Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.2% → 90.3%

Time: 28.5s

Alternatives: 26

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.2% 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: 90.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x - t_1 \cdot \left(z - y\right)\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-201}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t_1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (- x (* t_1 (- z y)))))
   (if (<= t_2 -2e-201)
     t_2
     (if (<= t_2 0.0) (+ t (/ x (/ 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 - (t_1 * (z - y));
	double tmp;
	if (t_2 <= -2e-201) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (x / (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(t_1 * Float64(z - y)))
	tmp = 0.0
	if (t_2 <= -2e-201)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(x / 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[(t$95$1 * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-201], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(x / 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)))) < -1.99999999999999989e-201

   1. Initial program 93.9%

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

   if -1.99999999999999989e-201 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 6.0%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. distribute-lft-out-- 77.5%

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

      3. div-sub 77.5%

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

      4. mul-1-neg 77.5%

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

      5. unsub-neg 77.5%

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

      6. distribute-rgt-out-- 77.5%

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

      7. associate-/l* 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in t around 0 77.7%

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

      1. associate-/l* 93.8%

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

      2. neg-mul-1 93.8%

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

      3. distribute-neg-frac 93.8%

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

   8. Simplified 93.8%

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

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

   1. Initial program 95.4%

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

      1. +-commutative 95.4%

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

      2. fma-def 95.4%

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

   3. Simplified 95.4%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq -2 \cdot 10^{-201}:\\ \;\;\;\;x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{elif}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq 0:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-201} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- t x) (- a z)) (- z y)))))
   (if (or (<= t_1 -2e-201) (not (<= t_1 0.0)))
     t_1
     (+ t (/ x (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if ((t_1 <= -2e-201) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (x / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((t - x) / (a - z)) * (z - y))
    if ((t_1 <= (-2d-201)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + (x / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if ((t_1 <= -2e-201) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (x / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((t - x) / (a - z)) * (z - y))
	tmp = 0
	if (t_1 <= -2e-201) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + (x / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) / Float64(a - z)) * Float64(z - y)))
	tmp = 0.0
	if ((t_1 <= -2e-201) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(x / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((t - x) / (a - z)) * (z - y));
	tmp = 0.0;
	if ((t_1 <= -2e-201) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + (x / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-201], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(x / 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)))) < -1.99999999999999989e-201 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.7%

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

   if -1.99999999999999989e-201 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 6.0%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. distribute-lft-out-- 77.5%

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

      3. div-sub 77.5%

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

      4. mul-1-neg 77.5%

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

      5. unsub-neg 77.5%

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

      6. distribute-rgt-out-- 77.5%

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

      7. associate-/l* 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in t around 0 77.7%

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

      1. associate-/l* 93.8%

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

      2. neg-mul-1 93.8%

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

      3. distribute-neg-frac 93.8%

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

   8. Simplified 93.8%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq -2 \cdot 10^{-201} \lor \neg \left(x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq 0\right):\\ \;\;\;\;x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -8.4 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-33}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -8.4e-33)
     t_2
     (if (<= a -1.5e-276)
       t_1
       (if (<= a 2.8e-291)
         (/ x (/ z y))
         (if (<= a 5e-106)
           t_1
           (if (<= a 8.6e-76)
             t_2
             (if (<= a 3.5e-33)
               (* (- t x) (/ y a))
               (if (<= a 1.8e+80)
                 (* x (/ (- y a) z))
                 (+ x (* t (/ y a))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -8.4e-33) {
		tmp = t_2;
	} else if (a <= -1.5e-276) {
		tmp = t_1;
	} else if (a <= 2.8e-291) {
		tmp = x / (z / y);
	} else if (a <= 5e-106) {
		tmp = t_1;
	} else if (a <= 8.6e-76) {
		tmp = t_2;
	} else if (a <= 3.5e-33) {
		tmp = (t - x) * (y / a);
	} else if (a <= 1.8e+80) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-8.4d-33)) then
        tmp = t_2
    else if (a <= (-1.5d-276)) then
        tmp = t_1
    else if (a <= 2.8d-291) then
        tmp = x / (z / y)
    else if (a <= 5d-106) then
        tmp = t_1
    else if (a <= 8.6d-76) then
        tmp = t_2
    else if (a <= 3.5d-33) then
        tmp = (t - x) * (y / a)
    else if (a <= 1.8d+80) then
        tmp = x * ((y - a) / z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -8.4e-33) {
		tmp = t_2;
	} else if (a <= -1.5e-276) {
		tmp = t_1;
	} else if (a <= 2.8e-291) {
		tmp = x / (z / y);
	} else if (a <= 5e-106) {
		tmp = t_1;
	} else if (a <= 8.6e-76) {
		tmp = t_2;
	} else if (a <= 3.5e-33) {
		tmp = (t - x) * (y / a);
	} else if (a <= 1.8e+80) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -8.4e-33:
		tmp = t_2
	elif a <= -1.5e-276:
		tmp = t_1
	elif a <= 2.8e-291:
		tmp = x / (z / y)
	elif a <= 5e-106:
		tmp = t_1
	elif a <= 8.6e-76:
		tmp = t_2
	elif a <= 3.5e-33:
		tmp = (t - x) * (y / a)
	elif a <= 1.8e+80:
		tmp = x * ((y - a) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -8.4e-33)
		tmp = t_2;
	elseif (a <= -1.5e-276)
		tmp = t_1;
	elseif (a <= 2.8e-291)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 5e-106)
		tmp = t_1;
	elseif (a <= 8.6e-76)
		tmp = t_2;
	elseif (a <= 3.5e-33)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (a <= 1.8e+80)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -8.4e-33)
		tmp = t_2;
	elseif (a <= -1.5e-276)
		tmp = t_1;
	elseif (a <= 2.8e-291)
		tmp = x / (z / y);
	elseif (a <= 5e-106)
		tmp = t_1;
	elseif (a <= 8.6e-76)
		tmp = t_2;
	elseif (a <= 3.5e-33)
		tmp = (t - x) * (y / a);
	elseif (a <= 1.8e+80)
		tmp = x * ((y - a) / z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.4e-33], t$95$2, If[LessEqual[a, -1.5e-276], t$95$1, If[LessEqual[a, 2.8e-291], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-106], t$95$1, If[LessEqual[a, 8.6e-76], t$95$2, If[LessEqual[a, 3.5e-33], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+80], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -8.4e-33 or 4.99999999999999983e-106 < a < 8.5999999999999998e-76

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0 58.8%

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

      1. associate-/l* 70.4%

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

      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 x around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   8. Simplified 58.5%

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

   if -8.4e-33 < a < -1.49999999999999994e-276 or 2.8e-291 < a < 4.99999999999999983e-106

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf 83.2%

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

      1. associate--l+ 83.2%

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

      2. distribute-lft-out-- 83.2%

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

      3. div-sub 83.2%

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

      4. mul-1-neg 83.2%

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

      5. unsub-neg 83.2%

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

      6. distribute-rgt-out-- 83.2%

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

      7. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in y around inf 83.3%

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

   7. Taylor expanded in t around inf 63.7%

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

   if -1.49999999999999994e-276 < a < 2.8e-291

   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 93.4%

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

      1. associate--l+ 93.4%

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

      2. distribute-lft-out-- 93.4%

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

      3. div-sub 93.4%

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

      4. mul-1-neg 93.4%

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

      5. unsub-neg 93.4%

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

      6. distribute-rgt-out-- 93.4%

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

      7. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 87.1%

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

      1. associate-/l* 93.8%

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

      2. neg-mul-1 93.8%

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

      3. distribute-neg-frac 93.8%

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

   8. Simplified 93.8%

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

   9. Taylor expanded in y around inf 74.2%

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

       1. associate-/l* 80.8%

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

   11. Simplified 80.8%

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

   if 8.5999999999999998e-76 < a < 3.4999999999999999e-33

   1. Initial program 87.8%

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

   3. Taylor expanded in y around inf 75.2%

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

      1. div-sub 75.2%

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

      2. associate-*r/ 64.0%

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

      3. associate-/l* 75.0%

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

      4. associate-/r/ 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in a around inf 51.8%

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

   if 3.4999999999999999e-33 < a < 1.79999999999999997e80

   1. Initial program 62.6%

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

   3. Taylor expanded in z around inf 69.6%

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

      1. associate--l+ 69.6%

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

      2. distribute-lft-out-- 69.6%

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

      3. div-sub 69.6%

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

      4. mul-1-neg 69.6%

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

      5. unsub-neg 69.6%

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

      6. distribute-rgt-out-- 69.6%

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

      7. associate-/l* 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in t around 0 61.3%

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

      1. associate-/l* 69.9%

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

      2. neg-mul-1 69.9%

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

      3. distribute-neg-frac 69.9%

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

   8. Simplified 69.9%

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

   9. Taylor expanded in t around 0 44.4%

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

       1. associate-*r/ 52.9%

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

   11. Simplified 52.9%

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

   if 1.79999999999999997e80 < a

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0 65.2%

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

      1. associate-/l* 76.8%

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

      2. associate-/r/ 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in t around inf 63.1%

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

      1. associate-*r/ 68.8%

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

   8. Simplified 68.8%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-33}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 34.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ t_2 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -1.46 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-208}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a y))) (t_2 (* x (/ y z))))
   (if (<= a -1.46e-19)
     x
     (if (<= a 1.65e-290)
       t_2
       (if (<= a 8.2e-208)
         t
         (if (<= a 2e-34)
           t_1
           (if (<= a 4.5e+44)
             t_2
             (if (<= a 1.45e+121) x (if (<= a 5.8e+163) t_1 x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double t_2 = x * (y / z);
	double tmp;
	if (a <= -1.46e-19) {
		tmp = x;
	} else if (a <= 1.65e-290) {
		tmp = t_2;
	} else if (a <= 8.2e-208) {
		tmp = t;
	} else if (a <= 2e-34) {
		tmp = t_1;
	} else if (a <= 4.5e+44) {
		tmp = t_2;
	} else if (a <= 1.45e+121) {
		tmp = x;
	} else if (a <= 5.8e+163) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (a / y)
    t_2 = x * (y / z)
    if (a <= (-1.46d-19)) then
        tmp = x
    else if (a <= 1.65d-290) then
        tmp = t_2
    else if (a <= 8.2d-208) then
        tmp = t
    else if (a <= 2d-34) then
        tmp = t_1
    else if (a <= 4.5d+44) then
        tmp = t_2
    else if (a <= 1.45d+121) then
        tmp = x
    else if (a <= 5.8d+163) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double t_2 = x * (y / z);
	double tmp;
	if (a <= -1.46e-19) {
		tmp = x;
	} else if (a <= 1.65e-290) {
		tmp = t_2;
	} else if (a <= 8.2e-208) {
		tmp = t;
	} else if (a <= 2e-34) {
		tmp = t_1;
	} else if (a <= 4.5e+44) {
		tmp = t_2;
	} else if (a <= 1.45e+121) {
		tmp = x;
	} else if (a <= 5.8e+163) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / y)
	t_2 = x * (y / z)
	tmp = 0
	if a <= -1.46e-19:
		tmp = x
	elif a <= 1.65e-290:
		tmp = t_2
	elif a <= 8.2e-208:
		tmp = t
	elif a <= 2e-34:
		tmp = t_1
	elif a <= 4.5e+44:
		tmp = t_2
	elif a <= 1.45e+121:
		tmp = x
	elif a <= 5.8e+163:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / y))
	t_2 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -1.46e-19)
		tmp = x;
	elseif (a <= 1.65e-290)
		tmp = t_2;
	elseif (a <= 8.2e-208)
		tmp = t;
	elseif (a <= 2e-34)
		tmp = t_1;
	elseif (a <= 4.5e+44)
		tmp = t_2;
	elseif (a <= 1.45e+121)
		tmp = x;
	elseif (a <= 5.8e+163)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / y);
	t_2 = x * (y / z);
	tmp = 0.0;
	if (a <= -1.46e-19)
		tmp = x;
	elseif (a <= 1.65e-290)
		tmp = t_2;
	elseif (a <= 8.2e-208)
		tmp = t;
	elseif (a <= 2e-34)
		tmp = t_1;
	elseif (a <= 4.5e+44)
		tmp = t_2;
	elseif (a <= 1.45e+121)
		tmp = x;
	elseif (a <= 5.8e+163)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.46e-19], x, If[LessEqual[a, 1.65e-290], t$95$2, If[LessEqual[a, 8.2e-208], t, If[LessEqual[a, 2e-34], t$95$1, If[LessEqual[a, 4.5e+44], t$95$2, If[LessEqual[a, 1.45e+121], x, If[LessEqual[a, 5.8e+163], t$95$1, x]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.46000000000000008e-19 or 4.5e44 < a < 1.45e121 or 5.79999999999999996e163 < a

