Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.5% → 94.9%

Time: 20.4s

Alternatives: 23

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.5% 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: 94.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-276} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-276) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (- 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 <= -2e-276) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = 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 <= -2e-276) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t - Float64(Float64(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, -2e-276], 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[(x / 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)))) < -2e-276 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. remove-double-neg 91.7%

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

      3. unsub-neg 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-*l/ 78.5%

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

      6. associate-/l* 95.7%

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

      7. fma-neg 95.7%

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

      8. remove-double-neg 95.7%

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

   3. Simplified 95.7%

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

   if -2e-276 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.0%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. associate--l+ 75.9%

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

      2. distribute-lft-out-- 75.9%

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

      3. div-sub 75.9%

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

      4. mul-1-neg 75.9%

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

      5. unsub-neg 75.9%

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

      6. div-sub 75.9%

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

      7. associate-/l* 93.6%

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

      8. associate-/l* 99.7%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 99.8%

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

      1. neg-mul-1 99.8%

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

      2. distribute-neg-frac2 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-276} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-276} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-276) (not (<= t_1 0.0)))
     t_1
     (- 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 <= -2e-276) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - ((x / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-276)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t - ((x / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-276) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = 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 <= -2e-276) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = 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 <= -2e-276) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(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 <= -2e-276) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t - ((x / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-276], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t - N[(N[(x / 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)))) < -2e-276 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.7%

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

   if -2e-276 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.0%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. associate--l+ 75.9%

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

      2. distribute-lft-out-- 75.9%

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

      3. div-sub 75.9%

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

      4. mul-1-neg 75.9%

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

      5. unsub-neg 75.9%

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

      6. div-sub 75.9%

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

      7. associate-/l* 93.6%

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

      8. associate-/l* 99.7%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 99.8%

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

      1. neg-mul-1 99.8%

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

      2. distribute-neg-frac2 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-276} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-276} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-276) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (- 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 <= -2e-276) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t - ((x / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-276)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t - ((x / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-276) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = 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 <= -2e-276) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = 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 <= -2e-276) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t - Float64(Float64(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 <= -2e-276) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = 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, -2e-276], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(x / 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)))) < -2e-276 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-*l/ 78.5%

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

      3. associate-*r/ 95.7%

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

      4. clear-num 95.6%

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

      5. un-div-inv 95.6%

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

   4. Applied egg-rr 95.6%

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

   if -2e-276 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.0%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. associate--l+ 75.9%

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

      2. distribute-lft-out-- 75.9%

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

      3. div-sub 75.9%

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

      4. mul-1-neg 75.9%

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

      5. unsub-neg 75.9%

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

      6. div-sub 75.9%

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

      7. associate-/l* 93.6%

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

      8. associate-/l* 99.7%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 99.8%

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

      1. neg-mul-1 99.8%

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

      2. distribute-neg-frac2 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-276} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 41.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+148}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= z -2.8e+148)
     t
     (if (<= z -1.8e+81)
       (* x (/ (- y a) z))
       (if (<= z -1.65e-94)
         t_1
         (if (<= z -2.4e-219)
           x
           (if (<= z 3.1e-131)
             t_1
             (if (<= z 1.7e-82)
               x
               (if (<= z 7.6e+51) (* t (/ y (- a z))) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -2.8e+148) {
		tmp = t;
	} else if (z <= -1.8e+81) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.65e-94) {
		tmp = t_1;
	} else if (z <= -2.4e-219) {
		tmp = x;
	} else if (z <= 3.1e-131) {
		tmp = t_1;
	} else if (z <= 1.7e-82) {
		tmp = x;
	} else if (z <= 7.6e+51) {
		tmp = t * (y / (a - z));
	} 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 = y * ((t - x) / a)
    if (z <= (-2.8d+148)) then
        tmp = t
    else if (z <= (-1.8d+81)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-1.65d-94)) then
        tmp = t_1
    else if (z <= (-2.4d-219)) then
        tmp = x
    else if (z <= 3.1d-131) then
        tmp = t_1
    else if (z <= 1.7d-82) then
        tmp = x
    else if (z <= 7.6d+51) then
        tmp = t * (y / (a - z))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -2.8e+148) {
		tmp = t;
	} else if (z <= -1.8e+81) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.65e-94) {
		tmp = t_1;
	} else if (z <= -2.4e-219) {
		tmp = x;
	} else if (z <= 3.1e-131) {
		tmp = t_1;
	} else if (z <= 1.7e-82) {
		tmp = x;
	} else if (z <= 7.6e+51) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if z <= -2.8e+148:
		tmp = t
	elif z <= -1.8e+81:
		tmp = x * ((y - a) / z)
	elif z <= -1.65e-94:
		tmp = t_1
	elif z <= -2.4e-219:
		tmp = x
	elif z <= 3.1e-131:
		tmp = t_1
	elif z <= 1.7e-82:
		tmp = x
	elif z <= 7.6e+51:
		tmp = t * (y / (a - z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -2.8e+148)
		tmp = t;
	elseif (z <= -1.8e+81)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -1.65e-94)
		tmp = t_1;
	elseif (z <= -2.4e-219)
		tmp = x;
	elseif (z <= 3.1e-131)
		tmp = t_1;
	elseif (z <= 1.7e-82)
		tmp = x;
	elseif (z <= 7.6e+51)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -2.8e+148)
		tmp = t;
	elseif (z <= -1.8e+81)
		tmp = x * ((y - a) / z);
	elseif (z <= -1.65e-94)
		tmp = t_1;
	elseif (z <= -2.4e-219)
		tmp = x;
	elseif (z <= 3.1e-131)
		tmp = t_1;
	elseif (z <= 1.7e-82)
		tmp = x;
	elseif (z <= 7.6e+51)
		tmp = t * (y / (a - z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+148], t, If[LessEqual[z, -1.8e+81], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e-94], t$95$1, If[LessEqual[z, -2.4e-219], x, If[LessEqual[z, 3.1e-131], t$95$1, If[LessEqual[z, 1.7e-82], x, If[LessEqual[z, 7.6e+51], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.7999999999999998e148 or 7.5999999999999994e51 < z

   1. Initial program 65.8%

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

   3. Taylor expanded in z around inf 55.2%

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

   if -2.7999999999999998e148 < z < -1.80000000000000003e81

   1. Initial program 67.5%

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

   3. Taylor expanded in z around inf 60.0%

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

      1. associate--l+ 60.0%

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

      2. distribute-lft-out-- 60.0%

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

      3. div-sub 60.0%

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

      4. mul-1-neg 60.0%

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

      5. unsub-neg 60.0%

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

      6. div-sub 60.0%

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

      7. associate-/l* 75.5%

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

      8. associate-/l* 75.5%

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

      9. distribute-rgt-out-- 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in t around 0 43.4%

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

      1. associate-/l* 58.9%

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

   8. Simplified 58.9%

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

   if -1.80000000000000003e81 < z < -1.6500000000000001e-94 or -2.40000000000000014e-219 < z < 3.10000000000000021e-131

   1. Initial program 88.6%

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

   3. Taylor expanded in y around inf 62.1%

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

      1. div-sub 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in a around inf 52.6%

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

   if -1.6500000000000001e-94 < z < -2.40000000000000014e-219 or 3.10000000000000021e-131 < z < 1.69999999999999988e-82

   1. Initial program 95.8%

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

   3. Taylor expanded in a around inf 52.5%

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

   if 1.69999999999999988e-82 < z < 7.5999999999999994e51

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 57.6%

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

      1. div-sub 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in t around inf 46.1%

