Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.0% → 95.0%

Time: 18.0s

Alternatives: 23

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: 80.0% 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: 95.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-279} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-279) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (- t (* (/ (- t x) z) (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	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[Or[LessEqual[t$95$1, -2e-279], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000011e-279 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.8%

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

      1. +-commutative 90.8%

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

      2. remove-double-neg 90.8%

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

      3. unsub-neg 90.8%

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

      4. *-commutative 90.8%

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

      5. associate-*l/ 77.1%

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

      6. associate-/l* 95.4%

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

      7. fma-neg 95.4%

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

      8. remove-double-neg 95.4%

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

   3. Simplified 95.4%

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

   if -2.00000000000000011e-279 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   3. Taylor expanded in z around inf 78.6%

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

      1. associate--l+ 78.6%

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

      2. distribute-lft-out-- 78.6%

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

      3. div-sub 78.6%

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

      4. mul-1-neg 78.6%

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

      5. unsub-neg 78.6%

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

      6. div-sub 78.6%

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

      7. associate-/l* 89.3%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-279} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-279} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-279) (not (<= t_1 0.0)))
     t_1
     (- t (* (/ (- t x) z) (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-279)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t - (((t - x) / z) * (y - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-279) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t - (((t - x) / z) * (y - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-279) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t - (((t - x) / z) * (y - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-279], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000011e-279 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.8%

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

   if -2.00000000000000011e-279 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   3. Taylor expanded in z around inf 78.6%

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

      1. associate--l+ 78.6%

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

      2. distribute-lft-out-- 78.6%

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

      3. div-sub 78.6%

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

      4. mul-1-neg 78.6%

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

      5. unsub-neg 78.6%

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

      6. div-sub 78.6%

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

      7. associate-/l* 89.3%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-279} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-279} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-279) (not (<= t_1 0.0)))
     (+ x (/ (- y z) (/ (- a z) (- t x))))
     (- t (* (/ (- t x) z) (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0)) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-279)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t - (((t - x) / z) * (y - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0)) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-279) or not (t_1 <= 0.0):
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t - (((t - x) / z) * (y - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-279) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-279) || ~((t_1 <= 0.0)))
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t - (((t - x) / z) * (y - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-279], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000011e-279 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.8%

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

      1. clear-num 90.7%

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

      2. un-div-inv 91.5%

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

   4. Applied egg-rr 91.5%

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

   if -2.00000000000000011e-279 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   3. Taylor expanded in z around inf 78.6%

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

      1. associate--l+ 78.6%

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

      2. distribute-lft-out-- 78.6%

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

      3. div-sub 78.6%

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

      4. mul-1-neg 78.6%

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

      5. unsub-neg 78.6%

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

      6. div-sub 78.6%

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

      7. associate-/l* 89.3%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-279} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+70}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-265}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))) (t_2 (+ x (/ (* y t) a))))
   (if (<= z -9e+70)
     t
     (if (<= z -3.1e-31)
       (* t (/ y (- a z)))
       (if (<= z -2.3e-144)
         t_1
         (if (<= z 3.8e-265)
           t_2
           (if (<= z 2.15e-162) t_1 (if (<= z 6e+90) t_2 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -9e+70) {
		tmp = t;
	} else if (z <= -3.1e-31) {
		tmp = t * (y / (a - z));
	} else if (z <= -2.3e-144) {
		tmp = t_1;
	} else if (z <= 3.8e-265) {
		tmp = t_2;
	} else if (z <= 2.15e-162) {
		tmp = t_1;
	} else if (z <= 6e+90) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    t_2 = x + ((y * t) / a)
    if (z <= (-9d+70)) then
        tmp = t
    else if (z <= (-3.1d-31)) then
        tmp = t * (y / (a - z))
    else if (z <= (-2.3d-144)) then
        tmp = t_1
    else if (z <= 3.8d-265) then
        tmp = t_2
    else if (z <= 2.15d-162) then
        tmp = t_1
    else if (z <= 6d+90) then
        tmp = t_2
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -9e+70) {
		tmp = t;
	} else if (z <= -3.1e-31) {
		tmp = t * (y / (a - z));
	} else if (z <= -2.3e-144) {
		tmp = t_1;
	} else if (z <= 3.8e-265) {
		tmp = t_2;
	} else if (z <= 2.15e-162) {
		tmp = t_1;
	} else if (z <= 6e+90) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	t_2 = x + ((y * t) / a)
	tmp = 0
	if z <= -9e+70:
		tmp = t
	elif z <= -3.1e-31:
		tmp = t * (y / (a - z))
	elif z <= -2.3e-144:
		tmp = t_1
	elif z <= 3.8e-265:
		tmp = t_2
	elif z <= 2.15e-162:
		tmp = t_1
	elif z <= 6e+90:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -9e+70)
		tmp = t;
	elseif (z <= -3.1e-31)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= -2.3e-144)
		tmp = t_1;
	elseif (z <= 3.8e-265)
		tmp = t_2;
	elseif (z <= 2.15e-162)
		tmp = t_1;
	elseif (z <= 6e+90)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	t_2 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -9e+70)
		tmp = t;
	elseif (z <= -3.1e-31)
		tmp = t * (y / (a - z));
	elseif (z <= -2.3e-144)
		tmp = t_1;
	elseif (z <= 3.8e-265)
		tmp = t_2;
	elseif (z <= 2.15e-162)
		tmp = t_1;
	elseif (z <= 6e+90)
		tmp = t_2;
	else
		tmp = t;
	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]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+70], t, If[LessEqual[z, -3.1e-31], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-144], t$95$1, If[LessEqual[z, 3.8e-265], t$95$2, If[LessEqual[z, 2.15e-162], t$95$1, If[LessEqual[z, 6e+90], t$95$2, t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.9999999999999999e70 or 5.99999999999999957e90 < z

   1. Initial program 66.6%

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

   3. Taylor expanded in z around inf 51.1%

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

   if -8.9999999999999999e70 < z < -3.1e-31

   1. Initial program 94.6%

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

   3. Taylor expanded in y around inf 46.4%

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

      1. div-sub 46.4%

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

   5. Simplified 46.4%

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

   6. Taylor expanded in t around inf 41.9%

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

      1. associate-/l* 51.5%

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

   8. Simplified 51.5%

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

   if -3.1e-31 < z < -2.3e-144 or 3.7999999999999998e-265 < z < 2.14999999999999998e-162

