Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 81.1% → 95.2%

Time: 15.3s

Alternatives: 22

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 81.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-308} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-308) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-308) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-308) || !(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(a - y)));
	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, -1e-308], 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[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999991e-309 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 86.9%

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

      1. +-commutative 86.9%

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

      2. remove-double-neg 86.9%

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

      3. unsub-neg 86.9%

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

      4. *-commutative 86.9%

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

      5. associate-*l/ 74.5%

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

      6. associate-/l* 92.8%

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

      7. fma-neg 92.9%

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

      8. remove-double-neg 92.9%

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

   3. Simplified 92.9%

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

   if -9.9999999999999991e-309 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 85.8%

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

      1. associate--l+ 85.8%

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

      2. distribute-lft-out-- 85.8%

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

      3. div-sub 85.8%

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

      4. mul-1-neg 85.8%

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

      5. unsub-neg 85.8%

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

      6. div-sub 85.8%

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

      7. associate-/l* 93.0%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.8%

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

   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 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-308} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-218} \lor \neg \left(t\_1 \leq 10^{-293}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-218) (not (<= t_1 1e-293)))
     t_1
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-218) || !(t_1 <= 1e-293)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-218)) .or. (.not. (t_1 <= 1d-293))) then
        tmp = t_1
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-218) || !(t_1 <= 1e-293)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-218) or not (t_1 <= 1e-293):
		tmp = t_1
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-218) || !(t_1 <= 1e-293))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-218) || ~((t_1 <= 1e-293)))
		tmp = t_1;
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-218], N[Not[LessEqual[t$95$1, 1e-293]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-218 or 1.0000000000000001e-293 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.8%

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

   if -1e-218 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.0000000000000001e-293

   1. Initial program 3.8%

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

   3. Taylor expanded in z around inf 80.8%

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

      1. associate--l+ 80.8%

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

      2. distribute-lft-out-- 80.8%

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

      3. div-sub 80.8%

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

      4. mul-1-neg 80.8%

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

      5. unsub-neg 80.8%

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

      6. div-sub 80.8%

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

      7. associate-/l* 86.3%

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

      8. associate-/l* 91.8%

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

      9. distribute-rgt-out-- 91.8%

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

   5. Simplified 91.8%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-218} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-293}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-293}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-218)
     t_1
     (if (<= t_1 1e-293)
       (+ t (* (/ (- t x) z) (- a y)))
       (+ x (/ (- y z) (/ (- a z) (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-218) {
		tmp = t_1;
	} else if (t_1 <= 1e-293) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-1d-218)) then
        tmp = t_1
    else if (t_1 <= 1d-293) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-218) {
		tmp = t_1;
	} else if (t_1 <= 1e-293) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -1e-218:
		tmp = t_1
	elif t_1 <= 1e-293:
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-218)
		tmp = t_1;
	elseif (t_1 <= 1e-293)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -1e-218)
		tmp = t_1;
	elseif (t_1 <= 1e-293)
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-218], t$95$1, If[LessEqual[t$95$1, 1e-293], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-218

   1. Initial program 88.9%

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

   if -1e-218 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.0000000000000001e-293

   1. Initial program 3.8%

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

   3. Taylor expanded in z around inf 80.8%

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

      1. associate--l+ 80.8%

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

      2. distribute-lft-out-- 80.8%

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

      3. div-sub 80.8%

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

      4. mul-1-neg 80.8%

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

      5. unsub-neg 80.8%

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

      6. div-sub 80.8%

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

      7. associate-/l* 86.3%

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

      8. associate-/l* 91.8%

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

      9. distribute-rgt-out-- 91.8%

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

   5. Simplified 91.8%

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

   if 1.0000000000000001e-293 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 90.8%

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

   4. Applied egg-rr 90.8%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-218}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-293}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+132}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-21}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-296}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -7e+132)
     t
     (if (<= z -2.5e-21)
       (+ x t)
       (if (<= z -2.05e-260)
         t_1
         (if (<= z -4.8e-296)
           (* t (/ y (- a z)))
           (if (<= z 2.45e-278)
             t_1
             (if (<= z 3.6e-232)
               (* y (/ (- t x) a))
               (if (<= z 6e+81) t_1 t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -7e+132) {
		tmp = t;
	} else if (z <= -2.5e-21) {
		tmp = x + t;
	} else if (z <= -2.05e-260) {
		tmp = t_1;
	} else if (z <= -4.8e-296) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.45e-278) {
		tmp = t_1;
	} else if (z <= 3.6e-232) {
		tmp = y * ((t - x) / a);
	} else if (z <= 6e+81) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-7d+132)) then
        tmp = t
    else if (z <= (-2.5d-21)) then
        tmp = x + t
    else if (z <= (-2.05d-260)) then
        tmp = t_1
    else if (z <= (-4.8d-296)) then
        tmp = t * (y / (a - z))
    else if (z <= 2.45d-278) then
        tmp = t_1
    else if (z <= 3.6d-232) then
        tmp = y * ((t - x) / a)
    else if (z <= 6d+81) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -7e+132) {
		tmp = t;
	} else if (z <= -2.5e-21) {
		tmp = x + t;
	} else if (z <= -2.05e-260) {
		tmp = t_1;
	} else if (z <= -4.8e-296) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.45e-278) {
		tmp = t_1;
	} else if (z <= 3.6e-232) {
		tmp = y * ((t - x) / a);
	} else if (z <= 6e+81) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -7e+132:
		tmp = t
	elif z <= -2.5e-21:
		tmp = x + t
	elif z <= -2.05e-260:
		tmp = t_1
	elif z <= -4.8e-296:
		tmp = t * (y / (a - z))
	elif z <= 2.45e-278:
		tmp = t_1
	elif z <= 3.6e-232:
		tmp = y * ((t - x) / a)
	elif z <= 6e+81:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -7e+132)
		tmp = t;
	elseif (z <= -2.5e-21)
		tmp = Float64(x + t);
	elseif (z <= -2.05e-260)
		tmp = t_1;
	elseif (z <= -4.8e-296)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 2.45e-278)
		tmp = t_1;
	elseif (z <= 3.6e-232)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 6e+81)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -7e+132)
		tmp = t;
	elseif (z <= -2.5e-21)
		tmp = x + t;
	elseif (z <= -2.05e-260)
		tmp = t_1;
	elseif (z <= -4.8e-296)
		tmp = t * (y / (a - z));
	elseif (z <= 2.45e-278)
		tmp = t_1;
	elseif (z <= 3.6e-232)
		tmp = y * ((t - x) / a);
	elseif (z <= 6e+81)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+132], t, If[LessEqual[z, -2.5e-21], N[(x + t), $MachinePrecision], If[LessEqual[z, -2.05e-260], t$95$1, If[LessEqual[z, -4.8e-296], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e-278], t$95$1, If[LessEqual[z, 3.6e-232], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+81], t$95$1, t]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.00000000000000041e132 or 5.99999999999999995e81 < z

   1. Initial program 54.5%

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

   3. Taylor expanded in z around inf 62.1%

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

   if -7.00000000000000041e132 < z < -2.49999999999999986e-21

   1. Initial program 89.0%

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

      1. clear-num 88.9%

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

      2. un-div-inv 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in t around inf 73.3%

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

   6. Taylor expanded in z around inf 55.5%

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

   if -2.49999999999999986e-21 < z < -2.04999999999999998e-260 or -4.79999999999999992e-296 < z < 2.4500000000000001e-278 or 3.60000000000000016e-232 < z < 5.99999999999999995e81

