Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.1% → 95.4%

Time: 15.0s

Alternatives: 22

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-307}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-307)
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (if (<= t_1 0.0)
       (+ t (* (/ (- t x) z) (- a y)))
       (fma (- t x) (/ (- y z) (- a z)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-307) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-307)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-307], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.99999999999999909e-308

   1. Initial program 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-*l/ 74.7%

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

      3. associate-*r/ 92.3%

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

      4. clear-num 92.2%

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

      5. un-div-inv 92.5%

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

   4. Applied egg-rr 92.5%

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

   if -9.99999999999999909e-308 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 85.0%

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

      1. associate--l+ 85.0%

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

      2. distribute-lft-out-- 85.0%

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

      3. div-sub 84.9%

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

      4. mul-1-neg 84.9%

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

      5. unsub-neg 84.9%

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

      6. div-sub 85.0%

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

      7. associate-/l* 88.7%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   5. Simplified 99.9%

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

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

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. remove-double-neg 90.0%

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

      3. unsub-neg 90.0%

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

      4. *-commutative 90.0%

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

      5. associate-*l/ 74.5%

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

      6. associate-/l* 93.4%

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

      7. fma-neg 93.4%

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

      8. remove-double-neg 93.4%

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

   3. Simplified 93.4%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-307}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-307} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-307) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-307) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-307)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-307) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-307) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-307) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-307) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-307], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.99999999999999909e-308 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-*l/ 74.6%

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

      3. associate-*r/ 92.8%

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

      4. clear-num 92.7%

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

      5. un-div-inv 92.9%

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

   4. Applied egg-rr 92.9%

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

   if -9.99999999999999909e-308 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 85.0%

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

      1. associate--l+ 85.0%

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

      2. distribute-lft-out-- 85.0%

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

      3. div-sub 84.9%

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

      4. mul-1-neg 84.9%

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

      5. unsub-neg 84.9%

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

      6. div-sub 85.0%

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

      7. associate-/l* 88.7%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-307} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-112} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -4e-112) (not (<= t_1 0.0)))
     t_1
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-112) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-4d-112)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-112) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -4e-112) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -4e-112) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -4e-112) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-112], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -3.9999999999999998e-112 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.0%

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

   if -3.9999999999999998e-112 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 11.7%

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

   3. Taylor expanded in z around inf 79.4%

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

      1. associate--l+ 79.4%

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

      2. distribute-lft-out-- 79.4%

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

      3. div-sub 79.4%

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

      4. mul-1-neg 79.4%

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

      5. unsub-neg 79.4%

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

      6. div-sub 79.4%

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

      7. associate-/l* 82.0%

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

      8. associate-/l* 89.6%

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

      9. distribute-rgt-out-- 89.6%

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

   5. Simplified 89.6%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-112} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -0.6:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-235}:\\ \;\;\;\;\frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-25}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* t (/ (- y z) a)))))
   (if (<= a -0.6)
     t_2
     (if (<= a -2.7e-224)
       t_1
       (if (<= a 6e-235)
         (* (/ (- t x) z) (- a y))
         (if (<= a 7.5e-119)
           t_1
           (if (<= a 5.4e-25)
             (* (- t x) (/ y (- a z)))
             (if (<= a 7.6e+56) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -0.6) {
		tmp = t_2;
	} else if (a <= -2.7e-224) {
		tmp = t_1;
	} else if (a <= 6e-235) {
		tmp = ((t - x) / z) * (a - y);
	} else if (a <= 7.5e-119) {
		tmp = t_1;
	} else if (a <= 5.4e-25) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 7.6e+56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (t * ((y - z) / a))
    if (a <= (-0.6d0)) then
        tmp = t_2
    else if (a <= (-2.7d-224)) then
        tmp = t_1
    else if (a <= 6d-235) then
        tmp = ((t - x) / z) * (a - y)
    else if (a <= 7.5d-119) then
        tmp = t_1
    else if (a <= 5.4d-25) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 7.6d+56) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -0.6) {
		tmp = t_2;
	} else if (a <= -2.7e-224) {
		tmp = t_1;
	} else if (a <= 6e-235) {
		tmp = ((t - x) / z) * (a - y);
	} else if (a <= 7.5e-119) {
		tmp = t_1;
	} else if (a <= 5.4e-25) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 7.6e+56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (t * ((y - z) / a))
	tmp = 0
	if a <= -0.6:
		tmp = t_2
	elif a <= -2.7e-224:
		tmp = t_1
	elif a <= 6e-235:
		tmp = ((t - x) / z) * (a - y)
	elif a <= 7.5e-119:
		tmp = t_1
	elif a <= 5.4e-25:
		tmp = (t - x) * (y / (a - z))
	elif a <= 7.6e+56:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(t * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -0.6)
		tmp = t_2;
	elseif (a <= -2.7e-224)
		tmp = t_1;
	elseif (a <= 6e-235)
		tmp = Float64(Float64(Float64(t - x) / z) * Float64(a - y));
	elseif (a <= 7.5e-119)
		tmp = t_1;
	elseif (a <= 5.4e-25)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 7.6e+56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (t * ((y - z) / a));
	tmp = 0.0;
	if (a <= -0.6)
		tmp = t_2;
	elseif (a <= -2.7e-224)
		tmp = t_1;
	elseif (a <= 6e-235)
		tmp = ((t - x) / z) * (a - y);
	elseif (a <= 7.5e-119)
		tmp = t_1;
	elseif (a <= 5.4e-25)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 7.6e+56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.6], t$95$2, If[LessEqual[a, -2.7e-224], t$95$1, If[LessEqual[a, 6e-235], N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-119], t$95$1, If[LessEqual[a, 5.4e-25], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e+56], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.599999999999999978 or 7.59999999999999991e56 < a

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

      2. associate-*l/ 68.0%

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

      3. associate-*r/ 91.3%

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

      4. clear-num 91.2%

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

      5. un-div-inv 91.3%

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

   4. Applied egg-rr 91.3%

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

   5. Taylor expanded in a around inf 80.9%

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

   6. Taylor expanded in t around inf 64.5%

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

      1. associate-*r/ 73.2%

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

   8. Simplified 73.2%

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

   if -0.599999999999999978 < a < -2.69999999999999998e-224 or 5.9999999999999997e-235 < a < 7.50000000000000044e-119 or 5.40000000000000032e-25 < a < 7.59999999999999991e56

   1. Initial program 68.9%

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

   3. Taylor expanded in x around 0 52.2%

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

      1. associate-/l* 66.1%

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

   5. Simplified 66.1%

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

   if -2.69999999999999998e-224 < a < 5.9999999999999997e-235

   1. Initial program 74.6%

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

   3. Taylor expanded in z around inf 90.9%

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

      1. associate--l+ 90.9%

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

      2. distribute-lft-out-- 90.9%

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

      3. div-sub 90.8%

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

      4. mul-1-neg 90.8%

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

      5. unsub-neg 90.8%

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

      6. div-sub 90.9%

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

      7. associate-/l* 94.0%

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

      8. associate-/l* 81.1%

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

      9. distribute-rgt-out-- 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in z around 0 71.5%