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 66.0%

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

      1. div-sub 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in a around inf 62.2%

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

   if -2.3e-144 < z < 3.7999999999999998e-265 or 2.14999999999999998e-162 < z < 5.99999999999999957e90

   1. Initial program 90.4%

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

      1. clear-num 90.4%

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

      2. un-div-inv 91.1%

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

   4. Applied egg-rr 91.1%

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

   5. Taylor expanded in t around inf 77.3%

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

   6. Taylor expanded in z around 0 61.0%

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

      1. +-commutative 61.0%

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

   8. Simplified 61.0%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+70}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-265}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-162}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+90}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-47}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= z -3.4e+69)
     t
     (if (<= z -8.6e-30)
       (* t (/ y (- a z)))
       (if (<= z -2.25e-144)
         (* y (/ (- t x) a))
         (if (<= z 4.8e-220)
           t_1
           (if (<= z 1.25e-47)
             (- x (* x (/ y a)))
             (if (<= z 1e+91) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -3.4e+69) {
		tmp = t;
	} else if (z <= -8.6e-30) {
		tmp = t * (y / (a - z));
	} else if (z <= -2.25e-144) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.8e-220) {
		tmp = t_1;
	} else if (z <= 1.25e-47) {
		tmp = x - (x * (y / a));
	} else if (z <= 1e+91) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (z <= (-3.4d+69)) then
        tmp = t
    else if (z <= (-8.6d-30)) then
        tmp = t * (y / (a - z))
    else if (z <= (-2.25d-144)) then
        tmp = y * ((t - x) / a)
    else if (z <= 4.8d-220) then
        tmp = t_1
    else if (z <= 1.25d-47) then
        tmp = x - (x * (y / a))
    else if (z <= 1d+91) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -3.4e+69) {
		tmp = t;
	} else if (z <= -8.6e-30) {
		tmp = t * (y / (a - z));
	} else if (z <= -2.25e-144) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.8e-220) {
		tmp = t_1;
	} else if (z <= 1.25e-47) {
		tmp = x - (x * (y / a));
	} else if (z <= 1e+91) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if z <= -3.4e+69:
		tmp = t
	elif z <= -8.6e-30:
		tmp = t * (y / (a - z))
	elif z <= -2.25e-144:
		tmp = y * ((t - x) / a)
	elif z <= 4.8e-220:
		tmp = t_1
	elif z <= 1.25e-47:
		tmp = x - (x * (y / a))
	elif z <= 1e+91:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -3.4e+69)
		tmp = t;
	elseif (z <= -8.6e-30)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= -2.25e-144)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 4.8e-220)
		tmp = t_1;
	elseif (z <= 1.25e-47)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= 1e+91)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -3.4e+69)
		tmp = t;
	elseif (z <= -8.6e-30)
		tmp = t * (y / (a - z));
	elseif (z <= -2.25e-144)
		tmp = y * ((t - x) / a);
	elseif (z <= 4.8e-220)
		tmp = t_1;
	elseif (z <= 1.25e-47)
		tmp = x - (x * (y / a));
	elseif (z <= 1e+91)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+69], t, If[LessEqual[z, -8.6e-30], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.25e-144], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-220], t$95$1, If[LessEqual[z, 1.25e-47], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+91], t$95$1, t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.39999999999999986e69 or 1.00000000000000008e91 < z

   1. Initial program 66.6%

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

   3. Taylor expanded in z around inf 51.1%

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

   if -3.39999999999999986e69 < z < -8.59999999999999932e-30

   1. Initial program 94.6%

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

   3. Taylor expanded in y around inf 46.4%

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

      1. div-sub 46.4%

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

   5. Simplified 46.4%

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

   6. Taylor expanded in t around inf 41.9%

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

      1. associate-/l* 51.5%

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

   8. Simplified 51.5%

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

   if -8.59999999999999932e-30 < z < -2.2499999999999999e-144

   1. Initial program 92.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in a around inf 55.8%

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

   if -2.2499999999999999e-144 < z < 4.8000000000000003e-220 or 1.25000000000000003e-47 < z < 1.00000000000000008e91

   1. Initial program 88.2%

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

      1. clear-num 88.1%

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

      2. un-div-inv 88.9%

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

   4. Applied egg-rr 88.9%

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

   5. Taylor expanded in t around inf 75.0%

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

   6. Taylor expanded in z around 0 64.5%

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

      1. +-commutative 64.5%

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

   8. Simplified 64.5%

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

   if 4.8000000000000003e-220 < z < 1.25000000000000003e-47

   1. Initial program 94.1%

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

   3. Taylor expanded in t around 0 55.3%

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

      1. mul-1-neg 55.3%

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

      2. associate-/l* 58.5%

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

      3. distribute-rgt-neg-in 58.5%

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

      4. distribute-frac-neg2 58.5%

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

      5. neg-sub0 58.5%

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

      6. associate--r- 58.5%

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

      7. neg-sub0 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in z around 0 55.1%

