Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 68.0% → 90.6%

Time: 28.3s

Alternatives: 27

Speedup: 0.6×

Specification

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 68.0% accurate, 1.0× speedup

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-290}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - z}{y - z}}{x - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -4e-290)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (if (<= t_1 0.0)
       (+ t (* x (/ (- y a) z)))
       (+ x (/ -1.0 (/ (/ (- a z) (- y z)) (- x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -4e-290) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -4e-290)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	else
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(Float64(a - z) / Float64(y - z)) / Float64(x - t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-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[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 / N[(N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.0000000000000003e-290

   1. Initial program 72.8%

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

      1. +-commutative 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-/l* 89.0%

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

      4. fma-define 89.0%

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

   3. Simplified 89.0%

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

   if -4.0000000000000003e-290 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.7%

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

      1. associate-/l* 7.5%

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

   3. Simplified 7.5%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. distribute-lft-out-- 99.5%

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

      3. div-sub 99.6%

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

      4. mul-1-neg 99.6%

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

      5. unsub-neg 99.6%

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

      6. div-sub 99.5%

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

      7. associate-/l* 92.6%

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

      8. associate-/l* 92.7%

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

      9. distribute-rgt-out-- 92.9%

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

   7. Simplified 92.9%

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

   8. Taylor expanded in t around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. associate-/l* 99.7%

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

      3. distribute-lft-neg-in 99.7%

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

   10. Simplified 99.7%

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

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

   1. Initial program 77.5%

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

      1. associate-/l* 88.4%

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

   3. Simplified 88.4%

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

      1. associate-*r/ 77.5%

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

      2. clear-num 77.3%

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

      3. associate-/r* 91.3%

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

   6. Applied egg-rr 91.3%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{y - z}}{t - x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -4 \cdot 10^{-290}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - z}{y - z}}{x - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+285}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -4e-290)
     t_1
     (if (<= t_2 0.0)
       (+ t (* x (/ (- y a) z)))
       (if (<= t_2 2e+285) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -4e-290) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (x * ((y - a) / z));
	} else if (t_2 <= 2e+285) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    t_2 = x + (((y - z) * (t - x)) / (a - z))
    if (t_2 <= (-4d-290)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t + (x * ((y - a) / z))
    else if (t_2 <= 2d+285) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -4e-290) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (x * ((y - a) / z));
	} else if (t_2 <= 2e+285) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -4e-290:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t + (x * ((y - a) / z))
	elif t_2 <= 2e+285:
		tmp = t_2
	else:
		tmp = t_1
	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))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -4e-290)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	elseif (t_2 <= 2e+285)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -4e-290)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t + (x * ((y - a) / z));
	elseif (t_2 <= 2e+285)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-290], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+285], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.0000000000000003e-290 or 2e285 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 64.1%

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

      1. associate-/l* 84.5%

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

   3. Simplified 84.5%

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

   if -4.0000000000000003e-290 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.7%

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

      1. associate-/l* 7.5%

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

   3. Simplified 7.5%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. distribute-lft-out-- 99.5%

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

      3. div-sub 99.6%

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

      4. mul-1-neg 99.6%

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

      5. unsub-neg 99.6%

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

      6. div-sub 99.5%

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

      7. associate-/l* 92.6%

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

      8. associate-/l* 92.7%

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

      9. distribute-rgt-out-- 92.9%

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

   7. Simplified 92.9%

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

   8. Taylor expanded in t around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. associate-/l* 99.7%

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

      3. distribute-lft-neg-in 99.7%

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

   10. Simplified 99.7%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2e285

   1. Initial program 98.3%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -4 \cdot 10^{-290}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{+285}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+285}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) (- t x)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -4e-290)
     t_1
     (if (<= t_2 0.0)
       (+ t (* x (/ (- y a) z)))
       (if (<= t_2 2e+285) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -4e-290) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (x * ((y - a) / z));
	} else if (t_2 <= 2e+285) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) / ((a - z) / (t - x)))
    t_2 = x + (((y - z) * (t - x)) / (a - z))
    if (t_2 <= (-4d-290)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t + (x * ((y - a) / z))
    else if (t_2 <= 2d+285) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -4e-290) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (x * ((y - a) / z));
	} else if (t_2 <= 2e+285) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / (t - x)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -4e-290:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t + (x * ((y - a) / z))
	elif t_2 <= 2e+285:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -4e-290)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	elseif (t_2 <= 2e+285)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((a - z) / (t - x)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -4e-290)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t + (x * ((y - a) / z));
	elseif (t_2 <= 2e+285)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-290], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+285], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.0000000000000003e-290 or 2e285 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 64.1%

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

      1. associate-/l* 84.5%

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

   3. Simplified 84.5%

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

      1. clear-num 84.5%

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

      2. un-div-inv 84.6%

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

   6. Applied egg-rr 84.6%

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

   if -4.0000000000000003e-290 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.7%

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

      1. associate-/l* 7.5%

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

   3. Simplified 7.5%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. distribute-lft-out-- 99.5%

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

      3. div-sub 99.6%

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

      4. mul-1-neg 99.6%

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

      5. unsub-neg 99.6%

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

      6. div-sub 99.5%

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

      7. associate-/l* 92.6%

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

      8. associate-/l* 92.7%

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

      9. distribute-rgt-out-- 92.9%

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

   7. Simplified 92.9%

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

   8. Taylor expanded in t around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. associate-/l* 99.7%

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

      3. distribute-lft-neg-in 99.7%

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

   10. Simplified 99.7%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2e285

   1. Initial program 98.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -4 \cdot 10^{-290}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{+285}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-290} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - z}{y - z}}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -4e-290) (not (<= t_1 0.0)))
     (+ x (/ -1.0 (/ (/ (- a z) (- y z)) (- x t))))
     (+ t (* x (/ (- y a) 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 <= -4e-290) || !(t_1 <= 0.0)) {
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)));
	} else {
		tmp = t + (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) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-4d-290)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((-1.0d0) / (((a - z) / (y - z)) / (x - t)))
    else
        tmp = t + (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 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -4e-290) || !(t_1 <= 0.0)) {
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)));
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -4e-290) or not (t_1 <= 0.0):
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)))
	else:
		tmp = t + (x * ((y - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -4e-290) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(Float64(a - z) / Float64(y - z)) / Float64(x - t))));
	else
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -4e-290) || ~((t_1 <= 0.0)))
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)));
	else
		tmp = t + (x * ((y - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-290], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(-1.0 / N[(N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.0000000000000003e-290 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 75.2%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

      1. associate-*r/ 75.2%

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

      2. clear-num 75.1%

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

      3. associate-/r* 90.1%

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

   6. Applied egg-rr 90.1%

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

   if -4.0000000000000003e-290 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.7%

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

      1. associate-/l* 7.5%

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

   3. Simplified 7.5%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. distribute-lft-out-- 99.5%

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

      3. div-sub 99.6%

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

      4. mul-1-neg 99.6%

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

      5. unsub-neg 99.6%

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

      6. div-sub 99.5%

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

      7. associate-/l* 92.6%

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

      8. associate-/l* 92.7%

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

      9. distribute-rgt-out-- 92.9%

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

   7. Simplified 92.9%

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

   8. Taylor expanded in t around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. associate-/l* 99.7%

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

      3. distribute-lft-neg-in 99.7%

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

   10. Simplified 99.7%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -4 \cdot 10^{-290} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - z}{y - z}}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 41.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z}{z - a}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-189}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-245}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ z (- z a)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -1.25e+90)
     t_2
     (if (<= a -4.2e-80)
       (* t (/ (- y z) a))
       (if (<= a -2.3e-189)
         t
         (if (<= a -2.85e-245)
           (/ (* x y) z)
           (if (<= a 9.5e-273)
             t_1
             (if (<= a 2.9e-60)
               (* x (/ (- y a) z))
               (if (<= a 9.5e+63) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.25e+90) {
		tmp = t_2;
	} else if (a <= -4.2e-80) {
		tmp = t * ((y - z) / a);
	} else if (a <= -2.3e-189) {
		tmp = t;
	} else if (a <= -2.85e-245) {
		tmp = (x * y) / z;
	} else if (a <= 9.5e-273) {
		tmp = t_1;
	} else if (a <= 2.9e-60) {
		tmp = x * ((y - a) / z);
	} else if (a <= 9.5e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (z / (z - a))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-1.25d+90)) then
        tmp = t_2
    else if (a <= (-4.2d-80)) then
        tmp = t * ((y - z) / a)
    else if (a <= (-2.3d-189)) then
        tmp = t
    else if (a <= (-2.85d-245)) then
        tmp = (x * y) / z
    else if (a <= 9.5d-273) then
        tmp = t_1
    else if (a <= 2.9d-60) then
        tmp = x * ((y - a) / z)
    else if (a <= 9.5d+63) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.25e+90) {
		tmp = t_2;
	} else if (a <= -4.2e-80) {
		tmp = t * ((y - z) / a);
	} else if (a <= -2.3e-189) {
		tmp = t;
	} else if (a <= -2.85e-245) {
		tmp = (x * y) / z;
	} else if (a <= 9.5e-273) {
		tmp = t_1;
	} else if (a <= 2.9e-60) {
		tmp = x * ((y - a) / z);
	} else if (a <= 9.5e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (z / (z - a))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -1.25e+90:
		tmp = t_2
	elif a <= -4.2e-80:
		tmp = t * ((y - z) / a)
	elif a <= -2.3e-189:
		tmp = t
	elif a <= -2.85e-245:
		tmp = (x * y) / z
	elif a <= 9.5e-273:
		tmp = t_1
	elif a <= 2.9e-60:
		tmp = x * ((y - a) / z)
	elif a <= 9.5e+63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z / Float64(z - a)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -1.25e+90)
		tmp = t_2;
	elseif (a <= -4.2e-80)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (a <= -2.3e-189)
		tmp = t;
	elseif (a <= -2.85e-245)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 9.5e-273)
		tmp = t_1;
	elseif (a <= 2.9e-60)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 9.5e+63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z / (z - a));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -1.25e+90)
		tmp = t_2;
	elseif (a <= -4.2e-80)
		tmp = t * ((y - z) / a);
	elseif (a <= -2.3e-189)
		tmp = t;
	elseif (a <= -2.85e-245)
		tmp = (x * y) / z;
	elseif (a <= 9.5e-273)
		tmp = t_1;
	elseif (a <= 2.9e-60)
		tmp = x * ((y - a) / z);
	elseif (a <= 9.5e+63)
		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[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e+90], t$95$2, If[LessEqual[a, -4.2e-80], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.3e-189], t, If[LessEqual[a, -2.85e-245], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 9.5e-273], t$95$1, If[LessEqual[a, 2.9e-60], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+63], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.2500000000000001e90 or 9.5000000000000003e63 < a

   1. Initial program 71.4%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in z around 0 58.1%

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

      1. associate-/l* 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in x around inf 58.6%

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

      1. mul-1-neg 58.6%

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

      2. unsub-neg 58.6%

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

   10. Simplified 58.6%

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

   if -1.2500000000000001e90 < a < -4.20000000000000003e-80

   1. Initial program 79.3%

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

      1. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in a around inf 61.3%

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

      1. +-commutative 61.3%

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

      2. associate-/l* 61.4%

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

      3. fma-define 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in t around inf 45.9%

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

      1. div-sub 45.9%

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

   10. Simplified 45.9%

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

   if -4.20000000000000003e-80 < a < -2.2999999999999998e-189

   1. Initial program 57.4%

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

      1. associate-/l* 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in z around inf 50.3%