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf 47.8%

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

   if -1.46000000000000008e-19 < a < 1.64999999999999993e-290 or 1.99999999999999986e-34 < a < 4.5e44

   1. Initial program 65.1%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. associate--l+ 78.1%

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

      2. distribute-lft-out-- 78.1%

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

      3. div-sub 78.1%

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

      4. mul-1-neg 78.1%

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

      5. unsub-neg 78.1%

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

      6. distribute-rgt-out-- 78.1%

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

      7. associate-/l* 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in y around inf 75.7%

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

   7. Taylor expanded in t around 0 37.9%

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

      1. associate-*r/ 43.1%

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

   9. Simplified 43.1%

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

   if 1.64999999999999993e-290 < a < 8.1999999999999998e-208

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf 51.1%

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

   if 8.1999999999999998e-208 < a < 1.99999999999999986e-34 or 1.45e121 < a < 5.79999999999999996e163

   1. Initial program 80.0%

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

   3. Taylor expanded in x around 0 48.6%

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

   4. Taylor expanded in y around inf 38.1%

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

      1. associate-/l* 47.3%

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

   6. Simplified 47.3%

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

   7. Taylor expanded in a around inf 35.5%

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

      1. associate-/l* 40.6%

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

   9. Simplified 40.6%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-208}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-34}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+163}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 34.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ t_2 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;a \leq -5.3 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-208}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a y))) (t_2 (/ x (/ z y))))
   (if (<= a -5.3e-20)
     x
     (if (<= a 2.4e-290)
       t_2
       (if (<= a 6.3e-208)
         t
         (if (<= a 8.8e-35)
           t_1
           (if (<= a 6.8e+48)
             t_2
             (if (<= a 3.05e+119) x (if (<= a 7.5e+163) t_1 x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double t_2 = x / (z / y);
	double tmp;
	if (a <= -5.3e-20) {
		tmp = x;
	} else if (a <= 2.4e-290) {
		tmp = t_2;
	} else if (a <= 6.3e-208) {
		tmp = t;
	} else if (a <= 8.8e-35) {
		tmp = t_1;
	} else if (a <= 6.8e+48) {
		tmp = t_2;
	} else if (a <= 3.05e+119) {
		tmp = x;
	} else if (a <= 7.5e+163) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (a / y)
    t_2 = x / (z / y)
    if (a <= (-5.3d-20)) then
        tmp = x
    else if (a <= 2.4d-290) then
        tmp = t_2
    else if (a <= 6.3d-208) then
        tmp = t
    else if (a <= 8.8d-35) then
        tmp = t_1
    else if (a <= 6.8d+48) then
        tmp = t_2
    else if (a <= 3.05d+119) then
        tmp = x
    else if (a <= 7.5d+163) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double t_2 = x / (z / y);
	double tmp;
	if (a <= -5.3e-20) {
		tmp = x;
	} else if (a <= 2.4e-290) {
		tmp = t_2;
	} else if (a <= 6.3e-208) {
		tmp = t;
	} else if (a <= 8.8e-35) {
		tmp = t_1;
	} else if (a <= 6.8e+48) {
		tmp = t_2;
	} else if (a <= 3.05e+119) {
		tmp = x;
	} else if (a <= 7.5e+163) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / y)
	t_2 = x / (z / y)
	tmp = 0
	if a <= -5.3e-20:
		tmp = x
	elif a <= 2.4e-290:
		tmp = t_2
	elif a <= 6.3e-208:
		tmp = t
	elif a <= 8.8e-35:
		tmp = t_1
	elif a <= 6.8e+48:
		tmp = t_2
	elif a <= 3.05e+119:
		tmp = x
	elif a <= 7.5e+163:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / y))
	t_2 = Float64(x / Float64(z / y))
	tmp = 0.0
	if (a <= -5.3e-20)
		tmp = x;
	elseif (a <= 2.4e-290)
		tmp = t_2;
	elseif (a <= 6.3e-208)
		tmp = t;
	elseif (a <= 8.8e-35)
		tmp = t_1;
	elseif (a <= 6.8e+48)
		tmp = t_2;
	elseif (a <= 3.05e+119)
		tmp = x;
	elseif (a <= 7.5e+163)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / y);
	t_2 = x / (z / y);
	tmp = 0.0;
	if (a <= -5.3e-20)
		tmp = x;
	elseif (a <= 2.4e-290)
		tmp = t_2;
	elseif (a <= 6.3e-208)
		tmp = t;
	elseif (a <= 8.8e-35)
		tmp = t_1;
	elseif (a <= 6.8e+48)
		tmp = t_2;
	elseif (a <= 3.05e+119)
		tmp = x;
	elseif (a <= 7.5e+163)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.3e-20], x, If[LessEqual[a, 2.4e-290], t$95$2, If[LessEqual[a, 6.3e-208], t, If[LessEqual[a, 8.8e-35], t$95$1, If[LessEqual[a, 6.8e+48], t$95$2, If[LessEqual[a, 3.05e+119], x, If[LessEqual[a, 7.5e+163], t$95$1, x]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.3000000000000002e-20 or 6.8000000000000006e48 < a < 3.05e119 or 7.50000000000000001e163 < a

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf 47.8%

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

   if -5.3000000000000002e-20 < a < 2.4000000000000001e-290 or 8.79999999999999975e-35 < a < 6.8000000000000006e48

   1. Initial program 65.1%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. associate--l+ 78.1%

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

      2. distribute-lft-out-- 78.1%

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

      3. div-sub 78.1%

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

      4. mul-1-neg 78.1%

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

      5. unsub-neg 78.1%

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

      6. distribute-rgt-out-- 78.1%

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

      7. associate-/l* 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in t around 0 72.0%

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

      1. associate-/l* 77.2%

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

      2. neg-mul-1 77.2%

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

      3. distribute-neg-frac 77.2%

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

   8. Simplified 77.2%

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

   9. Taylor expanded in y around inf 37.9%

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

       1. associate-/l* 43.1%

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

   11. Simplified 43.1%

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

   if 2.4000000000000001e-290 < a < 6.29999999999999993e-208

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf 51.1%

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

   if 6.29999999999999993e-208 < a < 8.79999999999999975e-35 or 3.05e119 < a < 7.50000000000000001e163

   1. Initial program 80.0%

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

   3. Taylor expanded in x around 0 48.6%

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

   4. Taylor expanded in y around inf 38.1%

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

      1. associate-/l* 47.3%

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

   6. Simplified 47.3%

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

   7. Taylor expanded in a around inf 35.5%

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

      1. associate-/l* 40.6%

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

   9. Simplified 40.6%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-208}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+163}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-243}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-160}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 540000000:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))))
   (if (<= a -6.2e-19)
     (* x (- 1.0 (/ y a)))
     (if (<= a 7.6e-243)
       (+ t (* x (/ y z)))
       (if (<= a 1.22e-160)
         (* t (- 1.0 (/ y z)))
         (if (<= a 4.8e-26)
           t_1
           (if (<= a 540000000.0)
             (- t (/ (* x a) z))
             (if (<= a 3.5e+74) t_1 (+ x (* t (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (a <= -6.2e-19) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 7.6e-243) {
		tmp = t + (x * (y / z));
	} else if (a <= 1.22e-160) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 4.8e-26) {
		tmp = t_1;
	} else if (a <= 540000000.0) {
		tmp = t - ((x * a) / z);
	} else if (a <= 3.5e+74) {
		tmp = t_1;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    if (a <= (-6.2d-19)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= 7.6d-243) then
        tmp = t + (x * (y / z))
    else if (a <= 1.22d-160) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 4.8d-26) then
        tmp = t_1
    else if (a <= 540000000.0d0) then
        tmp = t - ((x * a) / z)
    else if (a <= 3.5d+74) then
        tmp = t_1
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (a <= -6.2e-19) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 7.6e-243) {
		tmp = t + (x * (y / z));
	} else if (a <= 1.22e-160) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 4.8e-26) {
		tmp = t_1;
	} else if (a <= 540000000.0) {
		tmp = t - ((x * a) / z);
	} else if (a <= 3.5e+74) {
		tmp = t_1;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	tmp = 0
	if a <= -6.2e-19:
		tmp = x * (1.0 - (y / a))
	elif a <= 7.6e-243:
		tmp = t + (x * (y / z))
	elif a <= 1.22e-160:
		tmp = t * (1.0 - (y / z))
	elif a <= 4.8e-26:
		tmp = t_1
	elif a <= 540000000.0:
		tmp = t - ((x * a) / z)
	elif a <= 3.5e+74:
		tmp = t_1
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (a <= -6.2e-19)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= 7.6e-243)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (a <= 1.22e-160)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 4.8e-26)
		tmp = t_1;
	elseif (a <= 540000000.0)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	elseif (a <= 3.5e+74)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	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 (a <= -6.2e-19)
		tmp = x * (1.0 - (y / a));
	elseif (a <= 7.6e-243)
		tmp = t + (x * (y / z));
	elseif (a <= 1.22e-160)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 4.8e-26)
		tmp = t_1;
	elseif (a <= 540000000.0)
		tmp = t - ((x * a) / z);
	elseif (a <= 3.5e+74)
		tmp = t_1;
	else
		tmp = x + (t * (y / a));
	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]}, If[LessEqual[a, -6.2e-19], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e-243], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.22e-160], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-26], t$95$1, If[LessEqual[a, 540000000.0], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e+74], t$95$1, N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -6.1999999999999998e-19

   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 57.6%

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

      1. associate-/l* 71.3%

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

      2. associate-/r/ 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in x around inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. unsub-neg 57.3%

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

   8. Simplified 57.3%

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

   if -6.1999999999999998e-19 < a < 7.5999999999999996e-243

   1. Initial program 65.7%

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

   3. Taylor expanded in z around inf 82.8%

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

      1. associate--l+ 82.8%

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

      2. distribute-lft-out-- 82.8%

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

      3. div-sub 82.8%

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

      4. mul-1-neg 82.8%

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

      5. unsub-neg 82.8%

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

      6. distribute-rgt-out-- 82.8%

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

      7. associate-/l* 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in y around inf 84.1%

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

   7. Taylor expanded in t around 0 73.0%

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

      1. associate-*r/ 76.6%

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

      2. neg-mul-1 76.6%

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

      3. distribute-rgt-neg-in 76.6%

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

      4. distribute-neg-frac 76.6%

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

   9. Simplified 76.6%

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

   if 7.5999999999999996e-243 < a < 1.22000000000000003e-160

   1. Initial program 83.8%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. associate--l+ 83.8%

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

      2. distribute-lft-out-- 83.8%

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

      3. div-sub 83.8%

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

      4. mul-1-neg 83.8%

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

      5. unsub-neg 83.8%

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

      6. distribute-rgt-out-- 83.8%

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

      7. associate-/l* 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in y around inf 88.8%

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

   7. Taylor expanded in t around inf 88.8%

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

   if 1.22000000000000003e-160 < a < 4.8000000000000002e-26 or 5.4e8 < a < 3.50000000000000014e74

   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 75.3%

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

      1. div-sub 75.3%

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

      2. associate-*r/ 61.1%

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

      3. associate-/l* 75.3%

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

      4. associate-/r/ 75.3%

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

   5. Simplified 75.3%

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

   if 4.8000000000000002e-26 < a < 5.4e8

   1. Initial program 55.6%

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

   3. Taylor expanded in z around inf 83.5%

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

      1. associate--l+ 83.5%

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

      2. distribute-lft-out-- 83.5%

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

      3. div-sub 83.5%

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

      4. mul-1-neg 83.5%

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

      5. unsub-neg 83.5%

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

      6. distribute-rgt-out-- 83.5%

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

      7. associate-/l* 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in t around 0 77.1%

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

      1. associate-/l* 77.1%

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

      2. neg-mul-1 77.1%

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

      3. distribute-neg-frac 77.1%

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

   8. Simplified 77.1%

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

   9. Taylor expanded in y around 0 75.3%

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

   if 3.50000000000000014e74 < a

   1. Initial program 88.8%

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

   3. Taylor expanded in z around 0 64.1%

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

      1. associate-/l* 75.4%

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

      2. associate-/r/ 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in t around inf 62.0%