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

      1. mul-1-neg 55.1%

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

      2. unsub-neg 55.1%

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

      3. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-220}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-47}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 10^{+91}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ t_2 := t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-164}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) t))))
        (t_2 (- t (* (/ (- t x) z) (- y a)))))
   (if (<= z -7.2e+141)
     t_2
     (if (<= z -4.4e-223)
       t_1
       (if (<= z 5.3e-164)
         (+ x (/ (* y (- t x)) a))
         (if (<= z 1.12e+108) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / t));
	double t_2 = t - (((t - x) / z) * (y - a));
	double tmp;
	if (z <= -7.2e+141) {
		tmp = t_2;
	} else if (z <= -4.4e-223) {
		tmp = t_1;
	} else if (z <= 5.3e-164) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= 1.12e+108) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) / ((a - z) / t))
    t_2 = t - (((t - x) / z) * (y - a))
    if (z <= (-7.2d+141)) then
        tmp = t_2
    else if (z <= (-4.4d-223)) then
        tmp = t_1
    else if (z <= 5.3d-164) then
        tmp = x + ((y * (t - x)) / a)
    else if (z <= 1.12d+108) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / t));
	double t_2 = t - (((t - x) / z) * (y - a));
	double tmp;
	if (z <= -7.2e+141) {
		tmp = t_2;
	} else if (z <= -4.4e-223) {
		tmp = t_1;
	} else if (z <= 5.3e-164) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= 1.12e+108) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / t))
	t_2 = t - (((t - x) / z) * (y - a))
	tmp = 0
	if z <= -7.2e+141:
		tmp = t_2
	elif z <= -4.4e-223:
		tmp = t_1
	elif z <= 5.3e-164:
		tmp = x + ((y * (t - x)) / a)
	elif z <= 1.12e+108:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)))
	t_2 = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)))
	tmp = 0.0
	if (z <= -7.2e+141)
		tmp = t_2;
	elseif (z <= -4.4e-223)
		tmp = t_1;
	elseif (z <= 5.3e-164)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (z <= 1.12e+108)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((a - z) / t));
	t_2 = t - (((t - x) / z) * (y - a));
	tmp = 0.0;
	if (z <= -7.2e+141)
		tmp = t_2;
	elseif (z <= -4.4e-223)
		tmp = t_1;
	elseif (z <= 5.3e-164)
		tmp = x + ((y * (t - x)) / a);
	elseif (z <= 1.12e+108)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+141], t$95$2, If[LessEqual[z, -4.4e-223], t$95$1, If[LessEqual[z, 5.3e-164], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+108], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2000000000000003e141 or 1.11999999999999994e108 < z

   1. Initial program 60.1%

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

   3. Taylor expanded in z around inf 63.7%

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

      1. associate--l+ 63.7%

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

      2. distribute-lft-out-- 63.7%

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

      3. div-sub 63.7%

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

      4. mul-1-neg 63.7%

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

      5. unsub-neg 63.7%

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

      6. div-sub 63.7%

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

      7. associate-/l* 76.6%

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

      8. associate-/l* 89.1%

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

      9. distribute-rgt-out-- 89.1%

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

   5. Simplified 89.1%

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

   if -7.2000000000000003e141 < z < -4.40000000000000018e-223 or 5.30000000000000032e-164 < z < 1.11999999999999994e108

   1. Initial program 89.9%

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

      1. clear-num 89.8%

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

      2. un-div-inv 90.4%

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

   4. Applied egg-rr 90.4%

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

   5. Taylor expanded in t around inf 75.4%

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

   if -4.40000000000000018e-223 < z < 5.30000000000000032e-164

   1. Initial program 91.5%

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

      1. clear-num 91.4%

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

      2. un-div-inv 93.1%

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in z around 0 92.3%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+141}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-223}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-164}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-136}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 225000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.45e-140)
     t_2
     (if (<= t -3.4e-200)
       t_1
       (if (<= t 2.15e-136)
         (- x (* x (/ y a)))
         (if (<= t 225000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.45e-140) {
		tmp = t_2;
	} else if (t <= -3.4e-200) {
		tmp = t_1;
	} else if (t <= 2.15e-136) {
		tmp = x - (x * (y / a));
	} else if (t <= 225000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-1.45d-140)) then
        tmp = t_2
    else if (t <= (-3.4d-200)) then
        tmp = t_1
    else if (t <= 2.15d-136) then
        tmp = x - (x * (y / a))
    else if (t <= 225000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.45e-140) {
		tmp = t_2;
	} else if (t <= -3.4e-200) {
		tmp = t_1;
	} else if (t <= 2.15e-136) {
		tmp = x - (x * (y / a));
	} else if (t <= 225000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -1.45e-140:
		tmp = t_2
	elif t <= -3.4e-200:
		tmp = t_1
	elif t <= 2.15e-136:
		tmp = x - (x * (y / a))
	elif t <= 225000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -1.45e-140)
		tmp = t_2;
	elseif (t <= -3.4e-200)
		tmp = t_1;
	elseif (t <= 2.15e-136)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (t <= 225000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -1.45e-140)
		tmp = t_2;
	elseif (t <= -3.4e-200)
		tmp = t_1;
	elseif (t <= 2.15e-136)
		tmp = x - (x * (y / a));
	elseif (t <= 225000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e-140], t$95$2, If[LessEqual[t, -3.4e-200], t$95$1, If[LessEqual[t, 2.15e-136], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 225000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.44999999999999999e-140 or 225000 < t

   1. Initial program 89.5%

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

   3. Taylor expanded in x around 0 60.4%

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

      1. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

   if -1.44999999999999999e-140 < t < -3.4000000000000003e-200 or 2.15e-136 < t < 225000

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 60.1%

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

      1. div-sub 60.1%

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

   5. Simplified 60.1%

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

   if -3.4000000000000003e-200 < t < 2.15e-136

   1. Initial program 73.0%

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

   3. Taylor expanded in t around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. associate-/l* 73.9%

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

      3. distribute-rgt-neg-in 73.9%

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

      4. distribute-frac-neg2 73.9%

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

      5. neg-sub0 73.9%

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

      6. associate--r- 73.9%

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

      7. neg-sub0 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in z around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