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

   if -2.2999999999999998e-189 < a < -2.85e-245

   1. Initial program 54.4%

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

      1. associate-/l* 55.0%

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

   3. Simplified 55.0%

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

   5. Taylor expanded in z around inf 90.7%

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

      1. associate--l+ 90.7%

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

      2. distribute-lft-out-- 90.7%

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

      3. div-sub 90.7%

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

      4. mul-1-neg 90.7%

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

      5. unsub-neg 90.7%

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

      6. div-sub 90.7%

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

      7. associate-/l* 90.9%

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

      8. associate-/l* 80.0%

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

      9. distribute-rgt-out-- 90.9%

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

   7. Simplified 90.9%

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

   8. Taylor expanded in t around 0 70.8%

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

   9. Taylor expanded in y around inf 70.8%

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

       1. *-commutative 70.8%

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

   11. Simplified 70.8%

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

   if -2.85e-245 < a < 9.49999999999999925e-273 or 2.8999999999999999e-60 < a < 9.5000000000000003e63

   1. Initial program 67.1%

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

      1. associate-/l* 70.1%

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

   3. Simplified 70.1%

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

      1. associate-*r/ 67.1%

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

      2. clear-num 66.8%

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

      3. associate-/r* 74.8%

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

   6. Applied egg-rr 74.8%

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

   7. Taylor expanded in y around 0 48.1%

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

      1. associate-*r/ 48.1%

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

      2. neg-mul-1 48.1%

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

   9. Simplified 48.1%

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

   10. Taylor expanded in x around 0 47.0%

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

       1. associate-/l* 53.8%

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

   12. Simplified 53.8%

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

   if 9.49999999999999925e-273 < a < 2.8999999999999999e-60

   1. Initial program 60.6%

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

      1. associate-/l* 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in z around inf 79.3%

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

      1. associate--l+ 79.3%

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

      2. distribute-lft-out-- 79.3%

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

      3. div-sub 79.3%

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

      4. mul-1-neg 79.3%

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

      5. unsub-neg 79.3%

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

      6. div-sub 79.3%

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

      7. associate-/l* 80.8%

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

      8. associate-/l* 76.7%

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

      9. distribute-rgt-out-- 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in t around 0 42.1%

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

      1. associate-/l* 44.0%

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

   10. Simplified 44.0%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-189}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-245}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-273}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+99}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 210000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+117}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))) (t_2 (* t (/ z (- z a)))))
   (if (<= z -1.15e+99)
     t_2
     (if (<= z 1.05e-71)
       t_1
       (if (<= z 1.15e-28)
         (* x (/ y z))
         (if (<= z 210000000000.0)
           t_1
           (if (<= z 2.8e+67)
             t_2
             (if (<= z 2.4e+117)
               (- x (/ (* z t) a))
               (if (<= z 6.6e+137) (* x (/ (- y a) z)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -1.15e+99) {
		tmp = t_2;
	} else if (z <= 1.05e-71) {
		tmp = t_1;
	} else if (z <= 1.15e-28) {
		tmp = x * (y / z);
	} else if (z <= 210000000000.0) {
		tmp = t_1;
	} else if (z <= 2.8e+67) {
		tmp = t_2;
	} else if (z <= 2.4e+117) {
		tmp = x - ((z * t) / a);
	} else if (z <= 6.6e+137) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (t / a))
    t_2 = t * (z / (z - a))
    if (z <= (-1.15d+99)) then
        tmp = t_2
    else if (z <= 1.05d-71) then
        tmp = t_1
    else if (z <= 1.15d-28) then
        tmp = x * (y / z)
    else if (z <= 210000000000.0d0) then
        tmp = t_1
    else if (z <= 2.8d+67) then
        tmp = t_2
    else if (z <= 2.4d+117) then
        tmp = x - ((z * t) / a)
    else if (z <= 6.6d+137) then
        tmp = x * ((y - a) / z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -1.15e+99) {
		tmp = t_2;
	} else if (z <= 1.05e-71) {
		tmp = t_1;
	} else if (z <= 1.15e-28) {
		tmp = x * (y / z);
	} else if (z <= 210000000000.0) {
		tmp = t_1;
	} else if (z <= 2.8e+67) {
		tmp = t_2;
	} else if (z <= 2.4e+117) {
		tmp = x - ((z * t) / a);
	} else if (z <= 6.6e+137) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	t_2 = t * (z / (z - a))
	tmp = 0
	if z <= -1.15e+99:
		tmp = t_2
	elif z <= 1.05e-71:
		tmp = t_1
	elif z <= 1.15e-28:
		tmp = x * (y / z)
	elif z <= 210000000000.0:
		tmp = t_1
	elif z <= 2.8e+67:
		tmp = t_2
	elif z <= 2.4e+117:
		tmp = x - ((z * t) / a)
	elif z <= 6.6e+137:
		tmp = x * ((y - a) / z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	t_2 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -1.15e+99)
		tmp = t_2;
	elseif (z <= 1.05e-71)
		tmp = t_1;
	elseif (z <= 1.15e-28)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 210000000000.0)
		tmp = t_1;
	elseif (z <= 2.8e+67)
		tmp = t_2;
	elseif (z <= 2.4e+117)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	elseif (z <= 6.6e+137)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	t_2 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -1.15e+99)
		tmp = t_2;
	elseif (z <= 1.05e-71)
		tmp = t_1;
	elseif (z <= 1.15e-28)
		tmp = x * (y / z);
	elseif (z <= 210000000000.0)
		tmp = t_1;
	elseif (z <= 2.8e+67)
		tmp = t_2;
	elseif (z <= 2.4e+117)
		tmp = x - ((z * t) / a);
	elseif (z <= 6.6e+137)
		tmp = x * ((y - a) / z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+99], t$95$2, If[LessEqual[z, 1.05e-71], t$95$1, If[LessEqual[z, 1.15e-28], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 210000000000.0], t$95$1, If[LessEqual[z, 2.8e+67], t$95$2, If[LessEqual[z, 2.4e+117], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+137], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.1500000000000001e99 or 2.1e11 < z < 2.7999999999999998e67 or 6.60000000000000005e137 < z

   1. Initial program 42.6%

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

      1. associate-/l* 61.0%

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

   3. Simplified 61.0%

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

      1. associate-*r/ 42.6%

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

      2. clear-num 42.3%

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

      3. associate-/r* 66.9%

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

   6. Applied egg-rr 66.9%

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

   7. Taylor expanded in y around 0 52.2%

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

      1. associate-*r/ 52.2%

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

      2. neg-mul-1 52.2%

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

   9. Simplified 52.2%

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

   10. Taylor expanded in x around 0 43.4%

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

       1. associate-/l* 60.9%

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

   12. Simplified 60.9%

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

   if -1.1500000000000001e99 < z < 1.0500000000000001e-71 or 1.14999999999999993e-28 < z < 2.1e11

   1. Initial program 83.5%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around 0 64.2%

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

      1. associate-/l* 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in t around inf 55.3%

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

   if 1.0500000000000001e-71 < z < 1.14999999999999993e-28

   1. Initial program 79.2%

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

      1. associate-/l* 79.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in z around inf 58.1%

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

      1. associate--l+ 58.1%

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

      2. distribute-lft-out-- 58.1%

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

      3. div-sub 58.3%

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

      4. mul-1-neg 58.3%

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

      5. unsub-neg 58.3%

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

      6. div-sub 58.1%

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

      7. associate-/l* 57.8%

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

      8. associate-/l* 57.8%

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

      9. distribute-rgt-out-- 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in t around 0 51.6%

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

   9. Taylor expanded in y around inf 52.0%

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

       1. associate-/l* 58.7%

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

   11. Simplified 58.7%

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

   if 2.7999999999999998e67 < z < 2.3999999999999999e117

   1. Initial program 60.8%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in a around inf 28.5%

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

      1. +-commutative 28.5%

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

      2. associate-/l* 46.3%

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

      3. fma-define 46.3%

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

   7. Simplified 46.3%

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

   8. Taylor expanded in y around 0 34.7%

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

      1. mul-1-neg 34.7%

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

      2. unsub-neg 34.7%

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

   10. Simplified 34.7%

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

   11. Taylor expanded in t around inf 44.9%

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

   if 2.3999999999999999e117 < z < 6.60000000000000005e137

   1. Initial program 45.7%

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

      1. associate-/l* 45.9%

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

   3. Simplified 45.9%

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

   5. Taylor expanded in z around inf 56.9%

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

      1. associate--l+ 56.9%

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

      2. distribute-lft-out-- 56.9%

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

      3. div-sub 57.1%

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

      4. mul-1-neg 57.1%

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

      5. unsub-neg 57.1%

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

      6. div-sub 56.9%

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

      7. associate-/l* 56.7%

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

      8. associate-/l* 67.8%

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

      9. distribute-rgt-out-- 67.8%

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

   7. Simplified 67.8%

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

   8. Taylor expanded in t around 0 58.1%

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

      1. associate-/l* 58.2%

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

   10. Simplified 58.2%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+99}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-71}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 210000000000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+117}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1060000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+99} \lor \neg \left(z \leq 6.4 \cdot 10^{+137}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))) (t_2 (* t (/ z (- z a)))))
   (if (<= z -3.7e+87)
     t_2
     (if (<= z 1.05e-71)
       t_1
       (if (<= z 9e-30)
         (* x (/ y z))
         (if (<= z 1060000000000.0)
           t_1
           (if (or (<= z 2e+99) (not (<= z 6.4e+137)))
             t_2
             (* x (/ (- y a) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -3.7e+87) {
		tmp = t_2;
	} else if (z <= 1.05e-71) {
		tmp = t_1;
	} else if (z <= 9e-30) {
		tmp = x * (y / z);
	} else if (z <= 1060000000000.0) {
		tmp = t_1;
	} else if ((z <= 2e+99) || !(z <= 6.4e+137)) {
		tmp = t_2;
	} 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 = x + (y * (t / a))
    t_2 = t * (z / (z - a))
    if (z <= (-3.7d+87)) then
        tmp = t_2
    else if (z <= 1.05d-71) then
        tmp = t_1
    else if (z <= 9d-30) then
        tmp = x * (y / z)
    else if (z <= 1060000000000.0d0) then
        tmp = t_1
    else if ((z <= 2d+99) .or. (.not. (z <= 6.4d+137))) then
        tmp = t_2
    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 = x + (y * (t / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -3.7e+87) {
		tmp = t_2;
	} else if (z <= 1.05e-71) {
		tmp = t_1;
	} else if (z <= 9e-30) {
		tmp = x * (y / z);
	} else if (z <= 1060000000000.0) {
		tmp = t_1;
	} else if ((z <= 2e+99) || !(z <= 6.4e+137)) {
		tmp = t_2;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	t_2 = t * (z / (z - a))
	tmp = 0
	if z <= -3.7e+87:
		tmp = t_2
	elif z <= 1.05e-71:
		tmp = t_1
	elif z <= 9e-30:
		tmp = x * (y / z)
	elif z <= 1060000000000.0:
		tmp = t_1
	elif (z <= 2e+99) or not (z <= 6.4e+137):
		tmp = t_2
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	t_2 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -3.7e+87)
		tmp = t_2;
	elseif (z <= 1.05e-71)
		tmp = t_1;
	elseif (z <= 9e-30)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 1060000000000.0)
		tmp = t_1;
	elseif ((z <= 2e+99) || !(z <= 6.4e+137))
		tmp = t_2;
	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 = x + (y * (t / a));
	t_2 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -3.7e+87)
		tmp = t_2;
	elseif (z <= 1.05e-71)
		tmp = t_1;
	elseif (z <= 9e-30)
		tmp = x * (y / z);
	elseif (z <= 1060000000000.0)
		tmp = t_1;
	elseif ((z <= 2e+99) || ~((z <= 6.4e+137)))
		tmp = t_2;
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e+87], t$95$2, If[LessEqual[z, 1.05e-71], t$95$1, If[LessEqual[z, 9e-30], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1060000000000.0], t$95$1, If[Or[LessEqual[z, 2e+99], N[Not[LessEqual[z, 6.4e+137]], $MachinePrecision]], t$95$2, N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.70000000000000003e87 or 1.06e12 < z < 1.9999999999999999e99 or 6.40000000000000038e137 < z