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

      1. associate-*r/ 67.6%

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

   8. Simplified 67.6%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-243}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-160}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-26}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 540000000:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+74}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+120} \lor \neg \left(a \leq 5.8 \cdot 10^{+163}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -8.5e-34)
     t_2
     (if (<= a -1.5e-276)
       t_1
       (if (<= a 2.8e-291)
         (/ x (/ z y))
         (if (<= a 3.2e-107)
           t_1
           (if (or (<= a 9.8e+120) (not (<= a 5.8e+163)))
             t_2
             (/ t (/ a y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -8.5e-34) {
		tmp = t_2;
	} else if (a <= -1.5e-276) {
		tmp = t_1;
	} else if (a <= 2.8e-291) {
		tmp = x / (z / y);
	} else if (a <= 3.2e-107) {
		tmp = t_1;
	} else if ((a <= 9.8e+120) || !(a <= 5.8e+163)) {
		tmp = t_2;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-8.5d-34)) then
        tmp = t_2
    else if (a <= (-1.5d-276)) then
        tmp = t_1
    else if (a <= 2.8d-291) then
        tmp = x / (z / y)
    else if (a <= 3.2d-107) then
        tmp = t_1
    else if ((a <= 9.8d+120) .or. (.not. (a <= 5.8d+163))) then
        tmp = t_2
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -8.5e-34) {
		tmp = t_2;
	} else if (a <= -1.5e-276) {
		tmp = t_1;
	} else if (a <= 2.8e-291) {
		tmp = x / (z / y);
	} else if (a <= 3.2e-107) {
		tmp = t_1;
	} else if ((a <= 9.8e+120) || !(a <= 5.8e+163)) {
		tmp = t_2;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -8.5e-34:
		tmp = t_2
	elif a <= -1.5e-276:
		tmp = t_1
	elif a <= 2.8e-291:
		tmp = x / (z / y)
	elif a <= 3.2e-107:
		tmp = t_1
	elif (a <= 9.8e+120) or not (a <= 5.8e+163):
		tmp = t_2
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -8.5e-34)
		tmp = t_2;
	elseif (a <= -1.5e-276)
		tmp = t_1;
	elseif (a <= 2.8e-291)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 3.2e-107)
		tmp = t_1;
	elseif ((a <= 9.8e+120) || !(a <= 5.8e+163))
		tmp = t_2;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -8.5e-34)
		tmp = t_2;
	elseif (a <= -1.5e-276)
		tmp = t_1;
	elseif (a <= 2.8e-291)
		tmp = x / (z / y);
	elseif (a <= 3.2e-107)
		tmp = t_1;
	elseif ((a <= 9.8e+120) || ~((a <= 5.8e+163)))
		tmp = t_2;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e-34], t$95$2, If[LessEqual[a, -1.5e-276], t$95$1, If[LessEqual[a, 2.8e-291], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-107], t$95$1, If[Or[LessEqual[a, 9.8e+120], N[Not[LessEqual[a, 5.8e+163]], $MachinePrecision]], t$95$2, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.5000000000000001e-34 or 3.20000000000000013e-107 < a < 9.80000000000000021e120 or 5.79999999999999996e163 < a

   1. Initial program 85.4%

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

   3. Taylor expanded in z around 0 58.5%

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

      1. associate-/l* 67.1%

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

      2. associate-/r/ 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in x around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. unsub-neg 55.2%

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

   8. Simplified 55.2%

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

   if -8.5000000000000001e-34 < a < -1.49999999999999994e-276 or 2.8e-291 < a < 3.20000000000000013e-107

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf 83.2%

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

      1. associate--l+ 83.2%

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

      2. distribute-lft-out-- 83.2%

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

      3. div-sub 83.2%

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

      4. mul-1-neg 83.2%

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

      5. unsub-neg 83.2%

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

      6. distribute-rgt-out-- 83.2%

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

      7. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in y around inf 83.3%

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

   7. Taylor expanded in t around inf 63.7%

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

   if -1.49999999999999994e-276 < a < 2.8e-291

   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 93.4%

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

      1. associate--l+ 93.4%

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

      2. distribute-lft-out-- 93.4%

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

      3. div-sub 93.4%

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

      4. mul-1-neg 93.4%

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

      5. unsub-neg 93.4%

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

      6. distribute-rgt-out-- 93.4%

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

      7. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 87.1%

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

      1. associate-/l* 93.8%

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

      2. neg-mul-1 93.8%

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

      3. distribute-neg-frac 93.8%

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

   8. Simplified 93.8%

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

   9. Taylor expanded in y around inf 74.2%

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

       1. associate-/l* 80.8%

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

   11. Simplified 80.8%

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

   if 9.80000000000000021e120 < a < 5.79999999999999996e163

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0 42.1%

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

   4. Taylor expanded in y around inf 41.0%

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

      1. associate-/l* 50.5%

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

   6. Simplified 50.5%

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

   7. Taylor expanded in a around inf 42.6%

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

      1. associate-/l* 52.3%

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

   9. Simplified 52.3%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+120} \lor \neg \left(a \leq 5.8 \cdot 10^{+163}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -2.05 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-26} \lor \neg \left(a \leq 0.05\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -2.05e-35)
     t_2
     (if (<= a -1.2e-276)
       t_1
       (if (<= a 2.8e-291)
         (/ x (/ z y))
         (if (<= a 2.6e-106)
           t_1
           (if (or (<= a 1.5e-26) (not (<= a 0.05)))
             t_2
             (* x (/ (- y a) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -2.05e-35) {
		tmp = t_2;
	} else if (a <= -1.2e-276) {
		tmp = t_1;
	} else if (a <= 2.8e-291) {
		tmp = x / (z / y);
	} else if (a <= 2.6e-106) {
		tmp = t_1;
	} else if ((a <= 1.5e-26) || !(a <= 0.05)) {
		tmp = t_2;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-2.05d-35)) then
        tmp = t_2
    else if (a <= (-1.2d-276)) then
        tmp = t_1
    else if (a <= 2.8d-291) then
        tmp = x / (z / y)
    else if (a <= 2.6d-106) then
        tmp = t_1
    else if ((a <= 1.5d-26) .or. (.not. (a <= 0.05d0))) then
        tmp = t_2
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -2.05e-35) {
		tmp = t_2;
	} else if (a <= -1.2e-276) {
		tmp = t_1;
	} else if (a <= 2.8e-291) {
		tmp = x / (z / y);
	} else if (a <= 2.6e-106) {
		tmp = t_1;
	} else if ((a <= 1.5e-26) || !(a <= 0.05)) {
		tmp = t_2;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -2.05e-35:
		tmp = t_2
	elif a <= -1.2e-276:
		tmp = t_1
	elif a <= 2.8e-291:
		tmp = x / (z / y)
	elif a <= 2.6e-106:
		tmp = t_1
	elif (a <= 1.5e-26) or not (a <= 0.05):
		tmp = t_2
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -2.05e-35)
		tmp = t_2;
	elseif (a <= -1.2e-276)
		tmp = t_1;
	elseif (a <= 2.8e-291)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 2.6e-106)
		tmp = t_1;
	elseif ((a <= 1.5e-26) || !(a <= 0.05))
		tmp = t_2;
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -2.05e-35)
		tmp = t_2;
	elseif (a <= -1.2e-276)
		tmp = t_1;
	elseif (a <= 2.8e-291)
		tmp = x / (z / y);
	elseif (a <= 2.6e-106)
		tmp = t_1;
	elseif ((a <= 1.5e-26) || ~((a <= 0.05)))
		tmp = t_2;
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.05e-35], t$95$2, If[LessEqual[a, -1.2e-276], t$95$1, If[LessEqual[a, 2.8e-291], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-106], t$95$1, If[Or[LessEqual[a, 1.5e-26], N[Not[LessEqual[a, 0.05]], $MachinePrecision]], t$95$2, N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.05000000000000013e-35 or 2.6000000000000001e-106 < a < 1.50000000000000006e-26 or 0.050000000000000003 < a

   1. Initial program 87.0%

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

   3. Taylor expanded in z around 0 60.7%

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

      1. associate-/l* 70.6%

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

      2. associate-/r/ 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in x around inf 55.8%

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

      1. mul-1-neg 55.8%

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

      2. unsub-neg 55.8%

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

   8. Simplified 55.8%

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

   if -2.05000000000000013e-35 < a < -1.19999999999999991e-276 or 2.8e-291 < a < 2.6000000000000001e-106

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf 83.2%

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

      1. associate--l+ 83.2%

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

      2. distribute-lft-out-- 83.2%

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

      3. div-sub 83.2%

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

      4. mul-1-neg 83.2%

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

      5. unsub-neg 83.2%

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

      6. distribute-rgt-out-- 83.2%

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

      7. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in y around inf 83.3%

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

   7. Taylor expanded in t around inf 63.7%

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

   if -1.19999999999999991e-276 < a < 2.8e-291

   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 93.4%

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

      1. associate--l+ 93.4%

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

      2. distribute-lft-out-- 93.4%

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

      3. div-sub 93.4%

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

      4. mul-1-neg 93.4%

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

      5. unsub-neg 93.4%

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

      6. distribute-rgt-out-- 93.4%

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

      7. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 87.1%

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

      1. associate-/l* 93.8%

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

      2. neg-mul-1 93.8%

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

      3. distribute-neg-frac 93.8%

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

   8. Simplified 93.8%

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

   9. Taylor expanded in y around inf 74.2%

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

       1. associate-/l* 80.8%

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

   11. Simplified 80.8%

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

   if 1.50000000000000006e-26 < a < 0.050000000000000003

   1. Initial program 56.8%

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

   3. Taylor expanded in z around inf 90.3%

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

      1. associate--l+ 90.3%

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

      2. distribute-lft-out-- 90.3%

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

      3. div-sub 90.3%

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

      4. mul-1-neg 90.3%

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

      5. unsub-neg 90.3%

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

      6. distribute-rgt-out-- 90.3%

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

      7. associate-/l* 90.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in t around 0 82.7%

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

      1. associate-/l* 82.6%

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

      2. neg-mul-1 82.6%

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

      3. distribute-neg-frac 82.6%

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

   8. Simplified 82.6%

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

   9. Taylor expanded in t around 0 54.3%

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

       1. associate-*r/ 54.1%

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

   11. Simplified 54.1%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-26} \lor \neg \left(a \leq 0.05\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 86000000000000:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -1.3e-36)
     t_2
     (if (<= a -1.35e-276)
       t_1
       (if (<= a 5.5e-291)
         (/ x (/ z y))
         (if (<= a 5e-106)
           t_1
           (if (<= a 3.5e-26)
             t_2
             (if (<= a 86000000000000.0)
               (- t (/ (* x a) z))
               (+ x (* t (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.3e-36) {
		tmp = t_2;
	} else if (a <= -1.35e-276) {
		tmp = t_1;
	} else if (a <= 5.5e-291) {
		tmp = x / (z / y);
	} else if (a <= 5e-106) {
		tmp = t_1;
	} else if (a <= 3.5e-26) {
		tmp = t_2;
	} else if (a <= 86000000000000.0) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-1.3d-36)) then
        tmp = t_2
    else if (a <= (-1.35d-276)) then
        tmp = t_1
    else if (a <= 5.5d-291) then
        tmp = x / (z / y)
    else if (a <= 5d-106) then
        tmp = t_1
    else if (a <= 3.5d-26) then
        tmp = t_2
    else if (a <= 86000000000000.0d0) then
        tmp = t - ((x * a) / z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.3e-36) {
		tmp = t_2;
	} else if (a <= -1.35e-276) {
		tmp = t_1;
	} else if (a <= 5.5e-291) {
		tmp = x / (z / y);
	} else if (a <= 5e-106) {
		tmp = t_1;
	} else if (a <= 3.5e-26) {
		tmp = t_2;
	} else if (a <= 86000000000000.0) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -1.3e-36:
		tmp = t_2
	elif a <= -1.35e-276:
		tmp = t_1
	elif a <= 5.5e-291:
		tmp = x / (z / y)
	elif a <= 5e-106:
		tmp = t_1
	elif a <= 3.5e-26:
		tmp = t_2
	elif a <= 86000000000000.0:
		tmp = t - ((x * a) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -1.3e-36)
		tmp = t_2;
	elseif (a <= -1.35e-276)
		tmp = t_1;
	elseif (a <= 5.5e-291)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 5e-106)
		tmp = t_1;
	elseif (a <= 3.5e-26)
		tmp = t_2;
	elseif (a <= 86000000000000.0)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -1.3e-36)
		tmp = t_2;
	elseif (a <= -1.35e-276)
		tmp = t_1;
	elseif (a <= 5.5e-291)
		tmp = x / (z / y);
	elseif (a <= 5e-106)
		tmp = t_1;
	elseif (a <= 3.5e-26)
		tmp = t_2;
	elseif (a <= 86000000000000.0)
		tmp = t - ((x * a) / z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e-36], t$95$2, If[LessEqual[a, -1.35e-276], t$95$1, If[LessEqual[a, 5.5e-291], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-106], t$95$1, If[LessEqual[a, 3.5e-26], t$95$2, If[LessEqual[a, 86000000000000.0], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.3e-36 or 4.99999999999999983e-106 < a < 3.49999999999999985e-26