      3. associate-/l* 64.0%

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

   8. Simplified 64.0%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-136}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 225000:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{-41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-48}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))) (t_2 (* t (/ z (- z a)))))
   (if (<= z -4.1e-41)
     t_2
     (if (<= z 3.6e-220)
       t_1
       (if (<= z 1.6e-48) (- x (* x (/ y a))) (if (<= z 6e+90) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -4.1e-41) {
		tmp = t_2;
	} else if (z <= 3.6e-220) {
		tmp = t_1;
	} else if (z <= 1.6e-48) {
		tmp = x - (x * (y / a));
	} else if (z <= 6e+90) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    t_2 = t * (z / (z - a))
    if (z <= (-4.1d-41)) then
        tmp = t_2
    else if (z <= 3.6d-220) then
        tmp = t_1
    else if (z <= 1.6d-48) then
        tmp = x - (x * (y / a))
    else if (z <= 6d+90) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -4.1e-41) {
		tmp = t_2;
	} else if (z <= 3.6e-220) {
		tmp = t_1;
	} else if (z <= 1.6e-48) {
		tmp = x - (x * (y / a));
	} else if (z <= 6e+90) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	t_2 = t * (z / (z - a))
	tmp = 0
	if z <= -4.1e-41:
		tmp = t_2
	elif z <= 3.6e-220:
		tmp = t_1
	elif z <= 1.6e-48:
		tmp = x - (x * (y / a))
	elif z <= 6e+90:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	t_2 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -4.1e-41)
		tmp = t_2;
	elseif (z <= 3.6e-220)
		tmp = t_1;
	elseif (z <= 1.6e-48)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= 6e+90)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	t_2 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -4.1e-41)
		tmp = t_2;
	elseif (z <= 3.6e-220)
		tmp = t_1;
	elseif (z <= 1.6e-48)
		tmp = x - (x * (y / a));
	elseif (z <= 6e+90)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e-41], t$95$2, If[LessEqual[z, 3.6e-220], t$95$1, If[LessEqual[z, 1.6e-48], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+90], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.10000000000000014e-41 or 5.99999999999999957e90 < z

   1. Initial program 72.4%

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

   3. Taylor expanded in x around 0 43.8%

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

      1. associate-/l* 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in y around 0 53.8%

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

      1. neg-mul-1 53.8%

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

      2. distribute-neg-frac2 53.8%

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

      3. neg-sub0 53.8%

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

      4. associate--r- 53.8%

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

      5. neg-sub0 53.8%

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

   8. Simplified 53.8%

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

   if -4.10000000000000014e-41 < z < 3.60000000000000021e-220 or 1.5999999999999999e-48 < z < 5.99999999999999957e90

   1. Initial program 88.6%

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

      1. clear-num 88.5%

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

      2. un-div-inv 89.2%

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

   4. Applied egg-rr 89.2%

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

   5. Taylor expanded in t around inf 73.8%

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

   6. Taylor expanded in z around 0 61.4%

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

      1. +-commutative 61.4%

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

   8. Simplified 61.4%

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

   if 3.60000000000000021e-220 < z < 1.5999999999999999e-48

   1. Initial program 94.1%

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

   3. Taylor expanded in t around 0 55.3%

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

      1. mul-1-neg 55.3%

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

      2. associate-/l* 58.5%

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

      3. distribute-rgt-neg-in 58.5%

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

      4. distribute-frac-neg2 58.5%

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

      5. neg-sub0 58.5%

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

      6. associate--r- 58.5%

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

      7. neg-sub0 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in z around 0 55.1%

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

      1. mul-1-neg 55.1%

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

      2. unsub-neg 55.1%

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

      3. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-220}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-48}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+90}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= a -3.2e+127)
     t_1
     (if (<= a -7e+29)
       (* y (/ (- t x) a))
       (if (<= a -6.8e-17)
         t_1
         (if (<= a 1.2e+16) (* t (/ (- z y) z)) (- x (* x (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -3.2e+127) {
		tmp = t_1;
	} else if (a <= -7e+29) {
		tmp = y * ((t - x) / a);
	} else if (a <= -6.8e-17) {
		tmp = t_1;
	} else if (a <= 1.2e+16) {
		tmp = t * ((z - y) / z);
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (a <= (-3.2d+127)) then
        tmp = t_1
    else if (a <= (-7d+29)) then
        tmp = y * ((t - x) / a)
    else if (a <= (-6.8d-17)) then
        tmp = t_1
    else if (a <= 1.2d+16) then
        tmp = t * ((z - y) / z)
    else
        tmp = x - (x * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -3.2e+127) {
		tmp = t_1;
	} else if (a <= -7e+29) {
		tmp = y * ((t - x) / a);
	} else if (a <= -6.8e-17) {
		tmp = t_1;
	} else if (a <= 1.2e+16) {
		tmp = t * ((z - y) / z);
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if a <= -3.2e+127:
		tmp = t_1
	elif a <= -7e+29:
		tmp = y * ((t - x) / a)
	elif a <= -6.8e-17:
		tmp = t_1
	elif a <= 1.2e+16:
		tmp = t * ((z - y) / z)
	else:
		tmp = x - (x * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -3.2e+127)
		tmp = t_1;
	elseif (a <= -7e+29)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= -6.8e-17)
		tmp = t_1;
	elseif (a <= 1.2e+16)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	else
		tmp = Float64(x - Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -3.2e+127)
		tmp = t_1;
	elseif (a <= -7e+29)
		tmp = y * ((t - x) / a);
	elseif (a <= -6.8e-17)
		tmp = t_1;
	elseif (a <= 1.2e+16)
		tmp = t * ((z - y) / z);
	else
		tmp = x - (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e+127], t$95$1, If[LessEqual[a, -7e+29], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.8e-17], t$95$1, If[LessEqual[a, 1.2e+16], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.19999999999999976e127 or -6.99999999999999958e29 < a < -6.7999999999999996e-17

   1. Initial program 93.1%

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

      1. clear-num 93.0%

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

      2. un-div-inv 93.1%

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in t around inf 86.2%

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

   6. Taylor expanded in z around 0 74.4%

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

      1. +-commutative 74.4%

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

   8. Simplified 74.4%

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

   if -3.19999999999999976e127 < a < -6.99999999999999958e29

   1. Initial program 82.4%

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

   3. Taylor expanded in y around inf 69.1%

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

      1. div-sub 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in a around inf 51.8%

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

   if -6.7999999999999996e-17 < a < 1.2e16

   1. Initial program 74.7%

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

   3. Taylor expanded in x around 0 59.1%

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

      1. associate-/l* 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in a around 0 64.0%