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

      1. associate-*r/ 71.5%

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

      2. neg-mul-1 71.5%

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

      3. distribute-rgt-neg-in 71.5%

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

      4. associate-*l/ 74.6%

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

      5. distribute-rgt-neg-out 74.6%

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

      6. sub-neg 74.6%

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

      7. distribute-lft-out 61.7%

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

      8. associate-*l/ 55.7%

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

      9. associate-*r/ 56.0%

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

      10. +-commutative 56.0%

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

      11. *-commutative 56.0%

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

      12. distribute-lft-neg-out 56.0%

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

      13. associate-/l* 71.8%

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

      14. mul-1-neg 71.8%

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

      15. distribute-neg-in 71.8%

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

      16. mul-1-neg 71.8%

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

      17. remove-double-neg 71.8%

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

   8. Simplified 74.6%

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

   if 7.50000000000000044e-119 < a < 5.40000000000000032e-25

   1. Initial program 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-*l/ 65.8%

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

      3. associate-*r/ 76.4%

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

      4. clear-num 76.2%

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

      5. un-div-inv 76.2%

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

   4. Applied egg-rr 76.2%

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

   5. Taylor expanded in y around inf 71.6%

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

      1. div-sub 71.6%

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

      2. associate-*r/ 67.2%

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

      3. *-rgt-identity 67.2%

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

      4. times-frac 76.2%

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

      5. /-rgt-identity 76.2%

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

   7. Simplified 76.2%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.6:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-224}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-235}:\\ \;\;\;\;\frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-25}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y \cdot t}{z}\\ t_2 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -3 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* y t) z))) (t_2 (* y (/ (- t x) a))))
   (if (<= a -3e+122)
     x
     (if (<= a -4.6e+70)
       t_2
       (if (<= a -5.2e-85)
         x
         (if (<= a -1.85e-222)
           t_1
           (if (<= a 2.5e-17)
             (* y (/ (- x t) z))
             (if (<= a 1.4e+94) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * t) / z);
	double t_2 = y * ((t - x) / a);
	double tmp;
	if (a <= -3e+122) {
		tmp = x;
	} else if (a <= -4.6e+70) {
		tmp = t_2;
	} else if (a <= -5.2e-85) {
		tmp = x;
	} else if (a <= -1.85e-222) {
		tmp = t_1;
	} else if (a <= 2.5e-17) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.4e+94) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - ((y * t) / z)
    t_2 = y * ((t - x) / a)
    if (a <= (-3d+122)) then
        tmp = x
    else if (a <= (-4.6d+70)) then
        tmp = t_2
    else if (a <= (-5.2d-85)) then
        tmp = x
    else if (a <= (-1.85d-222)) then
        tmp = t_1
    else if (a <= 2.5d-17) then
        tmp = y * ((x - t) / z)
    else if (a <= 1.4d+94) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * t) / z);
	double t_2 = y * ((t - x) / a);
	double tmp;
	if (a <= -3e+122) {
		tmp = x;
	} else if (a <= -4.6e+70) {
		tmp = t_2;
	} else if (a <= -5.2e-85) {
		tmp = x;
	} else if (a <= -1.85e-222) {
		tmp = t_1;
	} else if (a <= 2.5e-17) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.4e+94) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y * t) / z)
	t_2 = y * ((t - x) / a)
	tmp = 0
	if a <= -3e+122:
		tmp = x
	elif a <= -4.6e+70:
		tmp = t_2
	elif a <= -5.2e-85:
		tmp = x
	elif a <= -1.85e-222:
		tmp = t_1
	elif a <= 2.5e-17:
		tmp = y * ((x - t) / z)
	elif a <= 1.4e+94:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y * t) / z))
	t_2 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (a <= -3e+122)
		tmp = x;
	elseif (a <= -4.6e+70)
		tmp = t_2;
	elseif (a <= -5.2e-85)
		tmp = x;
	elseif (a <= -1.85e-222)
		tmp = t_1;
	elseif (a <= 2.5e-17)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 1.4e+94)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y * t) / z);
	t_2 = y * ((t - x) / a);
	tmp = 0.0;
	if (a <= -3e+122)
		tmp = x;
	elseif (a <= -4.6e+70)
		tmp = t_2;
	elseif (a <= -5.2e-85)
		tmp = x;
	elseif (a <= -1.85e-222)
		tmp = t_1;
	elseif (a <= 2.5e-17)
		tmp = y * ((x - t) / z);
	elseif (a <= 1.4e+94)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3e+122], x, If[LessEqual[a, -4.6e+70], t$95$2, If[LessEqual[a, -5.2e-85], x, If[LessEqual[a, -1.85e-222], t$95$1, If[LessEqual[a, 2.5e-17], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+94], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.99999999999999986e122 or -4.59999999999999987e70 < a < -5.20000000000000023e-85

   1. Initial program 80.9%

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

   3. Taylor expanded in a around inf 53.3%

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

   if -2.99999999999999986e122 < a < -4.59999999999999987e70 or 1.39999999999999999e94 < a

   1. Initial program 90.4%

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

   3. Taylor expanded in y around inf 50.3%

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

      1. div-sub 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in a around inf 46.4%

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

   if -5.20000000000000023e-85 < a < -1.8499999999999999e-222 or 2.4999999999999999e-17 < a < 1.39999999999999999e94

   1. Initial program 74.9%

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

   3. Taylor expanded in a around 0 37.0%

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

      1. mul-1-neg 37.0%

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

      2. unsub-neg 37.0%

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

      3. associate-/l* 42.1%

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

      4. div-sub 42.2%

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

      5. sub-neg 42.2%

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

      6. *-inverses 42.2%

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

      7. metadata-eval 42.2%

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

   5. Simplified 42.2%

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

   6. Taylor expanded in x around 0 48.4%

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

      1. mul-1-neg 48.4%

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

      2. sub-neg 48.4%

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

      3. metadata-eval 48.4%

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

      4. distribute-rgt-neg-in 48.4%

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

      5. +-commutative 48.4%

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

      6. distribute-neg-in 48.4%

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

      7. metadata-eval 48.4%

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

      8. sub-neg 48.4%

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

   8. Simplified 48.4%

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

   9. Taylor expanded in y around 0 48.5%

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

       1. mul-1-neg 48.5%

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

       2. associate-*r/ 48.4%

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

       3. unsub-neg 48.4%

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

       4. *-commutative 48.4%

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

       5. associate-*l/ 48.5%

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

   11. Simplified 48.5%

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

   if -1.8499999999999999e-222 < a < 2.4999999999999999e-17

   1. Initial program 69.4%

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

   3. Taylor expanded in y around inf 62.6%

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

      1. div-sub 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in a around 0 52.3%

