Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.5% → 94.9%

Time: 15.2s

Alternatives: 22

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.5% 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

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-290}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-290)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (if (<= t_1 0.0)
       (+ t (* (/ (- t x) z) (- a y)))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-290) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-290)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-290], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.0000000000000001e-290

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. remove-double-neg 90.9%

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

      3. unsub-neg 90.9%

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

      4. *-commutative 90.9%

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

      5. associate-*l/ 77.9%

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

      6. associate-/l* 92.6%

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

      7. fma-neg 92.5%

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

      8. remove-double-neg 92.5%

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

   3. Simplified 92.5%

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

   if -1.0000000000000001e-290 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.8%

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

   3. Taylor expanded in z around inf 90.4%

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

      1. associate--l+ 90.4%

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

      2. distribute-lft-out-- 90.4%

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

      3. div-sub 90.4%

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

      4. mul-1-neg 90.4%

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

      5. unsub-neg 90.4%

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

      6. div-sub 90.4%

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

      7. associate-/l* 96.7%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   5. Simplified 99.9%

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

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

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

      2. associate-*l/ 77.4%

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

      3. associate-*r/ 95.3%

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

      4. clear-num 95.3%

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

      5. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-290}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-290} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-290) (not (<= t_1 0.0)))
     t_1
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-290) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-290)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-290) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-290) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-290) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-290) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-290], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.0000000000000001e-290 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.6%

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

   if -1.0000000000000001e-290 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.8%

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

   3. Taylor expanded in z around inf 90.4%

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

      1. associate--l+ 90.4%

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

      2. distribute-lft-out-- 90.4%

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

      3. div-sub 90.4%

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

      4. mul-1-neg 90.4%

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

      5. unsub-neg 90.4%

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

      6. div-sub 90.4%

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

      7. associate-/l* 96.7%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-290} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-290} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-290) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-290) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-290)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-290) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-290) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-290) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-290) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-290], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.0000000000000001e-290 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*l/ 77.7%

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

      3. associate-*r/ 93.9%

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

      4. clear-num 93.9%

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

      5. un-div-inv 94.5%

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

   4. Applied egg-rr 94.5%

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

   if -1.0000000000000001e-290 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.8%

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

   3. Taylor expanded in z around inf 90.4%

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

      1. associate--l+ 90.4%

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

      2. distribute-lft-out-- 90.4%

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

      3. div-sub 90.4%

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

      4. mul-1-neg 90.4%

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

      5. unsub-neg 90.4%

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

      6. div-sub 90.4%

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

      7. associate-/l* 96.7%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-290} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y}}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{-82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+59} \lor \neg \left(z \leq 2.15 \cdot 10^{+73}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a y)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.85e-82)
     t_2
     (if (<= z 3.7e-189)
       t_1
       (if (<= z 1.25e-42)
         (* y (/ (- t x) (- a z)))
         (if (<= z 4.7e+38)
           t_1
           (if (or (<= z 7.8e+59) (not (<= z 2.15e+73)))
             t_2
             (* x (- 1.0 (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / y));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.85e-82) {
		tmp = t_2;
	} else if (z <= 3.7e-189) {
		tmp = t_1;
	} else if (z <= 1.25e-42) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 4.7e+38) {
		tmp = t_1;
	} else if ((z <= 7.8e+59) || !(z <= 2.15e+73)) {
		tmp = t_2;
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) / (a / y))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-2.85d-82)) then
        tmp = t_2
    else if (z <= 3.7d-189) then
        tmp = t_1
    else if (z <= 1.25d-42) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 4.7d+38) then
        tmp = t_1
    else if ((z <= 7.8d+59) .or. (.not. (z <= 2.15d+73))) then
        tmp = t_2
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / y));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.85e-82) {
		tmp = t_2;
	} else if (z <= 3.7e-189) {
		tmp = t_1;
	} else if (z <= 1.25e-42) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 4.7e+38) {
		tmp = t_1;
	} else if ((z <= 7.8e+59) || !(z <= 2.15e+73)) {
		tmp = t_2;
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / y))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -2.85e-82:
		tmp = t_2
	elif z <= 3.7e-189:
		tmp = t_1
	elif z <= 1.25e-42:
		tmp = y * ((t - x) / (a - z))
	elif z <= 4.7e+38:
		tmp = t_1
	elif (z <= 7.8e+59) or not (z <= 2.15e+73):
		tmp = t_2
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / y)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.85e-82)
		tmp = t_2;
	elseif (z <= 3.7e-189)
		tmp = t_1;
	elseif (z <= 1.25e-42)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 4.7e+38)
		tmp = t_1;
	elseif ((z <= 7.8e+59) || !(z <= 2.15e+73))
		tmp = t_2;
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / y));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -2.85e-82)
		tmp = t_2;
	elseif (z <= 3.7e-189)
		tmp = t_1;
	elseif (z <= 1.25e-42)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 4.7e+38)
		tmp = t_1;
	elseif ((z <= 7.8e+59) || ~((z <= 2.15e+73)))
		tmp = t_2;
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.85e-82], t$95$2, If[LessEqual[z, 3.7e-189], t$95$1, If[LessEqual[z, 1.25e-42], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e+38], t$95$1, If[Or[LessEqual[z, 7.8e+59], N[Not[LessEqual[z, 2.15e+73]], $MachinePrecision]], t$95$2, N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.85000000000000001e-82 or 4.6999999999999999e38 < z < 7.80000000000000043e59 or 2.15000000000000007e73 < z

   1. Initial program 69.8%

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

   3. Taylor expanded in x around 0 49.0%

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

      1. associate-/l* 67.6%

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

   5. Simplified 67.6%

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

   if -2.85000000000000001e-82 < z < 3.70000000000000019e-189 or 1.25000000000000001e-42 < z < 4.6999999999999999e38

