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

Percentage Accurate: 68.3% → 88.2%

Time: 18.7s

Alternatives: 22

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: 68.3% 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: 88.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x - t}{z - a} \cdot \left(z - y\right)\\ t_2 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-250}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-260}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- x t) (- z a)) (- z y))))
        (t_2 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-250)
       t_2
       (if (<= t_2 5e-260) (+ t (/ (* (- t x) (- a y)) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((x - t) / (z - a)) * (z - y));
	double t_2 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-250) {
		tmp = t_2;
	} else if (t_2 <= 5e-260) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((x - t) / (z - a)) * (z - y));
	double t_2 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-250) {
		tmp = t_2;
	} else if (t_2 <= 5e-260) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((x - t) / (z - a)) * (z - y))
	t_2 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-250:
		tmp = t_2
	elif t_2 <= 5e-260:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(x - t) / Float64(z - a)) * Float64(z - y)))
	t_2 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-250)
		tmp = t_2;
	elseif (t_2 <= 5e-260)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((x - t) / (z - a)) * (z - y));
	t_2 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-250)
		tmp = t_2;
	elseif (t_2 <= 5e-260)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-250], t$95$2, If[LessEqual[t$95$2, 5e-260], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], 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))) < -inf.0 or 5.0000000000000003e-260 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 61.4%

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

      1. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.00000000000000027e-250

   1. Initial program 97.7%

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

   if -5.00000000000000027e-250 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.0000000000000003e-260

   1. Initial program 12.8%

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

      1. associate-/l* 5.2%

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

   3. Simplified 5.2%

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

   5. Taylor expanded in z around inf 99.0%

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

      1. associate--l+ 99.0%

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

      2. associate-*r/ 99.0%

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

      3. associate-*r/ 99.0%

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

      4. mul-1-neg 99.0%

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

      5. div-sub 99.0%

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

      6. mul-1-neg 99.0%

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

      7. distribute-lft-out-- 99.0%

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

      8. associate-*r/ 99.0%

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

      9. mul-1-neg 99.0%

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

      10. unsub-neg 99.0%

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

      11. distribute-rgt-out-- 99.0%

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

   7. Simplified 99.0%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -\infty:\\ \;\;\;\;x - \frac{x - t}{z - a} \cdot \left(z - y\right)\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -5 \cdot 10^{-250}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 5 \cdot 10^{-260}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{z - a} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-250} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-260}\right):\\ \;\;\;\;x + \frac{x - t}{\frac{z - a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (or (<= t_1 -5e-250) (not (<= t_1 5e-260)))
     (+ x (/ (- x t) (/ (- z a) (- y z))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-250) || !(t_1 <= 5e-260)) {
		tmp = x + ((x - t) / ((z - a) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) * (x - t)) / (a - z))
    if ((t_1 <= (-5d-250)) .or. (.not. (t_1 <= 5d-260))) then
        tmp = x + ((x - t) / ((z - a) / (y - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-250) || !(t_1 <= 5e-260)) {
		tmp = x + ((x - t) / ((z - a) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if (t_1 <= -5e-250) or not (t_1 <= 5e-260):
		tmp = x + ((x - t) / ((z - a) / (y - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -5e-250) || !(t_1 <= 5e-260))
		tmp = Float64(x + Float64(Float64(x - t) / Float64(Float64(z - a) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -5e-250) || ~((t_1 <= 5e-260)))
		tmp = x + ((x - t) / ((z - a) / (y - z)));
	else
		tmp = t + (((t - x) * (a - y)) / 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[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-250], N[Not[LessEqual[t$95$1, 5e-260]], $MachinePrecision]], N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.00000000000000027e-250 or 5.0000000000000003e-260 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 73.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative 85.3%

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

      2. associate-*l/ 73.4%

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

      3. associate-*r/ 88.4%

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

      4. clear-num 88.3%

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

      5. un-div-inv 88.7%

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

   6. Applied egg-rr 88.7%

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

   if -5.00000000000000027e-250 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.0000000000000003e-260

   1. Initial program 12.8%

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

      1. associate-/l* 5.2%

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

   3. Simplified 5.2%

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

   5. Taylor expanded in z around inf 99.0%

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

      1. associate--l+ 99.0%

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

      2. associate-*r/ 99.0%

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

      3. associate-*r/ 99.0%

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

      4. mul-1-neg 99.0%

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

      5. div-sub 99.0%

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

      6. mul-1-neg 99.0%

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

      7. distribute-lft-out-- 99.0%

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

      8. associate-*r/ 99.0%

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

      9. mul-1-neg 99.0%

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

      10. unsub-neg 99.0%

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

      11. distribute-rgt-out-- 99.0%

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

   7. Simplified 99.0%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -5 \cdot 10^{-250} \lor \neg \left(x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 5 \cdot 10^{-260}\right):\\ \;\;\;\;x + \frac{x - t}{\frac{z - a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{t - x}{\frac{z}{z - y} - \frac{a}{z - y}}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-260}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x - t}{\frac{z - a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (<= t_1 -5e-250)
     (+ x (/ (- t x) (- (/ z (- z y)) (/ a (- z y)))))
     (if (<= t_1 5e-260)
       (+ t (/ (* (- t x) (- a y)) z))
       (+ x (/ (- x t) (/ (- z a) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_1 <= -5e-250) {
		tmp = x + ((t - x) / ((z / (z - y)) - (a / (z - y))));
	} else if (t_1 <= 5e-260) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((x - t) / ((z - a) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) * (x - t)) / (a - z))
    if (t_1 <= (-5d-250)) then
        tmp = x + ((t - x) / ((z / (z - y)) - (a / (z - y))))
    else if (t_1 <= 5d-260) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = x + ((x - t) / ((z - a) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_1 <= -5e-250) {
		tmp = x + ((t - x) / ((z / (z - y)) - (a / (z - y))));
	} else if (t_1 <= 5e-260) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((x - t) / ((z - a) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if t_1 <= -5e-250:
		tmp = x + ((t - x) / ((z / (z - y)) - (a / (z - y))))
	elif t_1 <= 5e-260:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = x + ((x - t) / ((z - a) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -5e-250)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(z / Float64(z - y)) - Float64(a / Float64(z - y)))));
	elseif (t_1 <= 5e-260)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(Float64(x - t) / Float64(Float64(z - a) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if (t_1 <= -5e-250)
		tmp = x + ((t - x) / ((z / (z - y)) - (a / (z - y))));
	elseif (t_1 <= 5e-260)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = x + ((x - t) / ((z - a) / (y - 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[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-250], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-260], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / N[(y - z), $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))) < -5.00000000000000027e-250