   1. Initial program 88.0%

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

   3. Taylor expanded in z around 0 58.5%

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

      1. associate-/l* 68.9%

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

      2. associate-/r/ 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in x around inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. unsub-neg 56.0%

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

   8. Simplified 56.0%

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

   if -1.3e-36 < a < -1.34999999999999993e-276 or 5.5000000000000002e-291 < a < 4.99999999999999983e-106

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf 83.2%

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

      1. associate--l+ 83.2%

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

      2. distribute-lft-out-- 83.2%

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

      3. div-sub 83.2%

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

      4. mul-1-neg 83.2%

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

      5. unsub-neg 83.2%

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

      6. distribute-rgt-out-- 83.2%

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

      7. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in y around inf 83.3%

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

   7. Taylor expanded in t around inf 63.7%

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

   if -1.34999999999999993e-276 < a < 5.5000000000000002e-291

   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 93.4%

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

      1. associate--l+ 93.4%

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

      2. distribute-lft-out-- 93.4%

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

      3. div-sub 93.4%

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

      4. mul-1-neg 93.4%

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

      5. unsub-neg 93.4%

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

      6. distribute-rgt-out-- 93.4%

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

      7. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 87.1%

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

      1. associate-/l* 93.8%

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

      2. neg-mul-1 93.8%

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

      3. distribute-neg-frac 93.8%

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

   8. Simplified 93.8%

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

   9. Taylor expanded in y around inf 74.2%

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

       1. associate-/l* 80.8%

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

   11. Simplified 80.8%

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

   if 3.49999999999999985e-26 < a < 8.6e13

   1. Initial program 51.8%

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

   3. Taylor expanded in z around inf 84.8%

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

      1. associate--l+ 84.8%

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

      2. distribute-lft-out-- 84.8%

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

      3. div-sub 84.8%

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

      4. mul-1-neg 84.8%

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

      5. unsub-neg 84.8%

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

      6. distribute-rgt-out-- 84.8%

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

      7. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in t around 0 78.9%

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

      1. associate-/l* 78.9%

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

      2. neg-mul-1 78.9%

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

      3. distribute-neg-frac 78.9%

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

   8. Simplified 78.9%

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

   9. Taylor expanded in y around 0 70.1%

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

   if 8.6e13 < a

   1. Initial program 88.4%

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

   3. Taylor expanded in z around 0 64.9%

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

      1. associate-/l* 74.8%

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

      2. associate-/r/ 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in t around inf 59.9%

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

      1. associate-*r/ 64.8%

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

   8. Simplified 64.8%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 86000000000000:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-289}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+14}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -3.4e-33)
     t_2
     (if (<= a -1.5e-276)
       t_1
       (if (<= a 1.5e-289)
         (* (/ y z) (- x t))
         (if (<= a 5e-106)
           t_1
           (if (<= a 2.6e-26)
             t_2
             (if (<= a 1.6e+14) (- t (/ (* x a) z)) (+ x (* t (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -3.4e-33) {
		tmp = t_2;
	} else if (a <= -1.5e-276) {
		tmp = t_1;
	} else if (a <= 1.5e-289) {
		tmp = (y / z) * (x - t);
	} else if (a <= 5e-106) {
		tmp = t_1;
	} else if (a <= 2.6e-26) {
		tmp = t_2;
	} else if (a <= 1.6e+14) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-3.4d-33)) then
        tmp = t_2
    else if (a <= (-1.5d-276)) then
        tmp = t_1
    else if (a <= 1.5d-289) then
        tmp = (y / z) * (x - t)
    else if (a <= 5d-106) then
        tmp = t_1
    else if (a <= 2.6d-26) then
        tmp = t_2
    else if (a <= 1.6d+14) then
        tmp = t - ((x * a) / z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -3.4e-33) {
		tmp = t_2;
	} else if (a <= -1.5e-276) {
		tmp = t_1;
	} else if (a <= 1.5e-289) {
		tmp = (y / z) * (x - t);
	} else if (a <= 5e-106) {
		tmp = t_1;
	} else if (a <= 2.6e-26) {
		tmp = t_2;
	} else if (a <= 1.6e+14) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -3.4e-33:
		tmp = t_2
	elif a <= -1.5e-276:
		tmp = t_1
	elif a <= 1.5e-289:
		tmp = (y / z) * (x - t)
	elif a <= 5e-106:
		tmp = t_1
	elif a <= 2.6e-26:
		tmp = t_2
	elif a <= 1.6e+14:
		tmp = t - ((x * a) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -3.4e-33)
		tmp = t_2;
	elseif (a <= -1.5e-276)
		tmp = t_1;
	elseif (a <= 1.5e-289)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (a <= 5e-106)
		tmp = t_1;
	elseif (a <= 2.6e-26)
		tmp = t_2;
	elseif (a <= 1.6e+14)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -3.4e-33)
		tmp = t_2;
	elseif (a <= -1.5e-276)
		tmp = t_1;
	elseif (a <= 1.5e-289)
		tmp = (y / z) * (x - t);
	elseif (a <= 5e-106)
		tmp = t_1;
	elseif (a <= 2.6e-26)
		tmp = t_2;
	elseif (a <= 1.6e+14)
		tmp = t - ((x * a) / z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e-33], t$95$2, If[LessEqual[a, -1.5e-276], t$95$1, If[LessEqual[a, 1.5e-289], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-106], t$95$1, If[LessEqual[a, 2.6e-26], t$95$2, If[LessEqual[a, 1.6e+14], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.4000000000000001e-33 or 4.99999999999999983e-106 < a < 2.6000000000000001e-26

   1. Initial program 88.0%

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

   3. Taylor expanded in z around 0 58.5%

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

      1. associate-/l* 68.9%

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

      2. associate-/r/ 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in x around inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. unsub-neg 56.0%

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

   8. Simplified 56.0%

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

   if -3.4000000000000001e-33 < a < -1.49999999999999994e-276 or 1.4999999999999999e-289 < a < 4.99999999999999983e-106

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf 83.2%

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

      1. associate--l+ 83.2%

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

      2. distribute-lft-out-- 83.2%

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

      3. div-sub 83.2%

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

      4. mul-1-neg 83.2%

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

      5. unsub-neg 83.2%

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

      6. distribute-rgt-out-- 83.2%

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

      7. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in y around inf 83.3%

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

   7. Taylor expanded in t around inf 63.7%

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

   if -1.49999999999999994e-276 < a < 1.4999999999999999e-289

   1. Initial program 68.1%

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

   3. Taylor expanded in y around inf 81.2%

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

      1. div-sub 81.2%

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

      2. associate-*r/ 80.7%

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

      3. associate-/l* 81.2%

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

      4. associate-/r/ 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in a around 0 87.2%

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

      1. neg-mul-1 87.2%

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

      2. distribute-neg-frac 87.2%

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

   8. Simplified 87.2%

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

   if 2.6000000000000001e-26 < a < 1.6e14

   1. Initial program 51.8%

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

   3. Taylor expanded in z around inf 84.8%

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

      1. associate--l+ 84.8%

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

      2. distribute-lft-out-- 84.8%

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

      3. div-sub 84.8%

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

      4. mul-1-neg 84.8%

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

      5. unsub-neg 84.8%

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

      6. distribute-rgt-out-- 84.8%

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

      7. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in t around 0 78.9%

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

      1. associate-/l* 78.9%

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

      2. neg-mul-1 78.9%

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

      3. distribute-neg-frac 78.9%

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

   8. Simplified 78.9%

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

   9. Taylor expanded in y around 0 70.1%

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

   if 1.6e14 < a

   1. Initial program 88.4%

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

   3. Taylor expanded in z around 0 64.9%

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

      1. associate-/l* 74.8%

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

      2. associate-/r/ 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in t around inf 59.9%

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

      1. associate-*r/ 64.8%

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

   8. Simplified 64.8%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-289}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+14}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-243}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-109}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-34}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 4250000000:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= a -8.6e-19)
     t_1
     (if (<= a 6.2e-243)
       (+ t (* x (/ y z)))
       (if (<= a 7.5e-109)
         (* t (- 1.0 (/ y z)))
         (if (<= a 1.65e-75)
           t_1
           (if (<= a 5.4e-34)
             (* (- y z) (/ t (- a z)))
             (if (<= a 4250000000.0)
               (- t (/ (* x a) z))
               (+ x (* t (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -8.6e-19) {
		tmp = t_1;
	} else if (a <= 6.2e-243) {
		tmp = t + (x * (y / z));
	} else if (a <= 7.5e-109) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 1.65e-75) {
		tmp = t_1;
	} else if (a <= 5.4e-34) {
		tmp = (y - z) * (t / (a - z));
	} else if (a <= 4250000000.0) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (a <= (-8.6d-19)) then
        tmp = t_1
    else if (a <= 6.2d-243) then
        tmp = t + (x * (y / z))
    else if (a <= 7.5d-109) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 1.65d-75) then
        tmp = t_1
    else if (a <= 5.4d-34) then
        tmp = (y - z) * (t / (a - z))
    else if (a <= 4250000000.0d0) then
        tmp = t - ((x * a) / z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -8.6e-19) {
		tmp = t_1;
	} else if (a <= 6.2e-243) {
		tmp = t + (x * (y / z));
	} else if (a <= 7.5e-109) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 1.65e-75) {
		tmp = t_1;
	} else if (a <= 5.4e-34) {
		tmp = (y - z) * (t / (a - z));
	} else if (a <= 4250000000.0) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -8.6e-19:
		tmp = t_1
	elif a <= 6.2e-243:
		tmp = t + (x * (y / z))
	elif a <= 7.5e-109:
		tmp = t * (1.0 - (y / z))
	elif a <= 1.65e-75:
		tmp = t_1
	elif a <= 5.4e-34:
		tmp = (y - z) * (t / (a - z))
	elif a <= 4250000000.0:
		tmp = t - ((x * a) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -8.6e-19)
		tmp = t_1;
	elseif (a <= 6.2e-243)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (a <= 7.5e-109)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 1.65e-75)
		tmp = t_1;
	elseif (a <= 5.4e-34)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (a <= 4250000000.0)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	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 (a <= -8.6e-19)
		tmp = t_1;
	elseif (a <= 6.2e-243)
		tmp = t + (x * (y / z));
	elseif (a <= 7.5e-109)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 1.65e-75)
		tmp = t_1;
	elseif (a <= 5.4e-34)
		tmp = (y - z) * (t / (a - z));
	elseif (a <= 4250000000.0)
		tmp = t - ((x * a) / z);
	else
		tmp = x + (t * (y / a));
	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[a, -8.6e-19], t$95$1, If[LessEqual[a, 6.2e-243], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-109], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-75], t$95$1, If[LessEqual[a, 5.4e-34], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4250000000.0], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -8.6e-19 or 7.49999999999999982e-109 < a < 1.65e-75

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 60.8%

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

      1. associate-/l* 73.5%

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

      2. associate-/r/ 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in x around inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. unsub-neg 60.6%

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

   8. Simplified 60.6%

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

   if -8.6e-19 < a < 6.1999999999999999e-243

   1. Initial program 65.7%

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

   3. Taylor expanded in z around inf 82.8%

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

      1. associate--l+ 82.8%

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

      2. distribute-lft-out-- 82.8%

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

      3. div-sub 82.8%

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

      4. mul-1-neg 82.8%

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

      5. unsub-neg 82.8%

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

      6. distribute-rgt-out-- 82.8%

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

      7. associate-/l* 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in y around inf 84.1%