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

      2. associate-*l/ 85.4%

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

      3. associate-*r/ 95.2%

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

      4. clear-num 95.2%

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

      5. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in z around 0 87.9%

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

   if 3.70000000000000019e-189 < z < 1.25000000000000001e-42

   1. Initial program 86.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 78.3%

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

   5. Simplified 78.3%

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

   if 7.80000000000000043e59 < z < 2.15000000000000007e73

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 59.6%

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

   4. Taylor expanded in x around inf 88.1%

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

      1. mul-1-neg 88.1%

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

      2. sub-neg 88.1%

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

   6. Simplified 88.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-189}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+59} \lor \neg \left(z \leq 2.15 \cdot 10^{+73}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y}}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{-82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a y)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.85e-82)
     t_2
     (if (<= z 9.8e-192)
       t_1
       (if (<= z 1.85e-41)
         (* y (/ (- t x) (- a z)))
         (if (<= z 3.25e+39)
           t_1
           (if (<= z 1.05e+60)
             (/ t (/ (- a z) (- y z)))
             (if (<= z 3.1e+76) (* x (- 1.0 (/ y a))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / y));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.85e-82) {
		tmp = t_2;
	} else if (z <= 9.8e-192) {
		tmp = t_1;
	} else if (z <= 1.85e-41) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 3.25e+39) {
		tmp = t_1;
	} else if (z <= 1.05e+60) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 3.1e+76) {
		tmp = x * (1.0 - (y / 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 = x + ((t - x) / (a / y))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-2.85d-82)) then
        tmp = t_2
    else if (z <= 9.8d-192) then
        tmp = t_1
    else if (z <= 1.85d-41) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 3.25d+39) then
        tmp = t_1
    else if (z <= 1.05d+60) then
        tmp = t / ((a - z) / (y - z))
    else if (z <= 3.1d+76) then
        tmp = x * (1.0d0 - (y / 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 = x + ((t - x) / (a / y));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.85e-82) {
		tmp = t_2;
	} else if (z <= 9.8e-192) {
		tmp = t_1;
	} else if (z <= 1.85e-41) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 3.25e+39) {
		tmp = t_1;
	} else if (z <= 1.05e+60) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 3.1e+76) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / y))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -2.85e-82:
		tmp = t_2
	elif z <= 9.8e-192:
		tmp = t_1
	elif z <= 1.85e-41:
		tmp = y * ((t - x) / (a - z))
	elif z <= 3.25e+39:
		tmp = t_1
	elif z <= 1.05e+60:
		tmp = t / ((a - z) / (y - z))
	elif z <= 3.1e+76:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / y)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.85e-82)
		tmp = t_2;
	elseif (z <= 9.8e-192)
		tmp = t_1;
	elseif (z <= 1.85e-41)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 3.25e+39)
		tmp = t_1;
	elseif (z <= 1.05e+60)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (z <= 3.1e+76)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / y));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -2.85e-82)
		tmp = t_2;
	elseif (z <= 9.8e-192)
		tmp = t_1;
	elseif (z <= 1.85e-41)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 3.25e+39)
		tmp = t_1;
	elseif (z <= 1.05e+60)
		tmp = t / ((a - z) / (y - z));
	elseif (z <= 3.1e+76)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.85e-82], t$95$2, If[LessEqual[z, 9.8e-192], t$95$1, If[LessEqual[z, 1.85e-41], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.25e+39], t$95$1, If[LessEqual[z, 1.05e+60], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+76], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.85000000000000001e-82 or 3.10000000000000011e76 < z

   1. Initial program 69.7%

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

   3. Taylor expanded in x around 0 47.9%

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

      1. associate-/l* 68.1%

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

   5. Simplified 68.1%

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

   if -2.85000000000000001e-82 < z < 9.7999999999999999e-192 or 1.8500000000000001e-41 < z < 3.2500000000000001e39

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

      2. associate-*l/ 85.4%

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

      3. associate-*r/ 95.2%

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

      4. clear-num 95.2%

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

      5. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in z around 0 87.9%

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

   if 9.7999999999999999e-192 < z < 1.8500000000000001e-41

   1. Initial program 86.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 78.3%

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

   5. Simplified 78.3%

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

   if 3.2500000000000001e39 < z < 1.0500000000000001e60

   1. Initial program 71.0%

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

   3. Taylor expanded in x around 0 61.6%

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

      1. associate-/l* 61.4%

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

   5. Simplified 61.4%

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

      1. clear-num 61.4%

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

      2. div-inv 61.6%

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

   7. Applied egg-rr 61.6%

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

   if 1.0500000000000001e60 < z < 3.10000000000000011e76

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 59.6%

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

   4. Taylor expanded in x around inf 88.1%

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

      1. mul-1-neg 88.1%

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

      2. sub-neg 88.1%

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

   6. Simplified 88.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-192}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 45.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+20}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.15 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -8.6e+20)
     t
     (if (<= z -4.15e-82)
       (* t (/ (- y z) a))
       (if (<= z 7e-168)
         t_1
         (if (<= z 5.1e-54) (* t (/ y (- a z))) (if (<= z 1.4e+86) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -8.6e+20) {
		tmp = t;
	} else if (z <= -4.15e-82) {
		tmp = t * ((y - z) / a);
	} else if (z <= 7e-168) {
		tmp = t_1;
	} else if (z <= 5.1e-54) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.4e+86) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-8.6d+20)) then
        tmp = t
    else if (z <= (-4.15d-82)) then
        tmp = t * ((y - z) / a)
    else if (z <= 7d-168) then
        tmp = t_1
    else if (z <= 5.1d-54) then
        tmp = t * (y / (a - z))
    else if (z <= 1.4d+86) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -8.6e+20) {
		tmp = t;
	} else if (z <= -4.15e-82) {
		tmp = t * ((y - z) / a);
	} else if (z <= 7e-168) {
		tmp = t_1;
	} else if (z <= 5.1e-54) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.4e+86) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -8.6e+20:
		tmp = t
	elif z <= -4.15e-82:
		tmp = t * ((y - z) / a)
	elif z <= 7e-168:
		tmp = t_1
	elif z <= 5.1e-54:
		tmp = t * (y / (a - z))
	elif z <= 1.4e+86:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -8.6e+20)
		tmp = t;
	elseif (z <= -4.15e-82)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 7e-168)
		tmp = t_1;
	elseif (z <= 5.1e-54)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1.4e+86)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -8.6e+20)
		tmp = t;
	elseif (z <= -4.15e-82)
		tmp = t * ((y - z) / a);
	elseif (z <= 7e-168)
		tmp = t_1;
	elseif (z <= 5.1e-54)
		tmp = t * (y / (a - z));
	elseif (z <= 1.4e+86)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.6e+20], t, If[LessEqual[z, -4.15e-82], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-168], t$95$1, If[LessEqual[z, 5.1e-54], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+86], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.6e20 or 1.40000000000000002e86 < z

   1. Initial program 66.3%

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

   3. Taylor expanded in z around inf 54.3%

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

   if -8.6e20 < z < -4.14999999999999972e-82

   1. Initial program 80.0%

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

   3. Taylor expanded in x around 0 59.3%

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

      1. associate-/l* 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in a around inf 38.2%

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

      1. associate-/l* 48.0%

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

   8. Simplified 48.0%

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

   if -4.14999999999999972e-82 < z < 6.99999999999999964e-168 or 5.1000000000000001e-54 < z < 1.40000000000000002e86

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 67.2%

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

   4. Taylor expanded in x around inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. sub-neg 59.6%

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

   6. Simplified 59.6%

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

   if 6.99999999999999964e-168 < z < 5.1000000000000001e-54

   1. Initial program 83.1%

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

   3. Taylor expanded in x around 0 60.3%

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

      1. associate-/l* 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in y around inf 48.9%