   1. Initial program 89.3%

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

   3. Taylor expanded in x around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in z around 0 57.9%

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

   if -2.04999999999999998e-260 < z < -4.79999999999999992e-296

   1. Initial program 77.1%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. div-sub 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in t around inf 88.4%

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

      1. associate-/l* 99.6%

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

   8. Simplified 99.6%

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

   if 2.4500000000000001e-278 < z < 3.60000000000000016e-232

   1. Initial program 99.4%

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

   3. Taylor expanded in y around inf 99.4%

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

      1. div-sub 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in a around inf 99.4%

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

Alternative 5: 37.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-183}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-273}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-124}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+95}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -7.2e+145)
   (* x (/ y (- a)))
   (if (<= y -2.6e-183)
     (+ x t)
     (if (<= y 4.2e-273)
       t
       (if (<= y 1.1e-217)
         x
         (if (<= y 1.85e-124)
           t
           (if (<= y 1.8e+95) (+ x t) (* t (/ y (- a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.2e+145) {
		tmp = x * (y / -a);
	} else if (y <= -2.6e-183) {
		tmp = x + t;
	} else if (y <= 4.2e-273) {
		tmp = t;
	} else if (y <= 1.1e-217) {
		tmp = x;
	} else if (y <= 1.85e-124) {
		tmp = t;
	} else if (y <= 1.8e+95) {
		tmp = x + t;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-7.2d+145)) then
        tmp = x * (y / -a)
    else if (y <= (-2.6d-183)) then
        tmp = x + t
    else if (y <= 4.2d-273) then
        tmp = t
    else if (y <= 1.1d-217) then
        tmp = x
    else if (y <= 1.85d-124) then
        tmp = t
    else if (y <= 1.8d+95) then
        tmp = x + t
    else
        tmp = t * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.2e+145) {
		tmp = x * (y / -a);
	} else if (y <= -2.6e-183) {
		tmp = x + t;
	} else if (y <= 4.2e-273) {
		tmp = t;
	} else if (y <= 1.1e-217) {
		tmp = x;
	} else if (y <= 1.85e-124) {
		tmp = t;
	} else if (y <= 1.8e+95) {
		tmp = x + t;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -7.2e+145:
		tmp = x * (y / -a)
	elif y <= -2.6e-183:
		tmp = x + t
	elif y <= 4.2e-273:
		tmp = t
	elif y <= 1.1e-217:
		tmp = x
	elif y <= 1.85e-124:
		tmp = t
	elif y <= 1.8e+95:
		tmp = x + t
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -7.2e+145)
		tmp = Float64(x * Float64(y / Float64(-a)));
	elseif (y <= -2.6e-183)
		tmp = Float64(x + t);
	elseif (y <= 4.2e-273)
		tmp = t;
	elseif (y <= 1.1e-217)
		tmp = x;
	elseif (y <= 1.85e-124)
		tmp = t;
	elseif (y <= 1.8e+95)
		tmp = Float64(x + t);
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -7.2e+145)
		tmp = x * (y / -a);
	elseif (y <= -2.6e-183)
		tmp = x + t;
	elseif (y <= 4.2e-273)
		tmp = t;
	elseif (y <= 1.1e-217)
		tmp = x;
	elseif (y <= 1.85e-124)
		tmp = t;
	elseif (y <= 1.8e+95)
		tmp = x + t;
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -7.2e+145], N[(x * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e-183], N[(x + t), $MachinePrecision], If[LessEqual[y, 4.2e-273], t, If[LessEqual[y, 1.1e-217], x, If[LessEqual[y, 1.85e-124], t, If[LessEqual[y, 1.8e+95], N[(x + t), $MachinePrecision], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.19999999999999948e145

   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 inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. unsub-neg 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in z around 0 55.5%

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

   7. Taylor expanded in y around inf 39.4%

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

      1. mul-1-neg 39.4%

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

      2. associate-*r/ 47.5%

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

      3. *-commutative 47.5%

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

      4. distribute-rgt-neg-in 47.5%

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

   9. Simplified 47.5%

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

   if -7.19999999999999948e145 < y < -2.5999999999999999e-183 or 1.84999999999999995e-124 < y < 1.79999999999999989e95

   1. Initial program 83.3%

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

      1. clear-num 82.9%

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

      2. un-div-inv 83.0%

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

   4. Applied egg-rr 83.0%

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

   5. Taylor expanded in t around inf 71.2%

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

   6. Taylor expanded in z around inf 50.3%

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

   if -2.5999999999999999e-183 < y < 4.2000000000000004e-273 or 1.09999999999999991e-217 < y < 1.84999999999999995e-124

   1. Initial program 42.4%

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

   3. Taylor expanded in z around inf 68.1%

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

   if 4.2000000000000004e-273 < y < 1.09999999999999991e-217

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 71.4%

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

   if 1.79999999999999989e95 < y

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf 80.7%

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

      1. div-sub 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in t around inf 44.6%

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

      1. associate-/l* 55.9%

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

   8. Simplified 55.9%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-183}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-273}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-124}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+95}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{x - t}{a}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-193}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-234}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- x t) a)))))
   (if (<= a -1.75e+80)
     t_1
     (if (<= a -2.6e-193)
       (* t (/ (- y z) (- a z)))
       (if (<= a -5e-234)
         (/ y (/ (- a z) (- t x)))
         (if (<= a 1.16e-11)
           (/ t (/ (- a z) (- y z)))
           (if (<= a 2e+74) (+ x (/ (- y z) (/ (- a z) t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((x - t) / a));
	double tmp;
	if (a <= -1.75e+80) {
		tmp = t_1;
	} else if (a <= -2.6e-193) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= -5e-234) {
		tmp = y / ((a - z) / (t - x));
	} else if (a <= 1.16e-11) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 2e+74) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * ((x - t) / a))
    if (a <= (-1.75d+80)) then
        tmp = t_1
    else if (a <= (-2.6d-193)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= (-5d-234)) then
        tmp = y / ((a - z) / (t - x))
    else if (a <= 1.16d-11) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 2d+74) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((x - t) / a));
	double tmp;
	if (a <= -1.75e+80) {
		tmp = t_1;
	} else if (a <= -2.6e-193) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= -5e-234) {
		tmp = y / ((a - z) / (t - x));
	} else if (a <= 1.16e-11) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 2e+74) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((x - t) / a))
	tmp = 0
	if a <= -1.75e+80:
		tmp = t_1
	elif a <= -2.6e-193:
		tmp = t * ((y - z) / (a - z))
	elif a <= -5e-234:
		tmp = y / ((a - z) / (t - x))
	elif a <= 1.16e-11:
		tmp = t / ((a - z) / (y - z))
	elif a <= 2e+74:
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(x - t) / a)))
	tmp = 0.0
	if (a <= -1.75e+80)
		tmp = t_1;
	elseif (a <= -2.6e-193)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= -5e-234)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (a <= 1.16e-11)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 2e+74)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((x - t) / a));
	tmp = 0.0;
	if (a <= -1.75e+80)
		tmp = t_1;
	elseif (a <= -2.6e-193)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= -5e-234)
		tmp = y / ((a - z) / (t - x));
	elseif (a <= 1.16e-11)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 2e+74)
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+80], t$95$1, If[LessEqual[a, -2.6e-193], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e-234], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.16e-11], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+74], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.74999999999999997e80 or 1.9999999999999999e74 < a