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

   7. Taylor expanded in t around 0 73.0%

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

      1. associate-*r/ 76.6%

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

      2. neg-mul-1 76.6%

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

      3. distribute-rgt-neg-in 76.6%

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

      4. distribute-neg-frac 76.6%

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

   9. Simplified 76.6%

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

   if 6.1999999999999999e-243 < a < 7.49999999999999982e-109

   1. Initial program 75.8%

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

   3. Taylor expanded in z around inf 79.6%

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

      1. associate--l+ 79.6%

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

      2. distribute-lft-out-- 79.6%

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

      3. div-sub 79.6%

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

      4. mul-1-neg 79.6%

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

      5. unsub-neg 79.6%

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

      6. distribute-rgt-out-- 79.6%

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

      7. associate-/l* 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in y around inf 86.5%

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

   7. Taylor expanded in t around inf 79.5%

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

   if 1.65e-75 < a < 5.40000000000000034e-34

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 67.7%

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

      1. associate-/l* 82.9%

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

      2. associate-/r/ 82.9%

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

   5. Simplified 82.9%

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

   if 5.40000000000000034e-34 < a < 4.25e9

   1. Initial program 55.0%

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

   3. Taylor expanded in z around inf 76.1%

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

      1. associate--l+ 76.1%

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

      2. distribute-lft-out-- 76.1%

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

      3. div-sub 76.1%

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

      4. mul-1-neg 76.1%

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

      5. unsub-neg 76.1%

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

      6. distribute-rgt-out-- 76.1%

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

      7. associate-/l* 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in t around 0 71.4%

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

      1. associate-/l* 71.3%

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

      2. neg-mul-1 71.3%

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

      3. distribute-neg-frac 71.3%

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

   8. Simplified 71.3%

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

   9. Taylor expanded in y around 0 63.3%

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

   if 4.25e9 < a

   1. Initial program 88.4%

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

   3. Taylor expanded in z around 0 64.9%

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

      1. associate-/l* 74.8%

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

      2. associate-/r/ 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in t around inf 59.9%

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

      1. associate-*r/ 64.8%

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

   8. Simplified 64.8%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-243}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-109}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-34}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 4250000000:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-243}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4300000000000:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= a -1.9e-19)
     t_1
     (if (<= a 6.6e-243)
       (+ t (* x (/ y z)))
       (if (<= a 3.6e-106)
         (* t (- 1.0 (/ y z)))
         (if (<= a 5.8e-27)
           t_1
           (if (<= a 4300000000000.0)
             (- t (/ (* x a) z))
             (+ x (* t (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.9e-19) {
		tmp = t_1;
	} else if (a <= 6.6e-243) {
		tmp = t + (x * (y / z));
	} else if (a <= 3.6e-106) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 5.8e-27) {
		tmp = t_1;
	} else if (a <= 4300000000000.0) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (a <= (-1.9d-19)) then
        tmp = t_1
    else if (a <= 6.6d-243) then
        tmp = t + (x * (y / z))
    else if (a <= 3.6d-106) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 5.8d-27) then
        tmp = t_1
    else if (a <= 4300000000000.0d0) then
        tmp = t - ((x * a) / z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.9e-19) {
		tmp = t_1;
	} else if (a <= 6.6e-243) {
		tmp = t + (x * (y / z));
	} else if (a <= 3.6e-106) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 5.8e-27) {
		tmp = t_1;
	} else if (a <= 4300000000000.0) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -1.9e-19:
		tmp = t_1
	elif a <= 6.6e-243:
		tmp = t + (x * (y / z))
	elif a <= 3.6e-106:
		tmp = t * (1.0 - (y / z))
	elif a <= 5.8e-27:
		tmp = t_1
	elif a <= 4300000000000.0:
		tmp = t - ((x * a) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -1.9e-19)
		tmp = t_1;
	elseif (a <= 6.6e-243)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (a <= 3.6e-106)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 5.8e-27)
		tmp = t_1;
	elseif (a <= 4300000000000.0)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	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 (a <= -1.9e-19)
		tmp = t_1;
	elseif (a <= 6.6e-243)
		tmp = t + (x * (y / z));
	elseif (a <= 3.6e-106)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 5.8e-27)
		tmp = t_1;
	elseif (a <= 4300000000000.0)
		tmp = t - ((x * a) / z);
	else
		tmp = x + (t * (y / a));
	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[a, -1.9e-19], t$95$1, If[LessEqual[a, 6.6e-243], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e-106], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-27], t$95$1, If[LessEqual[a, 4300000000000.0], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.9e-19 or 3.60000000000000013e-106 < a < 5.80000000000000008e-27

   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 60.3%

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

      1. associate-/l* 71.5%

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

      2. associate-/r/ 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in x around inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. unsub-neg 57.6%

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

   8. Simplified 57.6%

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

   if -1.9e-19 < a < 6.60000000000000026e-243

   1. Initial program 65.7%

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

   3. Taylor expanded in z around inf 82.8%

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

      1. associate--l+ 82.8%

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

      2. distribute-lft-out-- 82.8%

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

      3. div-sub 82.8%

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

      4. mul-1-neg 82.8%

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

      5. unsub-neg 82.8%

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

      6. distribute-rgt-out-- 82.8%

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

      7. associate-/l* 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in y around inf 84.1%

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

   7. Taylor expanded in t around 0 73.0%

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

      1. associate-*r/ 76.6%

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

      2. neg-mul-1 76.6%

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

      3. distribute-rgt-neg-in 76.6%

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

      4. distribute-neg-frac 76.6%

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

   9. Simplified 76.6%

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

   if 6.60000000000000026e-243 < a < 3.60000000000000013e-106

   1. Initial program 75.8%

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

   3. Taylor expanded in z around inf 79.6%

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

      1. associate--l+ 79.6%

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

      2. distribute-lft-out-- 79.6%

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

      3. div-sub 79.6%

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

      4. mul-1-neg 79.6%

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

      5. unsub-neg 79.6%

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

      6. distribute-rgt-out-- 79.6%

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

      7. associate-/l* 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in y around inf 86.5%

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

   7. Taylor expanded in t around inf 79.5%

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

   if 5.80000000000000008e-27 < a < 4.3e12

   1. Initial program 51.8%

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

   3. Taylor expanded in z around inf 84.8%

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

      1. associate--l+ 84.8%

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

      2. distribute-lft-out-- 84.8%

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

      3. div-sub 84.8%

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

      4. mul-1-neg 84.8%

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

      5. unsub-neg 84.8%

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

      6. distribute-rgt-out-- 84.8%

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

      7. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in t around 0 78.9%

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

      1. associate-/l* 78.9%

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

      2. neg-mul-1 78.9%

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

      3. distribute-neg-frac 78.9%

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

   8. Simplified 78.9%

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

   9. Taylor expanded in y around 0 70.1%

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

   if 4.3e12 < a

   1. Initial program 88.4%

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

   3. Taylor expanded in z around 0 64.9%

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

      1. associate-/l* 74.8%

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

      2. associate-/r/ 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in t around inf 59.9%

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

      1. associate-*r/ 64.8%

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

   8. Simplified 64.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-243}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 4300000000000:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+42} \lor \neg \left(a \leq 5 \cdot 10^{-106} \lor \neg \left(a \leq 1.8 \cdot 10^{-26}\right) \land a \leq 1.9 \cdot 10^{+80}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1e+42)
         (not (or (<= a 5e-106) (and (not (<= a 1.8e-26)) (<= a 1.9e+80)))))
   (+ x (/ (- t x) (/ a (- y z))))
   (+ t (/ (- x t) (/ z (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1e+42) || !((a <= 5e-106) || (!(a <= 1.8e-26) && (a <= 1.9e+80)))) {
		tmp = x + ((t - x) / (a / (y - z)));
	} 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) :: tmp
    if ((a <= (-1d+42)) .or. (.not. (a <= 5d-106) .or. (.not. (a <= 1.8d-26)) .and. (a <= 1.9d+80))) then
        tmp = x + ((t - x) / (a / (y - z)))
    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 tmp;
	if ((a <= -1e+42) || !((a <= 5e-106) || (!(a <= 1.8e-26) && (a <= 1.9e+80)))) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1e+42) or not ((a <= 5e-106) or (not (a <= 1.8e-26) and (a <= 1.9e+80))):
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1e+42) || !((a <= 5e-106) || (!(a <= 1.8e-26) && (a <= 1.9e+80))))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	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)
	tmp = 0.0;
	if ((a <= -1e+42) || ~(((a <= 5e-106) || (~((a <= 1.8e-26)) && (a <= 1.9e+80)))))
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1e+42], N[Not[Or[LessEqual[a, 5e-106], And[N[Not[LessEqual[a, 1.8e-26]], $MachinePrecision], LessEqual[a, 1.9e+80]]]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 a < -1.00000000000000004e42 or 4.99999999999999983e-106 < a < 1.8000000000000001e-26 or 1.89999999999999999e80 < a

   1. Initial program 92.4%

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

   3. Taylor expanded in a around inf 68.6%

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

      1. associate-/l* 82.7%

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

   5. Simplified 82.7%

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

   if -1.00000000000000004e42 < a < 4.99999999999999983e-106 or 1.8000000000000001e-26 < a < 1.89999999999999999e80

   1. Initial program 66.9%

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

   3. Taylor expanded in z around inf 78.8%

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

      1. associate--l+ 78.8%

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

      2. distribute-lft-out-- 78.8%

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

      3. div-sub 78.8%

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

      4. mul-1-neg 78.8%

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

      5. unsub-neg 78.8%

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

      6. distribute-rgt-out-- 78.8%

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

      7. associate-/l* 84.4%

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

   5. Simplified 84.4%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+42} \lor \neg \left(a \leq 5 \cdot 10^{-106} \lor \neg \left(a \leq 1.8 \cdot 10^{-26}\right) \land a \leq 1.9 \cdot 10^{+80}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+132}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 8.1 \cdot 10^{+183}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.85e+132)
   (* (/ y z) (- t))
   (if (<= y -7e-286)
     t
     (if (<= y 2.95e+28)
       x
       (if (<= y 1.9e+103)
         (/ x (/ z y))
         (if (<= y 8.1e+183) (/ t (/ a y)) (* y (/ (- x) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.85e+132) {
		tmp = (y / z) * -t;
	} else if (y <= -7e-286) {
		tmp = t;
	} else if (y <= 2.95e+28) {
		tmp = x;
	} else if (y <= 1.9e+103) {
		tmp = x / (z / y);
	} else if (y <= 8.1e+183) {
		tmp = t / (a / y);
	} else {
		tmp = y * (-x / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.85d+132)) then
        tmp = (y / z) * -t
    else if (y <= (-7d-286)) then
        tmp = t
    else if (y <= 2.95d+28) then
        tmp = x
    else if (y <= 1.9d+103) then
        tmp = x / (z / y)
    else if (y <= 8.1d+183) then
        tmp = t / (a / y)
    else
        tmp = y * (-x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.85e+132) {
		tmp = (y / z) * -t;
	} else if (y <= -7e-286) {
		tmp = t;
	} else if (y <= 2.95e+28) {
		tmp = x;
	} else if (y <= 1.9e+103) {
		tmp = x / (z / y);
	} else if (y <= 8.1e+183) {
		tmp = t / (a / y);
	} else {
		tmp = y * (-x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.85e+132:
		tmp = (y / z) * -t
	elif y <= -7e-286:
		tmp = t
	elif y <= 2.95e+28:
		tmp = x
	elif y <= 1.9e+103:
		tmp = x / (z / y)
	elif y <= 8.1e+183:
		tmp = t / (a / y)
	else:
		tmp = y * (-x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.85e+132)
		tmp = Float64(Float64(y / z) * Float64(-t));
	elseif (y <= -7e-286)
		tmp = t;
	elseif (y <= 2.95e+28)
		tmp = x;
	elseif (y <= 1.9e+103)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= 8.1e+183)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = Float64(y * Float64(Float64(-x) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.85e+132)
		tmp = (y / z) * -t;
	elseif (y <= -7e-286)
		tmp = t;
	elseif (y <= 2.95e+28)
		tmp = x;
	elseif (y <= 1.9e+103)
		tmp = x / (z / y);
	elseif (y <= 8.1e+183)
		tmp = t / (a / y);
	else
		tmp = y * (-x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.85e+132], N[(N[(y / z), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[y, -7e-286], t, If[LessEqual[y, 2.95e+28], x, If[LessEqual[y, 1.9e+103], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.1e+183], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(y * N[((-x) / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.8499999999999999e132