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

      1. associate-/l* 49.2%

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

   8. Simplified 49.2%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+20}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.15 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-43}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -6.5e+21)
     t
     (if (<= z -4.5e-82)
       (* t (/ (- y z) a))
       (if (<= z -5.5e-226)
         t_1
         (if (<= z 1.2e-43) (+ x (/ (* y t) a)) (if (<= z 7.6e+85) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -6.5e+21) {
		tmp = t;
	} else if (z <= -4.5e-82) {
		tmp = t * ((y - z) / a);
	} else if (z <= -5.5e-226) {
		tmp = t_1;
	} else if (z <= 1.2e-43) {
		tmp = x + ((y * t) / a);
	} else if (z <= 7.6e+85) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-6.5d+21)) then
        tmp = t
    else if (z <= (-4.5d-82)) then
        tmp = t * ((y - z) / a)
    else if (z <= (-5.5d-226)) then
        tmp = t_1
    else if (z <= 1.2d-43) then
        tmp = x + ((y * t) / a)
    else if (z <= 7.6d+85) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -6.5e+21) {
		tmp = t;
	} else if (z <= -4.5e-82) {
		tmp = t * ((y - z) / a);
	} else if (z <= -5.5e-226) {
		tmp = t_1;
	} else if (z <= 1.2e-43) {
		tmp = x + ((y * t) / a);
	} else if (z <= 7.6e+85) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -6.5e+21:
		tmp = t
	elif z <= -4.5e-82:
		tmp = t * ((y - z) / a)
	elif z <= -5.5e-226:
		tmp = t_1
	elif z <= 1.2e-43:
		tmp = x + ((y * t) / a)
	elif z <= 7.6e+85:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -6.5e+21)
		tmp = t;
	elseif (z <= -4.5e-82)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= -5.5e-226)
		tmp = t_1;
	elseif (z <= 1.2e-43)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 7.6e+85)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -6.5e+21)
		tmp = t;
	elseif (z <= -4.5e-82)
		tmp = t * ((y - z) / a);
	elseif (z <= -5.5e-226)
		tmp = t_1;
	elseif (z <= 1.2e-43)
		tmp = x + ((y * t) / a);
	elseif (z <= 7.6e+85)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+21], t, If[LessEqual[z, -4.5e-82], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-226], t$95$1, If[LessEqual[z, 1.2e-43], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e+85], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5e21 or 7.59999999999999984e85 < z

   1. Initial program 66.3%

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

   3. Taylor expanded in z around inf 54.3%

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

   if -6.5e21 < z < -4.4999999999999998e-82

   1. Initial program 80.0%

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

   3. Taylor expanded in x around 0 59.3%

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

      1. associate-/l* 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in a around inf 38.2%

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

      1. associate-/l* 48.0%

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

   8. Simplified 48.0%

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

   if -4.4999999999999998e-82 < z < -5.5e-226 or 1.2000000000000001e-43 < z < 7.59999999999999984e85

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 57.5%

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

   4. Taylor expanded in x around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. sub-neg 60.0%

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

   6. Simplified 60.0%

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

   if -5.5e-226 < z < 1.2000000000000001e-43

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 69.7%

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

   4. Taylor expanded in t around inf 59.4%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-226}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-43}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-44}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (- t (* t (/ y z)))))
   (if (<= z -7.5e+20)
     t_2
     (if (<= z -6.2e-82)
       (* t (/ (- y z) a))
       (if (<= z -6.1e-226)
         t_1
         (if (<= z 6.2e-44)
           (+ x (/ (* y t) a))
           (if (<= z 6.5e+84) 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 - (t * (y / z));
	double tmp;
	if (z <= -7.5e+20) {
		tmp = t_2;
	} else if (z <= -6.2e-82) {
		tmp = t * ((y - z) / a);
	} else if (z <= -6.1e-226) {
		tmp = t_1;
	} else if (z <= 6.2e-44) {
		tmp = x + ((y * t) / a);
	} else if (z <= 6.5e+84) {
		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 - (t * (y / z))
    if (z <= (-7.5d+20)) then
        tmp = t_2
    else if (z <= (-6.2d-82)) then
        tmp = t * ((y - z) / a)
    else if (z <= (-6.1d-226)) then
        tmp = t_1
    else if (z <= 6.2d-44) then
        tmp = x + ((y * t) / a)
    else if (z <= 6.5d+84) 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 - (t * (y / z));
	double tmp;
	if (z <= -7.5e+20) {
		tmp = t_2;
	} else if (z <= -6.2e-82) {
		tmp = t * ((y - z) / a);
	} else if (z <= -6.1e-226) {
		tmp = t_1;
	} else if (z <= 6.2e-44) {
		tmp = x + ((y * t) / a);
	} else if (z <= 6.5e+84) {
		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 - (t * (y / z))
	tmp = 0
	if z <= -7.5e+20:
		tmp = t_2
	elif z <= -6.2e-82:
		tmp = t * ((y - z) / a)
	elif z <= -6.1e-226:
		tmp = t_1
	elif z <= 6.2e-44:
		tmp = x + ((y * t) / a)
	elif z <= 6.5e+84:
		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(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -7.5e+20)
		tmp = t_2;
	elseif (z <= -6.2e-82)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= -6.1e-226)
		tmp = t_1;
	elseif (z <= 6.2e-44)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 6.5e+84)
		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 - (t * (y / z));
	tmp = 0.0;
	if (z <= -7.5e+20)
		tmp = t_2;
	elseif (z <= -6.2e-82)
		tmp = t * ((y - z) / a);
	elseif (z <= -6.1e-226)
		tmp = t_1;
	elseif (z <= 6.2e-44)
		tmp = x + ((y * t) / a);
	elseif (z <= 6.5e+84)
		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[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+20], t$95$2, If[LessEqual[z, -6.2e-82], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.1e-226], t$95$1, If[LessEqual[z, 6.2e-44], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+84], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.5e20 or 6.50000000000000027e84 < z

   1. Initial program 66.3%

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

   3. Taylor expanded in x around 0 46.2%

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

      1. associate-/l* 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in a around 0 43.9%

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

      1. mul-1-neg 43.9%

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

      2. associate-/l* 62.5%

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

      3. distribute-lft-neg-in 62.5%

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

      4. div-sub 62.6%

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

      5. *-inverses 62.6%

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

   8. Simplified 62.6%

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

   9. Taylor expanded in y around 0 56.5%

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

       1. mul-1-neg 56.5%

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

       2. unsub-neg 56.5%

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

       3. associate-*r/ 62.6%

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

   11. Simplified 62.6%

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

   if -7.5e20 < z < -6.19999999999999999e-82

   1. Initial program 80.0%

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

   3. Taylor expanded in x around 0 59.3%

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

      1. associate-/l* 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in a around inf 38.2%

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

      1. associate-/l* 48.0%

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

   8. Simplified 48.0%

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

   if -6.19999999999999999e-82 < z < -6.0999999999999998e-226 or 6.19999999999999968e-44 < z < 6.50000000000000027e84