   1. Initial program 43.3%

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

      1. associate-/l* 62.6%

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

   3. Simplified 62.6%

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

      1. associate-*r/ 43.3%

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

      2. clear-num 43.0%

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

      3. associate-/r* 68.0%

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

   6. Applied egg-rr 68.0%

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

   7. Taylor expanded in y around 0 51.0%

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

      1. associate-*r/ 51.0%

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

      2. neg-mul-1 51.0%

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

   9. Simplified 51.0%

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

   10. Taylor expanded in x around 0 42.8%

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

       1. associate-/l* 59.1%

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

   12. Simplified 59.1%

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

   if -3.70000000000000003e87 < z < 1.0500000000000001e-71 or 8.99999999999999935e-30 < z < 1.06e12

   1. Initial program 83.5%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around 0 64.2%

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

      1. associate-/l* 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in t around inf 55.3%

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

   if 1.0500000000000001e-71 < z < 8.99999999999999935e-30

   1. Initial program 79.2%

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

      1. associate-/l* 79.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in z around inf 58.1%

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

      1. associate--l+ 58.1%

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

      2. distribute-lft-out-- 58.1%

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

      3. div-sub 58.3%

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

      4. mul-1-neg 58.3%

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

      5. unsub-neg 58.3%

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

      6. div-sub 58.1%

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

      7. associate-/l* 57.8%

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

      8. associate-/l* 57.8%

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

      9. distribute-rgt-out-- 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in t around 0 51.6%

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

   9. Taylor expanded in y around inf 52.0%

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

       1. associate-/l* 58.7%

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

   11. Simplified 58.7%

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

   if 1.9999999999999999e99 < z < 6.40000000000000038e137

   1. Initial program 56.1%

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

      1. associate-/l* 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in z around inf 57.1%

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

      1. associate--l+ 57.1%

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

      2. distribute-lft-out-- 57.1%

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

      3. div-sub 57.2%

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

      4. mul-1-neg 57.2%

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

      5. unsub-neg 57.2%

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

      6. div-sub 57.1%

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

      7. associate-/l* 57.1%

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

      8. associate-/l* 62.8%

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

      9. distribute-rgt-out-- 62.8%

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

   7. Simplified 62.8%

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

   8. Taylor expanded in t around 0 36.3%

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

      1. associate-/l* 36.5%

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

   10. Simplified 36.5%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-71}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1060000000000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+99} \lor \neg \left(z \leq 6.4 \cdot 10^{+137}\right):\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 700000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+52} \lor \neg \left(z \leq 1.1 \cdot 10^{+125}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))) (t_2 (* t (/ z (- z a)))))
   (if (<= z -1.02e+82)
     t_2
     (if (<= z 1.05e-71)
       t_1
       (if (<= z 7.4e-30)
         (* x (/ y z))
         (if (<= z 700000000000.0)
           t_1
           (if (or (<= z 1.25e+52) (not (<= z 1.1e+125)))
             t_2
             (* y (/ (- x t) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -1.02e+82) {
		tmp = t_2;
	} else if (z <= 1.05e-71) {
		tmp = t_1;
	} else if (z <= 7.4e-30) {
		tmp = x * (y / z);
	} else if (z <= 700000000000.0) {
		tmp = t_1;
	} else if ((z <= 1.25e+52) || !(z <= 1.1e+125)) {
		tmp = t_2;
	} else {
		tmp = y * ((x - t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (t / a))
    t_2 = t * (z / (z - a))
    if (z <= (-1.02d+82)) then
        tmp = t_2
    else if (z <= 1.05d-71) then
        tmp = t_1
    else if (z <= 7.4d-30) then
        tmp = x * (y / z)
    else if (z <= 700000000000.0d0) then
        tmp = t_1
    else if ((z <= 1.25d+52) .or. (.not. (z <= 1.1d+125))) then
        tmp = t_2
    else
        tmp = y * ((x - t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -1.02e+82) {
		tmp = t_2;
	} else if (z <= 1.05e-71) {
		tmp = t_1;
	} else if (z <= 7.4e-30) {
		tmp = x * (y / z);
	} else if (z <= 700000000000.0) {
		tmp = t_1;
	} else if ((z <= 1.25e+52) || !(z <= 1.1e+125)) {
		tmp = t_2;
	} else {
		tmp = y * ((x - t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	t_2 = t * (z / (z - a))
	tmp = 0
	if z <= -1.02e+82:
		tmp = t_2
	elif z <= 1.05e-71:
		tmp = t_1
	elif z <= 7.4e-30:
		tmp = x * (y / z)
	elif z <= 700000000000.0:
		tmp = t_1
	elif (z <= 1.25e+52) or not (z <= 1.1e+125):
		tmp = t_2
	else:
		tmp = y * ((x - t) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	t_2 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -1.02e+82)
		tmp = t_2;
	elseif (z <= 1.05e-71)
		tmp = t_1;
	elseif (z <= 7.4e-30)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 700000000000.0)
		tmp = t_1;
	elseif ((z <= 1.25e+52) || !(z <= 1.1e+125))
		tmp = t_2;
	else
		tmp = Float64(y * Float64(Float64(x - t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	t_2 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -1.02e+82)
		tmp = t_2;
	elseif (z <= 1.05e-71)
		tmp = t_1;
	elseif (z <= 7.4e-30)
		tmp = x * (y / z);
	elseif (z <= 700000000000.0)
		tmp = t_1;
	elseif ((z <= 1.25e+52) || ~((z <= 1.1e+125)))
		tmp = t_2;
	else
		tmp = y * ((x - t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+82], t$95$2, If[LessEqual[z, 1.05e-71], t$95$1, If[LessEqual[z, 7.4e-30], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 700000000000.0], t$95$1, If[Or[LessEqual[z, 1.25e+52], N[Not[LessEqual[z, 1.1e+125]], $MachinePrecision]], t$95$2, N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.0200000000000001e82 or 7e11 < z < 1.25e52 or 1.09999999999999995e125 < z

   1. Initial program 42.3%

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

      1. associate-/l* 60.1%

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

   3. Simplified 60.1%

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

      1. associate-*r/ 42.3%

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

      2. clear-num 42.0%

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

      3. associate-/r* 65.8%

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

   6. Applied egg-rr 65.8%

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

   7. Taylor expanded in y around 0 51.6%

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

      1. associate-*r/ 51.6%

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

      2. neg-mul-1 51.6%

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

   9. Simplified 51.6%

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

   10. Taylor expanded in x around 0 42.0%

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

       1. associate-/l* 58.9%

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

   12. Simplified 58.9%

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

   if -1.0200000000000001e82 < z < 1.0500000000000001e-71 or 7.4000000000000006e-30 < z < 7e11

   1. Initial program 83.5%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around 0 64.2%

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

      1. associate-/l* 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in t around inf 55.3%

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

   if 1.0500000000000001e-71 < z < 7.4000000000000006e-30

   1. Initial program 79.2%

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

      1. associate-/l* 79.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in z around inf 58.1%

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

      1. associate--l+ 58.1%

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

      2. distribute-lft-out-- 58.1%

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

      3. div-sub 58.3%

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

      4. mul-1-neg 58.3%

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

      5. unsub-neg 58.3%

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

      6. div-sub 58.1%

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

      7. associate-/l* 57.8%

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

      8. associate-/l* 57.8%

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

      9. distribute-rgt-out-- 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in t around 0 51.6%

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

   9. Taylor expanded in y around inf 52.0%

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

       1. associate-/l* 58.7%

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

   11. Simplified 58.7%

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

   if 1.25e52 < z < 1.09999999999999995e125

   1. Initial program 58.2%

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

      1. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 54.1%

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

      1. associate--l+ 54.1%

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

      2. distribute-lft-out-- 54.1%

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

      3. div-sub 54.1%

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

      4. mul-1-neg 54.1%

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

      5. unsub-neg 54.1%

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

      6. div-sub 54.1%

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

      7. associate-/l* 58.6%

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

      8. associate-/l* 63.4%

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

      9. distribute-rgt-out-- 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in y around -inf 42.9%

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

      1. mul-1-neg 42.9%

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

      2. associate-/l* 47.3%

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

      3. distribute-rgt-neg-in 47.3%

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

      4. distribute-neg-frac2 47.3%

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

   10. Simplified 47.3%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-71}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 700000000000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+52} \lor \neg \left(z \leq 1.1 \cdot 10^{+125}\right):\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{z}{z - a}\\ t_3 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -5.9 \cdot 10^{+91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-177}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 22000000000:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a))))
        (t_2 (* t (/ z (- z a))))
        (t_3 (* t (/ (- y z) a))))
   (if (<= z -5.9e+91)
     t_2
     (if (<= z 4.8e-229)
       t_1
       (if (<= z 7.4e-177)
         t_3
         (if (<= z 7.4e-72)
           t_1
           (if (<= z 5.8e-31)
             (* x (/ y z))
             (if (<= z 22000000000.0) t_3 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 * (z / (z - a));
	double t_3 = t * ((y - z) / a);
	double tmp;
	if (z <= -5.9e+91) {
		tmp = t_2;
	} else if (z <= 4.8e-229) {
		tmp = t_1;
	} else if (z <= 7.4e-177) {
		tmp = t_3;
	} else if (z <= 7.4e-72) {
		tmp = t_1;
	} else if (z <= 5.8e-31) {
		tmp = x * (y / z);
	} else if (z <= 22000000000.0) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = t * (z / (z - a))
    t_3 = t * ((y - z) / a)
    if (z <= (-5.9d+91)) then
        tmp = t_2
    else if (z <= 4.8d-229) then
        tmp = t_1
    else if (z <= 7.4d-177) then
        tmp = t_3
    else if (z <= 7.4d-72) then
        tmp = t_1
    else if (z <= 5.8d-31) then
        tmp = x * (y / z)
    else if (z <= 22000000000.0d0) then
        tmp = t_3
    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 * (z / (z - a));
	double t_3 = t * ((y - z) / a);
	double tmp;
	if (z <= -5.9e+91) {
		tmp = t_2;
	} else if (z <= 4.8e-229) {
		tmp = t_1;
	} else if (z <= 7.4e-177) {
		tmp = t_3;
	} else if (z <= 7.4e-72) {
		tmp = t_1;
	} else if (z <= 5.8e-31) {
		tmp = x * (y / z);
	} else if (z <= 22000000000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * (z / (z - a))
	t_3 = t * ((y - z) / a)
	tmp = 0
	if z <= -5.9e+91:
		tmp = t_2
	elif z <= 4.8e-229:
		tmp = t_1
	elif z <= 7.4e-177:
		tmp = t_3
	elif z <= 7.4e-72:
		tmp = t_1
	elif z <= 5.8e-31:
		tmp = x * (y / z)
	elif z <= 22000000000.0:
		tmp = t_3
	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(z / Float64(z - a)))
	t_3 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (z <= -5.9e+91)
		tmp = t_2;
	elseif (z <= 4.8e-229)
		tmp = t_1;
	elseif (z <= 7.4e-177)
		tmp = t_3;
	elseif (z <= 7.4e-72)
		tmp = t_1;
	elseif (z <= 5.8e-31)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 22000000000.0)
		tmp = t_3;
	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 * (z / (z - a));
	t_3 = t * ((y - z) / a);
	tmp = 0.0;
	if (z <= -5.9e+91)
		tmp = t_2;
	elseif (z <= 4.8e-229)
		tmp = t_1;
	elseif (z <= 7.4e-177)
		tmp = t_3;
	elseif (z <= 7.4e-72)
		tmp = t_1;
	elseif (z <= 5.8e-31)
		tmp = x * (y / z);
	elseif (z <= 22000000000.0)
		tmp = t_3;
	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[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.9e+91], t$95$2, If[LessEqual[z, 4.8e-229], t$95$1, If[LessEqual[z, 7.4e-177], t$95$3, If[LessEqual[z, 7.4e-72], t$95$1, If[LessEqual[z, 5.8e-31], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 22000000000.0], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.9000000000000002e91 or 2.2e10 < z