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

      1. associate-/l* 54.7%

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

   8. Simplified 54.7%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+148}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-131}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+146}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-132}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.35e+146)
   t
   (if (<= z -2.2e+81)
     (* x (/ (- y a) z))
     (if (<= z -1.45e-95)
       (* y (/ (- t x) a))
       (if (<= z -1.1e-220)
         x
         (if (<= z 5.6e-132)
           (/ (* y (- t x)) a)
           (if (<= z 4.4e-82)
             x
             (if (<= z 4.5e+51) (* t (/ y (- a z))) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.35e+146) {
		tmp = t;
	} else if (z <= -2.2e+81) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.45e-95) {
		tmp = y * ((t - x) / a);
	} else if (z <= -1.1e-220) {
		tmp = x;
	} else if (z <= 5.6e-132) {
		tmp = (y * (t - x)) / a;
	} else if (z <= 4.4e-82) {
		tmp = x;
	} else if (z <= 4.5e+51) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.35d+146)) then
        tmp = t
    else if (z <= (-2.2d+81)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-1.45d-95)) then
        tmp = y * ((t - x) / a)
    else if (z <= (-1.1d-220)) then
        tmp = x
    else if (z <= 5.6d-132) then
        tmp = (y * (t - x)) / a
    else if (z <= 4.4d-82) then
        tmp = x
    else if (z <= 4.5d+51) then
        tmp = t * (y / (a - z))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.35e+146) {
		tmp = t;
	} else if (z <= -2.2e+81) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.45e-95) {
		tmp = y * ((t - x) / a);
	} else if (z <= -1.1e-220) {
		tmp = x;
	} else if (z <= 5.6e-132) {
		tmp = (y * (t - x)) / a;
	} else if (z <= 4.4e-82) {
		tmp = x;
	} else if (z <= 4.5e+51) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.35e+146:
		tmp = t
	elif z <= -2.2e+81:
		tmp = x * ((y - a) / z)
	elif z <= -1.45e-95:
		tmp = y * ((t - x) / a)
	elif z <= -1.1e-220:
		tmp = x
	elif z <= 5.6e-132:
		tmp = (y * (t - x)) / a
	elif z <= 4.4e-82:
		tmp = x
	elif z <= 4.5e+51:
		tmp = t * (y / (a - z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.35e+146)
		tmp = t;
	elseif (z <= -2.2e+81)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -1.45e-95)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= -1.1e-220)
		tmp = x;
	elseif (z <= 5.6e-132)
		tmp = Float64(Float64(y * Float64(t - x)) / a);
	elseif (z <= 4.4e-82)
		tmp = x;
	elseif (z <= 4.5e+51)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.35e+146)
		tmp = t;
	elseif (z <= -2.2e+81)
		tmp = x * ((y - a) / z);
	elseif (z <= -1.45e-95)
		tmp = y * ((t - x) / a);
	elseif (z <= -1.1e-220)
		tmp = x;
	elseif (z <= 5.6e-132)
		tmp = (y * (t - x)) / a;
	elseif (z <= 4.4e-82)
		tmp = x;
	elseif (z <= 4.5e+51)
		tmp = t * (y / (a - z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.35e+146], t, If[LessEqual[z, -2.2e+81], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.45e-95], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-220], x, If[LessEqual[z, 5.6e-132], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 4.4e-82], x, If[LessEqual[z, 4.5e+51], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.34999999999999988e146 or 4.5e51 < z

   1. Initial program 65.8%

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

   3. Taylor expanded in z around inf 55.2%

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

   if -2.34999999999999988e146 < z < -2.19999999999999987e81

   1. Initial program 67.5%

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

   3. Taylor expanded in z around inf 60.0%

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

      1. associate--l+ 60.0%

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

      2. distribute-lft-out-- 60.0%

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

      3. div-sub 60.0%

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

      4. mul-1-neg 60.0%

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

      5. unsub-neg 60.0%

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

      6. div-sub 60.0%

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

      7. associate-/l* 75.5%

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

      8. associate-/l* 75.5%

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

      9. distribute-rgt-out-- 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in t around 0 43.4%

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

      1. associate-/l* 58.9%

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

   8. Simplified 58.9%

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

   if -2.19999999999999987e81 < z < -1.45000000000000001e-95

   1. Initial program 86.5%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. div-sub 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in a around inf 47.9%

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

   if -1.45000000000000001e-95 < z < -1.09999999999999993e-220 or 5.60000000000000005e-132 < z < 4.39999999999999971e-82

   1. Initial program 95.8%

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

   3. Taylor expanded in a around inf 52.5%

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

   if -1.09999999999999993e-220 < z < 5.60000000000000005e-132

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf 62.5%

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

      1. div-sub 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in a around inf 56.0%

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

      1. associate-*r/ 56.9%

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

      2. *-commutative 56.9%

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

   8. Applied egg-rr 56.9%

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

   if 4.39999999999999971e-82 < z < 4.5e51

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 57.6%

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

      1. div-sub 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in t around inf 46.1%

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

      1. associate-/l* 54.7%

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

   8. Simplified 54.7%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+146}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-132}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 45.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+145}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-274}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -4e+145)
     t
     (if (<= z -2.2e+81)
       (* x (/ (- y a) z))
       (if (<= z -5.8e-53)
         (* y (/ (- t x) a))
         (if (<= z -2.6e-250)
           t_1
           (if (<= z 6.8e-274)
             (/ (* y (- t x)) a)
             (if (<= z 2.5e-81)
               t_1
               (if (<= z 2.7e+51) (* t (/ y (- a z))) 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 <= -4e+145) {
		tmp = t;
	} else if (z <= -2.2e+81) {
		tmp = x * ((y - a) / z);
	} else if (z <= -5.8e-53) {
		tmp = y * ((t - x) / a);
	} else if (z <= -2.6e-250) {
		tmp = t_1;
	} else if (z <= 6.8e-274) {
		tmp = (y * (t - x)) / a;
	} else if (z <= 2.5e-81) {
		tmp = t_1;
	} else if (z <= 2.7e+51) {
		tmp = t * (y / (a - z));
	} 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 <= (-4d+145)) then
        tmp = t
    else if (z <= (-2.2d+81)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-5.8d-53)) then
        tmp = y * ((t - x) / a)
    else if (z <= (-2.6d-250)) then
        tmp = t_1
    else if (z <= 6.8d-274) then
        tmp = (y * (t - x)) / a
    else if (z <= 2.5d-81) then
        tmp = t_1
    else if (z <= 2.7d+51) then
        tmp = t * (y / (a - z))
    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 <= -4e+145) {
		tmp = t;
	} else if (z <= -2.2e+81) {
		tmp = x * ((y - a) / z);
	} else if (z <= -5.8e-53) {
		tmp = y * ((t - x) / a);
	} else if (z <= -2.6e-250) {
		tmp = t_1;
	} else if (z <= 6.8e-274) {
		tmp = (y * (t - x)) / a;
	} else if (z <= 2.5e-81) {
		tmp = t_1;
	} else if (z <= 2.7e+51) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -4e+145:
		tmp = t
	elif z <= -2.2e+81:
		tmp = x * ((y - a) / z)
	elif z <= -5.8e-53:
		tmp = y * ((t - x) / a)
	elif z <= -2.6e-250:
		tmp = t_1
	elif z <= 6.8e-274:
		tmp = (y * (t - x)) / a
	elif z <= 2.5e-81:
		tmp = t_1
	elif z <= 2.7e+51:
		tmp = t * (y / (a - z))
	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 <= -4e+145)
		tmp = t;
	elseif (z <= -2.2e+81)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -5.8e-53)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= -2.6e-250)
		tmp = t_1;
	elseif (z <= 6.8e-274)
		tmp = Float64(Float64(y * Float64(t - x)) / a);
	elseif (z <= 2.5e-81)
		tmp = t_1;
	elseif (z <= 2.7e+51)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	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 <= -4e+145)
		tmp = t;
	elseif (z <= -2.2e+81)
		tmp = x * ((y - a) / z);
	elseif (z <= -5.8e-53)
		tmp = y * ((t - x) / a);
	elseif (z <= -2.6e-250)
		tmp = t_1;
	elseif (z <= 6.8e-274)
		tmp = (y * (t - x)) / a;
	elseif (z <= 2.5e-81)
		tmp = t_1;
	elseif (z <= 2.7e+51)
		tmp = t * (y / (a - z));
	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, -4e+145], t, If[LessEqual[z, -2.2e+81], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e-53], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-250], t$95$1, If[LessEqual[z, 6.8e-274], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 2.5e-81], t$95$1, If[LessEqual[z, 2.7e+51], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4e145 or 2.69999999999999992e51 < z