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 57.5%

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

   4. Taylor expanded in x around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. sub-neg 60.0%

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

   6. Simplified 60.0%

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

   if -6.0999999999999998e-226 < z < 6.19999999999999968e-44

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 69.7%

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

   4. Taylor expanded in t around inf 59.4%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+20}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-226}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-44}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (- t (* t (/ y z)))))
   (if (<= z -3.3e+20)
     t_2
     (if (<= z -6.4e-82)
       (/ t (/ a (- y z)))
       (if (<= z -5.2e-226)
         t_1
         (if (<= z 1.02e-47)
           (+ x (/ (* y t) a))
           (if (<= z 1.5e+85) 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 - (t * (y / z));
	double tmp;
	if (z <= -3.3e+20) {
		tmp = t_2;
	} else if (z <= -6.4e-82) {
		tmp = t / (a / (y - z));
	} else if (z <= -5.2e-226) {
		tmp = t_1;
	} else if (z <= 1.02e-47) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.5e+85) {
		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 - (t * (y / z))
    if (z <= (-3.3d+20)) then
        tmp = t_2
    else if (z <= (-6.4d-82)) then
        tmp = t / (a / (y - z))
    else if (z <= (-5.2d-226)) then
        tmp = t_1
    else if (z <= 1.02d-47) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.5d+85) 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 - (t * (y / z));
	double tmp;
	if (z <= -3.3e+20) {
		tmp = t_2;
	} else if (z <= -6.4e-82) {
		tmp = t / (a / (y - z));
	} else if (z <= -5.2e-226) {
		tmp = t_1;
	} else if (z <= 1.02e-47) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.5e+85) {
		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 - (t * (y / z))
	tmp = 0
	if z <= -3.3e+20:
		tmp = t_2
	elif z <= -6.4e-82:
		tmp = t / (a / (y - z))
	elif z <= -5.2e-226:
		tmp = t_1
	elif z <= 1.02e-47:
		tmp = x + ((y * t) / a)
	elif z <= 1.5e+85:
		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(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -3.3e+20)
		tmp = t_2;
	elseif (z <= -6.4e-82)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (z <= -5.2e-226)
		tmp = t_1;
	elseif (z <= 1.02e-47)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.5e+85)
		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 - (t * (y / z));
	tmp = 0.0;
	if (z <= -3.3e+20)
		tmp = t_2;
	elseif (z <= -6.4e-82)
		tmp = t / (a / (y - z));
	elseif (z <= -5.2e-226)
		tmp = t_1;
	elseif (z <= 1.02e-47)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.5e+85)
		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[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+20], t$95$2, If[LessEqual[z, -6.4e-82], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.2e-226], t$95$1, If[LessEqual[z, 1.02e-47], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+85], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3e20 or 1.5e85 < z

   1. Initial program 66.3%

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

   3. Taylor expanded in x around 0 46.2%

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

      1. associate-/l* 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in a around 0 43.9%

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

      1. mul-1-neg 43.9%

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

      2. associate-/l* 62.5%

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

      3. distribute-lft-neg-in 62.5%

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

      4. div-sub 62.6%

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

      5. *-inverses 62.6%

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

   8. Simplified 62.6%

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

   9. Taylor expanded in y around 0 56.5%

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

       1. mul-1-neg 56.5%

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

       2. unsub-neg 56.5%

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

       3. associate-*r/ 62.6%

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

   11. Simplified 62.6%

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

   if -3.3e20 < z < -6.4000000000000002e-82

   1. Initial program 80.0%

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

   3. Taylor expanded in x around 0 59.3%

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

      1. associate-/l* 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in a around inf 38.2%

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

      1. associate-/l* 48.0%

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

   8. Simplified 48.0%

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

      1. clear-num 47.9%

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

      2. un-div-inv 48.1%

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

   10. Applied egg-rr 48.1%

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

   if -6.4000000000000002e-82 < z < -5.1999999999999997e-226 or 1.02000000000000002e-47 < z < 1.5e85

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 57.5%

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

   4. Taylor expanded in x around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. sub-neg 60.0%

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

   6. Simplified 60.0%

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

   if -5.1999999999999997e-226 < z < 1.02000000000000002e-47

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 69.7%

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

   4. Taylor expanded in t around inf 59.4%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+20}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-226}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := t - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))) (t_2 (- t (* t (/ y z)))))
   (if (<= z -6.4e-82)
     (* t (/ z (- z a)))
     (if (<= z 6.6e-157)
       t_1
       (if (<= z 1.35e-70)
         t_2
         (if (<= z 6.8e-51)
           t_1
           (if (<= z 1.8e+85) (* x (- 1.0 (/ y a))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = t - (t * (y / z));
	double tmp;
	if (z <= -6.4e-82) {
		tmp = t * (z / (z - a));
	} else if (z <= 6.6e-157) {
		tmp = t_1;
	} else if (z <= 1.35e-70) {
		tmp = t_2;
	} else if (z <= 6.8e-51) {
		tmp = t_1;
	} else if (z <= 1.8e+85) {
		tmp = x * (1.0 - (y / 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 = x + ((y * t) / a)
    t_2 = t - (t * (y / z))
    if (z <= (-6.4d-82)) then
        tmp = t * (z / (z - a))
    else if (z <= 6.6d-157) then
        tmp = t_1
    else if (z <= 1.35d-70) then
        tmp = t_2
    else if (z <= 6.8d-51) then
        tmp = t_1
    else if (z <= 1.8d+85) then
        tmp = x * (1.0d0 - (y / 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 = x + ((y * t) / a);
	double t_2 = t - (t * (y / z));
	double tmp;
	if (z <= -6.4e-82) {
		tmp = t * (z / (z - a));
	} else if (z <= 6.6e-157) {
		tmp = t_1;
	} else if (z <= 1.35e-70) {
		tmp = t_2;
	} else if (z <= 6.8e-51) {
		tmp = t_1;
	} else if (z <= 1.8e+85) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	t_2 = t - (t * (y / z))
	tmp = 0
	if z <= -6.4e-82:
		tmp = t * (z / (z - a))
	elif z <= 6.6e-157:
		tmp = t_1
	elif z <= 1.35e-70:
		tmp = t_2
	elif z <= 6.8e-51:
		tmp = t_1
	elif z <= 1.8e+85:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	t_2 = Float64(t - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -6.4e-82)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (z <= 6.6e-157)
		tmp = t_1;
	elseif (z <= 1.35e-70)
		tmp = t_2;
	elseif (z <= 6.8e-51)
		tmp = t_1;
	elseif (z <= 1.8e+85)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	t_2 = t - (t * (y / z));
	tmp = 0.0;
	if (z <= -6.4e-82)
		tmp = t * (z / (z - a));
	elseif (z <= 6.6e-157)
		tmp = t_1;
	elseif (z <= 1.35e-70)
		tmp = t_2;
	elseif (z <= 6.8e-51)
		tmp = t_1;
	elseif (z <= 1.8e+85)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e-82], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-157], t$95$1, If[LessEqual[z, 1.35e-70], t$95$2, If[LessEqual[z, 6.8e-51], t$95$1, If[LessEqual[z, 1.8e+85], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.4000000000000002e-82

   1. Initial program 70.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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* 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in y around 0 44.1%

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

      1. mul-1-neg 44.1%

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

      2. associate-/l* 55.2%

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

      3. distribute-rgt-neg-in 55.2%

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

      4. mul-1-neg 55.2%

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

      5. associate-*r/ 55.2%

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

      6. neg-mul-1 55.2%

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

   8. Simplified 55.2%

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

   if -6.4000000000000002e-82 < z < 6.59999999999999998e-157 or 1.3500000000000001e-70 < z < 6.80000000000000005e-51

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 77.6%

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

   4. Taylor expanded in t around inf 64.5%

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

   if 6.59999999999999998e-157 < z < 1.3500000000000001e-70 or 1.7999999999999999e85 < z

   1. Initial program 70.1%

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

   3. Taylor expanded in x around 0 50.6%

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

      1. associate-/l* 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in a around 0 50.5%