   1. Initial program 45.5%

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

      1. associate-/l* 63.4%

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

   3. Simplified 63.4%

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

      1. associate-*r/ 45.5%

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

      2. clear-num 45.2%

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

      3. associate-/r* 67.9%

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

   6. Applied egg-rr 67.9%

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

   7. Taylor expanded in y around 0 49.2%

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

      1. associate-*r/ 49.2%

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

      2. neg-mul-1 49.2%

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

   9. Simplified 49.2%

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

   10. Taylor expanded in x around 0 37.8%

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

       1. associate-/l* 51.4%

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

   12. Simplified 51.4%

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

   if -5.9000000000000002e91 < z < 4.8e-229 or 7.39999999999999986e-177 < z < 7.3999999999999997e-72

   1. Initial program 84.3%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around 0 65.5%

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

      1. associate-/l* 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in x around inf 50.2%

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

      1. mul-1-neg 50.2%

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

      2. unsub-neg 50.2%

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

   10. Simplified 50.2%

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

   if 4.8e-229 < z < 7.39999999999999986e-177 or 5.8000000000000001e-31 < z < 2.2e10

   1. Initial program 79.1%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in a around inf 62.9%

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

      1. +-commutative 62.9%

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

      2. associate-/l* 78.3%

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

      3. fma-define 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in t around inf 68.7%

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

      1. div-sub 68.7%

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

   10. Simplified 68.7%

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

   if 7.3999999999999997e-72 < z < 5.8000000000000001e-31

   1. Initial program 77.6%

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

      1. associate-/l* 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in z around inf 62.5%

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

      1. associate--l+ 62.5%

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

      2. distribute-lft-out-- 62.5%

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

      3. div-sub 62.8%

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

      4. mul-1-neg 62.8%

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

      5. unsub-neg 62.8%

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

      6. div-sub 62.5%

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

      7. associate-/l* 62.3%

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

      8. associate-/l* 62.3%

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

      9. distribute-rgt-out-- 62.5%

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

   7. Simplified 62.5%

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

   8. Taylor expanded in t around 0 55.6%

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

   9. Taylor expanded in y around inf 55.9%

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

       1. associate-/l* 63.1%

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

   11. Simplified 63.1%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-177}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 22000000000:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+166}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -5.6e+94)
     (+ x (* y (/ (- t x) a)))
     (if (<= a -1.22e-136)
       t_1
       (if (<= a 1.65e-72)
         (+ t (/ (* y (- x t)) z))
         (if (<= a 1.85e+66)
           t_1
           (if (<= a 4e+166)
             (- x (/ (* z t) a))
             (+ x (/ y (/ a (- t x)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -5.6e+94) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -1.22e-136) {
		tmp = t_1;
	} else if (a <= 1.65e-72) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.85e+66) {
		tmp = t_1;
	} else if (a <= 4e+166) {
		tmp = x - ((z * t) / a);
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-5.6d+94)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= (-1.22d-136)) then
        tmp = t_1
    else if (a <= 1.65d-72) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 1.85d+66) then
        tmp = t_1
    else if (a <= 4d+166) then
        tmp = x - ((z * t) / a)
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -5.6e+94) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -1.22e-136) {
		tmp = t_1;
	} else if (a <= 1.65e-72) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.85e+66) {
		tmp = t_1;
	} else if (a <= 4e+166) {
		tmp = x - ((z * t) / a);
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -5.6e+94:
		tmp = x + (y * ((t - x) / a))
	elif a <= -1.22e-136:
		tmp = t_1
	elif a <= 1.65e-72:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 1.85e+66:
		tmp = t_1
	elif a <= 4e+166:
		tmp = x - ((z * t) / a)
	else:
		tmp = x + (y / (a / (t - x)))
	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 (a <= -5.6e+94)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= -1.22e-136)
		tmp = t_1;
	elseif (a <= 1.65e-72)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 1.85e+66)
		tmp = t_1;
	elseif (a <= 4e+166)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	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 (a <= -5.6e+94)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= -1.22e-136)
		tmp = t_1;
	elseif (a <= 1.65e-72)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 1.85e+66)
		tmp = t_1;
	elseif (a <= 4e+166)
		tmp = x - ((z * t) / a);
	else
		tmp = x + (y / (a / (t - x)));
	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[a, -5.6e+94], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.22e-136], t$95$1, If[LessEqual[a, 1.65e-72], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+66], t$95$1, If[LessEqual[a, 4e+166], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.59999999999999997e94

   1. Initial program 62.2%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around 0 55.9%

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

      1. associate-/l* 75.5%

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

   7. Simplified 75.5%

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

   if -5.59999999999999997e94 < a < -1.22000000000000001e-136 or 1.65e-72 < a < 1.85e66

   1. Initial program 68.2%

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

      1. associate-/l* 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in x around 0 57.2%

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

      1. associate-/l* 68.0%

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

   7. Simplified 68.0%

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

   if -1.22000000000000001e-136 < a < 1.65e-72

   1. Initial program 61.6%

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

      1. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in z around inf 85.2%

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

      1. associate--l+ 85.2%

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

      2. distribute-lft-out-- 85.2%

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

      3. div-sub 85.2%

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

      4. mul-1-neg 85.2%

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

      5. unsub-neg 85.2%

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

      6. div-sub 85.2%

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

      7. associate-/l* 84.9%

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

      8. associate-/l* 81.1%

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

      9. distribute-rgt-out-- 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in y around inf 80.5%

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

   if 1.85e66 < a < 3.99999999999999976e166

   1. Initial program 82.6%

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

      1. associate-/l* 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in a around inf 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 70.9%

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

      3. fma-define 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in y around 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. unsub-neg 65.3%

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

   10. Simplified 65.3%

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

   11. Taylor expanded in t around inf 65.4%

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

   if 3.99999999999999976e166 < a

   1. Initial program 80.7%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 78.5%

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

   7. Simplified 78.5%

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

      1. clear-num 78.5%

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

      2. un-div-inv 78.6%

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

   9. Applied egg-rr 78.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-136}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+166}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-136}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-63}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+85}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+166}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.6e+94)
   (+ x (* y (/ (- t x) a)))
   (if (<= a -1.3e-136)
     (* t (/ (- y z) (- a z)))
     (if (<= a 2.05e-63)
       (+ t (/ (* y (- x t)) z))
       (if (<= a 6e+85)
         (+ t (* x (/ (- y a) z)))
         (if (<= a 4e+166) (- x (/ (* z t) a)) (+ x (/ y (/ a (- t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e+94) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -1.3e-136) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 2.05e-63) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 6e+85) {
		tmp = t + (x * ((y - a) / z));
	} else if (a <= 4e+166) {
		tmp = x - ((z * t) / a);
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.6d+94)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= (-1.3d-136)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 2.05d-63) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 6d+85) then
        tmp = t + (x * ((y - a) / z))
    else if (a <= 4d+166) then
        tmp = x - ((z * t) / a)
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e+94) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -1.3e-136) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 2.05e-63) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 6e+85) {
		tmp = t + (x * ((y - a) / z));
	} else if (a <= 4e+166) {
		tmp = x - ((z * t) / a);
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.6e+94:
		tmp = x + (y * ((t - x) / a))
	elif a <= -1.3e-136:
		tmp = t * ((y - z) / (a - z))
	elif a <= 2.05e-63:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 6e+85:
		tmp = t + (x * ((y - a) / z))
	elif a <= 4e+166:
		tmp = x - ((z * t) / a)
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.6e+94)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= -1.3e-136)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 2.05e-63)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 6e+85)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	elseif (a <= 4e+166)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.6e+94)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= -1.3e-136)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 2.05e-63)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 6e+85)
		tmp = t + (x * ((y - a) / z));
	elseif (a <= 4e+166)
		tmp = x - ((z * t) / a);
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.6e+94], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.3e-136], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.05e-63], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+85], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+166], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -5.59999999999999997e94

   1. Initial program 62.2%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around 0 55.9%

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

      1. associate-/l* 75.5%

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

   7. Simplified 75.5%

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

   if -5.59999999999999997e94 < a < -1.29999999999999998e-136

   1. Initial program 69.9%

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

      1. associate-/l* 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in x around 0 59.7%

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

      1. associate-/l* 71.3%

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

   7. Simplified 71.3%

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

   if -1.29999999999999998e-136 < a < 2.0499999999999999e-63

   1. Initial program 61.9%

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

      1. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in z around inf 84.5%

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

      1. associate--l+ 84.6%

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

      2. distribute-lft-out-- 84.6%

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

      3. div-sub 84.6%

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

      4. mul-1-neg 84.6%

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

      5. unsub-neg 84.6%

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

      6. div-sub 84.6%

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

      7. associate-/l* 84.3%

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

      8. associate-/l* 80.6%

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

      9. distribute-rgt-out-- 84.4%

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

   7. Simplified 84.4%

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

   8. Taylor expanded in y around inf 78.9%

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

   if 2.0499999999999999e-63 < a < 6.0000000000000001e85

   1. Initial program 65.0%

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

      1. associate-/l* 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in z around inf 54.8%

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

      1. associate--l+ 54.8%

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

      2. distribute-lft-out-- 54.8%

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

      3. div-sub 55.0%

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

      4. mul-1-neg 55.0%

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

      5. unsub-neg 55.0%

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

      6. div-sub 54.8%

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

      7. associate-/l* 58.1%

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

      8. associate-/l* 61.1%

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

      9. distribute-rgt-out-- 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in t around 0 61.4%

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

      1. mul-1-neg 61.4%

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

      2. associate-/l* 61.4%

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

      3. distribute-lft-neg-in 61.4%

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

   10. Simplified 61.4%

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

   if 6.0000000000000001e85 < a < 3.99999999999999976e166

   1. Initial program 86.0%

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

      1. associate-/l* 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in a around inf 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-/l* 78.4%