   1. Initial program 91.0%

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

   3. Taylor expanded in z around 0 67.0%

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

      1. associate-/l* 85.3%

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

   5. Simplified 85.3%

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

   if -1.74999999999999997e80 < a < -2.60000000000000008e-193

   1. Initial program 73.1%

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

   3. Taylor expanded in x around 0 60.2%

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

      1. associate-/l* 76.6%

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

   5. Simplified 76.6%

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

   if -2.60000000000000008e-193 < a < -4.99999999999999979e-234

   1. Initial program 70.8%

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

   3. Taylor expanded in y around inf 87.4%

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

      1. div-sub 87.5%

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

   5. Simplified 87.5%

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

      1. clear-num 87.7%

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

      2. div-inv 87.7%

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

   7. Applied egg-rr 87.7%

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

   if -4.99999999999999979e-234 < a < 1.1600000000000001e-11

   1. Initial program 66.4%

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

   3. Taylor expanded in x around 0 61.2%

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

      1. associate-/l* 73.5%

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

   5. Simplified 73.5%

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

      1. clear-num 73.5%

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

      2. un-div-inv 73.5%

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

   7. Applied egg-rr 73.5%

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

   if 1.1600000000000001e-11 < a < 1.9999999999999999e74

   1. Initial program 89.0%

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

      1. clear-num 89.0%

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

      2. un-div-inv 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in t around inf 83.7%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+80}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-193}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-234}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-183}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-272}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-119}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+96}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.6e+147)
   (* x (/ y (- a)))
   (if (<= y -6.8e-183)
     (+ x t)
     (if (<= y 6.2e-272)
       t
       (if (<= y 7.8e-215)
         x
         (if (<= y 1.12e-119)
           t
           (if (<= y 1.66e+96) (+ x t) (* t (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.6e+147) {
		tmp = x * (y / -a);
	} else if (y <= -6.8e-183) {
		tmp = x + t;
	} else if (y <= 6.2e-272) {
		tmp = t;
	} else if (y <= 7.8e-215) {
		tmp = x;
	} else if (y <= 1.12e-119) {
		tmp = t;
	} else if (y <= 1.66e+96) {
		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 (y <= (-6.6d+147)) then
        tmp = x * (y / -a)
    else if (y <= (-6.8d-183)) then
        tmp = x + t
    else if (y <= 6.2d-272) then
        tmp = t
    else if (y <= 7.8d-215) then
        tmp = x
    else if (y <= 1.12d-119) then
        tmp = t
    else if (y <= 1.66d+96) 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 (y <= -6.6e+147) {
		tmp = x * (y / -a);
	} else if (y <= -6.8e-183) {
		tmp = x + t;
	} else if (y <= 6.2e-272) {
		tmp = t;
	} else if (y <= 7.8e-215) {
		tmp = x;
	} else if (y <= 1.12e-119) {
		tmp = t;
	} else if (y <= 1.66e+96) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.6e+147:
		tmp = x * (y / -a)
	elif y <= -6.8e-183:
		tmp = x + t
	elif y <= 6.2e-272:
		tmp = t
	elif y <= 7.8e-215:
		tmp = x
	elif y <= 1.12e-119:
		tmp = t
	elif y <= 1.66e+96:
		tmp = x + t
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.6e+147)
		tmp = Float64(x * Float64(y / Float64(-a)));
	elseif (y <= -6.8e-183)
		tmp = Float64(x + t);
	elseif (y <= 6.2e-272)
		tmp = t;
	elseif (y <= 7.8e-215)
		tmp = x;
	elseif (y <= 1.12e-119)
		tmp = t;
	elseif (y <= 1.66e+96)
		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 (y <= -6.6e+147)
		tmp = x * (y / -a);
	elseif (y <= -6.8e-183)
		tmp = x + t;
	elseif (y <= 6.2e-272)
		tmp = t;
	elseif (y <= 7.8e-215)
		tmp = x;
	elseif (y <= 1.12e-119)
		tmp = t;
	elseif (y <= 1.66e+96)
		tmp = x + t;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.6e+147], N[(x * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.8e-183], N[(x + t), $MachinePrecision], If[LessEqual[y, 6.2e-272], t, If[LessEqual[y, 7.8e-215], x, If[LessEqual[y, 1.12e-119], t, If[LessEqual[y, 1.66e+96], N[(x + t), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.60000000000000049e147

   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 inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. unsub-neg 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in z around 0 55.5%

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

   7. Taylor expanded in y around inf 39.4%

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

      1. mul-1-neg 39.4%

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

      2. associate-*r/ 47.5%

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

      3. *-commutative 47.5%

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

      4. distribute-rgt-neg-in 47.5%

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

   9. Simplified 47.5%

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

   if -6.60000000000000049e147 < y < -6.80000000000000029e-183 or 1.11999999999999998e-119 < y < 1.6599999999999999e96

   1. Initial program 83.3%

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

      1. clear-num 82.9%

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

      2. un-div-inv 83.0%

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

   4. Applied egg-rr 83.0%

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

   5. Taylor expanded in t around inf 71.2%

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

   6. Taylor expanded in z around inf 50.3%

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

   if -6.80000000000000029e-183 < y < 6.20000000000000059e-272 or 7.7999999999999999e-215 < y < 1.11999999999999998e-119

   1. Initial program 42.4%

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

   3. Taylor expanded in z around inf 68.1%

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

   if 6.20000000000000059e-272 < y < 7.7999999999999999e-215

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 71.4%

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

   if 1.6599999999999999e96 < y

   1. Initial program 84.8%

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

   3. Taylor expanded in x around 0 50.3%

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

      1. associate-/l* 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in z around 0 41.9%

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

      1. associate-/l* 51.6%

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

   8. Simplified 51.6%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-183}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-272}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-119}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+96}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+146}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-183}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-273}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-131}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+96}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.8e+146)
   (* (- y) (/ x a))
   (if (<= y -1.05e-183)
     (+ x t)
     (if (<= y 7.4e-273)
       t
       (if (<= y 8.5e-218)
         x
         (if (<= y 1.65e-131)
           t
           (if (<= y 1.65e+96) (+ x t) (* t (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.8e+146) {
		tmp = -y * (x / a);
	} else if (y <= -1.05e-183) {
		tmp = x + t;
	} else if (y <= 7.4e-273) {
		tmp = t;
	} else if (y <= 8.5e-218) {
		tmp = x;
	} else if (y <= 1.65e-131) {
		tmp = t;
	} else if (y <= 1.65e+96) {
		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 (y <= (-5.8d+146)) then
        tmp = -y * (x / a)
    else if (y <= (-1.05d-183)) then
        tmp = x + t
    else if (y <= 7.4d-273) then
        tmp = t
    else if (y <= 8.5d-218) then
        tmp = x
    else if (y <= 1.65d-131) then
        tmp = t
    else if (y <= 1.65d+96) 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 (y <= -5.8e+146) {
		tmp = -y * (x / a);
	} else if (y <= -1.05e-183) {
		tmp = x + t;
	} else if (y <= 7.4e-273) {
		tmp = t;
	} else if (y <= 8.5e-218) {
		tmp = x;
	} else if (y <= 1.65e-131) {
		tmp = t;
	} else if (y <= 1.65e+96) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.8e+146:
		tmp = -y * (x / a)
	elif y <= -1.05e-183:
		tmp = x + t
	elif y <= 7.4e-273:
		tmp = t
	elif y <= 8.5e-218:
		tmp = x
	elif y <= 1.65e-131:
		tmp = t
	elif y <= 1.65e+96:
		tmp = x + t
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.8e+146)
		tmp = Float64(Float64(-y) * Float64(x / a));
	elseif (y <= -1.05e-183)
		tmp = Float64(x + t);
	elseif (y <= 7.4e-273)
		tmp = t;
	elseif (y <= 8.5e-218)
		tmp = x;
	elseif (y <= 1.65e-131)
		tmp = t;
	elseif (y <= 1.65e+96)
		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 (y <= -5.8e+146)
		tmp = -y * (x / a);
	elseif (y <= -1.05e-183)
		tmp = x + t;
	elseif (y <= 7.4e-273)
		tmp = t;
	elseif (y <= 8.5e-218)
		tmp = x;
	elseif (y <= 1.65e-131)
		tmp = t;
	elseif (y <= 1.65e+96)
		tmp = x + t;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.8e+146], N[((-y) * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.05e-183], N[(x + t), $MachinePrecision], If[LessEqual[y, 7.4e-273], t, If[LessEqual[y, 8.5e-218], x, If[LessEqual[y, 1.65e-131], t, If[LessEqual[y, 1.65e+96], N[(x + t), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.7999999999999997e146