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

      1. mul-1-neg 52.3%

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

      2. associate-/l* 58.1%

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

      3. distribute-rgt-neg-in 58.1%

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

      4. distribute-neg-frac2 58.1%

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

   8. Simplified 58.1%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-222}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 32.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-215}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-290}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.45e-68)
   x
   (if (<= a -2.2e-215)
     t
     (if (<= a 2.05e-290)
       (* t (/ (- y) z))
       (if (<= a 8e+57) t (if (<= a 5.6e+102) x (/ t (/ a y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.45e-68) {
		tmp = x;
	} else if (a <= -2.2e-215) {
		tmp = t;
	} else if (a <= 2.05e-290) {
		tmp = t * (-y / z);
	} else if (a <= 8e+57) {
		tmp = t;
	} else if (a <= 5.6e+102) {
		tmp = x;
	} 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) :: tmp
    if (a <= (-1.45d-68)) then
        tmp = x
    else if (a <= (-2.2d-215)) then
        tmp = t
    else if (a <= 2.05d-290) then
        tmp = t * (-y / z)
    else if (a <= 8d+57) then
        tmp = t
    else if (a <= 5.6d+102) then
        tmp = x
    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 tmp;
	if (a <= -1.45e-68) {
		tmp = x;
	} else if (a <= -2.2e-215) {
		tmp = t;
	} else if (a <= 2.05e-290) {
		tmp = t * (-y / z);
	} else if (a <= 8e+57) {
		tmp = t;
	} else if (a <= 5.6e+102) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.45e-68:
		tmp = x
	elif a <= -2.2e-215:
		tmp = t
	elif a <= 2.05e-290:
		tmp = t * (-y / z)
	elif a <= 8e+57:
		tmp = t
	elif a <= 5.6e+102:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.45e-68)
		tmp = x;
	elseif (a <= -2.2e-215)
		tmp = t;
	elseif (a <= 2.05e-290)
		tmp = Float64(t * Float64(Float64(-y) / z));
	elseif (a <= 8e+57)
		tmp = t;
	elseif (a <= 5.6e+102)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.45e-68)
		tmp = x;
	elseif (a <= -2.2e-215)
		tmp = t;
	elseif (a <= 2.05e-290)
		tmp = t * (-y / z);
	elseif (a <= 8e+57)
		tmp = t;
	elseif (a <= 5.6e+102)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.45e-68], x, If[LessEqual[a, -2.2e-215], t, If[LessEqual[a, 2.05e-290], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+57], t, If[LessEqual[a, 5.6e+102], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.45e-68 or 8.00000000000000039e57 < a < 5.60000000000000037e102

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 48.2%

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

   if -1.45e-68 < a < -2.19999999999999996e-215 or 2.0500000000000001e-290 < a < 8.00000000000000039e57

   1. Initial program 67.8%

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

   3. Taylor expanded in z around inf 34.8%

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

   if -2.19999999999999996e-215 < a < 2.0500000000000001e-290

   1. Initial program 88.7%

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

   3. Taylor expanded in a around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. unsub-neg 77.6%

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

      3. associate-/l* 81.7%

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

      4. div-sub 81.7%

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

      5. sub-neg 81.7%

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

      6. *-inverses 81.7%

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

      7. metadata-eval 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in x around 0 59.3%

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

      1. mul-1-neg 59.3%

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

      2. sub-neg 59.3%

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

      3. metadata-eval 59.3%

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

      4. distribute-rgt-neg-in 59.3%

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

      5. +-commutative 59.3%

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

      6. distribute-neg-in 59.3%

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

      7. metadata-eval 59.3%

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

      8. sub-neg 59.3%

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

   8. Simplified 59.3%

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

   9. Taylor expanded in y around inf 41.3%

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

       1. associate-*r/ 42.7%

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

       2. neg-mul-1 42.7%

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

       3. distribute-rgt-neg-in 42.7%

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

       4. distribute-neg-frac2 42.7%

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

   11. Simplified 42.7%

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

   if 5.60000000000000037e102 < a

   1. Initial program 90.4%

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

   3. Taylor expanded in y around inf 46.0%

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

      1. div-sub 46.0%

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

   5. Simplified 46.0%

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

   6. Taylor expanded in a around inf 43.5%

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

   7. Taylor expanded in t around inf 29.0%

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

      1. associate-/l* 40.8%

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

   9. Simplified 40.8%

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

       1. clear-num 40.7%

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

       2. un-div-inv 40.8%

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

   11. Applied egg-rr 40.8%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-215}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-290}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 30.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{+154}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-128}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 19000000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= t -5.6e+241)
     t_1
     (if (<= t -1.02e+154)
       t
       (if (<= t -5.4e+100)
         x
         (if (<= t -2e-128) t (if (<= t 19000000000000.0) x t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -5.6e+241) {
		tmp = t_1;
	} else if (t <= -1.02e+154) {
		tmp = t;
	} else if (t <= -5.4e+100) {
		tmp = x;
	} else if (t <= -2e-128) {
		tmp = t;
	} else if (t <= 19000000000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (t <= (-5.6d+241)) then
        tmp = t_1
    else if (t <= (-1.02d+154)) then
        tmp = t
    else if (t <= (-5.4d+100)) then
        tmp = x
    else if (t <= (-2d-128)) then
        tmp = t
    else if (t <= 19000000000000.0d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -5.6e+241) {
		tmp = t_1;
	} else if (t <= -1.02e+154) {
		tmp = t;
	} else if (t <= -5.4e+100) {
		tmp = x;
	} else if (t <= -2e-128) {
		tmp = t;
	} else if (t <= 19000000000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if t <= -5.6e+241:
		tmp = t_1
	elif t <= -1.02e+154:
		tmp = t
	elif t <= -5.4e+100:
		tmp = x
	elif t <= -2e-128:
		tmp = t
	elif t <= 19000000000000.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (t <= -5.6e+241)
		tmp = t_1;
	elseif (t <= -1.02e+154)
		tmp = t;
	elseif (t <= -5.4e+100)
		tmp = x;
	elseif (t <= -2e-128)
		tmp = t;
	elseif (t <= 19000000000000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (t <= -5.6e+241)
		tmp = t_1;
	elseif (t <= -1.02e+154)
		tmp = t;
	elseif (t <= -5.4e+100)
		tmp = x;
	elseif (t <= -2e-128)
		tmp = t;
	elseif (t <= 19000000000000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+241], t$95$1, If[LessEqual[t, -1.02e+154], t, If[LessEqual[t, -5.4e+100], x, If[LessEqual[t, -2e-128], t, If[LessEqual[t, 19000000000000.0], x, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.60000000000000052e241 or 1.9e13 < t

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf 56.2%

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

      1. div-sub 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in a around inf 54.1%

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

   7. Taylor expanded in t around inf 39.4%

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

      1. associate-/l* 51.5%

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

   9. Simplified 51.5%

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

   if -5.60000000000000052e241 < t < -1.02000000000000007e154 or -5.39999999999999997e100 < t < -2.00000000000000011e-128

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf 34.1%

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

   if -1.02000000000000007e154 < t < -5.39999999999999997e100 or -2.00000000000000011e-128 < t < 1.9e13