   1. Initial program 65.8%

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

   3. Taylor expanded in z around inf 55.2%

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

   if -4e145 < z < -2.19999999999999987e81

   1. Initial program 67.5%

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

   3. Taylor expanded in z around inf 60.0%

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

      1. associate--l+ 60.0%

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

      2. distribute-lft-out-- 60.0%

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

      3. div-sub 60.0%

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

      4. mul-1-neg 60.0%

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

      5. unsub-neg 60.0%

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

      6. div-sub 60.0%

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

      7. associate-/l* 75.5%

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

      8. associate-/l* 75.5%

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

      9. distribute-rgt-out-- 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in t around 0 43.4%

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

      1. associate-/l* 58.9%

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

   8. Simplified 58.9%

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

   if -2.19999999999999987e81 < z < -5.7999999999999996e-53

   1. Initial program 83.9%

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

   3. Taylor expanded in y around inf 63.6%

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

      1. div-sub 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in a around inf 50.1%

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

   if -5.7999999999999996e-53 < z < -2.60000000000000008e-250 or 6.79999999999999962e-274 < z < 2.4999999999999999e-81

   1. Initial program 95.3%

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

   3. Taylor expanded in x around -inf 74.3%

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

      1. mul-1-neg 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in z around 0 65.1%

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

   if -2.60000000000000008e-250 < z < 6.79999999999999962e-274

   1. Initial program 83.3%

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

   3. Taylor expanded in y around inf 71.5%

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

      1. div-sub 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in a around inf 69.9%

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

      1. associate-*r/ 77.6%

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

      2. *-commutative 77.6%

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

   8. Applied egg-rr 77.6%

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

   if 2.4999999999999999e-81 < z < 2.69999999999999992e51

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 57.6%

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

      1. div-sub 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in t around inf 46.1%

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

      1. associate-/l* 54.7%

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

   8. Simplified 54.7%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+145}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-274}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{-37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-185}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -7.2e-37)
     t_2
     (if (<= t -1.8e-60)
       t_1
       (if (<= t -8.8e-185)
         (/ (* x y) (- z a))
         (if (<= t 1.05e-288)
           t_1
           (if (<= t 2.4e-209)
             (* x (/ (- y a) z))
             (if (<= t 2.8e-68) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -7.2e-37) {
		tmp = t_2;
	} else if (t <= -1.8e-60) {
		tmp = t_1;
	} else if (t <= -8.8e-185) {
		tmp = (x * y) / (z - a);
	} else if (t <= 1.05e-288) {
		tmp = t_1;
	} else if (t <= 2.4e-209) {
		tmp = x * ((y - a) / z);
	} else if (t <= 2.8e-68) {
		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 * (1.0d0 - (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-7.2d-37)) then
        tmp = t_2
    else if (t <= (-1.8d-60)) then
        tmp = t_1
    else if (t <= (-8.8d-185)) then
        tmp = (x * y) / (z - a)
    else if (t <= 1.05d-288) then
        tmp = t_1
    else if (t <= 2.4d-209) then
        tmp = x * ((y - a) / z)
    else if (t <= 2.8d-68) 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 * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -7.2e-37) {
		tmp = t_2;
	} else if (t <= -1.8e-60) {
		tmp = t_1;
	} else if (t <= -8.8e-185) {
		tmp = (x * y) / (z - a);
	} else if (t <= 1.05e-288) {
		tmp = t_1;
	} else if (t <= 2.4e-209) {
		tmp = x * ((y - a) / z);
	} else if (t <= 2.8e-68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -7.2e-37:
		tmp = t_2
	elif t <= -1.8e-60:
		tmp = t_1
	elif t <= -8.8e-185:
		tmp = (x * y) / (z - a)
	elif t <= 1.05e-288:
		tmp = t_1
	elif t <= 2.4e-209:
		tmp = x * ((y - a) / z)
	elif t <= 2.8e-68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -7.2e-37)
		tmp = t_2;
	elseif (t <= -1.8e-60)
		tmp = t_1;
	elseif (t <= -8.8e-185)
		tmp = Float64(Float64(x * y) / Float64(z - a));
	elseif (t <= 1.05e-288)
		tmp = t_1;
	elseif (t <= 2.4e-209)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (t <= 2.8e-68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -7.2e-37)
		tmp = t_2;
	elseif (t <= -1.8e-60)
		tmp = t_1;
	elseif (t <= -8.8e-185)
		tmp = (x * y) / (z - a);
	elseif (t <= 1.05e-288)
		tmp = t_1;
	elseif (t <= 2.4e-209)
		tmp = x * ((y - a) / z);
	elseif (t <= 2.8e-68)
		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[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e-37], t$95$2, If[LessEqual[t, -1.8e-60], t$95$1, If[LessEqual[t, -8.8e-185], N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-288], t$95$1, If[LessEqual[t, 2.4e-209], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-68], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.20000000000000014e-37 or 2.8000000000000001e-68 < t

   1. Initial program 85.9%

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

   3. Taylor expanded in x around 0 52.2%

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

      1. associate-/l* 72.4%

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

   5. Simplified 72.4%

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

   if -7.20000000000000014e-37 < t < -1.8e-60 or -8.8000000000000002e-185 < t < 1.04999999999999998e-288 or 2.4000000000000001e-209 < t < 2.8000000000000001e-68

   1. Initial program 74.1%

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

   3. Taylor expanded in x around -inf 76.5%

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

      1. mul-1-neg 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in z around 0 64.0%

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

   if -1.8e-60 < t < -8.8000000000000002e-185

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. div-sub 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in t around 0 65.4%

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

      1. associate-*r/ 65.4%

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

      2. mul-1-neg 65.4%

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

      3. distribute-lft-neg-out 65.4%

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

      4. *-commutative 65.4%

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

   8. Simplified 65.4%

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

   if 1.04999999999999998e-288 < t < 2.4000000000000001e-209

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf 56.8%

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

      1. associate--l+ 56.8%

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

      2. distribute-lft-out-- 56.8%

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

      3. div-sub 57.3%

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

      4. mul-1-neg 57.3%

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

      5. unsub-neg 57.3%

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

      6. div-sub 56.8%

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

      7. associate-/l* 56.8%

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

      8. associate-/l* 63.2%

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

      9. distribute-rgt-out-- 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in t around 0 46.3%