   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 inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. unsub-neg 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in z around 0 55.5%

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

   7. Taylor expanded in y around inf 39.4%

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

      1. mul-1-neg 39.4%

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

      2. associate-*r/ 47.5%

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

      3. *-commutative 47.5%

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

      4. distribute-rgt-neg-in 47.5%

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

   9. Simplified 47.5%

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

   10. Taylor expanded in y around 0 39.4%

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

       1. mul-1-neg 39.4%

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

       2. *-commutative 39.4%

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

       3. distribute-frac-neg2 39.4%

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

       4. associate-/l* 41.2%

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

   12. Simplified 41.2%

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

   if -5.7999999999999997e146 < y < -1.0500000000000001e-183 or 1.6500000000000001e-131 < y < 1.64999999999999992e96

   1. Initial program 83.3%

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

      1. clear-num 82.9%

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

      2. un-div-inv 83.0%

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

   4. Applied egg-rr 83.0%

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

   5. Taylor expanded in t around inf 71.2%

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

   6. Taylor expanded in z around inf 50.3%

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

   if -1.0500000000000001e-183 < y < 7.4000000000000007e-273 or 8.5000000000000004e-218 < y < 1.6500000000000001e-131

   1. Initial program 42.4%

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

   3. Taylor expanded in z around inf 68.1%

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

   if 7.4000000000000007e-273 < y < 8.5000000000000004e-218

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 71.4%

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

   if 1.64999999999999992e96 < y

   1. Initial program 84.8%

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

   3. Taylor expanded in x around 0 50.3%

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

      1. associate-/l* 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in z around 0 41.9%

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

      1. associate-/l* 51.6%

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

   8. Simplified 51.6%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+146}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-183}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-273}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-131}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+96}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-183}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-272}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-130}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{+94}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= y -5.5e+208)
     t_1
     (if (<= y -1.7e-183)
       (+ x t)
       (if (<= y 1.05e-272)
         t
         (if (<= y 7e-218)
           x
           (if (<= y 5e-130) t (if (<= y 6.7e+94) (+ x t) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (y <= -5.5e+208) {
		tmp = t_1;
	} else if (y <= -1.7e-183) {
		tmp = x + t;
	} else if (y <= 1.05e-272) {
		tmp = t;
	} else if (y <= 7e-218) {
		tmp = x;
	} else if (y <= 5e-130) {
		tmp = t;
	} else if (y <= 6.7e+94) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (y <= (-5.5d+208)) then
        tmp = t_1
    else if (y <= (-1.7d-183)) then
        tmp = x + t
    else if (y <= 1.05d-272) then
        tmp = t
    else if (y <= 7d-218) then
        tmp = x
    else if (y <= 5d-130) then
        tmp = t
    else if (y <= 6.7d+94) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (y <= -5.5e+208) {
		tmp = t_1;
	} else if (y <= -1.7e-183) {
		tmp = x + t;
	} else if (y <= 1.05e-272) {
		tmp = t;
	} else if (y <= 7e-218) {
		tmp = x;
	} else if (y <= 5e-130) {
		tmp = t;
	} else if (y <= 6.7e+94) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if y <= -5.5e+208:
		tmp = t_1
	elif y <= -1.7e-183:
		tmp = x + t
	elif y <= 1.05e-272:
		tmp = t
	elif y <= 7e-218:
		tmp = x
	elif y <= 5e-130:
		tmp = t
	elif y <= 6.7e+94:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (y <= -5.5e+208)
		tmp = t_1;
	elseif (y <= -1.7e-183)
		tmp = Float64(x + t);
	elseif (y <= 1.05e-272)
		tmp = t;
	elseif (y <= 7e-218)
		tmp = x;
	elseif (y <= 5e-130)
		tmp = t;
	elseif (y <= 6.7e+94)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (y <= -5.5e+208)
		tmp = t_1;
	elseif (y <= -1.7e-183)
		tmp = x + t;
	elseif (y <= 1.05e-272)
		tmp = t;
	elseif (y <= 7e-218)
		tmp = x;
	elseif (y <= 5e-130)
		tmp = t;
	elseif (y <= 6.7e+94)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+208], t$95$1, If[LessEqual[y, -1.7e-183], N[(x + t), $MachinePrecision], If[LessEqual[y, 1.05e-272], t, If[LessEqual[y, 7e-218], x, If[LessEqual[y, 5e-130], t, If[LessEqual[y, 6.7e+94], N[(x + t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.4999999999999997e208 or 6.699999999999999e94 < y

   1. Initial program 87.4%

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

   3. Taylor expanded in x around 0 50.6%

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

      1. associate-/l* 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in z around 0 41.6%

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

      1. associate-/l* 51.4%

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

   8. Simplified 51.4%

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

   if -5.4999999999999997e208 < y < -1.70000000000000007e-183 or 4.9999999999999996e-130 < y < 6.699999999999999e94

   1. Initial program 83.4%

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

      1. clear-num 83.0%

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

      2. un-div-inv 83.1%

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

   4. Applied egg-rr 83.1%

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

   5. Taylor expanded in t around inf 68.9%

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

   6. Taylor expanded in z around inf 47.7%

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

   if -1.70000000000000007e-183 < y < 1.04999999999999993e-272 or 7e-218 < y < 4.9999999999999996e-130

   1. Initial program 42.4%

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

   3. Taylor expanded in z around inf 68.1%

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

   if 1.04999999999999993e-272 < y < 7e-218

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 71.4%

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

Alternative 10: 48.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+129}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-21}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.36 \cdot 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-296}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -4.5e+129)
     t
     (if (<= z -9.8e-21)
       (+ x t)
       (if (<= z -2.36e-259)
         t_1
         (if (<= z -7e-296) (* t (/ y (- a z))) (if (<= z 2.5e+82) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -4.5e+129) {
		tmp = t;
	} else if (z <= -9.8e-21) {
		tmp = x + t;
	} else if (z <= -2.36e-259) {
		tmp = t_1;
	} else if (z <= -7e-296) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.5e+82) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-4.5d+129)) then
        tmp = t
    else if (z <= (-9.8d-21)) then
        tmp = x + t
    else if (z <= (-2.36d-259)) then
        tmp = t_1
    else if (z <= (-7d-296)) then
        tmp = t * (y / (a - z))
    else if (z <= 2.5d+82) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -4.5e+129) {
		tmp = t;
	} else if (z <= -9.8e-21) {
		tmp = x + t;
	} else if (z <= -2.36e-259) {
		tmp = t_1;
	} else if (z <= -7e-296) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.5e+82) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -4.5e+129:
		tmp = t
	elif z <= -9.8e-21:
		tmp = x + t
	elif z <= -2.36e-259:
		tmp = t_1
	elif z <= -7e-296:
		tmp = t * (y / (a - z))
	elif z <= 2.5e+82:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -4.5e+129)
		tmp = t;
	elseif (z <= -9.8e-21)
		tmp = Float64(x + t);
	elseif (z <= -2.36e-259)
		tmp = t_1;
	elseif (z <= -7e-296)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 2.5e+82)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -4.5e+129)
		tmp = t;
	elseif (z <= -9.8e-21)
		tmp = x + t;
	elseif (z <= -2.36e-259)
		tmp = t_1;
	elseif (z <= -7e-296)
		tmp = t * (y / (a - z));
	elseif (z <= 2.5e+82)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+129], t, If[LessEqual[z, -9.8e-21], N[(x + t), $MachinePrecision], If[LessEqual[z, -2.36e-259], t$95$1, If[LessEqual[z, -7e-296], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+82], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5000000000000001e129 or 2.50000000000000008e82 < z