   1. Initial program 74.2%

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

   3. Taylor expanded in a around inf 38.4%

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

Alternative 8: 66.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+71}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+188} \lor \neg \left(z \leq 5.5 \cdot 10^{+203}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -4.3e+27)
     t_1
     (if (<= z 2.05e+71)
       (+ x (/ (- t x) (/ a y)))
       (if (or (<= z 9e+188) (not (<= z 5.5e+203)))
         t_1
         (* (/ (- t x) z) (- a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.3e+27) {
		tmp = t_1;
	} else if (z <= 2.05e+71) {
		tmp = x + ((t - x) / (a / y));
	} else if ((z <= 9e+188) || !(z <= 5.5e+203)) {
		tmp = t_1;
	} else {
		tmp = ((t - x) / z) * (a - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-4.3d+27)) then
        tmp = t_1
    else if (z <= 2.05d+71) then
        tmp = x + ((t - x) / (a / y))
    else if ((z <= 9d+188) .or. (.not. (z <= 5.5d+203))) then
        tmp = t_1
    else
        tmp = ((t - x) / z) * (a - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.3e+27) {
		tmp = t_1;
	} else if (z <= 2.05e+71) {
		tmp = x + ((t - x) / (a / y));
	} else if ((z <= 9e+188) || !(z <= 5.5e+203)) {
		tmp = t_1;
	} else {
		tmp = ((t - x) / z) * (a - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -4.3e+27:
		tmp = t_1
	elif z <= 2.05e+71:
		tmp = x + ((t - x) / (a / y))
	elif (z <= 9e+188) or not (z <= 5.5e+203):
		tmp = t_1
	else:
		tmp = ((t - x) / z) * (a - y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -4.3e+27)
		tmp = t_1;
	elseif (z <= 2.05e+71)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif ((z <= 9e+188) || !(z <= 5.5e+203))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(t - x) / z) * Float64(a - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -4.3e+27)
		tmp = t_1;
	elseif (z <= 2.05e+71)
		tmp = x + ((t - x) / (a / y));
	elseif ((z <= 9e+188) || ~((z <= 5.5e+203)))
		tmp = t_1;
	else
		tmp = ((t - x) / z) * (a - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+27], t$95$1, If[LessEqual[z, 2.05e+71], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 9e+188], N[Not[LessEqual[z, 5.5e+203]], $MachinePrecision]], t$95$1, N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.30000000000000008e27 or 2.0500000000000001e71 < z < 9.00000000000000021e188 or 5.50000000000000029e203 < z

   1. Initial program 63.4%

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

   3. Taylor expanded in x around 0 43.6%

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

      1. associate-/l* 65.9%

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

   5. Simplified 65.9%

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

   if -4.30000000000000008e27 < z < 2.0500000000000001e71

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-*l/ 85.1%

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

      3. associate-*r/ 95.8%

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

      4. clear-num 95.7%

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

      5. un-div-inv 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in z around 0 75.5%

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

   if 9.00000000000000021e188 < z < 5.50000000000000029e203

   1. Initial program 41.3%

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

   3. Taylor expanded in z around inf 45.9%

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

      1. associate--l+ 45.9%

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

      2. distribute-lft-out-- 45.9%

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

      3. div-sub 45.9%

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

      4. mul-1-neg 45.9%

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

      5. unsub-neg 45.9%

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

      6. div-sub 45.9%

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

      7. associate-/l* 86.8%

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

      8. associate-/l* 86.8%

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

      9. distribute-rgt-out-- 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in z around 0 45.9%

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

      1. associate-*r/ 45.9%

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

      2. neg-mul-1 45.9%

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

      3. distribute-rgt-neg-in 45.9%

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

      4. associate-*l/ 81.0%

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

      5. distribute-rgt-neg-out 81.0%

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

      6. sub-neg 81.0%

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

      7. distribute-lft-out 81.0%

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

      8. associate-*l/ 45.9%

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

      9. associate-*r/ 80.5%

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

      10. +-commutative 80.5%

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

      11. *-commutative 80.5%

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

      12. distribute-lft-neg-out 80.5%

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

      13. associate-/l* 80.5%

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

      14. mul-1-neg 80.5%

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

      15. distribute-neg-in 80.5%

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

      16. mul-1-neg 80.5%

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

      17. remove-double-neg 80.5%

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

   8. Simplified 81.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+71}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+188} \lor \neg \left(z \leq 5.5 \cdot 10^{+203}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+71}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+188} \lor \neg \left(z \leq 6.8 \cdot 10^{+203}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -8e+20)
     t_1
     (if (<= z 2.5e+71)
       (+ x (* y (/ (- t x) a)))
       (if (or (<= z 9.5e+188) (not (<= z 6.8e+203)))
         t_1
         (* (/ (- t x) z) (- a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -8e+20) {
		tmp = t_1;
	} else if (z <= 2.5e+71) {
		tmp = x + (y * ((t - x) / a));
	} else if ((z <= 9.5e+188) || !(z <= 6.8e+203)) {
		tmp = t_1;
	} else {
		tmp = ((t - x) / z) * (a - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-8d+20)) then
        tmp = t_1
    else if (z <= 2.5d+71) then
        tmp = x + (y * ((t - x) / a))
    else if ((z <= 9.5d+188) .or. (.not. (z <= 6.8d+203))) then
        tmp = t_1
    else
        tmp = ((t - x) / z) * (a - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -8e+20) {
		tmp = t_1;
	} else if (z <= 2.5e+71) {
		tmp = x + (y * ((t - x) / a));
	} else if ((z <= 9.5e+188) || !(z <= 6.8e+203)) {
		tmp = t_1;
	} else {
		tmp = ((t - x) / z) * (a - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -8e+20:
		tmp = t_1
	elif z <= 2.5e+71:
		tmp = x + (y * ((t - x) / a))
	elif (z <= 9.5e+188) or not (z <= 6.8e+203):
		tmp = t_1
	else:
		tmp = ((t - x) / z) * (a - y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -8e+20)
		tmp = t_1;
	elseif (z <= 2.5e+71)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif ((z <= 9.5e+188) || !(z <= 6.8e+203))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(t - x) / z) * Float64(a - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -8e+20)
		tmp = t_1;
	elseif (z <= 2.5e+71)
		tmp = x + (y * ((t - x) / a));
	elseif ((z <= 9.5e+188) || ~((z <= 6.8e+203)))
		tmp = t_1;
	else
		tmp = ((t - x) / z) * (a - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+20], t$95$1, If[LessEqual[z, 2.5e+71], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 9.5e+188], N[Not[LessEqual[z, 6.8e+203]], $MachinePrecision]], t$95$1, N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8e20 or 2.49999999999999986e71 < z < 9.4999999999999996e188 or 6.8000000000000002e203 < z

   1. Initial program 62.8%

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

   3. Taylor expanded in x around 0 44.2%

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

      1. associate-/l* 66.3%

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

   5. Simplified 66.3%

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

   if -8e20 < z < 2.49999999999999986e71

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0 63.5%

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

      1. associate-/l* 73.4%

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

   5. Simplified 73.4%

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

   if 9.4999999999999996e188 < z < 6.8000000000000002e203

   1. Initial program 41.3%

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

   3. Taylor expanded in z around inf 45.9%

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

      1. associate--l+ 45.9%

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

      2. distribute-lft-out-- 45.9%

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

      3. div-sub 45.9%

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

      4. mul-1-neg 45.9%

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

      5. unsub-neg 45.9%

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

      6. div-sub 45.9%

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

      7. associate-/l* 86.8%

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

      8. associate-/l* 86.8%

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

      9. distribute-rgt-out-- 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in z around 0 45.9%