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0 30.5%

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

   4. Taylor expanded in y around inf 29.6%

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

      1. associate-/l* 52.0%

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

   6. Simplified 52.0%

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

   7. Taylor expanded in a around 0 27.4%

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

      1. mul-1-neg 27.4%

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

      2. associate-*r/ 38.2%

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

   9. Simplified 38.2%

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

   if -2.8499999999999999e132 < y < -6.99999999999999977e-286

   1. Initial program 65.0%

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

   3. Taylor expanded in z around inf 39.0%

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

   if -6.99999999999999977e-286 < y < 2.9500000000000001e28

   1. Initial program 75.4%

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

   3. Taylor expanded in a around inf 43.0%

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

   if 2.9500000000000001e28 < y < 1.8999999999999998e103

   1. Initial program 74.8%

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

   3. Taylor expanded in z around inf 53.7%

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

      1. associate--l+ 53.7%

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

      2. distribute-lft-out-- 53.7%

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

      3. div-sub 53.7%

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

      4. mul-1-neg 53.7%

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

      5. unsub-neg 53.7%

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

      6. distribute-rgt-out-- 53.7%

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

      7. associate-/l* 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in t around 0 47.8%

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

      1. associate-/l* 51.3%

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

      2. neg-mul-1 51.3%

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

      3. distribute-neg-frac 51.3%

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

   8. Simplified 51.3%

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

   9. Taylor expanded in y around inf 35.9%

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

       1. associate-/l* 39.4%

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

   11. Simplified 39.4%

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

   if 1.8999999999999998e103 < y < 8.09999999999999993e183

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 65.4%

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

   4. Taylor expanded in y around inf 64.8%

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

      1. associate-/l* 76.5%

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

   6. Simplified 76.5%

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

   7. Taylor expanded in a around inf 65.4%

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

      1. associate-/l* 77.3%

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

   9. Simplified 77.3%

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

   if 8.09999999999999993e183 < y

   1. Initial program 94.8%

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

   3. Taylor expanded in t around 0 75.3%

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

      1. neg-mul-1 75.3%

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

      2. distribute-neg-frac 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in y around inf 65.7%

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

      1. mul-1-neg 65.7%

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

      2. associate-*l/ 80.4%

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

      3. *-commutative 80.4%

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

      4. distribute-rgt-neg-in 80.4%

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

      5. distribute-neg-frac 80.4%

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

   8. Simplified 80.4%

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

   9. Taylor expanded in a around inf 51.2%

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

       1. associate-*r/ 51.2%

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

       2. mul-1-neg 51.2%

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

   11. Simplified 51.2%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+132}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 8.1 \cdot 10^{+183}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+132}:\\ \;\;\;\;\frac{t}{\frac{-z}{y}}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-284}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+181}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.8e+132)
   (/ t (/ (- z) y))
   (if (<= y -1.1e-284)
     t
     (if (<= y 5.2e+28)
       x
       (if (<= y 3.9e+105)
         (/ x (/ z y))
         (if (<= y 5.8e+181) (/ t (/ a y)) (* y (/ (- x) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.8e+132) {
		tmp = t / (-z / y);
	} else if (y <= -1.1e-284) {
		tmp = t;
	} else if (y <= 5.2e+28) {
		tmp = x;
	} else if (y <= 3.9e+105) {
		tmp = x / (z / y);
	} else if (y <= 5.8e+181) {
		tmp = t / (a / y);
	} else {
		tmp = y * (-x / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.8d+132)) then
        tmp = t / (-z / y)
    else if (y <= (-1.1d-284)) then
        tmp = t
    else if (y <= 5.2d+28) then
        tmp = x
    else if (y <= 3.9d+105) then
        tmp = x / (z / y)
    else if (y <= 5.8d+181) then
        tmp = t / (a / y)
    else
        tmp = y * (-x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.8e+132) {
		tmp = t / (-z / y);
	} else if (y <= -1.1e-284) {
		tmp = t;
	} else if (y <= 5.2e+28) {
		tmp = x;
	} else if (y <= 3.9e+105) {
		tmp = x / (z / y);
	} else if (y <= 5.8e+181) {
		tmp = t / (a / y);
	} else {
		tmp = y * (-x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.8e+132:
		tmp = t / (-z / y)
	elif y <= -1.1e-284:
		tmp = t
	elif y <= 5.2e+28:
		tmp = x
	elif y <= 3.9e+105:
		tmp = x / (z / y)
	elif y <= 5.8e+181:
		tmp = t / (a / y)
	else:
		tmp = y * (-x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.8e+132)
		tmp = Float64(t / Float64(Float64(-z) / y));
	elseif (y <= -1.1e-284)
		tmp = t;
	elseif (y <= 5.2e+28)
		tmp = x;
	elseif (y <= 3.9e+105)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= 5.8e+181)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = Float64(y * Float64(Float64(-x) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.8e+132)
		tmp = t / (-z / y);
	elseif (y <= -1.1e-284)
		tmp = t;
	elseif (y <= 5.2e+28)
		tmp = x;
	elseif (y <= 3.9e+105)
		tmp = x / (z / y);
	elseif (y <= 5.8e+181)
		tmp = t / (a / y);
	else
		tmp = y * (-x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.8e+132], N[(t / N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e-284], t, If[LessEqual[y, 5.2e+28], x, If[LessEqual[y, 3.9e+105], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+181], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(y * N[((-x) / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.7999999999999999e132

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0 30.5%

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

   4. Taylor expanded in y around inf 29.6%

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

      1. associate-/l* 52.0%

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

   6. Simplified 52.0%

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

   7. Taylor expanded in a around 0 38.2%

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

      1. mul-1-neg 38.2%

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

      2. distribute-frac-neg 38.2%

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

   9. Simplified 38.2%

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

   if -2.7999999999999999e132 < y < -1.1e-284

   1. Initial program 65.0%

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

   3. Taylor expanded in z around inf 39.0%

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

   if -1.1e-284 < y < 5.2000000000000004e28

   1. Initial program 75.4%

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

   3. Taylor expanded in a around inf 43.0%

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

   if 5.2000000000000004e28 < y < 3.89999999999999978e105

   1. Initial program 74.8%

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

   3. Taylor expanded in z around inf 53.7%

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

      1. associate--l+ 53.7%

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

      2. distribute-lft-out-- 53.7%

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

      3. div-sub 53.7%

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

      4. mul-1-neg 53.7%

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

      5. unsub-neg 53.7%

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

      6. distribute-rgt-out-- 53.7%

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

      7. associate-/l* 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in t around 0 47.8%

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

      1. associate-/l* 51.3%

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

      2. neg-mul-1 51.3%

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

      3. distribute-neg-frac 51.3%

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

   8. Simplified 51.3%

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

   9. Taylor expanded in y around inf 35.9%

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

       1. associate-/l* 39.4%

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

   11. Simplified 39.4%

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

   if 3.89999999999999978e105 < y < 5.8e181

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 65.4%

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

   4. Taylor expanded in y around inf 64.8%

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

      1. associate-/l* 76.5%

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

   6. Simplified 76.5%

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

   7. Taylor expanded in a around inf 65.4%

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

      1. associate-/l* 77.3%

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

   9. Simplified 77.3%

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

   if 5.8e181 < y

   1. Initial program 94.8%

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

   3. Taylor expanded in t around 0 75.3%

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

      1. neg-mul-1 75.3%

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

      2. distribute-neg-frac 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in y around inf 65.7%

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

      1. mul-1-neg 65.7%

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

      2. associate-*l/ 80.4%

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

      3. *-commutative 80.4%

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

      4. distribute-rgt-neg-in 80.4%

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

      5. distribute-neg-frac 80.4%

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

   8. Simplified 80.4%

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

   9. Taylor expanded in a around inf 51.2%

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

       1. associate-*r/ 51.2%

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

       2. mul-1-neg 51.2%

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

   11. Simplified 51.2%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+132}:\\ \;\;\;\;\frac{t}{\frac{-z}{y}}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-284}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+181}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-106}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{-27} \lor \neg \left(a \leq 1.9 \cdot 10^{+80}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a (- y z))))))
   (if (<= a -5.4e-19)
     t_1
     (if (<= a 5e-106)
       (+ t (/ (- x t) (/ z y)))
       (if (or (<= a 3.05e-27) (not (<= a 1.9e+80)))
         t_1
         (+ t (/ x (/ z (- y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -5.4e-19) {
		tmp = t_1;
	} else if (a <= 5e-106) {
		tmp = t + ((x - t) / (z / y));
	} else if ((a <= 3.05e-27) || !(a <= 1.9e+80)) {
		tmp = t_1;
	} else {
		tmp = t + (x / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) / (a / (y - z)))
    if (a <= (-5.4d-19)) then
        tmp = t_1
    else if (a <= 5d-106) then
        tmp = t + ((x - t) / (z / y))
    else if ((a <= 3.05d-27) .or. (.not. (a <= 1.9d+80))) then
        tmp = t_1
    else
        tmp = t + (x / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -5.4e-19) {
		tmp = t_1;
	} else if (a <= 5e-106) {
		tmp = t + ((x - t) / (z / y));
	} else if ((a <= 3.05e-27) || !(a <= 1.9e+80)) {
		tmp = t_1;
	} else {
		tmp = t + (x / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / (y - z)))
	tmp = 0
	if a <= -5.4e-19:
		tmp = t_1
	elif a <= 5e-106:
		tmp = t + ((x - t) / (z / y))
	elif (a <= 3.05e-27) or not (a <= 1.9e+80):
		tmp = t_1
	else:
		tmp = t + (x / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -5.4e-19)
		tmp = t_1;
	elseif (a <= 5e-106)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif ((a <= 3.05e-27) || !(a <= 1.9e+80))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(x / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / (y - z)));
	tmp = 0.0;
	if (a <= -5.4e-19)
		tmp = t_1;
	elseif (a <= 5e-106)
		tmp = t + ((x - t) / (z / y));
	elseif ((a <= 3.05e-27) || ~((a <= 1.9e+80)))
		tmp = t_1;
	else
		tmp = t + (x / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.4e-19], t$95$1, If[LessEqual[a, 5e-106], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 3.05e-27], N[Not[LessEqual[a, 1.9e+80]], $MachinePrecision]], t$95$1, N[(t + N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.4000000000000002e-19 or 4.99999999999999983e-106 < a < 3.05e-27 or 1.89999999999999999e80 < a

   1. Initial program 90.5%

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

   3. Taylor expanded in a around inf 67.4%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   if -5.4000000000000002e-19 < a < 4.99999999999999983e-106

   1. Initial program 68.3%

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

   3. Taylor expanded in z around inf 82.0%

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

      1. associate--l+ 82.0%

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

      2. distribute-lft-out-- 82.0%

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

      3. div-sub 82.0%

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

      4. mul-1-neg 82.0%

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

      5. unsub-neg 82.0%

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

      6. distribute-rgt-out-- 82.0%

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

      7. associate-/l* 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in y around inf 84.7%

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

   if 3.05e-27 < a < 1.89999999999999999e80

   1. Initial program 60.8%

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

   3. Taylor expanded in z around inf 72.5%

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

      1. associate--l+ 72.5%

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

      2. distribute-lft-out-- 72.5%

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

      3. div-sub 72.5%

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

      4. mul-1-neg 72.5%

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

      5. unsub-neg 72.5%

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

      6. distribute-rgt-out-- 72.5%

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

      7. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in t around 0 63.7%

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

      1. associate-/l* 72.8%

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

      2. neg-mul-1 72.8%

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

      3. distribute-neg-frac 72.8%

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

   8. Simplified 72.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-106}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{-27} \lor \neg \left(a \leq 1.9 \cdot 10^{+80}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 31.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.14 \cdot 10^{+133}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-287}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 10^{+251}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.14e+133)
   (* (/ y z) (- t))
   (if (<= y -1.42e-287)
     t
     (if (<= y 2.5e+28)
       x
       (if (<= y 6.5e+104)
         (/ x (/ z y))
         (if (<= y 1e+251) (/ t (/ a y)) (* x (/ y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.14e+133) {
		tmp = (y / z) * -t;
	} else if (y <= -1.42e-287) {
		tmp = t;
	} else if (y <= 2.5e+28) {
		tmp = x;
	} else if (y <= 6.5e+104) {
		tmp = x / (z / y);
	} else if (y <= 1e+251) {
		tmp = t / (a / y);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.14d+133)) then
        tmp = (y / z) * -t
    else if (y <= (-1.42d-287)) then
        tmp = t
    else if (y <= 2.5d+28) then
        tmp = x
    else if (y <= 6.5d+104) then
        tmp = x / (z / y)
    else if (y <= 1d+251) then
        tmp = t / (a / y)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.14e+133) {
		tmp = (y / z) * -t;
	} else if (y <= -1.42e-287) {
		tmp = t;
	} else if (y <= 2.5e+28) {
		tmp = x;
	} else if (y <= 6.5e+104) {
		tmp = x / (z / y);
	} else if (y <= 1e+251) {
		tmp = t / (a / y);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.14e+133:
		tmp = (y / z) * -t
	elif y <= -1.42e-287:
		tmp = t
	elif y <= 2.5e+28:
		tmp = x
	elif y <= 6.5e+104:
		tmp = x / (z / y)
	elif y <= 1e+251:
		tmp = t / (a / y)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.14e+133)
		tmp = Float64(Float64(y / z) * Float64(-t));
	elseif (y <= -1.42e-287)
		tmp = t;
	elseif (y <= 2.5e+28)
		tmp = x;
	elseif (y <= 6.5e+104)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= 1e+251)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.14e+133)
		tmp = (y / z) * -t;
	elseif (y <= -1.42e-287)
		tmp = t;
	elseif (y <= 2.5e+28)
		tmp = x;
	elseif (y <= 6.5e+104)
		tmp = x / (z / y);
	elseif (y <= 1e+251)
		tmp = t / (a / y);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.14e+133], N[(N[(y / z), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[y, -1.42e-287], t, If[LessEqual[y, 2.5e+28], x, If[LessEqual[y, 6.5e+104], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+251], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.14e133