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

      1. associate-*r/ 64.0%

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

      2. neg-mul-1 64.0%

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

   8. Simplified 64.0%

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

   if 1.2e16 < a

   1. Initial program 90.0%

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

   3. Taylor expanded in t around 0 39.5%

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

      1. mul-1-neg 39.5%

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

      2. associate-/l* 52.4%

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

      3. distribute-rgt-neg-in 52.4%

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

      4. distribute-frac-neg2 52.4%

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

      5. neg-sub0 52.4%

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

      6. associate--r- 52.4%

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

      7. neg-sub0 52.4%

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

   5. Simplified 52.4%

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

   6. Taylor expanded in z around 0 39.1%

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

      1. mul-1-neg 39.1%

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

      2. unsub-neg 39.1%

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

      3. associate-/l* 48.0%

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

   8. Simplified 48.0%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+127}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 16500:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) t)))))
   (if (<= t -1.25e-135)
     t_1
     (if (<= t -3.5e-199)
       (* y (/ (- t x) (- a z)))
       (if (<= t 16500.0) (* x (+ (/ (- y z) (- z a)) 1.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (t <= -1.25e-135) {
		tmp = t_1;
	} else if (t <= -3.5e-199) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 16500.0) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) / ((a - z) / t))
    if (t <= (-1.25d-135)) then
        tmp = t_1
    else if (t <= (-3.5d-199)) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= 16500.0d0) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (t <= -1.25e-135) {
		tmp = t_1;
	} else if (t <= -3.5e-199) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 16500.0) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / t))
	tmp = 0
	if t <= -1.25e-135:
		tmp = t_1
	elif t <= -3.5e-199:
		tmp = y * ((t - x) / (a - z))
	elif t <= 16500.0:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -1.25e-135)
		tmp = t_1;
	elseif (t <= -3.5e-199)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= 16500.0)
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((a - z) / t));
	tmp = 0.0;
	if (t <= -1.25e-135)
		tmp = t_1;
	elseif (t <= -3.5e-199)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= 16500.0)
		tmp = x * (((y - z) / (z - a)) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e-135], t$95$1, If[LessEqual[t, -3.5e-199], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 16500.0], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25000000000000005e-135 or 16500 < t

   1. Initial program 90.0%

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

      1. clear-num 89.8%

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

      2. un-div-inv 90.4%

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

   4. Applied egg-rr 90.4%

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

   5. Taylor expanded in t around inf 86.2%

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

   if -1.25000000000000005e-135 < t < -3.4999999999999999e-199

   1. Initial program 43.8%

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

   3. Taylor expanded in y around inf 65.7%

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

      1. div-sub 65.7%

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

   5. Simplified 65.7%

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

   if -3.4999999999999999e-199 < t < 16500

   1. Initial program 73.8%

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

   3. Taylor expanded in x around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

   5. Simplified 67.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-135}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 16500:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+70}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4000:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-46} \lor \neg \left(z \leq 7.5 \cdot 10^{-87}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+70)
   t
   (if (<= z -4000.0)
     (* t (/ y (- z)))
     (if (or (<= z -1.62e-46) (not (<= z 7.5e-87))) (+ x t) (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+70) {
		tmp = t;
	} else if (z <= -4000.0) {
		tmp = t * (y / -z);
	} else if ((z <= -1.62e-46) || !(z <= 7.5e-87)) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.05d+70)) then
        tmp = t
    else if (z <= (-4000.0d0)) then
        tmp = t * (y / -z)
    else if ((z <= (-1.62d-46)) .or. (.not. (z <= 7.5d-87))) then
        tmp = x + t
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+70) {
		tmp = t;
	} else if (z <= -4000.0) {
		tmp = t * (y / -z);
	} else if ((z <= -1.62e-46) || !(z <= 7.5e-87)) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+70:
		tmp = t
	elif z <= -4000.0:
		tmp = t * (y / -z)
	elif (z <= -1.62e-46) or not (z <= 7.5e-87):
		tmp = x + t
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+70)
		tmp = t;
	elseif (z <= -4000.0)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif ((z <= -1.62e-46) || !(z <= 7.5e-87))
		tmp = Float64(x + t);
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+70)
		tmp = t;
	elseif (z <= -4000.0)
		tmp = t * (y / -z);
	elseif ((z <= -1.62e-46) || ~((z <= 7.5e-87)))
		tmp = x + t;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+70], t, If[LessEqual[z, -4000.0], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.62e-46], N[Not[LessEqual[z, 7.5e-87]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.05000000000000004e70

   1. Initial program 70.7%

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

   3. Taylor expanded in z around inf 53.8%

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

   if -1.05000000000000004e70 < z < -4e3

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf 57.1%

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

      1. div-sub 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in t around inf 57.2%

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

   7. Taylor expanded in a around 0 47.3%

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

      1. mul-1-neg 47.3%

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

      2. associate-/l* 56.7%

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

      3. distribute-rgt-neg-in 56.7%

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

   9. Simplified 56.7%

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

   if -4e3 < z < -1.6200000000000001e-46 or 7.5000000000000002e-87 < z

   1. Initial program 78.0%

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

      1. clear-num 77.9%

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

      2. un-div-inv 78.1%

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

   4. Applied egg-rr 78.1%

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

   5. Taylor expanded in t around inf 63.2%

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

   6. Taylor expanded in z around inf 38.8%

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

   if -1.6200000000000001e-46 < z < 7.5000000000000002e-87

   1. Initial program 90.4%

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

   3. Taylor expanded in x around 0 52.5%

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

      1. associate-/l* 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in z around 0 39.7%