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

      1. associate-/l* 57.9%

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

   8. Simplified 57.9%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-185}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-288}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-192}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 4.55 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -6.8e-37)
     t_2
     (if (<= t -1.05e-59)
       t_1
       (if (<= t -1.35e-192)
         (* y (/ (- t x) (- a z)))
         (if (<= t 4.55e-287)
           t_1
           (if (<= t 1.2e-209)
             (* x (/ (- y a) z))
             (if (<= t 2.25e-71) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -6.8e-37) {
		tmp = t_2;
	} else if (t <= -1.05e-59) {
		tmp = t_1;
	} else if (t <= -1.35e-192) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 4.55e-287) {
		tmp = t_1;
	} else if (t <= 1.2e-209) {
		tmp = x * ((y - a) / z);
	} else if (t <= 2.25e-71) {
		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 * (1.0d0 - (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-6.8d-37)) then
        tmp = t_2
    else if (t <= (-1.05d-59)) then
        tmp = t_1
    else if (t <= (-1.35d-192)) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= 4.55d-287) then
        tmp = t_1
    else if (t <= 1.2d-209) then
        tmp = x * ((y - a) / z)
    else if (t <= 2.25d-71) 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 * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -6.8e-37) {
		tmp = t_2;
	} else if (t <= -1.05e-59) {
		tmp = t_1;
	} else if (t <= -1.35e-192) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 4.55e-287) {
		tmp = t_1;
	} else if (t <= 1.2e-209) {
		tmp = x * ((y - a) / z);
	} else if (t <= 2.25e-71) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -6.8e-37:
		tmp = t_2
	elif t <= -1.05e-59:
		tmp = t_1
	elif t <= -1.35e-192:
		tmp = y * ((t - x) / (a - z))
	elif t <= 4.55e-287:
		tmp = t_1
	elif t <= 1.2e-209:
		tmp = x * ((y - a) / z)
	elif t <= 2.25e-71:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -6.8e-37)
		tmp = t_2;
	elseif (t <= -1.05e-59)
		tmp = t_1;
	elseif (t <= -1.35e-192)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= 4.55e-287)
		tmp = t_1;
	elseif (t <= 1.2e-209)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (t <= 2.25e-71)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -6.8e-37)
		tmp = t_2;
	elseif (t <= -1.05e-59)
		tmp = t_1;
	elseif (t <= -1.35e-192)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= 4.55e-287)
		tmp = t_1;
	elseif (t <= 1.2e-209)
		tmp = x * ((y - a) / z);
	elseif (t <= 2.25e-71)
		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[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e-37], t$95$2, If[LessEqual[t, -1.05e-59], t$95$1, If[LessEqual[t, -1.35e-192], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.55e-287], t$95$1, If[LessEqual[t, 1.2e-209], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e-71], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.80000000000000037e-37 or 2.2500000000000001e-71 < t

   1. Initial program 85.9%

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

   3. Taylor expanded in x around 0 52.2%

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

      1. associate-/l* 72.4%

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

   5. Simplified 72.4%

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

   if -6.80000000000000037e-37 < t < -1.04999999999999998e-59 or -1.34999999999999996e-192 < t < 4.5499999999999999e-287 or 1.2000000000000001e-209 < t < 2.2500000000000001e-71

   1. Initial program 75.3%

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

   3. Taylor expanded in x around -inf 77.8%

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

      1. mul-1-neg 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in z around 0 66.0%

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

   if -1.04999999999999998e-59 < t < -1.34999999999999996e-192

   1. Initial program 67.7%

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

   3. Taylor expanded in y around inf 71.2%

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

      1. div-sub 71.2%

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

   5. Simplified 71.2%

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

   if 4.5499999999999999e-287 < t < 1.2000000000000001e-209

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf 56.8%

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

      1. associate--l+ 56.8%

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

      2. distribute-lft-out-- 56.8%

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

      3. div-sub 57.3%

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

      4. mul-1-neg 57.3%

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

      5. unsub-neg 57.3%

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

      6. div-sub 56.8%

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

      7. associate-/l* 56.8%

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

      8. associate-/l* 63.2%

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

      9. distribute-rgt-out-- 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in t around 0 46.3%

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

      1. associate-/l* 57.9%

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

   8. Simplified 57.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-192}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 4.55 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -9 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-205}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 850:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -9e+101)
     t_2
     (if (<= a 1.8e-301)
       t_1
       (if (<= a 9.5e-205)
         (* x (/ y z))
         (if (<= a 850.0)
           t_1
           (if (<= a 1.56e+53)
             (* y (/ (- t x) a))
             (if (<= a 2.3e+93) (* x (/ (- y a) z)) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -9e+101) {
		tmp = t_2;
	} else if (a <= 1.8e-301) {
		tmp = t_1;
	} else if (a <= 9.5e-205) {
		tmp = x * (y / z);
	} else if (a <= 850.0) {
		tmp = t_1;
	} else if (a <= 1.56e+53) {
		tmp = y * ((t - x) / a);
	} else if (a <= 2.3e+93) {
		tmp = x * ((y - a) / z);
	} 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 * (1.0d0 - (y / z))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-9d+101)) then
        tmp = t_2
    else if (a <= 1.8d-301) then
        tmp = t_1
    else if (a <= 9.5d-205) then
        tmp = x * (y / z)
    else if (a <= 850.0d0) then
        tmp = t_1
    else if (a <= 1.56d+53) then
        tmp = y * ((t - x) / a)
    else if (a <= 2.3d+93) then
        tmp = x * ((y - a) / z)
    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 * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -9e+101) {
		tmp = t_2;
	} else if (a <= 1.8e-301) {
		tmp = t_1;
	} else if (a <= 9.5e-205) {
		tmp = x * (y / z);
	} else if (a <= 850.0) {
		tmp = t_1;
	} else if (a <= 1.56e+53) {
		tmp = y * ((t - x) / a);
	} else if (a <= 2.3e+93) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -9e+101:
		tmp = t_2
	elif a <= 1.8e-301:
		tmp = t_1
	elif a <= 9.5e-205:
		tmp = x * (y / z)
	elif a <= 850.0:
		tmp = t_1
	elif a <= 1.56e+53:
		tmp = y * ((t - x) / a)
	elif a <= 2.3e+93:
		tmp = x * ((y - a) / z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -9e+101)
		tmp = t_2;
	elseif (a <= 1.8e-301)
		tmp = t_1;
	elseif (a <= 9.5e-205)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 850.0)
		tmp = t_1;
	elseif (a <= 1.56e+53)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= 2.3e+93)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -9e+101)
		tmp = t_2;
	elseif (a <= 1.8e-301)
		tmp = t_1;
	elseif (a <= 9.5e-205)
		tmp = x * (y / z);
	elseif (a <= 850.0)
		tmp = t_1;
	elseif (a <= 1.56e+53)
		tmp = y * ((t - x) / a);
	elseif (a <= 2.3e+93)
		tmp = x * ((y - a) / z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e+101], t$95$2, If[LessEqual[a, 1.8e-301], t$95$1, If[LessEqual[a, 9.5e-205], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 850.0], t$95$1, If[LessEqual[a, 1.56e+53], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+93], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -9.0000000000000004e101 or 2.3000000000000002e93 < a

   1. Initial program 91.8%

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

   3. Taylor expanded in x around -inf 64.1%

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

      1. mul-1-neg 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in z around 0 61.8%

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

   if -9.0000000000000004e101 < a < 1.80000000000000004e-301 or 9.49999999999999957e-205 < a < 850

   1. Initial program 77.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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* 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in a around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. div-sub 60.9%

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

      3. sub-neg 60.9%

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

      4. *-inverses 60.9%

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

      5. metadata-eval 60.9%

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

   8. Simplified 60.9%

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

   if 1.80000000000000004e-301 < a < 9.49999999999999957e-205

   1. Initial program 57.7%

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

   3. Taylor expanded in x around -inf 62.6%

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

      1. mul-1-neg 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in a around 0 58.4%

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

      1. associate-*r/ 58.4%

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

      2. neg-mul-1 58.4%

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

   8. Simplified 58.4%

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

   if 850 < a < 1.56e53

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf 75.0%

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

      1. div-sub 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in a around inf 75.1%

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

   if 1.56e53 < a < 2.3000000000000002e93

   1. Initial program 73.7%

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

   3. Taylor expanded in z around inf 55.9%

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

      1. associate--l+ 55.9%

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

      2. distribute-lft-out-- 55.9%

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

      3. div-sub 55.9%

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

      4. mul-1-neg 55.9%

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

      5. unsub-neg 55.9%

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

      6. div-sub 55.9%

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

      7. associate-/l* 47.6%

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

      8. associate-/l* 56.6%

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

      9. distribute-rgt-out-- 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in t around 0 30.5%