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

      3. fma-define 78.4%

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

   7. Simplified 78.4%

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

   8. Taylor expanded in y around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. unsub-neg 78.5%

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

   10. Simplified 78.5%

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

   11. Taylor expanded in t around inf 78.5%

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

   if 3.99999999999999976e166 < a

   1. Initial program 80.7%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 78.5%

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

   7. Simplified 78.5%

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

      1. clear-num 78.5%

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

      2. un-div-inv 78.6%

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

   9. Applied egg-rr 78.6%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-136}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-63}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+85}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+166}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+95}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-136}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-62}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+84}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+166}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.4e+95)
   (+ x (* y (/ (- t x) a)))
   (if (<= a -3.7e-136)
     (* t (/ (- y z) (- a z)))
     (if (<= a 1.35e-62)
       (+ t (/ (* y (- x t)) z))
       (if (<= a 5.6e+84)
         (+ t (* (- y a) (/ x z)))
         (if (<= a 4.5e+166)
           (- x (/ (* z t) a))
           (+ x (/ y (/ a (- t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.4e+95) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -3.7e-136) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.35e-62) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 5.6e+84) {
		tmp = t + ((y - a) * (x / z));
	} else if (a <= 4.5e+166) {
		tmp = x - ((z * t) / a);
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.4d+95)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= (-3.7d-136)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 1.35d-62) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 5.6d+84) then
        tmp = t + ((y - a) * (x / z))
    else if (a <= 4.5d+166) then
        tmp = x - ((z * t) / a)
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.4e+95) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -3.7e-136) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.35e-62) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 5.6e+84) {
		tmp = t + ((y - a) * (x / z));
	} else if (a <= 4.5e+166) {
		tmp = x - ((z * t) / a);
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.4e+95:
		tmp = x + (y * ((t - x) / a))
	elif a <= -3.7e-136:
		tmp = t * ((y - z) / (a - z))
	elif a <= 1.35e-62:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 5.6e+84:
		tmp = t + ((y - a) * (x / z))
	elif a <= 4.5e+166:
		tmp = x - ((z * t) / a)
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.4e+95)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= -3.7e-136)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 1.35e-62)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 5.6e+84)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	elseif (a <= 4.5e+166)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.4e+95)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= -3.7e-136)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 1.35e-62)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 5.6e+84)
		tmp = t + ((y - a) * (x / z));
	elseif (a <= 4.5e+166)
		tmp = x - ((z * t) / a);
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.4e+95], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.7e-136], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-62], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e+84], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+166], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.3999999999999998e95

   1. Initial program 62.2%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around 0 55.9%

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

      1. associate-/l* 75.5%

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

   7. Simplified 75.5%

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

   if -4.3999999999999998e95 < a < -3.7e-136

   1. Initial program 69.9%

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

      1. associate-/l* 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in x around 0 59.7%

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

      1. associate-/l* 71.3%

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

   7. Simplified 71.3%

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

   if -3.7e-136 < a < 1.3500000000000001e-62

   1. Initial program 61.9%

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

      1. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in z around inf 84.5%

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

      1. associate--l+ 84.6%

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

      2. distribute-lft-out-- 84.6%

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

      3. div-sub 84.6%

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

      4. mul-1-neg 84.6%

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

      5. unsub-neg 84.6%

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

      6. div-sub 84.6%

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

      7. associate-/l* 84.3%

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

      8. associate-/l* 80.6%

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

      9. distribute-rgt-out-- 84.4%

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

   7. Simplified 84.4%

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

   8. Taylor expanded in y around inf 78.9%

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

   if 1.3500000000000001e-62 < a < 5.59999999999999963e84

   1. Initial program 65.0%

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

      1. associate-/l* 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in z around inf 54.8%

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

      1. associate--l+ 54.8%

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

      2. distribute-lft-out-- 54.8%

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

      3. div-sub 55.0%

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

      4. mul-1-neg 55.0%

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

      5. unsub-neg 55.0%

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

      6. div-sub 54.8%

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

      7. associate-/l* 58.1%

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

      8. associate-/l* 61.1%

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

      9. distribute-rgt-out-- 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in t around 0 61.5%

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

      1. neg-mul-1 61.5%

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

      2. distribute-neg-frac2 61.5%

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

   10. Simplified 61.5%

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

   if 5.59999999999999963e84 < a < 4.5000000000000003e166

   1. Initial program 86.0%

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

      1. associate-/l* 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in a around inf 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-/l* 78.4%

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

      3. fma-define 78.4%

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

   7. Simplified 78.4%

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

   8. Taylor expanded in y around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. unsub-neg 78.5%

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

   10. Simplified 78.5%

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

   11. Taylor expanded in t around inf 78.5%

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

   if 4.5000000000000003e166 < a

   1. Initial program 80.7%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 78.5%

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

   7. Simplified 78.5%

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

      1. clear-num 78.5%

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

      2. un-div-inv 78.6%

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

   9. Applied egg-rr 78.6%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+95}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-136}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-62}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+84}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+166}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-188}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-273}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -5.6e+94)
     x
     (if (<= a -6e-188)
       t
       (if (<= a -1.25e-246)
         t_1
         (if (<= a 3.4e-273)
           t
           (if (<= a 1.1e-58) t_1 (if (<= a 5.8e+60) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -5.6e+94) {
		tmp = x;
	} else if (a <= -6e-188) {
		tmp = t;
	} else if (a <= -1.25e-246) {
		tmp = t_1;
	} else if (a <= 3.4e-273) {
		tmp = t;
	} else if (a <= 1.1e-58) {
		tmp = t_1;
	} else if (a <= 5.8e+60) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-5.6d+94)) then
        tmp = x
    else if (a <= (-6d-188)) then
        tmp = t
    else if (a <= (-1.25d-246)) then
        tmp = t_1
    else if (a <= 3.4d-273) then
        tmp = t
    else if (a <= 1.1d-58) then
        tmp = t_1
    else if (a <= 5.8d+60) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -5.6e+94) {
		tmp = x;
	} else if (a <= -6e-188) {
		tmp = t;
	} else if (a <= -1.25e-246) {
		tmp = t_1;
	} else if (a <= 3.4e-273) {
		tmp = t;
	} else if (a <= 1.1e-58) {
		tmp = t_1;
	} else if (a <= 5.8e+60) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -5.6e+94:
		tmp = x
	elif a <= -6e-188:
		tmp = t
	elif a <= -1.25e-246:
		tmp = t_1
	elif a <= 3.4e-273:
		tmp = t
	elif a <= 1.1e-58:
		tmp = t_1
	elif a <= 5.8e+60:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -5.6e+94)
		tmp = x;
	elseif (a <= -6e-188)
		tmp = t;
	elseif (a <= -1.25e-246)
		tmp = t_1;
	elseif (a <= 3.4e-273)
		tmp = t;
	elseif (a <= 1.1e-58)
		tmp = t_1;
	elseif (a <= 5.8e+60)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -5.6e+94)
		tmp = x;
	elseif (a <= -6e-188)
		tmp = t;
	elseif (a <= -1.25e-246)
		tmp = t_1;
	elseif (a <= 3.4e-273)
		tmp = t;
	elseif (a <= 1.1e-58)
		tmp = t_1;
	elseif (a <= 5.8e+60)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+94], x, If[LessEqual[a, -6e-188], t, If[LessEqual[a, -1.25e-246], t$95$1, If[LessEqual[a, 3.4e-273], t, If[LessEqual[a, 1.1e-58], t$95$1, If[LessEqual[a, 5.8e+60], t, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.59999999999999997e94 or 5.79999999999999999e60 < a

   1. Initial program 72.1%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in a around inf 48.5%

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

   if -5.59999999999999997e94 < a < -6.00000000000000033e-188 or -1.2499999999999999e-246 < a < 3.39999999999999991e-273 or 1.10000000000000003e-58 < a < 5.79999999999999999e60

   1. Initial program 68.0%

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

      1. associate-/l* 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in z around inf 41.9%

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

   if -6.00000000000000033e-188 < a < -1.2499999999999999e-246 or 3.39999999999999991e-273 < a < 1.10000000000000003e-58

   1. Initial program 59.6%

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

      1. associate-/l* 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in z around inf 81.2%

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

      1. associate--l+ 81.2%

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

      2. distribute-lft-out-- 81.2%

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

      3. div-sub 81.2%

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

      4. mul-1-neg 81.2%

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

      5. unsub-neg 81.2%

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

      6. div-sub 81.2%

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

      7. associate-/l* 82.5%

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

      8. associate-/l* 77.3%

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

      9. distribute-rgt-out-- 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in t around 0 46.9%

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

   9. Taylor expanded in y around inf 41.4%

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

       1. associate-/l* 42.6%

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

   11. Simplified 42.6%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-188}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-273}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-188}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-229}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.56 \cdot 10^{-272}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+63}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.8e+94)
   x
   (if (<= a -3e-188)
     t
     (if (<= a -4.2e-229)
       (/ (* x y) z)
       (if (<= a 2.56e-272)
         t
         (if (<= a 7.2e-58) (* x (/ y z)) (if (<= a 7.5e+63) t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e+94) {
		tmp = x;
	} else if (a <= -3e-188) {
		tmp = t;
	} else if (a <= -4.2e-229) {
		tmp = (x * y) / z;
	} else if (a <= 2.56e-272) {
		tmp = t;
	} else if (a <= 7.2e-58) {
		tmp = x * (y / z);
	} else if (a <= 7.5e+63) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.8d+94)) then
        tmp = x
    else if (a <= (-3d-188)) then
        tmp = t
    else if (a <= (-4.2d-229)) then
        tmp = (x * y) / z
    else if (a <= 2.56d-272) then
        tmp = t
    else if (a <= 7.2d-58) then
        tmp = x * (y / z)
    else if (a <= 7.5d+63) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e+94) {
		tmp = x;
	} else if (a <= -3e-188) {
		tmp = t;
	} else if (a <= -4.2e-229) {
		tmp = (x * y) / z;
	} else if (a <= 2.56e-272) {
		tmp = t;
	} else if (a <= 7.2e-58) {
		tmp = x * (y / z);
	} else if (a <= 7.5e+63) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.8e+94:
		tmp = x
	elif a <= -3e-188:
		tmp = t
	elif a <= -4.2e-229:
		tmp = (x * y) / z
	elif a <= 2.56e-272:
		tmp = t
	elif a <= 7.2e-58:
		tmp = x * (y / z)
	elif a <= 7.5e+63:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.8e+94)
		tmp = x;
	elseif (a <= -3e-188)
		tmp = t;
	elseif (a <= -4.2e-229)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 2.56e-272)
		tmp = t;
	elseif (a <= 7.2e-58)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 7.5e+63)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.8e+94)
		tmp = x;
	elseif (a <= -3e-188)
		tmp = t;
	elseif (a <= -4.2e-229)
		tmp = (x * y) / z;
	elseif (a <= 2.56e-272)
		tmp = t;
	elseif (a <= 7.2e-58)
		tmp = x * (y / z);
	elseif (a <= 7.5e+63)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.8e+94], x, If[LessEqual[a, -3e-188], t, If[LessEqual[a, -4.2e-229], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.56e-272], t, If[LessEqual[a, 7.2e-58], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e+63], t, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.7999999999999997e94 or 7.5000000000000005e63 < a

   1. Initial program 72.1%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in a around inf 48.5%

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

   if -5.7999999999999997e94 < a < -3.00000000000000017e-188 or -4.19999999999999967e-229 < a < 2.55999999999999991e-272 or 7.20000000000000019e-58 < a < 7.5000000000000005e63

   1. Initial program 68.0%

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

      1. associate-/l* 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in z around inf 41.9%