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0 30.5%

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

   4. Taylor expanded in y around inf 29.6%

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

      1. associate-/l* 52.0%

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

   6. Simplified 52.0%

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

   7. Taylor expanded in a around 0 27.4%

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

      1. mul-1-neg 27.4%

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

      2. associate-*r/ 38.2%

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

   9. Simplified 38.2%

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

   if -1.14e133 < y < -1.42000000000000009e-287

   1. Initial program 65.0%

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

   3. Taylor expanded in z around inf 39.0%

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

   if -1.42000000000000009e-287 < y < 2.49999999999999979e28

   1. Initial program 75.4%

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

   3. Taylor expanded in a around inf 43.0%

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

   if 2.49999999999999979e28 < y < 6.5000000000000005e104

   1. Initial program 74.8%

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

   3. Taylor expanded in z around inf 53.7%

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

      1. associate--l+ 53.7%

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

      2. distribute-lft-out-- 53.7%

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

      3. div-sub 53.7%

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

      4. mul-1-neg 53.7%

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

      5. unsub-neg 53.7%

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

      6. distribute-rgt-out-- 53.7%

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

      7. associate-/l* 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in t around 0 47.8%

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

      1. associate-/l* 51.3%

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

      2. neg-mul-1 51.3%

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

      3. distribute-neg-frac 51.3%

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

   8. Simplified 51.3%

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

   9. Taylor expanded in y around inf 35.9%

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

       1. associate-/l* 39.4%

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

   11. Simplified 39.4%

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

   if 6.5000000000000005e104 < y < 1e251

   1. Initial program 97.4%

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

   3. Taylor expanded in x around 0 45.9%

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

   4. Taylor expanded in y around inf 45.5%

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

      1. associate-/l* 50.3%

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

   6. Simplified 50.3%

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

   7. Taylor expanded in a around inf 49.5%

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

      1. associate-/l* 54.3%

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

   9. Simplified 54.3%

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

   if 1e251 < y

   1. Initial program 93.8%

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

   3. Taylor expanded in z around inf 58.4%

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

      1. associate--l+ 58.4%

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

      2. distribute-lft-out-- 58.4%

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

      3. div-sub 58.4%

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

      4. mul-1-neg 58.4%

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

      5. unsub-neg 58.4%

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

      6. distribute-rgt-out-- 58.4%

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

      7. associate-/l* 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in y around inf 64.8%

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

   7. Taylor expanded in t around 0 46.3%

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

      1. associate-*r/ 52.6%

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

   9. Simplified 52.6%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.14 \cdot 10^{+133}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-287}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 10^{+251}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 68.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-110}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-26}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 270000000:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))))
   (if (<= a -3.5e-19)
     t_1
     (if (<= a 1.6e-110)
       (- t (/ y (/ z (- t x))))
       (if (<= a 4.9e-26)
         (* (- t x) (/ y (- a z)))
         (if (<= a 270000000.0) (- t (/ (* x a) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -3.5e-19) {
		tmp = t_1;
	} else if (a <= 1.6e-110) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 4.9e-26) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 270000000.0) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    if (a <= (-3.5d-19)) then
        tmp = t_1
    else if (a <= 1.6d-110) then
        tmp = t - (y / (z / (t - x)))
    else if (a <= 4.9d-26) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 270000000.0d0) then
        tmp = t - ((x * a) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -3.5e-19) {
		tmp = t_1;
	} else if (a <= 1.6e-110) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 4.9e-26) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 270000000.0) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -3.5e-19:
		tmp = t_1
	elif a <= 1.6e-110:
		tmp = t - (y / (z / (t - x)))
	elif a <= 4.9e-26:
		tmp = (t - x) * (y / (a - z))
	elif a <= 270000000.0:
		tmp = t - ((x * a) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -3.5e-19)
		tmp = t_1;
	elseif (a <= 1.6e-110)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	elseif (a <= 4.9e-26)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 270000000.0)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -3.5e-19)
		tmp = t_1;
	elseif (a <= 1.6e-110)
		tmp = t - (y / (z / (t - x)));
	elseif (a <= 4.9e-26)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 270000000.0)
		tmp = t - ((x * a) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e-19], t$95$1, If[LessEqual[a, 1.6e-110], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e-26], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 270000000.0], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.50000000000000015e-19 or 2.7e8 < a

   1. Initial program 89.2%

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

   3. Taylor expanded in z around 0 61.2%

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

      1. associate-/l* 73.0%

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

      2. associate-/r/ 73.0%

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

   5. Simplified 73.0%

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

   if -3.50000000000000015e-19 < a < 1.60000000000000014e-110

   1. Initial program 68.8%

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

   3. Taylor expanded in z around inf 81.8%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 81.8%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 81.8%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 81.8%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 81.8%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 81.8%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 81.8%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 88.1%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 88.1%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 79.4%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 83.0%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

   8. Simplified 83.0%

      \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

   if 1.60000000000000014e-110 < a < 4.8999999999999999e-26

   1. Initial program 82.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.3%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 69.3%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

      2. associate-*r/ 63.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

      3. associate-/l* 69.3%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - z}{t - x}}} \]

      4. associate-/r/ 69.5%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   5. Simplified 69.5%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   if 4.8999999999999999e-26 < a < 2.7e8

   1. Initial program 55.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.5%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 83.5%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 83.5%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 83.5%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 83.5%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 83.5%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 83.5%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 83.4%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 83.4%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in t around 0 77.1%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 77.1%

         \[\leadsto t - -1 \cdot \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. neg-mul-1 77.1%

         \[\leadsto t - \color{blue}{\left(-\frac{x}{\frac{z}{y - a}}\right)} \]

      3. distribute-neg-frac 77.1%

         \[\leadsto t - \color{blue}{\frac{-x}{\frac{z}{y - a}}} \]

   8. Simplified 77.1%

      \[\leadsto t - \color{blue}{\frac{-x}{\frac{z}{y - a}}} \]

   9. Taylor expanded in y around 0 75.3%

      \[\leadsto t - \color{blue}{\frac{a \cdot x}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-19}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-110}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-26}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 270000000:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 69.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -4.05 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-106}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-26}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2080000000:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))))
   (if (<= a -4.05e-19)
     t_1
     (if (<= a 4.6e-106)
       (+ t (/ (- x t) (/ z y)))
       (if (<= a 5.2e-26)
         (* (- t x) (/ y (- a z)))
         (if (<= a 2080000000.0) (- t (/ (* x a) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -4.05e-19) {
		tmp = t_1;
	} else if (a <= 4.6e-106) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 5.2e-26) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 2080000000.0) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    if (a <= (-4.05d-19)) then
        tmp = t_1
    else if (a <= 4.6d-106) then
        tmp = t + ((x - t) / (z / y))
    else if (a <= 5.2d-26) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 2080000000.0d0) then
        tmp = t - ((x * a) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -4.05e-19) {
		tmp = t_1;
	} else if (a <= 4.6e-106) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 5.2e-26) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 2080000000.0) {
		tmp = t - ((x * a) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -4.05e-19:
		tmp = t_1
	elif a <= 4.6e-106:
		tmp = t + ((x - t) / (z / y))
	elif a <= 5.2e-26:
		tmp = (t - x) * (y / (a - z))
	elif a <= 2080000000.0:
		tmp = t - ((x * a) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -4.05e-19)
		tmp = t_1;
	elseif (a <= 4.6e-106)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif (a <= 5.2e-26)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 2080000000.0)
		tmp = Float64(t - Float64(Float64(x * a) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -4.05e-19)
		tmp = t_1;
	elseif (a <= 4.6e-106)
		tmp = t + ((x - t) / (z / y));
	elseif (a <= 5.2e-26)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 2080000000.0)
		tmp = t - ((x * a) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.05e-19], t$95$1, If[LessEqual[a, 4.6e-106], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-26], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2080000000.0], N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.05000000000000012e-19 or 2.08e9 < a

   1. Initial program 89.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 61.2%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 73.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

      2. associate-/r/ 73.0%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(t - x\right)} \]

   5. Simplified 73.0%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - x\right)} \]

   if -4.05000000000000012e-19 < a < 4.6000000000000002e-106

   1. Initial program 68.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 82.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 82.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 82.0%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 82.0%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 82.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 82.0%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 82.0%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 88.2%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 88.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 84.7%

      \[\leadsto t - \frac{t - x}{\color{blue}{\frac{z}{y}}} \]

   if 4.6000000000000002e-106 < a < 5.2000000000000002e-26

   1. Initial program 87.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.8%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 73.8%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

      2. associate-*r/ 67.7%

         \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

      3. associate-/l* 73.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - z}{t - x}}} \]

      4. associate-/r/ 74.0%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   5. Simplified 74.0%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   if 5.2000000000000002e-26 < a < 2.08e9

   1. Initial program 55.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.5%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 83.5%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 83.5%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 83.5%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 83.5%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 83.5%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 83.5%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 83.4%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 83.4%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in t around 0 77.1%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 77.1%

         \[\leadsto t - -1 \cdot \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. neg-mul-1 77.1%

         \[\leadsto t - \color{blue}{\left(-\frac{x}{\frac{z}{y - a}}\right)} \]

      3. distribute-neg-frac 77.1%

         \[\leadsto t - \color{blue}{\frac{-x}{\frac{z}{y - a}}} \]

   8. Simplified 77.1%

      \[\leadsto t - \color{blue}{\frac{-x}{\frac{z}{y - a}}} \]

   9. Taylor expanded in y around 0 75.3%

      \[\leadsto t - \color{blue}{\frac{a \cdot x}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.05 \cdot 10^{-19}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-106}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-26}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2080000000:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 46.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -9.5e-28)
     x
     (if (<= a -1.2e-276)
       t_1
       (if (<= a 1.85e-290) (/ x (/ z y)) (if (<= a 6.5e+19) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -9.5e-28) {
		tmp = x;
	} else if (a <= -1.2e-276) {
		tmp = t_1;
	} else if (a <= 1.85e-290) {
		tmp = x / (z / y);
	} else if (a <= 6.5e+19) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-9.5d-28)) then
        tmp = x
    else if (a <= (-1.2d-276)) then
        tmp = t_1
    else if (a <= 1.85d-290) then
        tmp = x / (z / y)
    else if (a <= 6.5d+19) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -9.5e-28) {
		tmp = x;
	} else if (a <= -1.2e-276) {
		tmp = t_1;
	} else if (a <= 1.85e-290) {
		tmp = x / (z / y);
	} else if (a <= 6.5e+19) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -9.5e-28:
		tmp = x
	elif a <= -1.2e-276:
		tmp = t_1
	elif a <= 1.85e-290:
		tmp = x / (z / y)
	elif a <= 6.5e+19:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -9.5e-28)
		tmp = x;
	elseif (a <= -1.2e-276)
		tmp = t_1;
	elseif (a <= 1.85e-290)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 6.5e+19)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -9.5e-28)
		tmp = x;
	elseif (a <= -1.2e-276)
		tmp = t_1;
	elseif (a <= 1.85e-290)
		tmp = x / (z / y);
	elseif (a <= 6.5e+19)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e-28], x, If[LessEqual[a, -1.2e-276], t$95$1, If[LessEqual[a, 1.85e-290], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+19], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.50000000000000001e-28 or 6.5e19 < a