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

      1. associate-/l* 39.0%

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

   8. Simplified 39.0%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-301}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-205}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 850:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.56 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-205}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 880:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.86 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -1.45e+102)
     t_2
     (if (<= a 4.3e-299)
       t_1
       (if (<= a 2.6e-205)
         (* x (/ y z))
         (if (<= a 880.0)
           t_1
           (if (<= a 1.86e+56)
             (* y (/ (- t x) a))
             (if (<= a 1.5e+63) (* t (/ z (- z a))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.45e+102) {
		tmp = t_2;
	} else if (a <= 4.3e-299) {
		tmp = t_1;
	} else if (a <= 2.6e-205) {
		tmp = x * (y / z);
	} else if (a <= 880.0) {
		tmp = t_1;
	} else if (a <= 1.86e+56) {
		tmp = y * ((t - x) / a);
	} else if (a <= 1.5e+63) {
		tmp = t * (z / (z - a));
	} 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 * (1.0d0 - (y / z))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-1.45d+102)) then
        tmp = t_2
    else if (a <= 4.3d-299) then
        tmp = t_1
    else if (a <= 2.6d-205) then
        tmp = x * (y / z)
    else if (a <= 880.0d0) then
        tmp = t_1
    else if (a <= 1.86d+56) then
        tmp = y * ((t - x) / a)
    else if (a <= 1.5d+63) then
        tmp = t * (z / (z - a))
    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 * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.45e+102) {
		tmp = t_2;
	} else if (a <= 4.3e-299) {
		tmp = t_1;
	} else if (a <= 2.6e-205) {
		tmp = x * (y / z);
	} else if (a <= 880.0) {
		tmp = t_1;
	} else if (a <= 1.86e+56) {
		tmp = y * ((t - x) / a);
	} else if (a <= 1.5e+63) {
		tmp = t * (z / (z - a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -1.45e+102:
		tmp = t_2
	elif a <= 4.3e-299:
		tmp = t_1
	elif a <= 2.6e-205:
		tmp = x * (y / z)
	elif a <= 880.0:
		tmp = t_1
	elif a <= 1.86e+56:
		tmp = y * ((t - x) / a)
	elif a <= 1.5e+63:
		tmp = t * (z / (z - a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -1.45e+102)
		tmp = t_2;
	elseif (a <= 4.3e-299)
		tmp = t_1;
	elseif (a <= 2.6e-205)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 880.0)
		tmp = t_1;
	elseif (a <= 1.86e+56)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= 1.5e+63)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -1.45e+102)
		tmp = t_2;
	elseif (a <= 4.3e-299)
		tmp = t_1;
	elseif (a <= 2.6e-205)
		tmp = x * (y / z);
	elseif (a <= 880.0)
		tmp = t_1;
	elseif (a <= 1.86e+56)
		tmp = y * ((t - x) / a);
	elseif (a <= 1.5e+63)
		tmp = t * (z / (z - a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e+102], t$95$2, If[LessEqual[a, 4.3e-299], t$95$1, If[LessEqual[a, 2.6e-205], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 880.0], t$95$1, If[LessEqual[a, 1.86e+56], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+63], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.4500000000000001e102 or 1.5e63 < a

   1. Initial program 89.6%

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

   3. Taylor expanded in x around -inf 63.1%

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

      1. mul-1-neg 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in z around 0 58.9%

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

   if -1.4500000000000001e102 < a < 4.29999999999999979e-299 or 2.5999999999999998e-205 < a < 880

   1. Initial program 77.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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* 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in a around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. div-sub 60.9%

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

      3. sub-neg 60.9%

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

      4. *-inverses 60.9%

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

      5. metadata-eval 60.9%

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

   8. Simplified 60.9%

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

   if 4.29999999999999979e-299 < a < 2.5999999999999998e-205

   1. Initial program 57.7%

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

   3. Taylor expanded in x around -inf 62.6%

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

      1. mul-1-neg 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in a around 0 58.4%

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

      1. associate-*r/ 58.4%

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

      2. neg-mul-1 58.4%

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

   8. Simplified 58.4%

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

   if 880 < a < 1.86000000000000007e56

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf 75.0%

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

      1. div-sub 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in a around inf 75.1%

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

   if 1.86000000000000007e56 < a < 1.5e63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-neg-frac2 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate--r- 100.0%

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

      5. neg-sub0 100.0%

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

   8. Simplified 100.0%

      \[\leadsto t \cdot \color{blue}{\frac{z}{\left(-a\right) + z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-205}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 880:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.86 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.75 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{elif}\;a \leq 1500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -6.2e+102)
     t_2
     (if (<= a 1.9e-299)
       t_1
       (if (<= a 3.75e-187)
         (* y (/ x (- z a)))
         (if (<= a 1500.0)
           t_1
           (if (<= a 9.8e+55)
             (* y (/ (- t x) a))
             (if (<= a 2.4e+63) (* t (/ z (- z a))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -6.2e+102) {
		tmp = t_2;
	} else if (a <= 1.9e-299) {
		tmp = t_1;
	} else if (a <= 3.75e-187) {
		tmp = y * (x / (z - a));
	} else if (a <= 1500.0) {
		tmp = t_1;
	} else if (a <= 9.8e+55) {
		tmp = y * ((t - x) / a);
	} else if (a <= 2.4e+63) {
		tmp = t * (z / (z - a));
	} 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 * (1.0d0 - (y / z))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-6.2d+102)) then
        tmp = t_2
    else if (a <= 1.9d-299) then
        tmp = t_1
    else if (a <= 3.75d-187) then
        tmp = y * (x / (z - a))
    else if (a <= 1500.0d0) then
        tmp = t_1
    else if (a <= 9.8d+55) then
        tmp = y * ((t - x) / a)
    else if (a <= 2.4d+63) then
        tmp = t * (z / (z - a))
    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 * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -6.2e+102) {
		tmp = t_2;
	} else if (a <= 1.9e-299) {
		tmp = t_1;
	} else if (a <= 3.75e-187) {
		tmp = y * (x / (z - a));
	} else if (a <= 1500.0) {
		tmp = t_1;
	} else if (a <= 9.8e+55) {
		tmp = y * ((t - x) / a);
	} else if (a <= 2.4e+63) {
		tmp = t * (z / (z - a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -6.2e+102:
		tmp = t_2
	elif a <= 1.9e-299:
		tmp = t_1
	elif a <= 3.75e-187:
		tmp = y * (x / (z - a))
	elif a <= 1500.0:
		tmp = t_1
	elif a <= 9.8e+55:
		tmp = y * ((t - x) / a)
	elif a <= 2.4e+63:
		tmp = t * (z / (z - a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -6.2e+102)
		tmp = t_2;
	elseif (a <= 1.9e-299)
		tmp = t_1;
	elseif (a <= 3.75e-187)
		tmp = Float64(y * Float64(x / Float64(z - a)));
	elseif (a <= 1500.0)
		tmp = t_1;
	elseif (a <= 9.8e+55)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= 2.4e+63)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -6.2e+102)
		tmp = t_2;
	elseif (a <= 1.9e-299)
		tmp = t_1;
	elseif (a <= 3.75e-187)
		tmp = y * (x / (z - a));
	elseif (a <= 1500.0)
		tmp = t_1;
	elseif (a <= 9.8e+55)
		tmp = y * ((t - x) / a);
	elseif (a <= 2.4e+63)
		tmp = t * (z / (z - a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e+102], t$95$2, If[LessEqual[a, 1.9e-299], t$95$1, If[LessEqual[a, 3.75e-187], N[(y * N[(x / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1500.0], t$95$1, If[LessEqual[a, 9.8e+55], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+63], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.19999999999999973e102 or 2.4e63 < a

   1. Initial program 89.6%

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

   3. Taylor expanded in x around -inf 63.1%

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

      1. mul-1-neg 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in z around 0 58.9%

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

   if -6.19999999999999973e102 < a < 1.9000000000000001e-299 or 3.7500000000000002e-187 < a < 1500

   1. Initial program 76.3%

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

   3. Taylor expanded in x around 0 50.2%

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

      1. associate-/l* 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in a around 0 61.4%