   1. Initial program 54.5%

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

   3. Taylor expanded in z around inf 62.1%

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

   if -4.5000000000000001e129 < z < -9.8000000000000003e-21

   1. Initial program 89.0%

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

      1. clear-num 88.9%

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

      2. un-div-inv 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in t around inf 73.3%

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

   6. Taylor expanded in z around inf 55.5%

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

   if -9.8000000000000003e-21 < z < -2.36e-259 or -6.9999999999999998e-296 < z < 2.50000000000000008e82

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in z around 0 55.7%

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

   if -2.36e-259 < z < -6.9999999999999998e-296

   1. Initial program 77.1%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. div-sub 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in t around inf 88.4%

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

      1. associate-/l* 99.6%

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

   8. Simplified 99.6%

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

Alternative 11: 64.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{x - t}{a}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-193}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-234}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 0.0305:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- x t) a)))))
   (if (<= a -6e+84)
     t_1
     (if (<= a -2e-193)
       (* t (/ (- y z) (- a z)))
       (if (<= a -1.6e-234)
         (/ y (/ (- a z) (- t x)))
         (if (<= a 0.0305) (/ t (/ (- a z) (- y z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((x - t) / a));
	double tmp;
	if (a <= -6e+84) {
		tmp = t_1;
	} else if (a <= -2e-193) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= -1.6e-234) {
		tmp = y / ((a - z) / (t - x));
	} else if (a <= 0.0305) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * ((x - t) / a))
    if (a <= (-6d+84)) then
        tmp = t_1
    else if (a <= (-2d-193)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= (-1.6d-234)) then
        tmp = y / ((a - z) / (t - x))
    else if (a <= 0.0305d0) then
        tmp = t / ((a - z) / (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((x - t) / a));
	double tmp;
	if (a <= -6e+84) {
		tmp = t_1;
	} else if (a <= -2e-193) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= -1.6e-234) {
		tmp = y / ((a - z) / (t - x));
	} else if (a <= 0.0305) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((x - t) / a))
	tmp = 0
	if a <= -6e+84:
		tmp = t_1
	elif a <= -2e-193:
		tmp = t * ((y - z) / (a - z))
	elif a <= -1.6e-234:
		tmp = y / ((a - z) / (t - x))
	elif a <= 0.0305:
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(x - t) / a)))
	tmp = 0.0
	if (a <= -6e+84)
		tmp = t_1;
	elseif (a <= -2e-193)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= -1.6e-234)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (a <= 0.0305)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((x - t) / a));
	tmp = 0.0;
	if (a <= -6e+84)
		tmp = t_1;
	elseif (a <= -2e-193)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= -1.6e-234)
		tmp = y / ((a - z) / (t - x));
	elseif (a <= 0.0305)
		tmp = t / ((a - z) / (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+84], t$95$1, If[LessEqual[a, -2e-193], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.6e-234], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.0305], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.99999999999999992e84 or 0.030499999999999999 < a

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 65.5%

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

      1. associate-/l* 81.5%

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

   5. Simplified 81.5%

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

   if -5.99999999999999992e84 < a < -2.0000000000000001e-193

   1. Initial program 73.1%

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

   3. Taylor expanded in x around 0 60.2%

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

      1. associate-/l* 76.6%

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

   5. Simplified 76.6%

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

   if -2.0000000000000001e-193 < a < -1.5999999999999999e-234

   1. Initial program 70.8%

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

   3. Taylor expanded in y around inf 87.4%

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

      1. div-sub 87.5%

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

   5. Simplified 87.5%

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

      1. clear-num 87.7%

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

      2. div-inv 87.7%

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

   7. Applied egg-rr 87.7%

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

   if -1.5999999999999999e-234 < a < 0.030499999999999999

   1. Initial program 67.1%

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

   3. Taylor expanded in x around 0 61.2%

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

      1. associate-/l* 72.9%

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

   5. Simplified 72.9%

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

      1. clear-num 72.9%

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

      2. un-div-inv 72.9%

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

   7. Applied egg-rr 72.9%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+84}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-193}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-234}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 0.0305:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{x - t}{a}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-195}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-238}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 0.019:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- x t) a)))))
   (if (<= a -1.35e+95)
     t_1
     (if (<= a -1.95e-195)
       (* t (/ (- y z) (- a z)))
       (if (<= a -4.8e-238)
         (* y (/ (- t x) (- a z)))
         (if (<= a 0.019) (/ t (/ (- a z) (- y z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((x - t) / a));
	double tmp;
	if (a <= -1.35e+95) {
		tmp = t_1;
	} else if (a <= -1.95e-195) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= -4.8e-238) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 0.019) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * ((x - t) / a))
    if (a <= (-1.35d+95)) then
        tmp = t_1
    else if (a <= (-1.95d-195)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= (-4.8d-238)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 0.019d0) then
        tmp = t / ((a - z) / (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((x - t) / a));
	double tmp;
	if (a <= -1.35e+95) {
		tmp = t_1;
	} else if (a <= -1.95e-195) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= -4.8e-238) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 0.019) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((x - t) / a))
	tmp = 0
	if a <= -1.35e+95:
		tmp = t_1
	elif a <= -1.95e-195:
		tmp = t * ((y - z) / (a - z))
	elif a <= -4.8e-238:
		tmp = y * ((t - x) / (a - z))
	elif a <= 0.019:
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(x - t) / a)))
	tmp = 0.0
	if (a <= -1.35e+95)
		tmp = t_1;
	elseif (a <= -1.95e-195)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= -4.8e-238)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 0.019)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((x - t) / a));
	tmp = 0.0;
	if (a <= -1.35e+95)
		tmp = t_1;
	elseif (a <= -1.95e-195)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= -4.8e-238)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 0.019)
		tmp = t / ((a - z) / (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.35e+95], t$95$1, If[LessEqual[a, -1.95e-195], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.8e-238], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.019], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.35e95 or 0.0189999999999999995 < a