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

      1. associate-*r/ 45.9%

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

      2. neg-mul-1 45.9%

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

      3. distribute-rgt-neg-in 45.9%

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

      4. associate-*l/ 81.0%

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

      5. distribute-rgt-neg-out 81.0%

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

      6. sub-neg 81.0%

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

      7. distribute-lft-out 81.0%

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

      8. associate-*l/ 45.9%

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

      9. associate-*r/ 80.5%

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

      10. +-commutative 80.5%

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

      11. *-commutative 80.5%

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

      12. distribute-lft-neg-out 80.5%

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

      13. associate-/l* 80.5%

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

      14. mul-1-neg 80.5%

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

      15. distribute-neg-in 80.5%

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

      16. mul-1-neg 80.5%

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

      17. remove-double-neg 80.5%

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

   8. Simplified 81.0%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+71}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+188} \lor \neg \left(z \leq 6.8 \cdot 10^{+203}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -1 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= a -1e+120)
     x
     (if (<= a -4.2e+70)
       t_1
       (if (<= a -5.2e-85)
         x
         (if (<= a 1.65e+93) (* t (- 1.0 (/ y z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (a <= -1e+120) {
		tmp = x;
	} else if (a <= -4.2e+70) {
		tmp = t_1;
	} else if (a <= -5.2e-85) {
		tmp = x;
	} else if (a <= 1.65e+93) {
		tmp = t * (1.0 - (y / 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 = y * ((t - x) / a)
    if (a <= (-1d+120)) then
        tmp = x
    else if (a <= (-4.2d+70)) then
        tmp = t_1
    else if (a <= (-5.2d-85)) then
        tmp = x
    else if (a <= 1.65d+93) then
        tmp = t * (1.0d0 - (y / 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 = y * ((t - x) / a);
	double tmp;
	if (a <= -1e+120) {
		tmp = x;
	} else if (a <= -4.2e+70) {
		tmp = t_1;
	} else if (a <= -5.2e-85) {
		tmp = x;
	} else if (a <= 1.65e+93) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if a <= -1e+120:
		tmp = x
	elif a <= -4.2e+70:
		tmp = t_1
	elif a <= -5.2e-85:
		tmp = x
	elif a <= 1.65e+93:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (a <= -1e+120)
		tmp = x;
	elseif (a <= -4.2e+70)
		tmp = t_1;
	elseif (a <= -5.2e-85)
		tmp = x;
	elseif (a <= 1.65e+93)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (a <= -1e+120)
		tmp = x;
	elseif (a <= -4.2e+70)
		tmp = t_1;
	elseif (a <= -5.2e-85)
		tmp = x;
	elseif (a <= 1.65e+93)
		tmp = t * (1.0 - (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e+120], x, If[LessEqual[a, -4.2e+70], t$95$1, If[LessEqual[a, -5.2e-85], x, If[LessEqual[a, 1.65e+93], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.9999999999999998e119 or -4.20000000000000015e70 < a < -5.20000000000000023e-85

   1. Initial program 80.9%

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

   3. Taylor expanded in a around inf 53.3%

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

   if -9.9999999999999998e119 < a < -4.20000000000000015e70 or 1.65000000000000004e93 < a

   1. Initial program 90.4%

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

   3. Taylor expanded in y around inf 50.3%

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

      1. div-sub 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in a around inf 46.4%

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

   if -5.20000000000000023e-85 < a < 1.65000000000000004e93

   1. Initial program 72.2%

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

   3. Taylor expanded in a around 0 46.6%

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

      1. mul-1-neg 46.6%

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

      2. unsub-neg 46.6%

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

      3. associate-/l* 53.7%

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

      4. div-sub 53.8%

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

      5. sub-neg 53.8%

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

      6. *-inverses 53.8%

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

      7. metadata-eval 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in x around 0 48.3%

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

      1. mul-1-neg 48.3%

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

      2. sub-neg 48.3%

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

      3. metadata-eval 48.3%

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

      4. distribute-rgt-neg-in 48.3%

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

      5. +-commutative 48.3%

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

      6. distribute-neg-in 48.3%

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

      7. metadata-eval 48.3%

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

      8. sub-neg 48.3%

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

   8. Simplified 48.3%

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

Alternative 11: 40.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 10^{-15}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -5.2e-85)
     x
     (if (<= a 1.9e-118)
       t_1
       (if (<= a 1e-15)
         (* x (/ (- y a) z))
         (if (<= a 1.9e+91) t_1 (* t (/ 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 tmp;
	if (a <= -5.2e-85) {
		tmp = x;
	} else if (a <= 1.9e-118) {
		tmp = t_1;
	} else if (a <= 1e-15) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.9e+91) {
		tmp = t_1;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-5.2d-85)) then
        tmp = x
    else if (a <= 1.9d-118) then
        tmp = t_1
    else if (a <= 1d-15) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.9d+91) then
        tmp = t_1
    else
        tmp = t * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -5.2e-85) {
		tmp = x;
	} else if (a <= 1.9e-118) {
		tmp = t_1;
	} else if (a <= 1e-15) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.9e+91) {
		tmp = t_1;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -5.2e-85:
		tmp = x
	elif a <= 1.9e-118:
		tmp = t_1
	elif a <= 1e-15:
		tmp = x * ((y - a) / z)
	elif a <= 1.9e+91:
		tmp = t_1
	else:
		tmp = t * (y / (a - z))
	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 <= -5.2e-85)
		tmp = x;
	elseif (a <= 1.9e-118)
		tmp = t_1;
	elseif (a <= 1e-15)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.9e+91)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -5.2e-85)
		tmp = x;
	elseif (a <= 1.9e-118)
		tmp = t_1;
	elseif (a <= 1e-15)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.9e+91)
		tmp = t_1;
	else
		tmp = t * (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]}, If[LessEqual[a, -5.2e-85], x, If[LessEqual[a, 1.9e-118], t$95$1, If[LessEqual[a, 1e-15], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+91], t$95$1, N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.20000000000000023e-85

   1. Initial program 82.2%

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

   3. Taylor expanded in a around inf 47.6%

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

   if -5.20000000000000023e-85 < a < 1.9e-118 or 1.0000000000000001e-15 < a < 1.8999999999999999e91

   1. Initial program 73.1%

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

   3. Taylor expanded in a around 0 46.5%

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

      1. mul-1-neg 46.5%

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

      2. unsub-neg 46.5%

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

      3. associate-/l* 53.3%

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

      4. div-sub 53.3%

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

      5. sub-neg 53.3%

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

      6. *-inverses 53.3%

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

      7. metadata-eval 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in x around 0 52.2%

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

      1. mul-1-neg 52.2%

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

      2. sub-neg 52.2%

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

      3. metadata-eval 52.2%

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

      4. distribute-rgt-neg-in 52.2%

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

      5. +-commutative 52.2%

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

      6. distribute-neg-in 52.2%

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

      7. metadata-eval 52.2%

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

      8. sub-neg 52.2%

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

   8. Simplified 52.2%

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

   if 1.9e-118 < a < 1.0000000000000001e-15

   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 72.1%

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

      1. associate--l+ 72.1%

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

      2. distribute-lft-out-- 72.1%

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

      3. div-sub 72.1%

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

      4. mul-1-neg 72.1%

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

      5. unsub-neg 72.1%

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

      6. div-sub 72.1%

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

      7. associate-/l* 79.7%

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

      8. associate-/l* 79.7%

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

      9. distribute-rgt-out-- 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in t around 0 47.8%