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

      1. mul-1-neg 61.4%

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

      2. div-sub 61.4%

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

      3. sub-neg 61.4%

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

      4. *-inverses 61.4%

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

      5. metadata-eval 61.4%

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

   8. Simplified 61.4%

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

   if 1.9000000000000001e-299 < a < 3.7500000000000002e-187

   1. Initial program 66.4%

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

   3. Taylor expanded in y around inf 73.8%

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

      1. div-sub 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in t around 0 60.0%

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

      1. neg-mul-1 60.0%

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

      2. distribute-neg-frac 60.0%

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

   8. Simplified 60.0%

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

   if 1500 < a < 9.80000000000000029e55

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf 75.0%

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

      1. div-sub 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in a around inf 75.1%

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

   if 9.80000000000000029e55 < a < 2.4e63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-neg-frac2 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate--r- 100.0%

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

      5. neg-sub0 100.0%

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

   8. Simplified 100.0%

      \[\leadsto t \cdot \color{blue}{\frac{z}{\left(-a\right) + z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 3.75 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{elif}\;a \leq 1500:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1050:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -1.02e+113)
     t_2
     (if (<= a 3.2e-300)
       t_1
       (if (<= a 3.9e-63)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1050.0) 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 * ((t - x) / a));
	double tmp;
	if (a <= -1.02e+113) {
		tmp = t_2;
	} else if (a <= 3.2e-300) {
		tmp = t_1;
	} else if (a <= 3.9e-63) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1050.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-1.02d+113)) then
        tmp = t_2
    else if (a <= 3.2d-300) then
        tmp = t_1
    else if (a <= 3.9d-63) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1050.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -1.02e+113) {
		tmp = t_2;
	} else if (a <= 3.2e-300) {
		tmp = t_1;
	} else if (a <= 3.9e-63) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1050.0) {
		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 * ((t - x) / a))
	tmp = 0
	if a <= -1.02e+113:
		tmp = t_2
	elif a <= 3.2e-300:
		tmp = t_1
	elif a <= 3.9e-63:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1050.0:
		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(t - x) / a)))
	tmp = 0.0
	if (a <= -1.02e+113)
		tmp = t_2;
	elseif (a <= 3.2e-300)
		tmp = t_1;
	elseif (a <= 3.9e-63)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1050.0)
		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 * ((t - x) / a));
	tmp = 0.0;
	if (a <= -1.02e+113)
		tmp = t_2;
	elseif (a <= 3.2e-300)
		tmp = t_1;
	elseif (a <= 3.9e-63)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1050.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.02e+113], t$95$2, If[LessEqual[a, 3.2e-300], t$95$1, If[LessEqual[a, 3.9e-63], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1050.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.02000000000000002e113 or 1050 < a

   1. Initial program 90.2%

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

   3. Taylor expanded in z around 0 64.2%

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

      1. associate-/l* 72.0%

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

   5. Simplified 72.0%

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

   if -1.02000000000000002e113 < a < 3.20000000000000021e-300 or 3.90000000000000022e-63 < a < 1050

   1. Initial program 76.9%

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

   3. Taylor expanded in x around 0 49.6%

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

      1. associate-/l* 67.2%

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

   5. Simplified 67.2%

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

   if 3.20000000000000021e-300 < a < 3.90000000000000022e-63

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 73.6%

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

      1. div-sub 75.6%

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

   5. Simplified 75.6%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+113}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-300}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1050:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 19000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ (- t x) (/ a y)))))
   (if (<= a -2.3e+111)
     t_2
     (if (<= a 1.7e-299)
       t_1
       (if (<= a 1.1e-66)
         (* y (/ (- t x) (- a z)))
         (if (<= a 19000.0) 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 - x) / (a / y));
	double tmp;
	if (a <= -2.3e+111) {
		tmp = t_2;
	} else if (a <= 1.7e-299) {
		tmp = t_1;
	} else if (a <= 1.1e-66) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 19000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + ((t - x) / (a / y))
    if (a <= (-2.3d+111)) then
        tmp = t_2
    else if (a <= 1.7d-299) then
        tmp = t_1
    else if (a <= 1.1d-66) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 19000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((t - x) / (a / y));
	double tmp;
	if (a <= -2.3e+111) {
		tmp = t_2;
	} else if (a <= 1.7e-299) {
		tmp = t_1;
	} else if (a <= 1.1e-66) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 19000.0) {
		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 - x) / (a / y))
	tmp = 0
	if a <= -2.3e+111:
		tmp = t_2
	elif a <= 1.7e-299:
		tmp = t_1
	elif a <= 1.1e-66:
		tmp = y * ((t - x) / (a - z))
	elif a <= 19000.0:
		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(Float64(t - x) / Float64(a / y)))
	tmp = 0.0
	if (a <= -2.3e+111)
		tmp = t_2;
	elseif (a <= 1.7e-299)
		tmp = t_1;
	elseif (a <= 1.1e-66)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 19000.0)
		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 - x) / (a / y));
	tmp = 0.0;
	if (a <= -2.3e+111)
		tmp = t_2;
	elseif (a <= 1.7e-299)
		tmp = t_1;
	elseif (a <= 1.1e-66)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 19000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e+111], t$95$2, If[LessEqual[a, 1.7e-299], t$95$1, If[LessEqual[a, 1.1e-66], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 19000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.30000000000000002e111 or 19000 < a

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

      2. associate-*l/ 69.6%

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

      3. associate-*r/ 91.6%

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

      4. clear-num 91.6%

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

      5. un-div-inv 91.6%

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

   4. Applied egg-rr 91.6%

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

   5. Taylor expanded in z around 0 73.2%

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

   if -2.30000000000000002e111 < a < 1.6999999999999999e-299 or 1.1000000000000001e-66 < a < 19000

   1. Initial program 77.1%

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

   3. Taylor expanded in x around 0 50.0%

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

      1. associate-/l* 67.5%

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

   5. Simplified 67.5%

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

   if 1.6999999999999999e-299 < a < 1.1000000000000001e-66

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 73.6%

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

      1. div-sub 75.6%

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

   5. Simplified 75.6%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+111}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 19000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+117}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-244}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -2.35e+117)
     t
     (if (<= z -6.4e-52)
       t_1
       (if (<= z -1.5e-244)
         x
         (if (<= z 7e-275) t_1 (if (<= z 2.4e-17) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -2.35e+117) {
		tmp = t;
	} else if (z <= -6.4e-52) {
		tmp = t_1;
	} else if (z <= -1.5e-244) {
		tmp = x;
	} else if (z <= 7e-275) {
		tmp = t_1;
	} else if (z <= 2.4e-17) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-2.35d+117)) then
        tmp = t
    else if (z <= (-6.4d-52)) then
        tmp = t_1
    else if (z <= (-1.5d-244)) then
        tmp = x
    else if (z <= 7d-275) then
        tmp = t_1
    else if (z <= 2.4d-17) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -2.35e+117) {
		tmp = t;
	} else if (z <= -6.4e-52) {
		tmp = t_1;
	} else if (z <= -1.5e-244) {
		tmp = x;
	} else if (z <= 7e-275) {
		tmp = t_1;
	} else if (z <= 2.4e-17) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -2.35e+117:
		tmp = t
	elif z <= -6.4e-52:
		tmp = t_1
	elif z <= -1.5e-244:
		tmp = x
	elif z <= 7e-275:
		tmp = t_1
	elif z <= 2.4e-17:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -2.35e+117)
		tmp = t;
	elseif (z <= -6.4e-52)
		tmp = t_1;
	elseif (z <= -1.5e-244)
		tmp = x;
	elseif (z <= 7e-275)
		tmp = t_1;
	elseif (z <= 2.4e-17)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -2.35e+117)
		tmp = t;
	elseif (z <= -6.4e-52)
		tmp = t_1;
	elseif (z <= -1.5e-244)
		tmp = x;
	elseif (z <= 7e-275)
		tmp = t_1;
	elseif (z <= 2.4e-17)
		tmp = x;
	else
		tmp = t;
	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[z, -2.35e+117], t, If[LessEqual[z, -6.4e-52], t$95$1, If[LessEqual[z, -1.5e-244], x, If[LessEqual[z, 7e-275], t$95$1, If[LessEqual[z, 2.4e-17], x, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.35000000000000003e117 or 2.39999999999999986e-17 < z