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 65.5%

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

      1. associate-/l* 81.5%

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

   5. Simplified 81.5%

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

   if -1.35e95 < a < -1.95e-195

   1. Initial program 73.1%

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

   3. Taylor expanded in x around 0 60.2%

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

      1. associate-/l* 76.6%

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

   5. Simplified 76.6%

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

   if -1.95e-195 < a < -4.7999999999999997e-238

   1. Initial program 70.8%

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

   3. Taylor expanded in y around inf 87.4%

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

      1. div-sub 87.5%

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

   5. Simplified 87.5%

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

   if -4.7999999999999997e-238 < a < 0.0189999999999999995

   1. Initial program 67.1%

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

   3. Taylor expanded in x around 0 61.2%

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

      1. associate-/l* 72.9%

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

   5. Simplified 72.9%

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

      1. clear-num 72.9%

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

      2. un-div-inv 72.9%

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

   7. Applied egg-rr 72.9%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+95}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-195}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-238}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 0.019:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - y \cdot \frac{x - t}{a}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-233}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 0.0255:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (- x (* y (/ (- x t) a)))))
   (if (<= a -4.5e+86)
     t_2
     (if (<= a -1.35e-195)
       t_1
       (if (<= a -5.2e-233)
         (* y (/ (- t x) (- a z)))
         (if (<= a 0.0255) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (y * ((x - t) / a));
	double tmp;
	if (a <= -4.5e+86) {
		tmp = t_2;
	} else if (a <= -1.35e-195) {
		tmp = t_1;
	} else if (a <= -5.2e-233) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 0.0255) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x - (y * ((x - t) / a))
    if (a <= (-4.5d+86)) then
        tmp = t_2
    else if (a <= (-1.35d-195)) then
        tmp = t_1
    else if (a <= (-5.2d-233)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 0.0255d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (y * ((x - t) / a));
	double tmp;
	if (a <= -4.5e+86) {
		tmp = t_2;
	} else if (a <= -1.35e-195) {
		tmp = t_1;
	} else if (a <= -5.2e-233) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 0.0255) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - (y * ((x - t) / a))
	tmp = 0
	if a <= -4.5e+86:
		tmp = t_2
	elif a <= -1.35e-195:
		tmp = t_1
	elif a <= -5.2e-233:
		tmp = y * ((t - x) / (a - z))
	elif a <= 0.0255:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(y * Float64(Float64(x - t) / a)))
	tmp = 0.0
	if (a <= -4.5e+86)
		tmp = t_2;
	elseif (a <= -1.35e-195)
		tmp = t_1;
	elseif (a <= -5.2e-233)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 0.0255)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - (y * ((x - t) / a));
	tmp = 0.0;
	if (a <= -4.5e+86)
		tmp = t_2;
	elseif (a <= -1.35e-195)
		tmp = t_1;
	elseif (a <= -5.2e-233)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 0.0255)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+86], t$95$2, If[LessEqual[a, -1.35e-195], t$95$1, If[LessEqual[a, -5.2e-233], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.0255], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.49999999999999993e86 or 0.0254999999999999984 < a

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 65.5%

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

      1. associate-/l* 81.5%

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

   5. Simplified 81.5%

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

   if -4.49999999999999993e86 < a < -1.35e-195 or -5.1999999999999996e-233 < a < 0.0254999999999999984

   1. Initial program 69.0%

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

   3. Taylor expanded in x around 0 60.9%

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

      1. associate-/l* 74.1%

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

   5. Simplified 74.1%

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

   if -1.35e-195 < a < -5.1999999999999996e-233

   1. Initial program 70.8%

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

   3. Taylor expanded in y around inf 87.4%

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

      1. div-sub 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+86}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-195}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-233}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 0.0255:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+108}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 0.031:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -3.1e+108)
     t_2
     (if (<= a -3.2e-195)
       t_1
       (if (<= a -1.35e-232)
         (* y (/ (- t x) (- a z)))
         (if (<= a 0.031) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -3.1e+108) {
		tmp = t_2;
	} else if (a <= -3.2e-195) {
		tmp = t_1;
	} else if (a <= -1.35e-232) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 0.031) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (t * (y / a))
    if (a <= (-3.1d+108)) then
        tmp = t_2
    else if (a <= (-3.2d-195)) then
        tmp = t_1
    else if (a <= (-1.35d-232)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 0.031d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -3.1e+108) {
		tmp = t_2;
	} else if (a <= -3.2e-195) {
		tmp = t_1;
	} else if (a <= -1.35e-232) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 0.031) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (t * (y / a))
	tmp = 0
	if a <= -3.1e+108:
		tmp = t_2
	elif a <= -3.2e-195:
		tmp = t_1
	elif a <= -1.35e-232:
		tmp = y * ((t - x) / (a - z))
	elif a <= 0.031:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -3.1e+108)
		tmp = t_2;
	elseif (a <= -3.2e-195)
		tmp = t_1;
	elseif (a <= -1.35e-232)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 0.031)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -3.1e+108)
		tmp = t_2;
	elseif (a <= -3.2e-195)
		tmp = t_1;
	elseif (a <= -1.35e-232)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 0.031)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e+108], t$95$2, If[LessEqual[a, -3.2e-195], t$95$1, If[LessEqual[a, -1.35e-232], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.031], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.1000000000000001e108 or 0.031 < a

   1. Initial program 91.1%

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

      1. clear-num 91.2%

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

      2. un-div-inv 91.0%

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

   4. Applied egg-rr 91.0%

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

   5. Taylor expanded in t around inf 80.3%

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

   6. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 74.1%

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

   8. Simplified 74.1%

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

   if -3.1000000000000001e108 < a < -3.2000000000000001e-195 or -1.35e-232 < a < 0.031

   1. Initial program 69.2%

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

   3. Taylor expanded in x around 0 61.1%

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

      1. associate-/l* 74.2%

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

   5. Simplified 74.2%

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

   if -3.2000000000000001e-195 < a < -1.35e-232

   1. Initial program 70.8%

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

   3. Taylor expanded in y around inf 87.4%

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

      1. div-sub 87.5%

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

   5. Simplified 87.5%

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

Alternative 15: 60.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.28 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 0.031:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -2.1e+104)
     t_2
     (if (<= a -1.28e-216)
       t_1
       (if (<= a -1.5e-232) (* x (/ (- y a) z)) (if (<= a 0.031) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -2.1e+104) {
		tmp = t_2;
	} else if (a <= -1.28e-216) {
		tmp = t_1;
	} else if (a <= -1.5e-232) {
		tmp = x * ((y - a) / z);
	} else if (a <= 0.031) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (t * (y / a))
    if (a <= (-2.1d+104)) then
        tmp = t_2
    else if (a <= (-1.28d-216)) then
        tmp = t_1
    else if (a <= (-1.5d-232)) then
        tmp = x * ((y - a) / z)
    else if (a <= 0.031d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -2.1e+104) {
		tmp = t_2;
	} else if (a <= -1.28e-216) {
		tmp = t_1;
	} else if (a <= -1.5e-232) {
		tmp = x * ((y - a) / z);
	} else if (a <= 0.031) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (t * (y / a))
	tmp = 0
	if a <= -2.1e+104:
		tmp = t_2
	elif a <= -1.28e-216:
		tmp = t_1
	elif a <= -1.5e-232:
		tmp = x * ((y - a) / z)
	elif a <= 0.031:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -2.1e+104)
		tmp = t_2;
	elseif (a <= -1.28e-216)
		tmp = t_1;
	elseif (a <= -1.5e-232)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 0.031)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -2.1e+104)
		tmp = t_2;
	elseif (a <= -1.28e-216)
		tmp = t_1;
	elseif (a <= -1.5e-232)
		tmp = x * ((y - a) / z);
	elseif (a <= 0.031)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+104], t$95$2, If[LessEqual[a, -1.28e-216], t$95$1, If[LessEqual[a, -1.5e-232], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.031], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.0999999999999998e104 or 0.031 < a