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

      1. mul-1-neg 50.5%

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

      2. associate-/l* 66.2%

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

      3. distribute-lft-neg-in 66.2%

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

      4. div-sub 66.2%

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

      5. *-inverses 66.2%

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

   8. Simplified 66.2%

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

   9. Taylor expanded in y around 0 62.5%

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

       1. mul-1-neg 62.5%

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

       2. unsub-neg 62.5%

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

       3. associate-*r/ 66.2%

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

   11. Simplified 66.2%

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

   if 6.80000000000000005e-51 < z < 1.7999999999999999e85

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0 44.1%

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

   4. Taylor expanded in x around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. sub-neg 53.5%

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

   6. Simplified 53.5%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-70}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := t - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))) (t_2 (- t (* t (/ y z)))))
   (if (<= z -6.4e-82)
     (/ t (- 1.0 (/ a z)))
     (if (<= z 6.5e-157)
       t_1
       (if (<= z 3.2e-68)
         t_2
         (if (<= z 6.9e-47)
           t_1
           (if (<= z 7e+84) (* x (- 1.0 (/ y a))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = t - (t * (y / z));
	double tmp;
	if (z <= -6.4e-82) {
		tmp = t / (1.0 - (a / z));
	} else if (z <= 6.5e-157) {
		tmp = t_1;
	} else if (z <= 3.2e-68) {
		tmp = t_2;
	} else if (z <= 6.9e-47) {
		tmp = t_1;
	} else if (z <= 7e+84) {
		tmp = x * (1.0 - (y / 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 = x + ((y * t) / a)
    t_2 = t - (t * (y / z))
    if (z <= (-6.4d-82)) then
        tmp = t / (1.0d0 - (a / z))
    else if (z <= 6.5d-157) then
        tmp = t_1
    else if (z <= 3.2d-68) then
        tmp = t_2
    else if (z <= 6.9d-47) then
        tmp = t_1
    else if (z <= 7d+84) then
        tmp = x * (1.0d0 - (y / 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 = x + ((y * t) / a);
	double t_2 = t - (t * (y / z));
	double tmp;
	if (z <= -6.4e-82) {
		tmp = t / (1.0 - (a / z));
	} else if (z <= 6.5e-157) {
		tmp = t_1;
	} else if (z <= 3.2e-68) {
		tmp = t_2;
	} else if (z <= 6.9e-47) {
		tmp = t_1;
	} else if (z <= 7e+84) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	t_2 = t - (t * (y / z))
	tmp = 0
	if z <= -6.4e-82:
		tmp = t / (1.0 - (a / z))
	elif z <= 6.5e-157:
		tmp = t_1
	elif z <= 3.2e-68:
		tmp = t_2
	elif z <= 6.9e-47:
		tmp = t_1
	elif z <= 7e+84:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	t_2 = Float64(t - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -6.4e-82)
		tmp = Float64(t / Float64(1.0 - Float64(a / z)));
	elseif (z <= 6.5e-157)
		tmp = t_1;
	elseif (z <= 3.2e-68)
		tmp = t_2;
	elseif (z <= 6.9e-47)
		tmp = t_1;
	elseif (z <= 7e+84)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	t_2 = t - (t * (y / z));
	tmp = 0.0;
	if (z <= -6.4e-82)
		tmp = t / (1.0 - (a / z));
	elseif (z <= 6.5e-157)
		tmp = t_1;
	elseif (z <= 3.2e-68)
		tmp = t_2;
	elseif (z <= 6.9e-47)
		tmp = t_1;
	elseif (z <= 7e+84)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e-82], N[(t / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-157], t$95$1, If[LessEqual[z, 3.2e-68], t$95$2, If[LessEqual[z, 6.9e-47], t$95$1, If[LessEqual[z, 7e+84], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.4000000000000002e-82

   1. Initial program 70.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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* 69.9%

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

   5. Simplified 69.9%

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

      1. clear-num 69.8%

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

      2. div-inv 69.9%

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

   7. Applied egg-rr 69.9%

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

   8. Taylor expanded in y around 0 55.2%

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

      1. mul-1-neg 55.2%

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

      2. div-sub 55.3%

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

      3. sub-neg 55.3%

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

      4. *-inverses 55.3%

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

      5. metadata-eval 55.3%

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

   10. Simplified 55.3%

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

   if -6.4000000000000002e-82 < z < 6.5000000000000002e-157 or 3.1999999999999999e-68 < z < 6.89999999999999994e-47

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 77.6%

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

   4. Taylor expanded in t around inf 64.5%

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

   if 6.5000000000000002e-157 < z < 3.1999999999999999e-68 or 6.9999999999999998e84 < z

   1. Initial program 70.1%

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

   3. Taylor expanded in x around 0 50.6%

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

      1. associate-/l* 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in a around 0 50.5%

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

      1. mul-1-neg 50.5%

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

      2. associate-/l* 66.2%

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

      3. distribute-lft-neg-in 66.2%

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

      4. div-sub 66.2%

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

      5. *-inverses 66.2%

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

   8. Simplified 66.2%

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

   9. Taylor expanded in y around 0 62.5%

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

       1. mul-1-neg 62.5%

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

       2. unsub-neg 62.5%

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

       3. associate-*r/ 66.2%

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

   11. Simplified 66.2%

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

   if 6.89999999999999994e-47 < z < 6.9999999999999998e84

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0 44.1%

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

   4. Taylor expanded in x around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. sub-neg 53.5%

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

   6. Simplified 53.5%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-68}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-190}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -4.7e-82)
     t_1
     (if (<= z 8.4e-190)
       (+ x (/ (- t x) (/ a y)))
       (if (<= z 2.2e-39)
         (* y (/ (- t x) (- a z)))
         (if (<= z 8e+86) (* x (+ (/ (- y z) (- z a)) 1.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.7e-82) {
		tmp = t_1;
	} else if (z <= 8.4e-190) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 2.2e-39) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 8e+86) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-4.7d-82)) then
        tmp = t_1
    else if (z <= 8.4d-190) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 2.2d-39) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 8d+86) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.7e-82) {
		tmp = t_1;
	} else if (z <= 8.4e-190) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 2.2e-39) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 8e+86) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -4.7e-82:
		tmp = t_1
	elif z <= 8.4e-190:
		tmp = x + ((t - x) / (a / y))
	elif z <= 2.2e-39:
		tmp = y * ((t - x) / (a - z))
	elif z <= 8e+86:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -4.7e-82)
		tmp = t_1;
	elseif (z <= 8.4e-190)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 2.2e-39)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 8e+86)
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -4.7e-82)
		tmp = t_1;
	elseif (z <= 8.4e-190)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 2.2e-39)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 8e+86)
		tmp = x * (((y - z) / (z - a)) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.7e-82], t$95$1, If[LessEqual[z, 8.4e-190], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-39], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+86], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.7000000000000001e-82 or 8.0000000000000001e86 < z