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

   if -3.00000000000000017e-188 < a < -4.19999999999999967e-229

   1. Initial program 54.4%

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

      1. associate-/l* 55.0%

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

   3. Simplified 55.0%

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

   5. Taylor expanded in z around inf 90.7%

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

      1. associate--l+ 90.7%

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

      2. distribute-lft-out-- 90.7%

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

      3. div-sub 90.7%

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

      4. mul-1-neg 90.7%

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

      5. unsub-neg 90.7%

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

      6. div-sub 90.7%

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

      7. associate-/l* 90.9%

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

      8. associate-/l* 80.0%

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

      9. distribute-rgt-out-- 90.9%

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

   7. Simplified 90.9%

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

   8. Taylor expanded in t around 0 70.8%

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

   9. Taylor expanded in y around inf 70.8%

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

       1. *-commutative 70.8%

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

   11. Simplified 70.8%

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

   if 2.55999999999999991e-272 < a < 7.20000000000000019e-58

   1. Initial program 60.6%

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

      1. associate-/l* 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in z around inf 79.3%

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

      1. associate--l+ 79.3%

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

      2. distribute-lft-out-- 79.3%

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

      3. div-sub 79.3%

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

      4. mul-1-neg 79.3%

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

      5. unsub-neg 79.3%

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

      6. div-sub 79.3%

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

      7. associate-/l* 80.8%

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

      8. associate-/l* 76.7%

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

      9. distribute-rgt-out-- 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in t around 0 42.1%

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

   9. Taylor expanded in y around inf 35.4%

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

       1. associate-/l* 37.3%

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

   11. Simplified 37.3%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-188}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-229}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.56 \cdot 10^{-272}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+63}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y - z}{a}\right)\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ (- y z) a)))))
   (if (<= x -1.3e+251)
     t_1
     (if (<= x -6.5e+104)
       (* x (/ (- y a) z))
       (if (<= x -5.8e+21)
         t_1
         (if (<= x 1.15e+66)
           (* t (/ (- y z) (- a z)))
           (* x (- 1.0 (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - ((y - z) / a));
	double tmp;
	if (x <= -1.3e+251) {
		tmp = t_1;
	} else if (x <= -6.5e+104) {
		tmp = x * ((y - a) / z);
	} else if (x <= -5.8e+21) {
		tmp = t_1;
	} else if (x <= 1.15e+66) {
		tmp = t * ((y - z) / (a - z));
	} 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) :: tmp
    t_1 = x * (1.0d0 - ((y - z) / a))
    if (x <= (-1.3d+251)) then
        tmp = t_1
    else if (x <= (-6.5d+104)) then
        tmp = x * ((y - a) / z)
    else if (x <= (-5.8d+21)) then
        tmp = t_1
    else if (x <= 1.15d+66) then
        tmp = t * ((y - z) / (a - z))
    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 * (1.0 - ((y - z) / a));
	double tmp;
	if (x <= -1.3e+251) {
		tmp = t_1;
	} else if (x <= -6.5e+104) {
		tmp = x * ((y - a) / z);
	} else if (x <= -5.8e+21) {
		tmp = t_1;
	} else if (x <= 1.15e+66) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - ((y - z) / a))
	tmp = 0
	if x <= -1.3e+251:
		tmp = t_1
	elif x <= -6.5e+104:
		tmp = x * ((y - a) / z)
	elif x <= -5.8e+21:
		tmp = t_1
	elif x <= 1.15e+66:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (x <= -1.3e+251)
		tmp = t_1;
	elseif (x <= -6.5e+104)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (x <= -5.8e+21)
		tmp = t_1;
	elseif (x <= 1.15e+66)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	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 * (1.0 - ((y - z) / a));
	tmp = 0.0;
	if (x <= -1.3e+251)
		tmp = t_1;
	elseif (x <= -6.5e+104)
		tmp = x * ((y - a) / z);
	elseif (x <= -5.8e+21)
		tmp = t_1;
	elseif (x <= 1.15e+66)
		tmp = t * ((y - z) / (a - z));
	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[(1.0 - N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+251], t$95$1, If[LessEqual[x, -6.5e+104], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e+21], t$95$1, If[LessEqual[x, 1.15e+66], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.3000000000000001e251 or -6.5000000000000005e104 < x < -5.8e21

   1. Initial program 69.7%

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

      1. associate-/l* 79.8%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in a around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. associate-/l* 68.1%

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

      3. fma-define 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in t around 0 59.2%

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

      1. *-rgt-identity 59.2%

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

      2. mul-1-neg 59.2%

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

      3. associate-/l* 68.0%

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

      4. distribute-rgt-neg-in 68.0%

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

      5. mul-1-neg 68.0%

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

      6. distribute-lft-in 68.0%

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

      7. mul-1-neg 68.0%

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

      8. unsub-neg 68.0%

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

   10. Simplified 68.0%

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

   if -1.3000000000000001e251 < x < -6.5000000000000005e104

   1. Initial program 42.0%

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

      1. associate-/l* 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in z around inf 63.6%

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

      1. associate--l+ 63.6%

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

      2. distribute-lft-out-- 63.6%

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

      3. div-sub 63.6%

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

      4. mul-1-neg 63.6%

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

      5. unsub-neg 63.6%

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

      6. div-sub 63.6%

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

      7. associate-/l* 66.8%

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

      8. associate-/l* 69.8%

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

      9. distribute-rgt-out-- 73.5%

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

   7. Simplified 73.5%

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

   8. Taylor expanded in t around 0 47.0%

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

      1. associate-/l* 56.6%

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

   10. Simplified 56.6%

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

   if -5.8e21 < x < 1.15e66

   1. Initial program 75.4%

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

      1. associate-/l* 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in x around 0 60.5%

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

      1. associate-/l* 72.2%

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

   7. Simplified 72.2%

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

   if 1.15e66 < x

   1. Initial program 57.7%

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

      1. associate-/l* 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in z around 0 46.4%

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

      1. associate-/l* 53.8%

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

   7. Simplified 53.8%

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

   8. Taylor expanded in x around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. unsub-neg 51.8%

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

   10. Simplified 51.8%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+251}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a}\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 480000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))) (t_2 (* t (/ z (- z a)))))
   (if (<= z -2.05e+30)
     t_2
     (if (<= z 1.2e-73)
       t_1
       (if (<= z 7e-31) (* x (/ y z)) (if (<= z 480000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -2.05e+30) {
		tmp = t_2;
	} else if (z <= 1.2e-73) {
		tmp = t_1;
	} else if (z <= 7e-31) {
		tmp = x * (y / z);
	} else if (z <= 480000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / a)
    t_2 = t * (z / (z - a))
    if (z <= (-2.05d+30)) then
        tmp = t_2
    else if (z <= 1.2d-73) then
        tmp = t_1
    else if (z <= 7d-31) then
        tmp = x * (y / z)
    else if (z <= 480000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -2.05e+30) {
		tmp = t_2;
	} else if (z <= 1.2e-73) {
		tmp = t_1;
	} else if (z <= 7e-31) {
		tmp = x * (y / z);
	} else if (z <= 480000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	t_2 = t * (z / (z - a))
	tmp = 0
	if z <= -2.05e+30:
		tmp = t_2
	elif z <= 1.2e-73:
		tmp = t_1
	elif z <= 7e-31:
		tmp = x * (y / z)
	elif z <= 480000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	t_2 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -2.05e+30)
		tmp = t_2;
	elseif (z <= 1.2e-73)
		tmp = t_1;
	elseif (z <= 7e-31)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 480000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	t_2 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -2.05e+30)
		tmp = t_2;
	elseif (z <= 1.2e-73)
		tmp = t_1;
	elseif (z <= 7e-31)
		tmp = x * (y / z);
	elseif (z <= 480000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+30], t$95$2, If[LessEqual[z, 1.2e-73], t$95$1, If[LessEqual[z, 7e-31], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 480000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05000000000000003e30 or 4.8e11 < z

   1. Initial program 49.8%

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

      1. associate-/l* 66.3%

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

   3. Simplified 66.3%

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

      1. associate-*r/ 49.8%

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

      2. clear-num 49.6%

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

      3. associate-/r* 70.3%

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

   6. Applied egg-rr 70.3%

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

   7. Taylor expanded in y around 0 49.9%

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

      1. associate-*r/ 49.9%

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

      2. neg-mul-1 49.9%

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

   9. Simplified 49.9%

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

   10. Taylor expanded in x around 0 37.5%

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

       1. associate-/l* 49.3%

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

   12. Simplified 49.3%

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

   if -2.05000000000000003e30 < z < 1.20000000000000003e-73 or 6.99999999999999971e-31 < z < 4.8e11

   1. Initial program 83.7%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in a around inf 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 78.7%

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

      3. fma-define 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in t around inf 37.4%

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

      1. div-sub 37.4%

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

   10. Simplified 37.4%

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

   if 1.20000000000000003e-73 < z < 6.99999999999999971e-31

   1. Initial program 80.6%

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

      1. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in z around inf 54.5%

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

      1. associate--l+ 54.5%

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

      2. distribute-lft-out-- 54.5%

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

      3. div-sub 61.4%

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

      4. mul-1-neg 61.4%

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

      5. unsub-neg 61.4%

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

      6. div-sub 54.5%

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

      7. associate-/l* 54.3%

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

      8. associate-/l* 54.3%

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

      9. distribute-rgt-out-- 61.2%

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

   7. Simplified 61.2%

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

   8. Taylor expanded in t around 0 55.2%

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

   9. Taylor expanded in y around inf 55.5%

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

       1. associate-/l* 61.7%

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

   11. Simplified 61.7%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 480000000000:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+98}:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-83} \lor \neg \left(a \leq 2.1 \cdot 10^{-29}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.15e+98)
   (- x (* (/ (- y z) a) (- x t)))
   (if (or (<= a -2.55e-83) (not (<= a 2.1e-29)))
     (+ x (/ (- y z) (/ (- a z) t)))
     (+ t (/ (* y (- x t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.15e+98) {
		tmp = x - (((y - z) / a) * (x - t));
	} else if ((a <= -2.55e-83) || !(a <= 2.1e-29)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.15d+98)) then
        tmp = x - (((y - z) / a) * (x - t))
    else if ((a <= (-2.55d-83)) .or. (.not. (a <= 2.1d-29))) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t + ((y * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.15e+98) {
		tmp = x - (((y - z) / a) * (x - t));
	} else if ((a <= -2.55e-83) || !(a <= 2.1e-29)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.15e+98:
		tmp = x - (((y - z) / a) * (x - t))
	elif (a <= -2.55e-83) or not (a <= 2.1e-29):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t + ((y * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.15e+98)
		tmp = Float64(x - Float64(Float64(Float64(y - z) / a) * Float64(x - t)));
	elseif ((a <= -2.55e-83) || !(a <= 2.1e-29))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.15e+98)
		tmp = x - (((y - z) / a) * (x - t));
	elseif ((a <= -2.55e-83) || ~((a <= 2.1e-29)))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t + ((y * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.15e+98], N[(x - N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -2.55e-83], N[Not[LessEqual[a, 2.1e-29]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.15000000000000007e98

   1. Initial program 62.2%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in a around inf 55.3%

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

      1. associate-/l* 83.2%

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

   7. Simplified 83.2%

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

   if -1.15000000000000007e98 < a < -2.55000000000000018e-83 or 2.09999999999999989e-29 < a

   1. Initial program 76.4%

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

      1. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

      1. clear-num 85.3%

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

      2. un-div-inv 85.3%

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

   6. Applied egg-rr 85.3%

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

   7. Taylor expanded in t around inf 74.6%

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

   if -2.55000000000000018e-83 < a < 2.09999999999999989e-29

   1. Initial program 61.1%

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

      1. associate-/l* 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in z around inf 81.8%