   1. Initial program 91.1%

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

      1. clear-num 91.2%

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

      2. un-div-inv 91.0%

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

   4. Applied egg-rr 91.0%

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

   5. Taylor expanded in t around inf 80.3%

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

   6. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 74.1%

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

   8. Simplified 74.1%

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

   if -2.0999999999999998e104 < a < -1.28e-216 or -1.49999999999999995e-232 < a < 0.031

   1. Initial program 69.6%

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

   3. Taylor expanded in x around 0 61.7%

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

      1. associate-/l* 73.8%

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

   5. Simplified 73.8%

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

   if -1.28e-216 < a < -1.49999999999999995e-232

   1. Initial program 61.4%

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

   3. Taylor expanded in x around inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. unsub-neg 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. sub-neg 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+104}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.28 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 0.031:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 55.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.26 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -1.9e+45)
     t_2
     (if (<= a -1.75e-216)
       t_1
       (if (<= a -1.7e-233)
         (* x (/ (- y a) z))
         (if (<= a 2.26e-10) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -1.9e+45) {
		tmp = t_2;
	} else if (a <= -1.75e-216) {
		tmp = t_1;
	} else if (a <= -1.7e-233) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.26e-10) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    t_2 = x + (t * (y / a))
    if (a <= (-1.9d+45)) then
        tmp = t_2
    else if (a <= (-1.75d-216)) then
        tmp = t_1
    else if (a <= (-1.7d-233)) then
        tmp = x * ((y - a) / z)
    else if (a <= 2.26d-10) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -1.9e+45) {
		tmp = t_2;
	} else if (a <= -1.75e-216) {
		tmp = t_1;
	} else if (a <= -1.7e-233) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.26e-10) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	t_2 = x + (t * (y / a))
	tmp = 0
	if a <= -1.9e+45:
		tmp = t_2
	elif a <= -1.75e-216:
		tmp = t_1
	elif a <= -1.7e-233:
		tmp = x * ((y - a) / z)
	elif a <= 2.26e-10:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.9e+45)
		tmp = t_2;
	elseif (a <= -1.75e-216)
		tmp = t_1;
	elseif (a <= -1.7e-233)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 2.26e-10)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -1.9e+45)
		tmp = t_2;
	elseif (a <= -1.75e-216)
		tmp = t_1;
	elseif (a <= -1.7e-233)
		tmp = x * ((y - a) / z);
	elseif (a <= 2.26e-10)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+45], t$95$2, If[LessEqual[a, -1.75e-216], t$95$1, If[LessEqual[a, -1.7e-233], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.26e-10], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9000000000000001e45 or 2.26e-10 < a

   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 90.6%

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

      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 80.3%

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

   6. Taylor expanded in z around 0 65.4%

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

      1. associate-/l* 73.0%

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

   8. Simplified 73.0%

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

   if -1.9000000000000001e45 < a < -1.74999999999999991e-216 or -1.7000000000000001e-233 < a < 2.26e-10

   1. Initial program 68.6%

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

   3. Taylor expanded in x around 0 61.7%

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

      1. associate-/l* 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in a around 0 65.8%

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

      1. associate-*r/ 65.8%

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

      2. neg-mul-1 65.8%

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

   8. Simplified 65.8%

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

   if -1.74999999999999991e-216 < a < -1.7000000000000001e-233

   1. Initial program 61.4%

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

   3. Taylor expanded in x around inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. unsub-neg 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. sub-neg 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+45}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.26 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 55.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-239}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -1.65e+43)
     t_2
     (if (<= a -1.15e-216)
       t_1
       (if (<= a -6.6e-239) (* x (/ y z)) (if (<= a 1.75e-9) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -1.65e+43) {
		tmp = t_2;
	} else if (a <= -1.15e-216) {
		tmp = t_1;
	} else if (a <= -6.6e-239) {
		tmp = x * (y / z);
	} else if (a <= 1.75e-9) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    t_2 = x + (t * (y / a))
    if (a <= (-1.65d+43)) then
        tmp = t_2
    else if (a <= (-1.15d-216)) then
        tmp = t_1
    else if (a <= (-6.6d-239)) then
        tmp = x * (y / z)
    else if (a <= 1.75d-9) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -1.65e+43) {
		tmp = t_2;
	} else if (a <= -1.15e-216) {
		tmp = t_1;
	} else if (a <= -6.6e-239) {
		tmp = x * (y / z);
	} else if (a <= 1.75e-9) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	t_2 = x + (t * (y / a))
	tmp = 0
	if a <= -1.65e+43:
		tmp = t_2
	elif a <= -1.15e-216:
		tmp = t_1
	elif a <= -6.6e-239:
		tmp = x * (y / z)
	elif a <= 1.75e-9:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.65e+43)
		tmp = t_2;
	elseif (a <= -1.15e-216)
		tmp = t_1;
	elseif (a <= -6.6e-239)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.75e-9)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -1.65e+43)
		tmp = t_2;
	elseif (a <= -1.15e-216)
		tmp = t_1;
	elseif (a <= -6.6e-239)
		tmp = x * (y / z);
	elseif (a <= 1.75e-9)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e+43], t$95$2, If[LessEqual[a, -1.15e-216], t$95$1, If[LessEqual[a, -6.6e-239], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e-9], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6500000000000001e43 or 1.75e-9 < a

   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 90.6%

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

      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 80.3%

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

   6. Taylor expanded in z around 0 65.4%

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

      1. associate-/l* 73.0%

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

   8. Simplified 73.0%

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

   if -1.6500000000000001e43 < a < -1.14999999999999998e-216 or -6.5999999999999999e-239 < a < 1.75e-9

   1. Initial program 68.6%

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

   3. Taylor expanded in x around 0 61.7%

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

      1. associate-/l* 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in a around 0 65.8%

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

      1. associate-*r/ 65.8%

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

      2. neg-mul-1 65.8%

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

   8. Simplified 65.8%

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

   if -1.14999999999999998e-216 < a < -6.5999999999999999e-239

   1. Initial program 61.4%

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

   3. Taylor expanded in x around inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. unsub-neg 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in a around 0 95.4%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-239}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 54.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))) (t_2 (* t (/ z (- z a)))))
   (if (<= z -2.4e+96)
     t_2
     (if (<= z -2.1e-92)
       t_1
       (if (<= z -2.9e-259)
         (* x (- 1.0 (/ y a)))
         (if (<= z 3.1e+83) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -2.4e+96) {
		tmp = t_2;
	} else if (z <= -2.1e-92) {
		tmp = t_1;
	} else if (z <= -2.9e-259) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.1e+83) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    t_2 = t * (z / (z - a))
    if (z <= (-2.4d+96)) then
        tmp = t_2
    else if (z <= (-2.1d-92)) then
        tmp = t_1
    else if (z <= (-2.9d-259)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 3.1d+83) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -2.4e+96) {
		tmp = t_2;
	} else if (z <= -2.1e-92) {
		tmp = t_1;
	} else if (z <= -2.9e-259) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.1e+83) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = t * (z / (z - a))
	tmp = 0
	if z <= -2.4e+96:
		tmp = t_2
	elif z <= -2.1e-92:
		tmp = t_1
	elif z <= -2.9e-259:
		tmp = x * (1.0 - (y / a))
	elif z <= 3.1e+83:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -2.4e+96)
		tmp = t_2;
	elseif (z <= -2.1e-92)
		tmp = t_1;
	elseif (z <= -2.9e-259)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 3.1e+83)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	t_2 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -2.4e+96)
		tmp = t_2;
	elseif (z <= -2.1e-92)
		tmp = t_1;
	elseif (z <= -2.9e-259)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 3.1e+83)
		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[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+96], t$95$2, If[LessEqual[z, -2.1e-92], t$95$1, If[LessEqual[z, -2.9e-259], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+83], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999993e96 or 3.09999999999999992e83 < z