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

      1. associate-/l* 51.7%

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

   8. Simplified 51.7%

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

   if 1.8999999999999999e91 < a

   1. Initial program 90.8%

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

   3. Taylor expanded in y around inf 44.1%

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

      1. div-sub 44.1%

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

   5. Simplified 44.1%

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

   6. Taylor expanded in t around inf 28.0%

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

      1. associate-/l* 39.2%

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

   8. Simplified 39.2%

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

Alternative 12: 40.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -2.6e-86)
     x
     (if (<= a 2.35e-118)
       t_1
       (if (<= a 1.5e-23)
         (* x (* y (/ 1.0 z)))
         (if (<= a 4.7e+92) t_1 (* t (/ 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 tmp;
	if (a <= -2.6e-86) {
		tmp = x;
	} else if (a <= 2.35e-118) {
		tmp = t_1;
	} else if (a <= 1.5e-23) {
		tmp = x * (y * (1.0 / z));
	} else if (a <= 4.7e+92) {
		tmp = t_1;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-2.6d-86)) then
        tmp = x
    else if (a <= 2.35d-118) then
        tmp = t_1
    else if (a <= 1.5d-23) then
        tmp = x * (y * (1.0d0 / z))
    else if (a <= 4.7d+92) then
        tmp = t_1
    else
        tmp = t * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -2.6e-86) {
		tmp = x;
	} else if (a <= 2.35e-118) {
		tmp = t_1;
	} else if (a <= 1.5e-23) {
		tmp = x * (y * (1.0 / z));
	} else if (a <= 4.7e+92) {
		tmp = t_1;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -2.6e-86:
		tmp = x
	elif a <= 2.35e-118:
		tmp = t_1
	elif a <= 1.5e-23:
		tmp = x * (y * (1.0 / z))
	elif a <= 4.7e+92:
		tmp = t_1
	else:
		tmp = t * (y / (a - z))
	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 <= -2.6e-86)
		tmp = x;
	elseif (a <= 2.35e-118)
		tmp = t_1;
	elseif (a <= 1.5e-23)
		tmp = Float64(x * Float64(y * Float64(1.0 / z)));
	elseif (a <= 4.7e+92)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -2.6e-86)
		tmp = x;
	elseif (a <= 2.35e-118)
		tmp = t_1;
	elseif (a <= 1.5e-23)
		tmp = x * (y * (1.0 / z));
	elseif (a <= 4.7e+92)
		tmp = t_1;
	else
		tmp = t * (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]}, If[LessEqual[a, -2.6e-86], x, If[LessEqual[a, 2.35e-118], t$95$1, If[LessEqual[a, 1.5e-23], N[(x * N[(y * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.7e+92], t$95$1, N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.6000000000000001e-86

   1. Initial program 82.2%

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

   3. Taylor expanded in a around inf 47.6%

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

   if -2.6000000000000001e-86 < a < 2.34999999999999995e-118 or 1.50000000000000001e-23 < a < 4.7e92

   1. Initial program 72.0%

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

   3. Taylor expanded in a around 0 46.2%

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

      1. mul-1-neg 46.2%

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

      2. unsub-neg 46.2%

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

      3. associate-/l* 52.8%

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

      4. div-sub 52.8%

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

      5. sub-neg 52.8%

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

      6. *-inverses 52.8%

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

      7. metadata-eval 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in x around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. sub-neg 51.7%

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

      3. metadata-eval 51.7%

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

      4. distribute-rgt-neg-in 51.7%

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

      5. +-commutative 51.7%

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

      6. distribute-neg-in 51.7%

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

      7. metadata-eval 51.7%

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

      8. sub-neg 51.7%

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

   8. Simplified 51.7%

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

   if 2.34999999999999995e-118 < a < 1.50000000000000001e-23

   1. Initial program 73.0%

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

   3. Taylor expanded in a around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. unsub-neg 48.7%

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

      3. associate-/l* 58.9%

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

      4. div-sub 58.9%

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

      5. sub-neg 58.9%

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

      6. *-inverses 58.9%

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

      7. metadata-eval 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in x around inf 40.8%

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

      1. sub-neg 40.8%

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

      2. sub-neg 40.8%

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

      3. metadata-eval 40.8%

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

      4. neg-mul-1 40.8%

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

      5. remove-double-neg 40.8%

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

      6. +-commutative 40.8%

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

   8. Simplified 40.8%

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

      1. associate-+r+ 49.6%

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

      2. metadata-eval 49.6%

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

      3. +-lft-identity 49.6%

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

      4. div-inv 49.6%

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

   10. Applied egg-rr 49.6%

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

   if 4.7e92 < a

   1. Initial program 90.8%

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

   3. Taylor expanded in y around inf 44.1%

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

      1. div-sub 44.1%

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

   5. Simplified 44.1%

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

   6. Taylor expanded in t around inf 28.0%

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

      1. associate-/l* 39.2%

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

   8. Simplified 39.2%

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

Alternative 13: 40.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -5.2e-85)
     x
     (if (<= a 1.05e-118)
       t_1
       (if (<= a 3.3e-24)
         (* x (/ y z))
         (if (<= a 9.5e+95) t_1 (* t (/ 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 tmp;
	if (a <= -5.2e-85) {
		tmp = x;
	} else if (a <= 1.05e-118) {
		tmp = t_1;
	} else if (a <= 3.3e-24) {
		tmp = x * (y / z);
	} else if (a <= 9.5e+95) {
		tmp = t_1;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-5.2d-85)) then
        tmp = x
    else if (a <= 1.05d-118) then
        tmp = t_1
    else if (a <= 3.3d-24) then
        tmp = x * (y / z)
    else if (a <= 9.5d+95) then
        tmp = t_1
    else
        tmp = t * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -5.2e-85) {
		tmp = x;
	} else if (a <= 1.05e-118) {
		tmp = t_1;
	} else if (a <= 3.3e-24) {
		tmp = x * (y / z);
	} else if (a <= 9.5e+95) {
		tmp = t_1;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -5.2e-85:
		tmp = x
	elif a <= 1.05e-118:
		tmp = t_1
	elif a <= 3.3e-24:
		tmp = x * (y / z)
	elif a <= 9.5e+95:
		tmp = t_1
	else:
		tmp = t * (y / (a - z))
	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 <= -5.2e-85)
		tmp = x;
	elseif (a <= 1.05e-118)
		tmp = t_1;
	elseif (a <= 3.3e-24)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 9.5e+95)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -5.2e-85)
		tmp = x;
	elseif (a <= 1.05e-118)
		tmp = t_1;
	elseif (a <= 3.3e-24)
		tmp = x * (y / z);
	elseif (a <= 9.5e+95)
		tmp = t_1;
	else
		tmp = t * (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]}, If[LessEqual[a, -5.2e-85], x, If[LessEqual[a, 1.05e-118], t$95$1, If[LessEqual[a, 3.3e-24], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+95], t$95$1, N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.20000000000000023e-85

   1. Initial program 82.2%

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

   3. Taylor expanded in a around inf 47.6%

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

   if -5.20000000000000023e-85 < a < 1.05e-118 or 3.29999999999999984e-24 < a < 9.5000000000000004e95

   1. Initial program 72.0%

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

   3. Taylor expanded in a around 0 46.2%

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

      1. mul-1-neg 46.2%

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

      2. unsub-neg 46.2%

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

      3. associate-/l* 52.8%

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

      4. div-sub 52.8%

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

      5. sub-neg 52.8%

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

      6. *-inverses 52.8%

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

      7. metadata-eval 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in x around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. sub-neg 51.7%

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

      3. metadata-eval 51.7%

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

      4. distribute-rgt-neg-in 51.7%

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

      5. +-commutative 51.7%

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

      6. distribute-neg-in 51.7%

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

      7. metadata-eval 51.7%

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

      8. sub-neg 51.7%

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

   8. Simplified 51.7%

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

   if 1.05e-118 < a < 3.29999999999999984e-24

   1. Initial program 73.0%

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

   3. Taylor expanded in a around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. unsub-neg 48.7%

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

      3. associate-/l* 58.9%

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

      4. div-sub 58.9%

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

      5. sub-neg 58.9%

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

      6. *-inverses 58.9%

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

      7. metadata-eval 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in x around -inf 40.6%