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

      1. associate-/l* 40.8%

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

   8. Simplified 40.8%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+70}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4000:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-46} \lor \neg \left(z \leq 7.5 \cdot 10^{-87}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+70}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -35000:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-50} \lor \neg \left(z \leq 4.2 \cdot 10^{-83}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+70)
   t
   (if (<= z -35000.0)
     (* y (/ t (- z)))
     (if (or (<= z -6.4e-50) (not (<= z 4.2e-83))) (+ x t) (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+70) {
		tmp = t;
	} else if (z <= -35000.0) {
		tmp = y * (t / -z);
	} else if ((z <= -6.4e-50) || !(z <= 4.2e-83)) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.5d+70)) then
        tmp = t
    else if (z <= (-35000.0d0)) then
        tmp = y * (t / -z)
    else if ((z <= (-6.4d-50)) .or. (.not. (z <= 4.2d-83))) then
        tmp = x + t
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+70) {
		tmp = t;
	} else if (z <= -35000.0) {
		tmp = y * (t / -z);
	} else if ((z <= -6.4e-50) || !(z <= 4.2e-83)) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+70:
		tmp = t
	elif z <= -35000.0:
		tmp = y * (t / -z)
	elif (z <= -6.4e-50) or not (z <= 4.2e-83):
		tmp = x + t
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+70)
		tmp = t;
	elseif (z <= -35000.0)
		tmp = Float64(y * Float64(t / Float64(-z)));
	elseif ((z <= -6.4e-50) || !(z <= 4.2e-83))
		tmp = Float64(x + t);
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+70)
		tmp = t;
	elseif (z <= -35000.0)
		tmp = y * (t / -z);
	elseif ((z <= -6.4e-50) || ~((z <= 4.2e-83)))
		tmp = x + t;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+70], t, If[LessEqual[z, -35000.0], N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -6.4e-50], N[Not[LessEqual[z, 4.2e-83]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.4999999999999999e70

   1. Initial program 70.7%

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

   3. Taylor expanded in z around inf 53.8%

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

   if -4.4999999999999999e70 < z < -35000

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf 57.1%

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

      1. div-sub 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in t around inf 57.2%

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

   7. Taylor expanded in a around 0 56.9%

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

      1. associate-*r/ 56.9%

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

      2. neg-mul-1 56.9%

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

   9. Simplified 56.9%

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

   if -35000 < z < -6.4e-50 or 4.1999999999999998e-83 < z

   1. Initial program 78.0%

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

      1. clear-num 77.9%

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

      2. un-div-inv 78.1%

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

   4. Applied egg-rr 78.1%

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

   5. Taylor expanded in t around inf 63.2%

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

   6. Taylor expanded in z around inf 38.8%

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

   if -6.4e-50 < z < 4.1999999999999998e-83

   1. Initial program 90.4%

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

   3. Taylor expanded in x around 0 52.5%

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

      1. associate-/l* 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in z around 0 39.7%

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

      1. associate-/l* 40.8%

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

   8. Simplified 40.8%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+70}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -35000:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-50} \lor \neg \left(z \leq 4.2 \cdot 10^{-83}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+173}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-11} \lor \neg \left(a \leq 4.8 \cdot 10^{-11}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.8e+173)
   (+ x (/ (- y z) (/ a t)))
   (if (or (<= a -3.2e-11) (not (<= a 4.8e-11)))
     (+ x (* y (/ (- t x) a)))
     (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.8e+173) {
		tmp = x + ((y - z) / (a / t));
	} else if ((a <= -3.2e-11) || !(a <= 4.8e-11)) {
		tmp = x + (y * ((t - x) / a));
	} 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 (a <= (-6.8d+173)) then
        tmp = x + ((y - z) / (a / t))
    else if ((a <= (-3.2d-11)) .or. (.not. (a <= 4.8d-11))) then
        tmp = x + (y * ((t - x) / a))
    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 (a <= -6.8e+173) {
		tmp = x + ((y - z) / (a / t));
	} else if ((a <= -3.2e-11) || !(a <= 4.8e-11)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.8e+173:
		tmp = x + ((y - z) / (a / t))
	elif (a <= -3.2e-11) or not (a <= 4.8e-11):
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.8e+173)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / t)));
	elseif ((a <= -3.2e-11) || !(a <= 4.8e-11))
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	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 (a <= -6.8e+173)
		tmp = x + ((y - z) / (a / t));
	elseif ((a <= -3.2e-11) || ~((a <= 4.8e-11)))
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.8e+173], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -3.2e-11], N[Not[LessEqual[a, 4.8e-11]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.80000000000000042e173

   1. Initial program 99.8%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

   6. Taylor expanded in a around inf 91.4%

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

   if -6.80000000000000042e173 < a < -3.19999999999999994e-11 or 4.8000000000000002e-11 < a

   1. Initial program 85.6%

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

   3. Taylor expanded in z around 0 56.1%

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

      1. associate-/l* 65.9%

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

   5. Simplified 65.9%

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

   if -3.19999999999999994e-11 < a < 4.8000000000000002e-11

   1. Initial program 75.8%

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

   3. Taylor expanded in x around 0 60.6%

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

      1. associate-/l* 75.3%

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

   5. Simplified 75.3%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+173}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-11} \lor \neg \left(a \leq 4.8 \cdot 10^{-11}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-12}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.3e-142)
     t_1
     (if (<= t -4e-260)
       (* x (/ (- y a) z))
       (if (<= t 2.8e-12) (- x (* x (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.3e-142) {
		tmp = t_1;
	} else if (t <= -4e-260) {
		tmp = x * ((y - a) / z);
	} else if (t <= 2.8e-12) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (t <= (-1.3d-142)) then
        tmp = t_1
    else if (t <= (-4d-260)) then
        tmp = x * ((y - a) / z)
    else if (t <= 2.8d-12) then
        tmp = x - (x * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.3e-142) {
		tmp = t_1;
	} else if (t <= -4e-260) {
		tmp = x * ((y - a) / z);
	} else if (t <= 2.8e-12) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -1.3e-142:
		tmp = t_1
	elif t <= -4e-260:
		tmp = x * ((y - a) / z)
	elif t <= 2.8e-12:
		tmp = x - (x * (y / a))
	else:
		tmp = t_1
	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 (t <= -1.3e-142)
		tmp = t_1;
	elseif (t <= -4e-260)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (t <= 2.8e-12)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	else
		tmp = t_1;
	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 (t <= -1.3e-142)
		tmp = t_1;
	elseif (t <= -4e-260)
		tmp = x * ((y - a) / z);
	elseif (t <= 2.8e-12)
		tmp = x - (x * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e-142], t$95$1, If[LessEqual[t, -4e-260], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-12], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3e-142 or 2.8000000000000002e-12 < t