   1. Initial program 58.6%

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

   3. Taylor expanded in x around 0 43.2%

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

      1. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in y around 0 65.8%

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

      1. neg-mul-1 65.8%

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

      2. distribute-neg-frac2 65.8%

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

      3. neg-sub0 65.8%

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

      4. associate--r- 65.8%

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

      5. neg-sub0 65.8%

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

   8. Simplified 65.8%

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

   if -2.39999999999999993e96 < z < -2.1e-92 or -2.90000000000000009e-259 < z < 3.09999999999999992e83

   1. Initial program 88.4%

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

      1. clear-num 88.3%

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

      2. un-div-inv 88.3%

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

   4. Applied egg-rr 88.3%

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

   5. Taylor expanded in t around inf 72.9%

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

   6. Taylor expanded in z around 0 54.8%

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

      1. associate-/l* 60.4%

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

   8. Simplified 60.4%

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

   if -2.1e-92 < z < -2.90000000000000009e-259

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf 73.2%

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

      1. mul-1-neg 73.2%

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

      2. unsub-neg 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in z around 0 66.2%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-92}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+83}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 52.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -8.5e+97)
     t
     (if (<= z -2.2e-92)
       t_1
       (if (<= z -2.55e-259)
         (* x (- 1.0 (/ y a)))
         (if (<= z 1.1e+82) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -8.5e+97) {
		tmp = t;
	} else if (z <= -2.2e-92) {
		tmp = t_1;
	} else if (z <= -2.55e-259) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.1e+82) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (z <= (-8.5d+97)) then
        tmp = t
    else if (z <= (-2.2d-92)) then
        tmp = t_1
    else if (z <= (-2.55d-259)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.1d+82) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -8.5e+97) {
		tmp = t;
	} else if (z <= -2.2e-92) {
		tmp = t_1;
	} else if (z <= -2.55e-259) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.1e+82) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -8.5e+97:
		tmp = t
	elif z <= -2.2e-92:
		tmp = t_1
	elif z <= -2.55e-259:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.1e+82:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -8.5e+97)
		tmp = t;
	elseif (z <= -2.2e-92)
		tmp = t_1;
	elseif (z <= -2.55e-259)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.1e+82)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -8.5e+97)
		tmp = t;
	elseif (z <= -2.2e-92)
		tmp = t_1;
	elseif (z <= -2.55e-259)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.1e+82)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+97], t, If[LessEqual[z, -2.2e-92], t$95$1, If[LessEqual[z, -2.55e-259], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+82], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999993e97 or 1.1000000000000001e82 < z

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 62.2%

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

   if -8.4999999999999993e97 < z < -2.19999999999999987e-92 or -2.5499999999999999e-259 < z < 1.1000000000000001e82

   1. Initial program 88.4%

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

      1. clear-num 88.3%

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

      2. un-div-inv 88.3%

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

   4. Applied egg-rr 88.3%

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

   5. Taylor expanded in t around inf 72.9%

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

   6. Taylor expanded in z around 0 54.8%

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

      1. associate-/l* 60.4%

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

   8. Simplified 60.4%

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

   if -2.19999999999999987e-92 < z < -2.5499999999999999e-259

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf 73.2%

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

      1. mul-1-neg 73.2%

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

      2. unsub-neg 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in z around 0 66.2%

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

Alternative 20: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{-10}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) t)))))
   (if (<= a -1.6e+41)
     t_1
     (if (<= a 6.1e-10)
       (+ t (* (/ (- t x) z) (- a y)))
       (if (<= a 1.8e+74) t_1 (- x (* y (/ (- x t) a))))))))

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 (a <= -1.6e+41) {
		tmp = t_1;
	} else if (a <= 6.1e-10) {
		tmp = t + (((t - x) / z) * (a - y));
	} else if (a <= 1.8e+74) {
		tmp = t_1;
	} else {
		tmp = x - (y * ((x - t) / 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) / ((a - z) / t))
    if (a <= (-1.6d+41)) then
        tmp = t_1
    else if (a <= 6.1d-10) then
        tmp = t + (((t - x) / z) * (a - y))
    else if (a <= 1.8d+74) then
        tmp = t_1
    else
        tmp = x - (y * ((x - t) / 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) / ((a - z) / t));
	double tmp;
	if (a <= -1.6e+41) {
		tmp = t_1;
	} else if (a <= 6.1e-10) {
		tmp = t + (((t - x) / z) * (a - y));
	} else if (a <= 1.8e+74) {
		tmp = t_1;
	} else {
		tmp = x - (y * ((x - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / t))
	tmp = 0
	if a <= -1.6e+41:
		tmp = t_1
	elif a <= 6.1e-10:
		tmp = t + (((t - x) / z) * (a - y))
	elif a <= 1.8e+74:
		tmp = t_1
	else:
		tmp = x - (y * ((x - t) / a))
	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 (a <= -1.6e+41)
		tmp = t_1;
	elseif (a <= 6.1e-10)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	elseif (a <= 1.8e+74)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	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 (a <= -1.6e+41)
		tmp = t_1;
	elseif (a <= 6.1e-10)
		tmp = t + (((t - x) / z) * (a - y));
	elseif (a <= 1.8e+74)
		tmp = t_1;
	else
		tmp = x - (y * ((x - t) / 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[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+41], t$95$1, If[LessEqual[a, 6.1e-10], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+74], t$95$1, N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.60000000000000005e41 or 6.0999999999999996e-10 < a < 1.79999999999999994e74

   1. Initial program 89.8%

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

      1. clear-num 90.1%

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

      2. un-div-inv 89.8%

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

   4. Applied egg-rr 89.8%

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

   5. Taylor expanded in t around inf 82.0%

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

   if -1.60000000000000005e41 < a < 6.0999999999999996e-10

   1. Initial program 68.3%

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

   3. Taylor expanded in z around inf 76.8%

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

      1. associate--l+ 76.8%

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

      2. distribute-lft-out-- 76.8%

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

      3. div-sub 78.9%

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

      4. mul-1-neg 78.9%

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

      5. unsub-neg 78.9%

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

      6. div-sub 76.8%

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

      7. associate-/l* 80.0%

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

      8. associate-/l* 77.8%

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

      9. distribute-rgt-out-- 82.0%

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

   5. Simplified 82.0%

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

   if 1.79999999999999994e74 < a

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 72.7%

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

      1. associate-/l* 87.8%

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

   5. Simplified 87.8%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{-10}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 38.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-5}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e+101) x (if (<= a 7.4e-5) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+101) {
		tmp = x;
	} else if (a <= 7.4e-5) {
		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 <= (-7d+101)) then
        tmp = x
    else if (a <= 7.4d-5) 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 <= -7e+101) {
		tmp = x;
	} else if (a <= 7.4e-5) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e+101:
		tmp = x
	elif a <= 7.4e-5:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e+101)
		tmp = x;
	elseif (a <= 7.4e-5)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e+101)
		tmp = x;
	elseif (a <= 7.4e-5)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e+101], x, If[LessEqual[a, 7.4e-5], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -7.00000000000000046e101 or 7.39999999999999962e-5 < a

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf 53.2%

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

   if -7.00000000000000046e101 < a < 7.39999999999999962e-5

   1. Initial program 69.4%

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

   3. Taylor expanded in z around inf 46.2%

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

Alternative 22: 24.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.1%

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

3. Taylor expanded in z around inf 30.6%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(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)))))