   1. Initial program 67.7%

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

   3. Taylor expanded in z around inf 50.6%

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

   if -2.35000000000000003e117 < z < -6.4000000000000002e-52 or -1.5000000000000001e-244 < z < 6.99999999999999938e-275

   1. Initial program 80.7%

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

   3. Taylor expanded in x around 0 41.6%

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

      1. associate-/l* 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in z around 0 38.7%

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

   if -6.4000000000000002e-52 < z < -1.5000000000000001e-244 or 6.99999999999999938e-275 < z < 2.39999999999999986e-17

   1. Initial program 94.4%

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

   3. Taylor expanded in a around inf 43.2%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+117}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-244}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-275}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-300}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.4e+105)
   x
   (if (<= a 6.2e-300)
     t
     (if (<= a 5e-69) (* x (/ (- y a) z)) (if (<= a 2.3e+93) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.4e+105) {
		tmp = x;
	} else if (a <= 6.2e-300) {
		tmp = t;
	} else if (a <= 5e-69) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.3e+93) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.4d+105)) then
        tmp = x
    else if (a <= 6.2d-300) then
        tmp = t
    else if (a <= 5d-69) then
        tmp = x * ((y - a) / z)
    else if (a <= 2.3d+93) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.4e+105) {
		tmp = x;
	} else if (a <= 6.2e-300) {
		tmp = t;
	} else if (a <= 5e-69) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.3e+93) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.4e+105:
		tmp = x
	elif a <= 6.2e-300:
		tmp = t
	elif a <= 5e-69:
		tmp = x * ((y - a) / z)
	elif a <= 2.3e+93:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.4e+105)
		tmp = x;
	elseif (a <= 6.2e-300)
		tmp = t;
	elseif (a <= 5e-69)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 2.3e+93)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.4e+105)
		tmp = x;
	elseif (a <= 6.2e-300)
		tmp = t;
	elseif (a <= 5e-69)
		tmp = x * ((y - a) / z);
	elseif (a <= 2.3e+93)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.4e+105], x, If[LessEqual[a, 6.2e-300], t, If[LessEqual[a, 5e-69], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+93], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.40000000000000014e105 or 2.3000000000000002e93 < a

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf 55.2%

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

   if -4.40000000000000014e105 < a < 6.2000000000000005e-300 or 5.00000000000000033e-69 < a < 2.3000000000000002e93

   1. Initial program 77.4%

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

   3. Taylor expanded in z around inf 40.9%

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

   if 6.2000000000000005e-300 < a < 5.00000000000000033e-69

   1. Initial program 69.2%

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

   3. Taylor expanded in z around inf 75.5%

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

      1. associate--l+ 75.5%

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

      2. distribute-lft-out-- 75.5%

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

      3. div-sub 77.5%

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

      4. mul-1-neg 77.5%

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

      5. unsub-neg 77.5%

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

      6. div-sub 75.5%

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

      7. associate-/l* 80.6%

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

      8. associate-/l* 76.0%

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

      9. distribute-rgt-out-- 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in t around 0 43.8%

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

      1. associate-/l* 49.4%

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

   8. Simplified 49.4%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-300}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-300}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e+103)
   x
   (if (<= a 8.6e-300)
     t
     (if (<= a 4.1e-67) (* x (/ y z)) (if (<= a 2.5e+93) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+103) {
		tmp = x;
	} else if (a <= 8.6e-300) {
		tmp = t;
	} else if (a <= 4.1e-67) {
		tmp = x * (y / z);
	} else if (a <= 2.5e+93) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.5d+103)) then
        tmp = x
    else if (a <= 8.6d-300) then
        tmp = t
    else if (a <= 4.1d-67) then
        tmp = x * (y / z)
    else if (a <= 2.5d+93) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+103) {
		tmp = x;
	} else if (a <= 8.6e-300) {
		tmp = t;
	} else if (a <= 4.1e-67) {
		tmp = x * (y / z);
	} else if (a <= 2.5e+93) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e+103:
		tmp = x
	elif a <= 8.6e-300:
		tmp = t
	elif a <= 4.1e-67:
		tmp = x * (y / z)
	elif a <= 2.5e+93:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e+103)
		tmp = x;
	elseif (a <= 8.6e-300)
		tmp = t;
	elseif (a <= 4.1e-67)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 2.5e+93)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e+103)
		tmp = x;
	elseif (a <= 8.6e-300)
		tmp = t;
	elseif (a <= 4.1e-67)
		tmp = x * (y / z);
	elseif (a <= 2.5e+93)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e+103], x, If[LessEqual[a, 8.6e-300], t, If[LessEqual[a, 4.1e-67], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+93], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.50000000000000001e103 or 2.5000000000000001e93 < a

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf 55.2%

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

   if -4.50000000000000001e103 < a < 8.6000000000000001e-300 or 4.0999999999999997e-67 < a < 2.5000000000000001e93

   1. Initial program 77.4%

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

   3. Taylor expanded in z around inf 40.9%

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

   if 8.6000000000000001e-300 < a < 4.0999999999999997e-67

   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 -inf 55.3%

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

      1. mul-1-neg 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in a around 0 47.6%

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

      1. associate-*r/ 47.6%

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

      2. neg-mul-1 47.6%

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

   8. Simplified 47.6%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-300}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 70.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+101} \lor \neg \left(a \leq 740\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.5e+101) (not (<= a 740.0)))
   (+ x (* (- y z) (/ (- t x) a)))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e+101) || !(a <= 740.0)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-8.5d+101)) .or. (.not. (a <= 740.0d0))) then
        tmp = x + ((y - z) * ((t - x) / a))
    else
        tmp = t + (y * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e+101) || !(a <= 740.0)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.5e+101) or not (a <= 740.0):
		tmp = x + ((y - z) * ((t - x) / a))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.5e+101) || !(a <= 740.0))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.5e+101) || ~((a <= 740.0)))
		tmp = x + ((y - z) * ((t - x) / a));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.5e+101], N[Not[LessEqual[a, 740.0]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.5000000000000001e101 or 740 < a

   1. Initial program 89.6%

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

   3. Taylor expanded in a around inf 78.2%

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

   if -8.5000000000000001e101 < a < 740

   1. Initial program 74.4%

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

   3. Taylor expanded in z around inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. distribute-lft-out-- 69.4%

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

      3. div-sub 70.8%

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

      4. mul-1-neg 70.8%

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

      5. unsub-neg 70.8%

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

      6. div-sub 69.4%

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

      7. associate-/l* 79.7%

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

      8. associate-/l* 78.2%

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

      9. distribute-rgt-out-- 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in y around inf 67.8%

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

      1. associate-*r/ 78.2%

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

   8. Simplified 78.2%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+101} \lor \neg \left(a \leq 740\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+102}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1320:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.35e+102)
   (+ x (* (- y z) (/ (- t x) a)))
   (if (<= a 1320.0)
     (+ t (* y (/ (- x t) z)))
     (+ x (/ (- t x) (/ a (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e+102) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= 1320.0) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.35d+102)) then
        tmp = x + ((y - z) * ((t - x) / a))
    else if (a <= 1320.0d0) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + ((t - x) / (a / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e+102) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= 1320.0) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.35e+102:
		tmp = x + ((y - z) * ((t - x) / a))
	elif a <= 1320.0:
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + ((t - x) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.35e+102)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	elseif (a <= 1320.0)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.35e+102)
		tmp = x + ((y - z) * ((t - x) / a));
	elseif (a <= 1320.0)
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + ((t - x) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.35e+102], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1320.0], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3500000000000001e102