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 59.6%

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

      1. associate-/l* 78.0%

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

   5. Simplified 78.0%

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

   if -1.3e-142 < t < -3.99999999999999985e-260

   1. Initial program 42.5%

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

   3. Taylor expanded in x around inf 42.5%

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

      1. mul-1-neg 42.5%

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

      2. unsub-neg 42.5%

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

   5. Simplified 42.5%

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

   6. Taylor expanded in z around inf 53.5%

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

      1. associate-*r/ 53.5%

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

      2. neg-mul-1 53.5%

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

      3. sub-neg 53.5%

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

      4. mul-1-neg 53.5%

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

   8. Simplified 53.5%

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

   if -3.99999999999999985e-260 < t < 2.8000000000000002e-12

   1. Initial program 78.1%

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

   3. Taylor expanded in t around 0 53.8%

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

      1. mul-1-neg 53.8%

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

      2. associate-/l* 69.3%

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

      3. distribute-rgt-neg-in 69.3%

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

      4. distribute-frac-neg2 69.3%

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

      5. neg-sub0 69.3%

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

      6. associate--r- 69.3%

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

      7. neg-sub0 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in z around 0 48.0%

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

      1. mul-1-neg 48.0%

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

      2. unsub-neg 48.0%

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

      3. associate-/l* 59.2%

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

   8. Simplified 59.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-12}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 40.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+72)
   t
   (if (<= z -2.15e-31)
     (* t (/ y (- a z)))
     (if (<= z 2.4e-84) (* y (/ (- t x) a)) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+72) {
		tmp = t;
	} else if (z <= -2.15e-31) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.4e-84) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.5d+72)) then
        tmp = t
    else if (z <= (-2.15d-31)) then
        tmp = t * (y / (a - z))
    else if (z <= 2.4d-84) then
        tmp = y * ((t - x) / a)
    else
        tmp = x + 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 <= -4.5e+72) {
		tmp = t;
	} else if (z <= -2.15e-31) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.4e-84) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+72:
		tmp = t
	elif z <= -2.15e-31:
		tmp = t * (y / (a - z))
	elif z <= 2.4e-84:
		tmp = y * ((t - x) / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+72)
		tmp = t;
	elseif (z <= -2.15e-31)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 2.4e-84)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+72)
		tmp = t;
	elseif (z <= -2.15e-31)
		tmp = t * (y / (a - z));
	elseif (z <= 2.4e-84)
		tmp = y * ((t - x) / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+72], t, If[LessEqual[z, -2.15e-31], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-84], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.4999999999999998e72

   1. Initial program 70.7%

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

   3. Taylor expanded in z around inf 53.8%

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

   if -4.4999999999999998e72 < z < -2.15e-31

   1. Initial program 94.6%

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

   3. Taylor expanded in y around inf 46.4%

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

      1. div-sub 46.4%

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

   5. Simplified 46.4%

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

   6. Taylor expanded in t around inf 41.9%

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

      1. associate-/l* 51.5%

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

   8. Simplified 51.5%

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

   if -2.15e-31 < z < 2.40000000000000017e-84

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 63.1%

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

      1. div-sub 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in a around inf 59.3%

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

   if 2.40000000000000017e-84 < z

   1. Initial program 74.7%

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

      1. clear-num 74.6%

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

      2. un-div-inv 74.8%

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

   4. Applied egg-rr 74.8%

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

   5. Taylor expanded in t around inf 60.6%

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

   6. Taylor expanded in z around inf 39.6%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 64.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-133} \lor \neg \left(t \leq 19000\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.5e-133) (not (<= t 19000.0)))
   (* t (/ (- y z) (- a z)))
   (* x (+ (/ (- y z) (- z a)) 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e-133) || !(t <= 19000.0)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	}
	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 ((t <= (-2.5d-133)) .or. (.not. (t <= 19000.0d0))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e-133) || !(t <= 19000.0)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.5e-133) or not (t <= 19000.0):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.5e-133) || !(t <= 19000.0))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.5e-133) || ~((t <= 19000.0)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (((y - z) / (z - a)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.5e-133], N[Not[LessEqual[t, 19000.0]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5e-133 or 19000 < t

   1. Initial program 89.9%

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

   3. Taylor expanded in x around 0 60.8%

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

      1. associate-/l* 80.1%

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

   5. Simplified 80.1%

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

   if -2.5e-133 < t < 19000

   1. Initial program 69.1%

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

   3. Taylor expanded in x around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. unsub-neg 62.7%

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

   5. Simplified 62.7%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-133} \lor \neg \left(t \leq 19000\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-11} \lor \neg \left(a \leq 8.2 \cdot 10^{-11}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6e-11) (not (<= a 8.2e-11)))
   (+ x (* y (/ (- t x) a)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e-11) || !(a <= 8.2e-11)) {
		tmp = x + (y * ((t - x) / a));
	} 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 ((a <= (-6d-11)) .or. (.not. (a <= 8.2d-11))) then
        tmp = x + (y * ((t - x) / a))
    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 ((a <= -6e-11) || !(a <= 8.2e-11)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6e-11) or not (a <= 8.2e-11):
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6e-11) || !(a <= 8.2e-11))
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	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 ((a <= -6e-11) || ~((a <= 8.2e-11)))
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6e-11], N[Not[LessEqual[a, 8.2e-11]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $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 a < -6e-11 or 8.2000000000000001e-11 < a

   1. Initial program 88.2%

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

   3. Taylor expanded in z around 0 58.5%

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

      1. associate-/l* 67.2%

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

   5. Simplified 67.2%

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

   if -6e-11 < a < 8.2000000000000001e-11

   1. Initial program 75.8%

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

   3. Taylor expanded in x around 0 60.6%

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

      1. associate-/l* 75.3%

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

   5. Simplified 75.3%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-11} \lor \neg \left(a \leq 8.2 \cdot 10^{-11}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+74) t (if (<= z 4.2e-85) (* t (/ y (- a z))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+74) {
		tmp = t;
	} else if (z <= 4.2e-85) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.5d+74)) then
        tmp = t
    else if (z <= 4.2d-85) then
        tmp = t * (y / (a - z))
    else
        tmp = x + 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 <= -7.5e+74) {
		tmp = t;
	} else if (z <= 4.2e-85) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e+74:
		tmp = t
	elif z <= 4.2e-85:
		tmp = t * (y / (a - z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+74)
		tmp = t;
	elseif (z <= 4.2e-85)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e+74)
		tmp = t;
	elseif (z <= 4.2e-85)
		tmp = t * (y / (a - z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+74], t, If[LessEqual[z, 4.2e-85], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5e74