   1. Initial program 69.2%

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

   3. Taylor expanded in x around 0 48.9%

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

      1. associate-/l* 70.0%

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

   5. Simplified 70.0%

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

   if -4.7000000000000001e-82 < z < 8.39999999999999966e-190

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

      2. associate-*l/ 85.8%

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

      3. associate-*r/ 94.2%

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

      4. clear-num 94.2%

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

      5. un-div-inv 95.7%

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

   4. Applied egg-rr 95.7%

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

   5. Taylor expanded in z around 0 90.0%

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

   if 8.39999999999999966e-190 < z < 2.20000000000000001e-39

   1. Initial program 86.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 78.3%

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

   5. Simplified 78.3%

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

   if 2.20000000000000001e-39 < z < 8.0000000000000001e86

   1. Initial program 90.3%

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

   3. Taylor expanded in x around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. unsub-neg 62.6%

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

   5. Simplified 62.6%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-190}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-221}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-32}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ (- y z) a)))))
   (if (<= a -8.8e+133)
     t_1
     (if (<= a -1.3e-221)
       (* t (/ (- y z) (- a z)))
       (if (<= a 8.2e-89)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1.7e-32) (/ (* (- y z) t) (- a z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * ((y - z) / a));
	double tmp;
	if (a <= -8.8e+133) {
		tmp = t_1;
	} else if (a <= -1.3e-221) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 8.2e-89) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.7e-32) {
		tmp = ((y - z) * t) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) * ((y - z) / a))
    if (a <= (-8.8d+133)) then
        tmp = t_1
    else if (a <= (-1.3d-221)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 8.2d-89) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.7d-32) then
        tmp = ((y - z) * t) / (a - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * ((y - z) / a));
	double tmp;
	if (a <= -8.8e+133) {
		tmp = t_1;
	} else if (a <= -1.3e-221) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 8.2e-89) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.7e-32) {
		tmp = ((y - z) * t) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * ((y - z) / a))
	tmp = 0
	if a <= -8.8e+133:
		tmp = t_1
	elif a <= -1.3e-221:
		tmp = t * ((y - z) / (a - z))
	elif a <= 8.2e-89:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.7e-32:
		tmp = ((y - z) * t) / (a - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -8.8e+133)
		tmp = t_1;
	elseif (a <= -1.3e-221)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 8.2e-89)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1.7e-32)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * ((y - z) / a));
	tmp = 0.0;
	if (a <= -8.8e+133)
		tmp = t_1;
	elseif (a <= -1.3e-221)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 8.2e-89)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.7e-32)
		tmp = ((y - z) * t) / (a - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.8e+133], t$95$1, If[LessEqual[a, -1.3e-221], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e-89], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-32], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.8e133 or 1.69999999999999989e-32 < a

   1. Initial program 94.8%

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

   3. Taylor expanded in a around inf 68.3%

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

      1. associate-/l* 83.8%

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

   5. Simplified 83.8%

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

   if -8.8e133 < a < -1.3000000000000001e-221

   1. Initial program 74.3%

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

   3. Taylor expanded in x around 0 53.4%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   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 -1.3000000000000001e-221 < a < 8.1999999999999997e-89

   1. Initial program 72.6%

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

   3. Taylor expanded in y around inf 67.9%

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

      1. div-sub 72.6%

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

   5. Simplified 72.6%

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

   if 8.1999999999999997e-89 < a < 1.69999999999999989e-32

   1. Initial program 67.8%

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

   3. Taylor expanded in x around 0 83.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+133}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-221}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-32}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-5}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-31}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ (- y z) a)))))
   (if (<= a -8.8e+133)
     t_1
     (if (<= a -5.8e+52)
       (/ t (/ (- a z) (- y z)))
       (if (<= a -8.5e-5)
         (- x (* y (/ (- x t) a)))
         (if (<= a 3.8e-31) (+ t (* (/ (- t x) z) (- a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * ((y - z) / a));
	double tmp;
	if (a <= -8.8e+133) {
		tmp = t_1;
	} else if (a <= -5.8e+52) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -8.5e-5) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= 3.8e-31) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) * ((y - z) / a))
    if (a <= (-8.8d+133)) then
        tmp = t_1
    else if (a <= (-5.8d+52)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= (-8.5d-5)) then
        tmp = x - (y * ((x - t) / a))
    else if (a <= 3.8d-31) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * ((y - z) / a));
	double tmp;
	if (a <= -8.8e+133) {
		tmp = t_1;
	} else if (a <= -5.8e+52) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -8.5e-5) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= 3.8e-31) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * ((y - z) / a))
	tmp = 0
	if a <= -8.8e+133:
		tmp = t_1
	elif a <= -5.8e+52:
		tmp = t / ((a - z) / (y - z))
	elif a <= -8.5e-5:
		tmp = x - (y * ((x - t) / a))
	elif a <= 3.8e-31:
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -8.8e+133)
		tmp = t_1;
	elseif (a <= -5.8e+52)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= -8.5e-5)
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	elseif (a <= 3.8e-31)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * ((y - z) / a));
	tmp = 0.0;
	if (a <= -8.8e+133)
		tmp = t_1;
	elseif (a <= -5.8e+52)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= -8.5e-5)
		tmp = x - (y * ((x - t) / a));
	elseif (a <= 3.8e-31)
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.8e+133], t$95$1, If[LessEqual[a, -5.8e+52], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.5e-5], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-31], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.8e133 or 3.8e-31 < a

   1. Initial program 94.8%

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

   3. Taylor expanded in a around inf 68.3%

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

      1. associate-/l* 83.8%

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

   5. Simplified 83.8%

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

   if -8.8e133 < a < -5.8e52

   1. Initial program 84.8%

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

   3. Taylor expanded in x around 0 56.3%

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

      1. associate-/l* 79.8%

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

   5. Simplified 79.8%

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

      1. clear-num 79.9%

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

      2. div-inv 80.2%

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

   7. Applied egg-rr 80.2%

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

   if -5.8e52 < a < -8.500000000000001e-5

   1. Initial program 75.9%

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

   3. Taylor expanded in z around 0 65.1%

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

      1. associate-/l* 76.0%

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

   5. Simplified 76.0%

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

   if -8.500000000000001e-5 < a < 3.8e-31

   1. Initial program 71.0%

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

   3. Taylor expanded in z around inf 80.0%

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

      1. associate--l+ 80.0%

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

      2. distribute-lft-out-- 80.0%

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

      3. div-sub 80.0%

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

      4. mul-1-neg 80.0%

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

      5. unsub-neg 80.0%

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

      6. div-sub 80.0%

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

      7. associate-/l* 83.9%

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

      8. associate-/l* 78.9%

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

      9. distribute-rgt-out-- 84.0%

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

   5. Simplified 84.0%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+133}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-5}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-31}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+216}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= x -6e+74)
     t_2
     (if (<= x 2.1e+22)
       t_1
       (if (<= x 1.08e+71)
         t_2
         (if (<= x 2.9e+216) t_1 (* x (/ (- y a) z))))))))