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

      1. associate-/l* 49.6%

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

   8. Simplified 49.6%

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

   if 9.5000000000000004e95 < a

   1. Initial program 90.8%

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

   3. Taylor expanded in y around inf 44.1%

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

      1. div-sub 44.1%

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

   5. Simplified 44.1%

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

   6. Taylor expanded in t around inf 28.0%

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

      1. associate-/l* 39.2%

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

   8. Simplified 39.2%

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

Alternative 14: 40.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -5.2e-85)
     x
     (if (<= a 2.35e-118)
       t_1
       (if (<= a 2.3e-22)
         (* x (/ y z))
         (if (<= a 2.75e+91) t_1 (/ t (/ a y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -5.2e-85) {
		tmp = x;
	} else if (a <= 2.35e-118) {
		tmp = t_1;
	} else if (a <= 2.3e-22) {
		tmp = x * (y / z);
	} else if (a <= 2.75e+91) {
		tmp = t_1;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-5.2d-85)) then
        tmp = x
    else if (a <= 2.35d-118) then
        tmp = t_1
    else if (a <= 2.3d-22) then
        tmp = x * (y / z)
    else if (a <= 2.75d+91) then
        tmp = t_1
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -5.2e-85) {
		tmp = x;
	} else if (a <= 2.35e-118) {
		tmp = t_1;
	} else if (a <= 2.3e-22) {
		tmp = x * (y / z);
	} else if (a <= 2.75e+91) {
		tmp = t_1;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -5.2e-85:
		tmp = x
	elif a <= 2.35e-118:
		tmp = t_1
	elif a <= 2.3e-22:
		tmp = x * (y / z)
	elif a <= 2.75e+91:
		tmp = t_1
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -5.2e-85)
		tmp = x;
	elseif (a <= 2.35e-118)
		tmp = t_1;
	elseif (a <= 2.3e-22)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 2.75e+91)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -5.2e-85)
		tmp = x;
	elseif (a <= 2.35e-118)
		tmp = t_1;
	elseif (a <= 2.3e-22)
		tmp = x * (y / z);
	elseif (a <= 2.75e+91)
		tmp = t_1;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e-85], x, If[LessEqual[a, 2.35e-118], t$95$1, If[LessEqual[a, 2.3e-22], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.75e+91], t$95$1, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.20000000000000023e-85

   1. Initial program 82.2%

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

   3. Taylor expanded in a around inf 47.6%

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

   if -5.20000000000000023e-85 < a < 2.34999999999999995e-118 or 2.2999999999999998e-22 < a < 2.7499999999999999e91

   1. Initial program 72.0%

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

   3. Taylor expanded in a around 0 46.2%

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

      1. mul-1-neg 46.2%

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

      2. unsub-neg 46.2%

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

      3. associate-/l* 52.8%

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

      4. div-sub 52.8%

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

      5. sub-neg 52.8%

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

      6. *-inverses 52.8%

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

      7. metadata-eval 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in x around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. sub-neg 51.7%

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

      3. metadata-eval 51.7%

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

      4. distribute-rgt-neg-in 51.7%

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

      5. +-commutative 51.7%

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

      6. distribute-neg-in 51.7%

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

      7. metadata-eval 51.7%

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

      8. sub-neg 51.7%

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

   8. Simplified 51.7%

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

   if 2.34999999999999995e-118 < a < 2.2999999999999998e-22

   1. Initial program 73.0%

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

   3. Taylor expanded in a around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. unsub-neg 48.7%

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

      3. associate-/l* 58.9%

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

      4. div-sub 58.9%

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

      5. sub-neg 58.9%

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

      6. *-inverses 58.9%

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

      7. metadata-eval 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in x around -inf 40.6%

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

      1. associate-/l* 49.6%

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

   8. Simplified 49.6%

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

   if 2.7499999999999999e91 < a

   1. Initial program 90.8%

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

   3. Taylor expanded in y around inf 44.1%

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

      1. div-sub 44.1%

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

   5. Simplified 44.1%

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

   6. Taylor expanded in a around inf 41.7%

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

   7. Taylor expanded in t around inf 27.8%

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

      1. associate-/l* 39.0%

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

   9. Simplified 39.0%

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

       1. clear-num 39.0%

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

       2. un-div-inv 39.1%

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

   11. Applied egg-rr 39.1%

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

Alternative 15: 53.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+164}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.1e+118)
   x
   (if (<= x 8.5e+91)
     (* t (/ (- y z) (- a z)))
     (if (<= x 1.06e+164) (* y (/ (- t x) a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.1e+118) {
		tmp = x;
	} else if (x <= 8.5e+91) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 1.06e+164) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.1d+118)) then
        tmp = x
    else if (x <= 8.5d+91) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 1.06d+164) then
        tmp = y * ((t - x) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.1e+118) {
		tmp = x;
	} else if (x <= 8.5e+91) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 1.06e+164) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.1e+118:
		tmp = x
	elif x <= 8.5e+91:
		tmp = t * ((y - z) / (a - z))
	elif x <= 1.06e+164:
		tmp = y * ((t - x) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.1e+118)
		tmp = x;
	elseif (x <= 8.5e+91)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 1.06e+164)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.1e+118)
		tmp = x;
	elseif (x <= 8.5e+91)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 1.06e+164)
		tmp = y * ((t - x) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.1e+118], x, If[LessEqual[x, 8.5e+91], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.06e+164], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.09999999999999993e118 or 1.05999999999999997e164 < x

   1. Initial program 68.4%

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

   3. Taylor expanded in a around inf 42.1%

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

   if -1.09999999999999993e118 < x < 8.4999999999999995e91

   1. Initial program 81.5%

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

   3. Taylor expanded in x around 0 51.2%

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

      1. associate-/l* 65.3%

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

   5. Simplified 65.3%

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

   if 8.4999999999999995e91 < x < 1.05999999999999997e164

   1. Initial program 80.7%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. div-sub 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in a around inf 53.7%

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

Alternative 16: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+42} \lor \neg \left(z \leq 1.2 \cdot 10^{+67}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.5e+42) (not (<= z 1.2e+67)))
   (+ t (* (/ (- t x) z) (- a y)))
   (+ x (* (- t x) (/ (- y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e+42) || !(z <= 1.2e+67)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((t - x) * ((y - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7.5d+42)) .or. (.not. (z <= 1.2d+67))) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x + ((t - x) * ((y - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e+42) || !(z <= 1.2e+67)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((t - x) * ((y - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.5e+42) or not (z <= 1.2e+67):
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x + ((t - x) * ((y - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.5e+42) || !(z <= 1.2e+67))
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.5e+42) || ~((z <= 1.2e+67)))
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x + ((t - x) * ((y - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.5e+42], N[Not[LessEqual[z, 1.2e+67]], $MachinePrecision]], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000041e42 or 1.20000000000000001e67 < z