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

      1. associate--l+ 81.8%

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

      2. distribute-lft-out-- 81.8%

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

      3. div-sub 82.7%

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

      4. mul-1-neg 82.7%

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

      5. unsub-neg 82.7%

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

      6. div-sub 81.8%

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

      7. associate-/l* 82.5%

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

      8. associate-/l* 79.6%

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

      9. distribute-rgt-out-- 83.5%

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

   7. Simplified 83.5%

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

   8. Taylor expanded in y around inf 76.7%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+98}:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-83} \lor \neg \left(a \leq 2.1 \cdot 10^{-29}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-31}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- y z) a) (- x t)))))
   (if (<= a -9.2e+94)
     t_1
     (if (<= a -9.8e-135)
       (* t (/ (- y z) (- a z)))
       (if (<= a 2.7e-31) (+ t (/ (* y (- x t)) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) / a) * (x - t));
	double tmp;
	if (a <= -9.2e+94) {
		tmp = t_1;
	} else if (a <= -9.8e-135) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 2.7e-31) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) / a) * (x - t))
    if (a <= (-9.2d+94)) then
        tmp = t_1
    else if (a <= (-9.8d-135)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 2.7d-31) then
        tmp = t + ((y * (x - t)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) / a) * (x - t));
	double tmp;
	if (a <= -9.2e+94) {
		tmp = t_1;
	} else if (a <= -9.8e-135) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 2.7e-31) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) / a) * (x - t))
	tmp = 0
	if a <= -9.2e+94:
		tmp = t_1
	elif a <= -9.8e-135:
		tmp = t * ((y - z) / (a - z))
	elif a <= 2.7e-31:
		tmp = t + ((y * (x - t)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) / a) * Float64(x - t)))
	tmp = 0.0
	if (a <= -9.2e+94)
		tmp = t_1;
	elseif (a <= -9.8e-135)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 2.7e-31)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) / a) * (x - t));
	tmp = 0.0;
	if (a <= -9.2e+94)
		tmp = t_1;
	elseif (a <= -9.8e-135)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 2.7e-31)
		tmp = t + ((y * (x - t)) / 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[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.2e+94], t$95$1, If[LessEqual[a, -9.8e-135], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-31], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.1999999999999999e94 or 2.70000000000000014e-31 < a

   1. Initial program 71.4%

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

      1. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in a around inf 60.4%

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

      1. associate-/l* 77.2%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a}} \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{x + \left(t - x\right) \cdot \frac{y - z}{a}} \]

   if -9.1999999999999999e94 < a < -9.8000000000000005e-135

   1. Initial program 69.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 77.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 77.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 59.7%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 71.3%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 71.3%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if -9.8000000000000005e-135 < a < 2.70000000000000014e-31

   1. Initial program 61.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 67.0%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 67.0%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 84.5%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 84.5%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 84.5%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 84.5%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 84.5%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 84.5%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 84.5%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 84.2%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 80.7%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 84.3%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   7. Simplified 84.3%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   8. Taylor expanded in y around inf 79.2%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+94}:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-31}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+98}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- y z) a) (- x t)))))
   (if (<= a -2.6e+96)
     t_1
     (if (<= a -6.5e-68)
       (+ x (/ (- y z) (/ (- a z) t)))
       (if (<= a 5e+98) (+ t (* (- y a) (/ (- x t) z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) / a) * (x - t));
	double tmp;
	if (a <= -2.6e+96) {
		tmp = t_1;
	} else if (a <= -6.5e-68) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (a <= 5e+98) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) / a) * (x - t))
    if (a <= (-2.6d+96)) then
        tmp = t_1
    else if (a <= (-6.5d-68)) then
        tmp = x + ((y - z) / ((a - z) / t))
    else if (a <= 5d+98) then
        tmp = t + ((y - a) * ((x - t) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) / a) * (x - t));
	double tmp;
	if (a <= -2.6e+96) {
		tmp = t_1;
	} else if (a <= -6.5e-68) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (a <= 5e+98) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) / a) * (x - t))
	tmp = 0
	if a <= -2.6e+96:
		tmp = t_1
	elif a <= -6.5e-68:
		tmp = x + ((y - z) / ((a - z) / t))
	elif a <= 5e+98:
		tmp = t + ((y - a) * ((x - t) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) / a) * Float64(x - t)))
	tmp = 0.0
	if (a <= -2.6e+96)
		tmp = t_1;
	elseif (a <= -6.5e-68)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	elseif (a <= 5e+98)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) / a) * (x - t));
	tmp = 0.0;
	if (a <= -2.6e+96)
		tmp = t_1;
	elseif (a <= -6.5e-68)
		tmp = x + ((y - z) / ((a - z) / t));
	elseif (a <= 5e+98)
		tmp = t + ((y - a) * ((x - t) / 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[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+96], t$95$1, If[LessEqual[a, -6.5e-68], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+98], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.6e96 or 4.9999999999999998e98 < a

   1. Initial program 73.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.0%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 67.2%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 88.6%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a}} \]

   7. Simplified 88.6%

      \[\leadsto \color{blue}{x + \left(t - x\right) \cdot \frac{y - z}{a}} \]

   if -2.6e96 < a < -6.4999999999999997e-68

   1. Initial program 77.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 82.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 82.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 82.3%

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{t - x}}} \]

      2. un-div-inv 82.4%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 82.4%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   7. Taylor expanded in t around inf 73.7%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   if -6.4999999999999997e-68 < a < 4.9999999999999998e98

   1. Initial program 61.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 69.1%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 69.1%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 74.9%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 74.9%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 74.9%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 75.7%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 75.7%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 75.7%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 74.9%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 76.8%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 75.9%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 79.0%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   7. Simplified 79.0%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+96}:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+98}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+98}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- y z) a) (- x t)))))
   (if (<= a -5.8e+96)
     t_1
     (if (<= a -3.2e-74)
       (+ x (/ (- y z) (/ (- a z) t)))
       (if (<= a 6e+98) (+ t (/ (- y a) (/ z (- x t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) / a) * (x - t));
	double tmp;
	if (a <= -5.8e+96) {
		tmp = t_1;
	} else if (a <= -3.2e-74) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (a <= 6e+98) {
		tmp = t + ((y - a) / (z / (x - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) / a) * (x - t))
    if (a <= (-5.8d+96)) then
        tmp = t_1
    else if (a <= (-3.2d-74)) then
        tmp = x + ((y - z) / ((a - z) / t))
    else if (a <= 6d+98) then
        tmp = t + ((y - a) / (z / (x - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) / a) * (x - t));
	double tmp;
	if (a <= -5.8e+96) {
		tmp = t_1;
	} else if (a <= -3.2e-74) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (a <= 6e+98) {
		tmp = t + ((y - a) / (z / (x - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) / a) * (x - t))
	tmp = 0
	if a <= -5.8e+96:
		tmp = t_1
	elif a <= -3.2e-74:
		tmp = x + ((y - z) / ((a - z) / t))
	elif a <= 6e+98:
		tmp = t + ((y - a) / (z / (x - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) / a) * Float64(x - t)))
	tmp = 0.0
	if (a <= -5.8e+96)
		tmp = t_1;
	elseif (a <= -3.2e-74)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	elseif (a <= 6e+98)
		tmp = Float64(t + Float64(Float64(y - a) / Float64(z / Float64(x - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) / a) * (x - t));
	tmp = 0.0;
	if (a <= -5.8e+96)
		tmp = t_1;
	elseif (a <= -3.2e-74)
		tmp = x + ((y - z) / ((a - z) / t));
	elseif (a <= 6e+98)
		tmp = t + ((y - a) / (z / (x - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.8e+96], t$95$1, If[LessEqual[a, -3.2e-74], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+98], N[(t + N[(N[(y - a), $MachinePrecision] / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.79999999999999955e96 or 6.0000000000000003e98 < a

   1. Initial program 73.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.0%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 67.2%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 88.6%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a}} \]

   7. Simplified 88.6%

      \[\leadsto \color{blue}{x + \left(t - x\right) \cdot \frac{y - z}{a}} \]

   if -5.79999999999999955e96 < a < -3.1999999999999999e-74

   1. Initial program 77.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 82.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 82.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 82.3%

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{t - x}}} \]

      2. un-div-inv 82.4%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 82.4%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   7. Taylor expanded in t around inf 73.7%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   if -3.1999999999999999e-74 < a < 6.0000000000000003e98

   1. Initial program 61.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 69.1%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 69.1%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 74.9%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 74.9%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 74.9%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 75.7%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 75.7%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 75.7%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 74.9%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 76.8%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 75.9%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 79.0%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   7. Simplified 79.0%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]
   8. Step-by-step derivation

      1. *-commutative 79.0%

         \[\leadsto t - \color{blue}{\left(y - a\right) \cdot \frac{t - x}{z}} \]

      2. clear-num 79.1%

         \[\leadsto t - \left(y - a\right) \cdot \color{blue}{\frac{1}{\frac{z}{t - x}}} \]

      3. un-div-inv 79.1%

         \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   9. Applied egg-rr 79.1%

      \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+96}:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+98}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{a} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 65.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-72}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 310000:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -3.6e+19)
     t_1
     (if (<= z 1.7e-72)
       (+ x (* y (/ (- t x) a)))
       (if (<= z 310000.0) (* y (/ (- t x) (- a z))) 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 <= -3.6e+19) {
		tmp = t_1;
	} else if (z <= 1.7e-72) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 310000.0) {
		tmp = y * ((t - x) / (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 = t * ((y - z) / (a - z))
    if (z <= (-3.6d+19)) then
        tmp = t_1
    else if (z <= 1.7d-72) then
        tmp = x + (y * ((t - x) / a))
    else if (z <= 310000.0d0) then
        tmp = y * ((t - x) / (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 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -3.6e+19) {
		tmp = t_1;
	} else if (z <= 1.7e-72) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 310000.0) {
		tmp = y * ((t - x) / (a - z));
	} 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 <= -3.6e+19:
		tmp = t_1
	elif z <= 1.7e-72:
		tmp = x + (y * ((t - x) / a))
	elif z <= 310000.0:
		tmp = y * ((t - x) / (a - z))
	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 <= -3.6e+19)
		tmp = t_1;
	elseif (z <= 1.7e-72)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (z <= 310000.0)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	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 <= -3.6e+19)
		tmp = t_1;
	elseif (z <= 1.7e-72)
		tmp = x + (y * ((t - x) / a));
	elseif (z <= 310000.0)
		tmp = y * ((t - x) / (a - z));
	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, -3.6e+19], t$95$1, If[LessEqual[z, 1.7e-72], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 310000.0], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e19 or 3.1e5 < z

   1. Initial program 50.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 66.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 48.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 63.3%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 63.3%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if -3.6e19 < z < 1.6999999999999999e-72

   1. Initial program 84.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 90.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 67.6%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 74.4%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 74.4%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]

   if 1.6999999999999999e-72 < z < 3.1e5

   1. Initial program 79.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 83.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 63.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   6. Step-by-step derivation