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 * (1.0 - (y / a));
	double tmp;
	if (x <= -6e+74) {
		tmp = t_2;
	} else if (x <= 2.1e+22) {
		tmp = t_1;
	} else if (x <= 1.08e+71) {
		tmp = t_2;
	} else if (x <= 2.9e+216) {
		tmp = t_1;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    if (x <= (-6d+74)) then
        tmp = t_2
    else if (x <= 2.1d+22) then
        tmp = t_1
    else if (x <= 1.08d+71) then
        tmp = t_2
    else if (x <= 2.9d+216) then
        tmp = t_1
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -6e+74) {
		tmp = t_2;
	} else if (x <= 2.1e+22) {
		tmp = t_1;
	} else if (x <= 1.08e+71) {
		tmp = t_2;
	} else if (x <= 2.9e+216) {
		tmp = t_1;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -6e+74:
		tmp = t_2
	elif x <= 2.1e+22:
		tmp = t_1
	elif x <= 1.08e+71:
		tmp = t_2
	elif x <= 2.9e+216:
		tmp = t_1
	else:
		tmp = x * ((y - a) / z)
	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(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -6e+74)
		tmp = t_2;
	elseif (x <= 2.1e+22)
		tmp = t_1;
	elseif (x <= 1.08e+71)
		tmp = t_2;
	elseif (x <= 2.9e+216)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -6e+74)
		tmp = t_2;
	elseif (x <= 2.1e+22)
		tmp = t_1;
	elseif (x <= 1.08e+71)
		tmp = t_2;
	elseif (x <= 2.9e+216)
		tmp = t_1;
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+74], t$95$2, If[LessEqual[x, 2.1e+22], t$95$1, If[LessEqual[x, 1.08e+71], t$95$2, If[LessEqual[x, 2.9e+216], t$95$1, N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6e74 or 2.0999999999999998e22 < x < 1.08e71

   1. Initial program 86.5%

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

   3. Taylor expanded in z around 0 57.2%

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

   4. Taylor expanded in x around inf 68.9%

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

      1. mul-1-neg 68.9%

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

      2. sub-neg 68.9%

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

   6. Simplified 68.9%

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

   if -6e74 < x < 2.0999999999999998e22 or 1.08e71 < x < 2.9000000000000001e216

   1. Initial program 82.8%

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

   3. Taylor expanded in x around 0 53.1%

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

      1. associate-/l* 67.9%

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

   5. Simplified 67.9%

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

   if 2.9000000000000001e216 < x

   1. Initial program 67.6%

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

   3. Taylor expanded in x around inf 63.3%

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

      1. mul-1-neg 63.3%

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

      2. unsub-neg 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in z around inf 74.7%

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

      1. neg-mul-1 74.7%

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

      2. sub-neg 74.7%

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

      3. mul-1-neg 74.7%

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

   8. Simplified 74.7%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+22}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+216}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-293}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* y (/ (- t x) (- a z)))))
   (if (<= y -8.5e+90)
     t_2
     (if (<= y -3e-209)
       t_1
       (if (<= y -3.2e-293)
         (+ x (/ (* y t) a))
         (if (<= y 7.7e+25) 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 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -8.5e+90) {
		tmp = t_2;
	} else if (y <= -3e-209) {
		tmp = t_1;
	} else if (y <= -3.2e-293) {
		tmp = x + ((y * t) / a);
	} else if (y <= 7.7e+25) {
		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 = y * ((t - x) / (a - z))
    if (y <= (-8.5d+90)) then
        tmp = t_2
    else if (y <= (-3d-209)) then
        tmp = t_1
    else if (y <= (-3.2d-293)) then
        tmp = x + ((y * t) / a)
    else if (y <= 7.7d+25) 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 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -8.5e+90) {
		tmp = t_2;
	} else if (y <= -3e-209) {
		tmp = t_1;
	} else if (y <= -3.2e-293) {
		tmp = x + ((y * t) / a);
	} else if (y <= 7.7e+25) {
		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 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -8.5e+90:
		tmp = t_2
	elif y <= -3e-209:
		tmp = t_1
	elif y <= -3.2e-293:
		tmp = x + ((y * t) / a)
	elif y <= 7.7e+25:
		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(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -8.5e+90)
		tmp = t_2;
	elseif (y <= -3e-209)
		tmp = t_1;
	elseif (y <= -3.2e-293)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (y <= 7.7e+25)
		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 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -8.5e+90)
		tmp = t_2;
	elseif (y <= -3e-209)
		tmp = t_1;
	elseif (y <= -3.2e-293)
		tmp = x + ((y * t) / a);
	elseif (y <= 7.7e+25)
		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[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+90], t$95$2, If[LessEqual[y, -3e-209], t$95$1, If[LessEqual[y, -3.2e-293], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.7e+25], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5000000000000002e90 or 7.70000000000000025e25 < y

   1. Initial program 93.1%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 79.6%

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

   5. Simplified 79.6%

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

   if -8.5000000000000002e90 < y < -2.9999999999999999e-209 or -3.20000000000000005e-293 < y < 7.70000000000000025e25

   1. Initial program 72.2%

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

   3. Taylor expanded in x around 0 49.3%

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

      1. associate-/l* 63.2%

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

   5. Simplified 63.2%

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

   if -2.9999999999999999e-209 < y < -3.20000000000000005e-293

   1. Initial program 78.7%

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

   3. Taylor expanded in z around 0 59.6%

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

   4. Taylor expanded in t around inf 59.6%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-209}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-293}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 63.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{x - t}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{-82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- x t) a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.85e-82)
     t_2
     (if (<= z 2.4e-194)
       t_1
       (if (<= z 6e-42)
         (* y (/ (- t x) (- a z)))
         (if (<= z 3.8e+38) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((x - t) / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.85e-82) {
		tmp = t_2;
	} else if (z <= 2.4e-194) {
		tmp = t_1;
	} else if (z <= 6e-42) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 3.8e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * ((x - t) / a))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-2.85d-82)) then
        tmp = t_2
    else if (z <= 2.4d-194) then
        tmp = t_1
    else if (z <= 6d-42) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 3.8d+38) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((x - t) / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.85e-82) {
		tmp = t_2;
	} else if (z <= 2.4e-194) {
		tmp = t_1;
	} else if (z <= 6e-42) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 3.8e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((x - t) / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -2.85e-82:
		tmp = t_2
	elif z <= 2.4e-194:
		tmp = t_1
	elif z <= 6e-42:
		tmp = y * ((t - x) / (a - z))
	elif z <= 3.8e+38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(x - t) / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.85e-82)
		tmp = t_2;
	elseif (z <= 2.4e-194)
		tmp = t_1;
	elseif (z <= 6e-42)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 3.8e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((x - t) / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -2.85e-82)
		tmp = t_2;
	elseif (z <= 2.4e-194)
		tmp = t_1;
	elseif (z <= 6e-42)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 3.8e+38)
		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[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.85e-82], t$95$2, If[LessEqual[z, 2.4e-194], t$95$1, If[LessEqual[z, 6e-42], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+38], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.85000000000000001e-82 or 3.7999999999999998e38 < z

   1. Initial program 71.4%

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

   3. Taylor expanded in x around 0 47.4%

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

      1. associate-/l* 65.0%

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

   5. Simplified 65.0%

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

   if -2.85000000000000001e-82 < z < 2.4e-194 or 6.00000000000000054e-42 < z < 3.7999999999999998e38