   1. Initial program 61.9%

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

   3. Taylor expanded in z around inf 61.3%

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

      1. associate--l+ 61.3%

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

      2. distribute-lft-out-- 61.3%

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

      3. div-sub 61.3%

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

      4. mul-1-neg 61.3%

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

      5. unsub-neg 61.3%

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

      6. div-sub 61.3%

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

      7. associate-/l* 73.1%

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

      8. associate-/l* 80.2%

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

      9. distribute-rgt-out-- 80.2%

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

   5. Simplified 80.2%

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

   if -7.50000000000000041e42 < z < 1.20000000000000001e67

   1. Initial program 89.6%

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

   3. Taylor expanded in a around inf 68.3%

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

      1. associate-/l* 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+42} \lor \neg \left(z \leq 1.2 \cdot 10^{+67}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 71.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+116} \lor \neg \left(z \leq 9.5 \cdot 10^{+65}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.5e+116) (not (<= z 9.5e+65)))
   (+ t (* y (/ (- x t) z)))
   (+ x (* (- t x) (/ (- y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+116) || !(z <= 9.5e+65)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) * ((y - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.5d+116)) .or. (.not. (z <= 9.5d+65))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + ((t - x) * ((y - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+116) || !(z <= 9.5e+65)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) * ((y - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.5e+116) or not (z <= 9.5e+65):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + ((t - x) * ((y - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.5e+116) || !(z <= 9.5e+65))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.5e+116) || ~((z <= 9.5e+65)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + ((t - x) * ((y - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.5e+116], N[Not[LessEqual[z, 9.5e+65]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000002e116 or 9.5000000000000005e65 < z

   1. Initial program 57.6%

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

   3. Taylor expanded in z around inf 63.5%

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

      1. associate--l+ 63.5%

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

      2. distribute-lft-out-- 63.5%

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

      3. div-sub 63.5%

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

      4. mul-1-neg 63.5%

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

      5. unsub-neg 63.5%

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

      6. div-sub 63.5%

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

      7. associate-/l* 77.1%

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

      8. associate-/l* 84.7%

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

      9. distribute-rgt-out-- 84.7%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in y around inf 60.1%

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

      1. associate-*r/ 73.7%

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

   8. Simplified 73.7%

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

   if -8.5000000000000002e116 < z < 9.5000000000000005e65

   1. Initial program 89.6%

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

   3. Taylor expanded in a around inf 66.1%

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

      1. associate-/l* 77.5%

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

   5. Simplified 77.5%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+116} \lor \neg \left(z \leq 9.5 \cdot 10^{+65}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 69.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+42} \lor \neg \left(z \leq 2.2 \cdot 10^{+67}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+42) (not (<= z 2.2e+67)))
   (+ t (* y (/ (- x t) z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+42) || !(z <= 2.2e+67)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.2d+42)) .or. (.not. (z <= 2.2d+67))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+42) || !(z <= 2.2e+67)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e+42) or not (z <= 2.2e+67):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e+42) || !(z <= 2.2e+67))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.2e+42) || ~((z <= 2.2e+67)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.2e+42], N[Not[LessEqual[z, 2.2e+67]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000002e42 or 2.2e67 < z

   1. Initial program 61.9%

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

   3. Taylor expanded in z around inf 61.3%

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

      1. associate--l+ 61.3%

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

      2. distribute-lft-out-- 61.3%

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

      3. div-sub 61.3%

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

      4. mul-1-neg 61.3%

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

      5. unsub-neg 61.3%

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

      6. div-sub 61.3%

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

      7. associate-/l* 73.1%

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

      8. associate-/l* 80.2%

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

      9. distribute-rgt-out-- 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in y around inf 58.5%

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

      1. associate-*r/ 70.2%

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

   8. Simplified 70.2%

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

   if -3.20000000000000002e42 < z < 2.2e67

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-*l/ 85.1%

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

      3. associate-*r/ 95.8%

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

      4. clear-num 95.7%

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

      5. un-div-inv 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in z around 0 74.8%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+42} \lor \neg \left(z \leq 2.2 \cdot 10^{+67}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 56.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-75} \lor \neg \left(x \leq 9 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -5e-75) (not (<= x 9e+65)))
   (* y (/ (- t x) (- a z)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -5e-75) || !(x <= 9e+65)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-5d-75)) .or. (.not. (x <= 9d+65))) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -5e-75) || !(x <= 9e+65)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -5e-75) or not (x <= 9e+65):
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -5e-75) || !(x <= 9e+65))
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -5e-75) || ~((x <= 9e+65)))
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -5e-75], N[Not[LessEqual[x, 9e+65]], $MachinePrecision]], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.99999999999999979e-75 or 9e65 < x

   1. Initial program 74.5%

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

   3. Taylor expanded in y around inf 42.9%

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

      1. div-sub 46.0%

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

   5. Simplified 46.0%

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

   if -4.99999999999999979e-75 < x < 9e65

   1. Initial program 82.1%

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

   3. Taylor expanded in x around 0 59.5%

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

      1. associate-/l* 74.9%

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

   5. Simplified 74.9%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-75} \lor \neg \left(x \leq 9 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 57.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-70}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.6e-70)
   (* (- t x) (/ y (- a z)))
   (if (<= x 1.02e+67) (* t (/ (- y z) (- a z))) (* y (/ (- t x) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.6e-70) {
		tmp = (t - x) * (y / (a - z));
	} else if (x <= 1.02e+67) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = y * ((t - x) / (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) :: tmp
    if (x <= (-2.6d-70)) then
        tmp = (t - x) * (y / (a - z))
    else if (x <= 1.02d+67) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = y * ((t - x) / (a - 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 (x <= -2.6e-70) {
		tmp = (t - x) * (y / (a - z));
	} else if (x <= 1.02e+67) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = y * ((t - x) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.6e-70:
		tmp = (t - x) * (y / (a - z))
	elif x <= 1.02e+67:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = y * ((t - x) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.6e-70)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (x <= 1.02e+67)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.6e-70)
		tmp = (t - x) * (y / (a - z));
	elseif (x <= 1.02e+67)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = y * ((t - x) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.6e-70], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e+67], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.60000000000000002e-70

   1. Initial program 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-*l/ 60.8%

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

      3. associate-*r/ 76.1%

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

      4. clear-num 76.0%

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

      5. un-div-inv 76.4%

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

   4. Applied egg-rr 76.4%

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

   5. Taylor expanded in y around inf 42.5%

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

      1. div-sub 43.8%

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

      2. associate-*r/ 36.9%

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

      3. *-rgt-identity 36.9%

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

      4. times-frac 44.9%

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

      5. /-rgt-identity 44.9%

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

   7. Simplified 44.9%

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

   if -2.60000000000000002e-70 < x < 1.02000000000000002e67

   1. Initial program 82.1%

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

   3. Taylor expanded in x around 0 59.5%

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

      1. associate-/l* 74.9%

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

   5. Simplified 74.9%

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

   if 1.02000000000000002e67 < x

   1. Initial program 75.9%

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

   3. Taylor expanded in y around inf 43.5%

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

      1. div-sub 49.6%

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

   5. Simplified 49.6%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-70}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e+94) t (if (<= z 9.5e+101) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+94) {
		tmp = t;
	} else if (z <= 9.5e+101) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.9d+94)) then
        tmp = t
    else if (z <= 9.5d+101) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+94) {
		tmp = t;
	} else if (z <= 9.5e+101) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e+94:
		tmp = t
	elif z <= 9.5e+101:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e+94)
		tmp = t;
	elseif (z <= 9.5e+101)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e+94)
		tmp = t;
	elseif (z <= 9.5e+101)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e+94], t, If[LessEqual[z, 9.5e+101], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8999999999999998e94 or 9.49999999999999947e101 < z

   1. Initial program 56.7%

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

   3. Taylor expanded in z around inf 47.9%

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

   if -2.8999999999999998e94 < z < 9.49999999999999947e101

   1. Initial program 89.7%

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

   3. Taylor expanded in a around inf 33.9%

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

Alternative 22: 24.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.3%

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

3. Taylor expanded in z around inf 21.3%

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

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))