   1. Initial program 87.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 42.5%

      \[\leadsto \color{blue}{x} \]

   if -9.50000000000000001e-28 < a < -1.19999999999999991e-276 or 1.84999999999999989e-290 < a < 6.5e19

   1. Initial program 70.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 76.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 76.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 76.1%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 76.1%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 76.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 76.1%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 76.1%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 80.2%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 80.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 73.7%

      \[\leadsto t - \frac{t - x}{\color{blue}{\frac{z}{y}}} \]

   7. Taylor expanded in t around inf 55.0%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]

   if -1.19999999999999991e-276 < a < 1.84999999999999989e-290

   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 93.4%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 93.4%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 93.4%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 93.4%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 93.4%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 93.4%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 93.4%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 100.0%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in t around 0 87.1%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 93.8%

         \[\leadsto t - -1 \cdot \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. neg-mul-1 93.8%

         \[\leadsto t - \color{blue}{\left(-\frac{x}{\frac{z}{y - a}}\right)} \]

      3. distribute-neg-frac 93.8%

         \[\leadsto t - \color{blue}{\frac{-x}{\frac{z}{y - a}}} \]

   8. Simplified 93.8%

      \[\leadsto t - \color{blue}{\frac{-x}{\frac{z}{y - a}}} \]

   9. Taylor expanded in y around inf 74.2%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   10. Step-by-step derivation

       1. associate-/l* 80.8%

          \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   11. Simplified 80.8%

       \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 64.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.78 \cdot 10^{-19}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-203}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+92}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.78e-19)
   (+ t (* x (/ y z)))
   (if (<= z 4e-203)
     (+ x (* (- t x) (/ y a)))
     (if (<= z 6.2e+92) (* (- t x) (/ y (- a z))) (+ t (* y (/ x z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.78e-19) {
		tmp = t + (x * (y / z));
	} else if (z <= 4e-203) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 6.2e+92) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.78d-19)) then
        tmp = t + (x * (y / z))
    else if (z <= 4d-203) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 6.2d+92) then
        tmp = (t - x) * (y / (a - z))
    else
        tmp = t + (y * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.78e-19) {
		tmp = t + (x * (y / z));
	} else if (z <= 4e-203) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 6.2e+92) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.78e-19:
		tmp = t + (x * (y / z))
	elif z <= 4e-203:
		tmp = x + ((t - x) * (y / a))
	elif z <= 6.2e+92:
		tmp = (t - x) * (y / (a - z))
	else:
		tmp = t + (y * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.78e-19)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (z <= 4e-203)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 6.2e+92)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	else
		tmp = Float64(t + Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.78e-19)
		tmp = t + (x * (y / z));
	elseif (z <= 4e-203)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 6.2e+92)
		tmp = (t - x) * (y / (a - z));
	else
		tmp = t + (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.78e-19], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-203], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+92], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.78000000000000011e-19

   1. Initial program 54.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 67.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 67.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 67.1%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 67.1%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 67.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 67.1%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 67.1%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 75.9%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 75.9%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 58.9%

      \[\leadsto t - \frac{t - x}{\color{blue}{\frac{z}{y}}} \]

   7. Taylor expanded in t around 0 52.8%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 54.3%

         \[\leadsto t - -1 \cdot \color{blue}{\left(x \cdot \frac{y}{z}\right)} \]

      2. neg-mul-1 54.3%

         \[\leadsto t - \color{blue}{\left(-x \cdot \frac{y}{z}\right)} \]

      3. distribute-rgt-neg-in 54.3%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y}{z}\right)} \]

      4. distribute-neg-frac 54.3%

         \[\leadsto t - x \cdot \color{blue}{\frac{-y}{z}} \]

   9. Simplified 54.3%

      \[\leadsto t - \color{blue}{x \cdot \frac{-y}{z}} \]

   if -1.78000000000000011e-19 < z < 4.0000000000000001e-203

   1. Initial program 96.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 83.6%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 88.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

      2. associate-/r/ 86.8%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(t - x\right)} \]

   5. Simplified 86.8%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - x\right)} \]

   if 4.0000000000000001e-203 < z < 6.2000000000000004e92

   1. Initial program 88.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 58.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   4. Step-by-step derivation

      1. div-sub 59.1%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

      2. associate-*r/ 51.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

      3. associate-/l* 59.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - z}{t - x}}} \]

      4. associate-/r/ 62.6%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   5. Simplified 62.6%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   if 6.2000000000000004e92 < z

   1. Initial program 64.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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-- 67.3%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 84.8%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 84.8%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in t around 0 70.1%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 80.4%

         \[\leadsto t - -1 \cdot \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. neg-mul-1 80.4%

         \[\leadsto t - \color{blue}{\left(-\frac{x}{\frac{z}{y - a}}\right)} \]

      3. distribute-neg-frac 80.4%

         \[\leadsto t - \color{blue}{\frac{-x}{\frac{z}{y - a}}} \]

   8. Simplified 80.4%

      \[\leadsto t - \color{blue}{\frac{-x}{\frac{z}{y - a}}} \]

   9. Taylor expanded in y around inf 66.2%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 66.2%

          \[\leadsto t - \color{blue}{\left(-\frac{x \cdot y}{z}\right)} \]

       2. associate-*l/ 72.5%

          \[\leadsto t - \left(-\color{blue}{\frac{x}{z} \cdot y}\right) \]

       3. *-commutative 72.5%

          \[\leadsto t - \left(-\color{blue}{y \cdot \frac{x}{z}}\right) \]

       4. distribute-rgt-neg-in 72.5%

          \[\leadsto t - \color{blue}{y \cdot \left(-\frac{x}{z}\right)} \]

       5. distribute-neg-frac 72.5%

          \[\leadsto t - y \cdot \color{blue}{\frac{-x}{z}} \]

   11. Simplified 72.5%

       \[\leadsto t - \color{blue}{y \cdot \frac{-x}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.78 \cdot 10^{-19}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-203}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+92}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 69.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.15 \cdot 10^{-19}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-76}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.15e-19)
   (+ t (/ x (/ z (- y a))))
   (if (<= z 3.2e-76) (+ x (* (- t x) (/ y a))) (+ t (/ (- x t) (/ z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.15e-19) {
		tmp = t + (x / (z / (y - a)));
	} else if (z <= 3.2e-76) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.15d-19)) then
        tmp = t + (x / (z / (y - a)))
    else if (z <= 3.2d-76) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t + ((x - t) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.15e-19) {
		tmp = t + (x / (z / (y - a)));
	} else if (z <= 3.2e-76) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.15e-19:
		tmp = t + (x / (z / (y - a)))
	elif z <= 3.2e-76:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.15e-19)
		tmp = Float64(t + Float64(x / Float64(z / Float64(y - a))));
	elseif (z <= 3.2e-76)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.15e-19)
		tmp = t + (x / (z / (y - a)));
	elseif (z <= 3.2e-76)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.15e-19], N[(t + N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-76], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1500000000000001e-19

   1. Initial program 54.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 67.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 67.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 67.1%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 67.1%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 67.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 67.1%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 67.1%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 75.9%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 75.9%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in t around 0 65.8%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 71.6%

         \[\leadsto t - -1 \cdot \color{blue}{\frac{x}{\frac{z}{y - a}}} \]

      2. neg-mul-1 71.6%

         \[\leadsto t - \color{blue}{\left(-\frac{x}{\frac{z}{y - a}}\right)} \]

      3. distribute-neg-frac 71.6%

         \[\leadsto t - \color{blue}{\frac{-x}{\frac{z}{y - a}}} \]

   8. Simplified 71.6%

      \[\leadsto t - \color{blue}{\frac{-x}{\frac{z}{y - a}}} \]

   if -4.1500000000000001e-19 < z < 3.1999999999999998e-76

   1. Initial program 96.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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* 85.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

      2. associate-/r/ 83.4%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(t - x\right)} \]

   5. Simplified 83.4%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - x\right)} \]

   if 3.1999999999999998e-76 < z

   1. Initial program 73.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 66.7%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 66.7%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 66.7%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 66.7%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 66.7%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 66.7%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 68.0%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 80.4%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 80.4%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 73.3%

      \[\leadsto t - \frac{t - x}{\color{blue}{\frac{z}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.15 \cdot 10^{-19}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-76}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 37.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.6e-19)
   x
   (if (<= a 6.2e-290) (* x (/ y z)) (if (<= a 6.5e+19) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.6e-19) {
		tmp = x;
	} else if (a <= 6.2e-290) {
		tmp = x * (y / z);
	} else if (a <= 6.5e+19) {
		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 <= (-8.6d-19)) then
        tmp = x
    else if (a <= 6.2d-290) then
        tmp = x * (y / z)
    else if (a <= 6.5d+19) 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 <= -8.6e-19) {
		tmp = x;
	} else if (a <= 6.2e-290) {
		tmp = x * (y / z);
	} else if (a <= 6.5e+19) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.6e-19:
		tmp = x
	elif a <= 6.2e-290:
		tmp = x * (y / z)
	elif a <= 6.5e+19:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.6e-19)
		tmp = x;
	elseif (a <= 6.2e-290)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 6.5e+19)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.6e-19)
		tmp = x;
	elseif (a <= 6.2e-290)
		tmp = x * (y / z);
	elseif (a <= 6.5e+19)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.6e-19], x, If[LessEqual[a, 6.2e-290], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+19], t, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.6e-19 or 6.5e19 < a

   1. Initial program 89.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 42.9%

      \[\leadsto \color{blue}{x} \]

   if -8.6e-19 < a < 6.1999999999999998e-290

   1. Initial program 65.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 80.7%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ 80.7%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 80.7%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 80.7%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 80.7%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 80.7%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. distribute-rgt-out-- 80.7%

         \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

      7. associate-/l* 85.2%

         \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   5. Simplified 85.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   6. Taylor expanded in y around inf 82.1%

      \[\leadsto t - \frac{t - x}{\color{blue}{\frac{z}{y}}} \]

   7. Taylor expanded in t around 0 42.8%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 46.9%

         \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   9. Simplified 46.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   if 6.1999999999999998e-290 < a < 6.5e19

   1. Initial program 72.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 33.6%

      \[\leadsto \color{blue}{t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.2e-28) x (if (<= a 4.2e+19) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.2e-28) {
		tmp = x;
	} else if (a <= 4.2e+19) {
		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 <= (-9.2d-28)) then
        tmp = x
    else if (a <= 4.2d+19) 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 <= -9.2e-28) {
		tmp = x;
	} else if (a <= 4.2e+19) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.2e-28:
		tmp = x
	elif a <= 4.2e+19:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.2e-28)
		tmp = x;
	elseif (a <= 4.2e+19)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.2e-28)
		tmp = x;
	elseif (a <= 4.2e+19)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.2e-28], x, If[LessEqual[a, 4.2e+19], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.19999999999999942e-28 or 4.2e19 < a

   1. Initial program 87.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 42.5%

      \[\leadsto \color{blue}{x} \]

   if -9.19999999999999942e-28 < a < 4.2e19

   1. Initial program 70.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 34.1%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 78.4%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
2. Add Preprocessing

3. Taylor expanded in t around 0 44.1%

   \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(-1 \cdot \frac{x}{a - z}\right)} \]
4. Step-by-step derivation

   1. neg-mul-1 44.1%

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(-\frac{x}{a - z}\right)} \]

   2. distribute-neg-frac 44.1%

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{-x}{a - z}} \]

5. Simplified 44.1%

   \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{-x}{a - z}} \]

6. Taylor expanded in z around inf 2.8%

   \[\leadsto \color{blue}{x + -1 \cdot x} \]
7. Step-by-step derivation

   1. mul-1-neg 2.8%

      \[\leadsto x + \color{blue}{\left(-x\right)} \]

   2. sub-neg 2.8%

      \[\leadsto \color{blue}{x - x} \]

   3. +-inverses 2.8%

      \[\leadsto \color{blue}{0} \]

8. Simplified 2.8%

   \[\leadsto \color{blue}{0} \]

9. Final simplification 2.8%

   \[\leadsto 0 \]
10. Add Preprocessing

Alternative 26: 24.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t;
}

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 78.4%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf 22.8%

   \[\leadsto \color{blue}{t} \]

4. Final simplification 22.8%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024020 
(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)))))