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf 84.7%

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

   if -1.3500000000000001e102 < a < 1320

   1. Initial program 74.4%

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

   3. Taylor expanded in z around inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. distribute-lft-out-- 69.4%

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

      3. div-sub 70.8%

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

      4. mul-1-neg 70.8%

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

      5. unsub-neg 70.8%

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

      6. div-sub 69.4%

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

      7. associate-/l* 79.7%

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

      8. associate-/l* 78.2%

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

      9. distribute-rgt-out-- 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in y around inf 67.8%

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

      1. associate-*r/ 78.2%

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

   8. Simplified 78.2%

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

   if 1320 < a

   1. Initial program 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-*l/ 65.4%

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

      3. associate-*r/ 89.9%

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

      4. clear-num 89.8%

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

      5. un-div-inv 89.8%

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

   4. Applied egg-rr 89.8%

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

   5. Taylor expanded in a around inf 75.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+102}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1320:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+103}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 960:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.6e+103)
   (+ x (* (- y z) (/ (- t x) a)))
   (if (<= a 960.0)
     (+ t (* (- y a) (/ (- x t) z)))
     (+ x (/ (- t x) (/ a (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e+103) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= 960.0) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.6d+103)) then
        tmp = x + ((y - z) * ((t - x) / a))
    else if (a <= 960.0d0) then
        tmp = t + ((y - a) * ((x - t) / z))
    else
        tmp = x + ((t - x) / (a / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e+103) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= 960.0) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.6e+103:
		tmp = x + ((y - z) * ((t - x) / a))
	elif a <= 960.0:
		tmp = t + ((y - a) * ((x - t) / z))
	else:
		tmp = x + ((t - x) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.6e+103)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	elseif (a <= 960.0)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.6e+103)
		tmp = x + ((y - z) * ((t - x) / a));
	elseif (a <= 960.0)
		tmp = t + ((y - a) * ((x - t) / z));
	else
		tmp = x + ((t - x) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.6e+103], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 960.0], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.6000000000000002e103

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf 84.7%

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

   if -2.6000000000000002e103 < a < 960

   1. Initial program 74.4%

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

   3. Taylor expanded in z around inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. distribute-lft-out-- 69.4%

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

      3. div-sub 70.8%

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

      4. mul-1-neg 70.8%

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

      5. unsub-neg 70.8%

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

      6. div-sub 69.4%

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

      7. associate-/l* 79.7%

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

      8. associate-/l* 78.2%

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

      9. distribute-rgt-out-- 81.7%

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

   5. Simplified 81.7%

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

   if 960 < a

   1. Initial program 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-*l/ 65.4%

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

      3. associate-*r/ 89.9%

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

      4. clear-num 89.8%

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

      5. un-div-inv 89.8%

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

   4. Applied egg-rr 89.8%

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

   5. Taylor expanded in a around inf 75.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+103}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 960:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+101}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 780:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e+101)
   (+ x (* (- y z) (/ (- t x) a)))
   (if (<= a 780.0)
     (+ t (/ (- y a) (/ z (- x t))))
     (+ x (/ (- t x) (/ a (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e+101) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= 780.0) {
		tmp = t + ((y - a) / (z / (x - t)));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.5d+101)) then
        tmp = x + ((y - z) * ((t - x) / a))
    else if (a <= 780.0d0) then
        tmp = t + ((y - a) / (z / (x - t)))
    else
        tmp = x + ((t - x) / (a / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e+101) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= 780.0) {
		tmp = t + ((y - a) / (z / (x - t)));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e+101:
		tmp = x + ((y - z) * ((t - x) / a))
	elif a <= 780.0:
		tmp = t + ((y - a) / (z / (x - t)))
	else:
		tmp = x + ((t - x) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.5e+101)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	elseif (a <= 780.0)
		tmp = Float64(t + Float64(Float64(y - a) / Float64(z / Float64(x - t))));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.5e+101)
		tmp = x + ((y - z) * ((t - x) / a));
	elseif (a <= 780.0)
		tmp = t + ((y - a) / (z / (x - t)));
	else
		tmp = x + ((t - x) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.5e+101], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 780.0], N[(t + N[(N[(y - a), $MachinePrecision] / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.5000000000000001e101

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf 84.7%

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

   if -8.5000000000000001e101 < a < 780

   1. Initial program 74.4%

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

   3. Taylor expanded in z around inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. distribute-lft-out-- 69.4%

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

      3. div-sub 70.8%

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

      4. mul-1-neg 70.8%

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

      5. unsub-neg 70.8%

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

      6. div-sub 69.4%

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

      7. associate-/l* 79.7%

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

      8. associate-/l* 78.2%

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

      9. distribute-rgt-out-- 81.7%

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

   5. Simplified 81.7%

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

      1. *-commutative 81.7%

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

      2. clear-num 81.7%

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

      3. un-div-inv 81.8%

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

   7. Applied egg-rr 81.8%

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

   if 780 < a

   1. Initial program 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-*l/ 65.4%

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

      3. associate-*r/ 89.9%

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

      4. clear-num 89.8%

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

      5. un-div-inv 89.8%

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

   4. Applied egg-rr 89.8%

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

   5. Taylor expanded in a around inf 75.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+101}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 780:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+61} \lor \neg \left(a \leq 850\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.1e+61) (not (<= a 850.0)))
   (+ x (/ (- t x) (/ a y)))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.1e+61) || !(a <= 850.0)) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.1d+61)) .or. (.not. (a <= 850.0d0))) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t + (y * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.1e+61) || !(a <= 850.0)) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.1e+61) or not (a <= 850.0):
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.1e+61) || !(a <= 850.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.1e+61) || ~((a <= 850.0)))
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.1e+61], N[Not[LessEqual[a, 850.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.1000000000000001e61 or 850 < a

   1. Initial program 87.8%

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

      1. *-commutative 87.8%

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

      2. associate-*l/ 69.8%

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

      3. associate-*r/ 90.0%

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

      4. clear-num 89.9%

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

      5. un-div-inv 89.9%

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

   4. Applied egg-rr 89.9%

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

   5. Taylor expanded in z around 0 71.1%

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

   if -5.1000000000000001e61 < a < 850

   1. Initial program 75.0%

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

   3. Taylor expanded in z around inf 71.1%

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

      1. associate--l+ 71.1%

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

      2. distribute-lft-out-- 71.1%

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

      3. div-sub 72.5%

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

      4. mul-1-neg 72.5%

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

      5. unsub-neg 72.5%

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

      6. div-sub 71.1%

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

      7. associate-/l* 81.3%

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

      8. associate-/l* 79.8%

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

      9. distribute-rgt-out-- 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in y around inf 69.4%

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

      1. associate-*r/ 79.7%

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

   8. Simplified 79.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+61} \lor \neg \left(a \leq 850\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 37.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e-7) t (if (<= z 2.6e-17) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e-7) {
		tmp = t;
	} else if (z <= 2.6e-17) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6d-7)) then
        tmp = t
    else if (z <= 2.6d-17) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e-7) {
		tmp = t;
	} else if (z <= 2.6e-17) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e-7:
		tmp = t
	elif z <= 2.6e-17:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e-7)
		tmp = t;
	elseif (z <= 2.6e-17)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6e-7)
		tmp = t;
	elseif (z <= 2.6e-17)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e-7], t, If[LessEqual[z, 2.6e-17], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -5.9999999999999997e-7 or 2.60000000000000003e-17 < z

   1. Initial program 68.7%

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

   3. Taylor expanded in z around inf 43.5%

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

   if -5.9999999999999997e-7 < z < 2.60000000000000003e-17

   1. Initial program 93.3%

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

   3. Taylor expanded in a around inf 37.3%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 25.2% 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 80.6%

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

3. Taylor expanded in z around inf 25.6%

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

4. Final simplification 25.6%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024067 
(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)))))