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0 75.6%

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

      1. associate-/l* 87.2%

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

   5. Simplified 87.2%

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

   if 2.4e-194 < z < 6.00000000000000054e-42

   1. Initial program 86.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-194}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+38}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-207}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.35e+44)
   (* t (/ y a))
   (if (<= y -1.06e-207)
     t
     (if (<= y -3.1e-294) x (if (<= y 7.2e+14) t (* x (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.35e+44) {
		tmp = t * (y / a);
	} else if (y <= -1.06e-207) {
		tmp = t;
	} else if (y <= -3.1e-294) {
		tmp = x;
	} else if (y <= 7.2e+14) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.35d+44)) then
        tmp = t * (y / a)
    else if (y <= (-1.06d-207)) then
        tmp = t
    else if (y <= (-3.1d-294)) then
        tmp = x
    else if (y <= 7.2d+14) then
        tmp = t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.35e+44) {
		tmp = t * (y / a);
	} else if (y <= -1.06e-207) {
		tmp = t;
	} else if (y <= -3.1e-294) {
		tmp = x;
	} else if (y <= 7.2e+14) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.35e+44:
		tmp = t * (y / a)
	elif y <= -1.06e-207:
		tmp = t
	elif y <= -3.1e-294:
		tmp = x
	elif y <= 7.2e+14:
		tmp = t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.35e+44)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= -1.06e-207)
		tmp = t;
	elseif (y <= -3.1e-294)
		tmp = x;
	elseif (y <= 7.2e+14)
		tmp = t;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.35e+44)
		tmp = t * (y / a);
	elseif (y <= -1.06e-207)
		tmp = t;
	elseif (y <= -3.1e-294)
		tmp = x;
	elseif (y <= 7.2e+14)
		tmp = t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.35e+44], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.06e-207], t, If[LessEqual[y, -3.1e-294], x, If[LessEqual[y, 7.2e+14], t, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.35e44

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 45.3%

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

      1. associate-/l* 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in z around 0 28.9%

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

      1. associate-/l* 42.8%

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

   8. Simplified 42.8%

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

   if -1.35e44 < y < -1.05999999999999997e-207 or -3.10000000000000003e-294 < y < 7.2e14

   1. Initial program 69.7%

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

   3. Taylor expanded in z around inf 45.3%

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

   if -1.05999999999999997e-207 < y < -3.10000000000000003e-294

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 55.0%

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

   if 7.2e14 < y

   1. Initial program 93.4%

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

   3. Taylor expanded in x around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in a around 0 39.8%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-207}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-209}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -7.6e+43)
   (* t (/ y (- a z)))
   (if (<= y -6.2e-209)
     t
     (if (<= y -2.3e-293) x (if (<= y 7.5e+14) t (* x (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.6e+43) {
		tmp = t * (y / (a - z));
	} else if (y <= -6.2e-209) {
		tmp = t;
	} else if (y <= -2.3e-293) {
		tmp = x;
	} else if (y <= 7.5e+14) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-7.6d+43)) then
        tmp = t * (y / (a - z))
    else if (y <= (-6.2d-209)) then
        tmp = t
    else if (y <= (-2.3d-293)) then
        tmp = x
    else if (y <= 7.5d+14) then
        tmp = t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.6e+43) {
		tmp = t * (y / (a - z));
	} else if (y <= -6.2e-209) {
		tmp = t;
	} else if (y <= -2.3e-293) {
		tmp = x;
	} else if (y <= 7.5e+14) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -7.6e+43:
		tmp = t * (y / (a - z))
	elif y <= -6.2e-209:
		tmp = t
	elif y <= -2.3e-293:
		tmp = x
	elif y <= 7.5e+14:
		tmp = t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -7.6e+43)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (y <= -6.2e-209)
		tmp = t;
	elseif (y <= -2.3e-293)
		tmp = x;
	elseif (y <= 7.5e+14)
		tmp = t;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -7.6e+43)
		tmp = t * (y / (a - z));
	elseif (y <= -6.2e-209)
		tmp = t;
	elseif (y <= -2.3e-293)
		tmp = x;
	elseif (y <= 7.5e+14)
		tmp = t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -7.6e+43], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.2e-209], t, If[LessEqual[y, -2.3e-293], x, If[LessEqual[y, 7.5e+14], t, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.60000000000000016e43

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 45.3%

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

      1. associate-/l* 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in y around inf 39.3%

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

      1. associate-/l* 51.1%

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

   8. Simplified 51.1%

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

   if -7.60000000000000016e43 < y < -6.2e-209 or -2.29999999999999995e-293 < y < 7.5e14

   1. Initial program 69.7%

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

   3. Taylor expanded in z around inf 45.3%

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

   if -6.2e-209 < y < -2.29999999999999995e-293

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 55.0%

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

   if 7.5e14 < y

   1. Initial program 93.4%

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

   3. Taylor expanded in x around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in a around 0 39.8%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-209}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.08e+21)
   t
   (if (<= z 7e-40) (* t (/ y a)) (if (<= z 1.3e+87) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.08e+21) {
		tmp = t;
	} else if (z <= 7e-40) {
		tmp = t * (y / a);
	} else if (z <= 1.3e+87) {
		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 <= (-1.08d+21)) then
        tmp = t
    else if (z <= 7d-40) then
        tmp = t * (y / a)
    else if (z <= 1.3d+87) 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 <= -1.08e+21) {
		tmp = t;
	} else if (z <= 7e-40) {
		tmp = t * (y / a);
	} else if (z <= 1.3e+87) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.08e+21:
		tmp = t
	elif z <= 7e-40:
		tmp = t * (y / a)
	elif z <= 1.3e+87:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.08e+21)
		tmp = t;
	elseif (z <= 7e-40)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 1.3e+87)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.08e+21)
		tmp = t;
	elseif (z <= 7e-40)
		tmp = t * (y / a);
	elseif (z <= 1.3e+87)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.08e+21], t, If[LessEqual[z, 7e-40], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+87], x, t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.08e21 or 1.29999999999999999e87 < z

   1. Initial program 67.0%

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

   3. Taylor expanded in z around inf 54.9%

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

   if -1.08e21 < z < 7.0000000000000003e-40

   1. Initial program 90.8%

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

   3. Taylor expanded in x around 0 41.5%

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

      1. associate-/l* 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in z around 0 27.6%

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

      1. associate-/l* 34.9%

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

   8. Simplified 34.9%

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

   if 7.0000000000000003e-40 < z < 1.29999999999999999e87

   1. Initial program 90.3%

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

   3. Taylor expanded in a around inf 36.0%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-82}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.28e-82) t (if (<= z 5.2e+87) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.28e-82) {
		tmp = t;
	} else if (z <= 5.2e+87) {
		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 <= (-1.28d-82)) then
        tmp = t
    else if (z <= 5.2d+87) 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 <= -1.28e-82) {
		tmp = t;
	} else if (z <= 5.2e+87) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.28e-82:
		tmp = t
	elif z <= 5.2e+87:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.28e-82)
		tmp = t;
	elseif (z <= 5.2e+87)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.28e-82)
		tmp = t;
	elseif (z <= 5.2e+87)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.28e-82], t, If[LessEqual[z, 5.2e+87], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.28e-82 or 5.19999999999999997e87 < z

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf 48.5%

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

   if -1.28e-82 < z < 5.19999999999999997e87

   1. Initial program 92.0%

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

   3. Taylor expanded in a around inf 33.0%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-82}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 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 82.2%

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

3. Taylor expanded in z around inf 25.4%

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

4. Final simplification 25.4%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024075 
(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)))))