      1. div-sub 63.6%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   7. Simplified 63.6%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-72}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 310000:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 65.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 146000:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -8e+24)
     t_1
     (if (<= z 3.5e-72)
       (+ x (/ y (/ a (- t x))))
       (if (<= z 146000.0) (* y (/ (- t x) (- a z))) 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 <= -8e+24) {
		tmp = t_1;
	} else if (z <= 3.5e-72) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 146000.0) {
		tmp = y * ((t - x) / (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 = t * ((y - z) / (a - z))
    if (z <= (-8d+24)) then
        tmp = t_1
    else if (z <= 3.5d-72) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 146000.0d0) then
        tmp = y * ((t - x) / (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 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -8e+24) {
		tmp = t_1;
	} else if (z <= 3.5e-72) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 146000.0) {
		tmp = y * ((t - x) / (a - z));
	} 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 <= -8e+24:
		tmp = t_1
	elif z <= 3.5e-72:
		tmp = x + (y / (a / (t - x)))
	elif z <= 146000.0:
		tmp = y * ((t - x) / (a - z))
	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 <= -8e+24)
		tmp = t_1;
	elseif (z <= 3.5e-72)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 146000.0)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	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 <= -8e+24)
		tmp = t_1;
	elseif (z <= 3.5e-72)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 146000.0)
		tmp = y * ((t - x) / (a - z));
	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, -8e+24], t$95$1, If[LessEqual[z, 3.5e-72], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 146000.0], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.9999999999999999e24 or 146000 < z

   1. Initial program 50.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 66.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 48.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 63.3%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 63.3%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if -7.9999999999999999e24 < z < 3.5e-72

   1. Initial program 84.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 90.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 67.6%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 74.4%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 74.4%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]
   8. Step-by-step derivation

      1. clear-num 74.3%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a}{t - x}}} \]

      2. un-div-inv 74.4%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   9. Applied egg-rr 74.4%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   if 3.5e-72 < z < 146000

   1. Initial program 79.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 83.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 63.6%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   6. Step-by-step derivation

      1. div-sub 63.6%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   7. Simplified 63.6%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 146000:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+88}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+117}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e+88)
   (+ t (/ (- y a) (/ z (- x t))))
   (if (<= z 2.15e+117)
     (+ x (* (- y z) (/ (- t x) (- a z))))
     (+ t (* (- y a) (/ (- x t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+88) {
		tmp = t + ((y - a) / (z / (x - t)));
	} else if (z <= 2.15e+117) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + ((y - a) * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.2d+88)) then
        tmp = t + ((y - a) / (z / (x - t)))
    else if (z <= 2.15d+117) then
        tmp = x + ((y - z) * ((t - x) / (a - z)))
    else
        tmp = t + ((y - a) * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+88) {
		tmp = t + ((y - a) / (z / (x - t)));
	} else if (z <= 2.15e+117) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + ((y - a) * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e+88:
		tmp = t + ((y - a) / (z / (x - t)))
	elif z <= 2.15e+117:
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	else:
		tmp = t + ((y - a) * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e+88)
		tmp = Float64(t + Float64(Float64(y - a) / Float64(z / Float64(x - t))));
	elseif (z <= 2.15e+117)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.2e+88)
		tmp = t + ((y - a) / (z / (x - t)));
	elseif (z <= 2.15e+117)
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	else
		tmp = t + ((y - a) * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e+88], N[(t + N[(N[(y - a), $MachinePrecision] / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+117], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.20000000000000055e88

   1. Initial program 39.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 53.8%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 53.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 84.5%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 84.5%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 84.5%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 84.5%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 84.5%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 84.5%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 84.5%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 89.2%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 93.2%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 93.2%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   7. Simplified 93.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]
   8. Step-by-step derivation

      1. *-commutative 93.2%

         \[\leadsto t - \color{blue}{\left(y - a\right) \cdot \frac{t - x}{z}} \]

      2. clear-num 93.2%

         \[\leadsto t - \left(y - a\right) \cdot \color{blue}{\frac{1}{\frac{z}{t - x}}} \]

      3. un-div-inv 93.3%

         \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   9. Applied egg-rr 93.3%

      \[\leadsto t - \color{blue}{\frac{y - a}{\frac{z}{t - x}}} \]

   if -8.20000000000000055e88 < z < 2.14999999999999999e117

   1. Initial program 80.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 88.0%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   if 2.14999999999999999e117 < z

   1. Initial program 38.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 60.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 61.3%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 61.3%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 61.3%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 61.3%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 61.3%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 61.3%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 61.3%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 70.1%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 79.4%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 79.4%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   7. Simplified 79.4%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+88}:\\ \;\;\;\;t + \frac{y - a}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+117}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 40.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 28500:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ z (- z a)))))
   (if (<= z -3.5e+19)
     t_1
     (if (<= z 1.7e-74) x (if (<= z 28500.0) (* x (/ y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double tmp;
	if (z <= -3.5e+19) {
		tmp = t_1;
	} else if (z <= 1.7e-74) {
		tmp = x;
	} else if (z <= 28500.0) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (z / (z - a))
    if (z <= (-3.5d+19)) then
        tmp = t_1
    else if (z <= 1.7d-74) then
        tmp = x
    else if (z <= 28500.0d0) then
        tmp = x * (y / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double tmp;
	if (z <= -3.5e+19) {
		tmp = t_1;
	} else if (z <= 1.7e-74) {
		tmp = x;
	} else if (z <= 28500.0) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (z / (z - a))
	tmp = 0
	if z <= -3.5e+19:
		tmp = t_1
	elif z <= 1.7e-74:
		tmp = x
	elif z <= 28500.0:
		tmp = x * (y / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -3.5e+19)
		tmp = t_1;
	elseif (z <= 1.7e-74)
		tmp = x;
	elseif (z <= 28500.0)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -3.5e+19)
		tmp = t_1;
	elseif (z <= 1.7e-74)
		tmp = x;
	elseif (z <= 28500.0)
		tmp = x * (y / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+19], t$95$1, If[LessEqual[z, 1.7e-74], x, If[LessEqual[z, 28500.0], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5e19 or 28500 < z

   1. Initial program 50.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 66.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r/ 50.4%

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

      2. clear-num 50.2%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

      3. associate-/r* 70.6%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a - z}{y - z}}{t - x}}} \]

   6. Applied egg-rr 70.6%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{y - z}}{t - x}}} \]

   7. Taylor expanded in y around 0 49.5%

      \[\leadsto x + \frac{1}{\frac{\color{blue}{-1 \cdot \frac{a - z}{z}}}{t - x}} \]
   8. Step-by-step derivation

      1. associate-*r/ 49.5%

         \[\leadsto x + \frac{1}{\frac{\color{blue}{\frac{-1 \cdot \left(a - z\right)}{z}}}{t - x}} \]

      2. neg-mul-1 49.5%

         \[\leadsto x + \frac{1}{\frac{\frac{\color{blue}{-\left(a - z\right)}}{z}}{t - x}} \]

   9. Simplified 49.5%

      \[\leadsto x + \frac{1}{\frac{\color{blue}{\frac{-\left(a - z\right)}{z}}}{t - x}} \]

   10. Taylor expanded in x around 0 36.9%

       \[\leadsto \color{blue}{\frac{t \cdot z}{z - a}} \]
   11. Step-by-step derivation

       1. associate-/l* 48.6%

          \[\leadsto \color{blue}{t \cdot \frac{z}{z - a}} \]

   12. Simplified 48.6%

       \[\leadsto \color{blue}{t \cdot \frac{z}{z - a}} \]

   if -3.5e19 < z < 1.7e-74

   1. Initial program 83.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.1%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 90.1%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 31.8%

      \[\leadsto \color{blue}{x} \]

   if 1.7e-74 < z < 28500

   1. Initial program 82.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 85.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 56.3%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 56.3%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. distribute-lft-out-- 56.3%

         \[\leadsto t + \color{blue}{-1 \cdot \left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      3. div-sub 60.1%

         \[\leadsto t + -1 \cdot \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      4. mul-1-neg 60.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      5. unsub-neg 60.1%

         \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. div-sub 56.3%

         \[\leadsto t - \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z} - \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      7. associate-/l* 56.2%

         \[\leadsto t - \left(\color{blue}{y \cdot \frac{t - x}{z}} - \frac{a \cdot \left(t - x\right)}{z}\right) \]

      8. associate-/l* 56.3%

         \[\leadsto t - \left(y \cdot \frac{t - x}{z} - \color{blue}{a \cdot \frac{t - x}{z}}\right) \]

      9. distribute-rgt-out-- 60.1%

         \[\leadsto t - \color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)} \]

   7. Simplified 60.1%

      \[\leadsto \color{blue}{t - \frac{t - x}{z} \cdot \left(y - a\right)} \]

   8. Taylor expanded in t around 0 45.7%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]

   9. Taylor expanded in y around inf 42.6%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   10. Step-by-step derivation

       1. associate-/l* 46.1%

          \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   11. Simplified 46.1%

       \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 28500:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 59.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+21}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8.8e+21)
   (- x (* y (/ x a)))
   (if (<= x 1.18e+66) (* t (/ (- y z) (- a z))) (* x (- 1.0 (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.8e+21) {
		tmp = x - (y * (x / a));
	} else if (x <= 1.18e+66) {
		tmp = t * ((y - z) / (a - z));
	} 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) :: tmp
    if (x <= (-8.8d+21)) then
        tmp = x - (y * (x / a))
    else if (x <= 1.18d+66) then
        tmp = t * ((y - z) / (a - z))
    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 tmp;
	if (x <= -8.8e+21) {
		tmp = x - (y * (x / a));
	} else if (x <= 1.18e+66) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -8.8e+21:
		tmp = x - (y * (x / a))
	elif x <= 1.18e+66:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8.8e+21)
		tmp = Float64(x - Float64(y * Float64(x / a)));
	elseif (x <= 1.18e+66)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -8.8e+21)
		tmp = x - (y * (x / a));
	elseif (x <= 1.18e+66)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8.8e+21], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.18e+66], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.8e21

   1. Initial program 55.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 72.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 72.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 44.9%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 51.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 51.2%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]

   8. Taylor expanded in t around 0 47.9%

      \[\leadsto x + y \cdot \color{blue}{\left(-1 \cdot \frac{x}{a}\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 47.9%

         \[\leadsto x + y \cdot \color{blue}{\left(-\frac{x}{a}\right)} \]

      2. distribute-neg-frac2 47.9%

         \[\leadsto x + y \cdot \color{blue}{\frac{x}{-a}} \]

   10. Simplified 47.9%

       \[\leadsto x + y \cdot \color{blue}{\frac{x}{-a}} \]

   if -8.8e21 < x < 1.1800000000000001e66

   1. Initial program 75.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 83.0%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 83.0%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 60.5%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 72.2%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 72.2%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if 1.1800000000000001e66 < x

   1. Initial program 57.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 71.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 46.4%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 53.8%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 53.8%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]

   8. Taylor expanded in x around inf 51.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 51.8%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \]

      2. unsub-neg 51.8%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   10. Simplified 51.8%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+21}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 38.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+63}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.6e+94) x (if (<= a 2.3e+63) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e+94) {
		tmp = x;
	} else if (a <= 2.3e+63) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.6d+94)) then
        tmp = x
    else if (a <= 2.3d+63) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e+94) {
		tmp = x;
	} else if (a <= 2.3e+63) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.6e+94:
		tmp = x
	elif a <= 2.3e+63:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.6e+94)
		tmp = x;
	elseif (a <= 2.3e+63)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.6e+94)
		tmp = x;
	elseif (a <= 2.3e+63)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.6e+94], x, If[LessEqual[a, 2.3e+63], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.59999999999999997e94 or 2.29999999999999993e63 < a

   1. Initial program 72.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 89.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 48.5%

      \[\leadsto \color{blue}{x} \]

   if -5.59999999999999997e94 < a < 2.29999999999999993e63

   1. Initial program 65.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 72.5%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 34.4%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+63}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 24.2% 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 67.5%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. associate-/l* 78.4%

      \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

3. Simplified 78.4%

   \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 24.9%

   \[\leadsto \color{blue}{t} \]

6. Final simplification 24.9%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	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[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024045 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))