   1. Initial program 70.7%

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

   3. Taylor expanded in z around inf 53.8%

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

   if -7.5e74 < z < 4.2e-85

   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 60.7%

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

      1. div-sub 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in t around inf 43.2%

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

      1. associate-/l* 45.5%

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

   8. Simplified 45.5%

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

   if 4.2e-85 < z

   1. Initial program 74.7%

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

      1. clear-num 74.6%

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

      2. un-div-inv 74.8%

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

   4. Applied egg-rr 74.8%

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

   5. Taylor expanded in t around inf 60.6%

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

   6. Taylor expanded in z around inf 39.6%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 39.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-11}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.15e+98) x (if (<= a -2.4e-11) (+ x t) (if (<= a 2.3e+16) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.15e+98) {
		tmp = x;
	} else if (a <= -2.4e-11) {
		tmp = x + t;
	} else if (a <= 2.3e+16) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.15d+98)) then
        tmp = x
    else if (a <= (-2.4d-11)) then
        tmp = x + t
    else if (a <= 2.3d+16) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.15e+98) {
		tmp = x;
	} else if (a <= -2.4e-11) {
		tmp = x + t;
	} else if (a <= 2.3e+16) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.15e+98:
		tmp = x
	elif a <= -2.4e-11:
		tmp = x + t
	elif a <= 2.3e+16:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.15e+98)
		tmp = x;
	elseif (a <= -2.4e-11)
		tmp = Float64(x + t);
	elseif (a <= 2.3e+16)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.15e+98)
		tmp = x;
	elseif (a <= -2.4e-11)
		tmp = x + t;
	elseif (a <= 2.3e+16)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.15e+98], x, If[LessEqual[a, -2.4e-11], N[(x + t), $MachinePrecision], If[LessEqual[a, 2.3e+16], t, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1500000000000001e98 or 2.3e16 < a

   1. Initial program 90.7%

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

   3. Taylor expanded in a around inf 43.2%

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

   if -2.1500000000000001e98 < a < -2.4000000000000001e-11

   1. Initial program 85.2%

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

      1. clear-num 85.0%

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

      2. un-div-inv 85.1%

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

   4. Applied egg-rr 85.1%

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

   5. Taylor expanded in t around inf 56.1%

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

   6. Taylor expanded in z around inf 34.4%

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

   if -2.4000000000000001e-11 < a < 2.3e16

   1. Initial program 75.1%

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

   3. Taylor expanded in z around inf 39.1%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-11}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-44}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.1e-44) t (if (<= z 1.4e-84) (* t (/ y a)) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.1e-44) {
		tmp = t;
	} else if (z <= 1.4e-84) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.1d-44)) then
        tmp = t
    else if (z <= 1.4d-84) then
        tmp = t * (y / a)
    else
        tmp = x + 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 <= -4.1e-44) {
		tmp = t;
	} else if (z <= 1.4e-84) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.1e-44:
		tmp = t
	elif z <= 1.4e-84:
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.1e-44)
		tmp = t;
	elseif (z <= 1.4e-84)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.1e-44)
		tmp = t;
	elseif (z <= 1.4e-84)
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.1e-44], t, If[LessEqual[z, 1.4e-84], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.09999999999999992e-44

   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 44.8%

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

   if -4.09999999999999992e-44 < z < 1.39999999999999991e-84

   1. Initial program 89.5%

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

   3. Taylor expanded in x around 0 52.0%

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

      1. associate-/l* 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in z around 0 39.3%

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

      1. associate-/l* 40.4%

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

   8. Simplified 40.4%

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

   if 1.39999999999999991e-84 < z

   1. Initial program 74.7%

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

      1. clear-num 74.6%

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

      2. un-div-inv 74.8%

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

   4. Applied egg-rr 74.8%

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

   5. Taylor expanded in t around inf 60.6%

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

   6. Taylor expanded in z around inf 39.6%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-44}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.5e-11) x (if (<= a 1.3e+16) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e-11) {
		tmp = x;
	} else if (a <= 1.3e+16) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.5d-11)) then
        tmp = x
    else if (a <= 1.3d+16) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e-11) {
		tmp = x;
	} else if (a <= 1.3e+16) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.5e-11:
		tmp = x
	elif a <= 1.3e+16:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.5e-11)
		tmp = x;
	elseif (a <= 1.3e+16)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.5e-11)
		tmp = x;
	elseif (a <= 1.3e+16)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.5e-11], x, If[LessEqual[a, 1.3e+16], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.49999999999999953e-11 or 1.3e16 < a

   1. Initial program 89.5%

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

   3. Taylor expanded in a around inf 37.7%

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

   if -6.49999999999999953e-11 < a < 1.3e16

   1. Initial program 75.1%

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

   3. Taylor expanded in z around inf 39.1%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 81.6%

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

3. Taylor expanded in t around 0 31.5%

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

   1. mul-1-neg 31.5%

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

   2. associate-/l* 37.5%

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

   3. distribute-rgt-neg-in 37.5%

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

   4. distribute-frac-neg2 37.5%

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

   5. neg-sub0 37.5%

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

   6. associate--r- 37.5%

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

   7. neg-sub0 37.5%

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

5. Simplified 37.5%

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

6. Taylor expanded in z around inf 2.7%

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

   1. distribute-rgt1-in 2.7%

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

   2. metadata-eval 2.7%

      \[\leadsto \color{blue}{0} \cdot x \]

   3. mul0-lft 2.7%

      \[\leadsto \color{blue}{0} \]

8. Simplified 2.7%

   \[\leadsto \color{blue}{0} \]

9. Final simplification 2.7%

   \[\leadsto 0 \]
10. Add Preprocessing

Alternative 23: 24.5% 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 81.6%

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

3. Taylor expanded in z around inf 26.4%

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

4. Final simplification 26.4%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024071 
(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)))))