   1. Initial program 77.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. *-commutative 84.5%

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

      2. associate-*l/ 77.8%

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

      3. associate-*r/ 90.5%

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

      4. clear-num 90.4%

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

      5. un-div-inv 90.5%

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

   6. Applied egg-rr 90.5%

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

      1. div-sub 90.5%

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

   8. Applied egg-rr 90.5%

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

   if -5.00000000000000027e-250 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.0000000000000003e-260

   1. Initial program 12.8%

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

      1. associate-/l* 5.2%

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

   3. Simplified 5.2%

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

   5. Taylor expanded in z around inf 99.0%

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

      1. associate--l+ 99.0%

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

      2. associate-*r/ 99.0%

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

      3. associate-*r/ 99.0%

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

      4. mul-1-neg 99.0%

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

      5. div-sub 99.0%

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

      6. mul-1-neg 99.0%

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

      7. distribute-lft-out-- 99.0%

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

      8. associate-*r/ 99.0%

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

      9. mul-1-neg 99.0%

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

      10. unsub-neg 99.0%

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

      11. distribute-rgt-out-- 99.0%

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

   7. Simplified 99.0%

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

   if 5.0000000000000003e-260 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 68.9%

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

      1. *-commutative 86.0%

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

      2. associate-*l/ 68.9%

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

      3. associate-*r/ 86.2%

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

      4. clear-num 86.1%

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

      5. un-div-inv 86.8%

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

   6. Applied egg-rr 86.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -5 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{t - x}{\frac{z}{z - y} - \frac{a}{z - y}}\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 5 \cdot 10^{-260}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x - t}{\frac{z - a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+17} \lor \neg \left(x \leq 2.7 \cdot 10^{-86}\right):\\ \;\;\;\;x \cdot \left(\left(1 - \frac{z}{z - a}\right) + \left(t \cdot \frac{y - z}{x \cdot \left(a - z\right)} + \frac{y}{z - a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{z - a}{y - z}}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.7e+17) (not (<= x 2.7e-86)))
   (*
    x
    (+
     (- 1.0 (/ z (- z a)))
     (+ (* t (/ (- y z) (* x (- a z)))) (/ y (- z a)))))
   (+ x (/ -1.0 (/ (/ (- z a) (- y z)) (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.7e+17) || !(x <= 2.7e-86)) {
		tmp = x * ((1.0 - (z / (z - a))) + ((t * ((y - z) / (x * (a - z)))) + (y / (z - a))));
	} else {
		tmp = x + (-1.0 / (((z - a) / (y - z)) / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-4.7d+17)) .or. (.not. (x <= 2.7d-86))) then
        tmp = x * ((1.0d0 - (z / (z - a))) + ((t * ((y - z) / (x * (a - z)))) + (y / (z - a))))
    else
        tmp = x + ((-1.0d0) / (((z - a) / (y - z)) / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.7e+17) || !(x <= 2.7e-86)) {
		tmp = x * ((1.0 - (z / (z - a))) + ((t * ((y - z) / (x * (a - z)))) + (y / (z - a))));
	} else {
		tmp = x + (-1.0 / (((z - a) / (y - z)) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.7e+17) or not (x <= 2.7e-86):
		tmp = x * ((1.0 - (z / (z - a))) + ((t * ((y - z) / (x * (a - z)))) + (y / (z - a))))
	else:
		tmp = x + (-1.0 / (((z - a) / (y - z)) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.7e+17) || !(x <= 2.7e-86))
		tmp = Float64(x * Float64(Float64(1.0 - Float64(z / Float64(z - a))) + Float64(Float64(t * Float64(Float64(y - z) / Float64(x * Float64(a - z)))) + Float64(y / Float64(z - a)))));
	else
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(Float64(z - a) / Float64(y - z)) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -4.7e+17) || ~((x <= 2.7e-86)))
		tmp = x * ((1.0 - (z / (z - a))) + ((t * ((y - z) / (x * (a - z)))) + (y / (z - a))));
	else
		tmp = x + (-1.0 / (((z - a) / (y - z)) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.7e+17], N[Not[LessEqual[x, 2.7e-86]], $MachinePrecision]], N[(x * N[(N[(1.0 - N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(y - z), $MachinePrecision] / N[(x * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 / N[(N[(N[(z - a), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.7e17 or 2.69999999999999992e-86 < x

   1. Initial program 60.0%

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

      1. associate-/l* 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in x around -inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. *-commutative 77.1%

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

      3. distribute-rgt-neg-in 77.1%

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

      4. +-commutative 77.1%

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

      5. mul-1-neg 77.1%

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

      6. unsub-neg 77.1%

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

      7. associate-/l* 86.9%

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

      8. *-commutative 86.9%

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

   7. Simplified 86.9%

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

   if -4.7e17 < x < 2.69999999999999992e-86

   1. Initial program 82.4%

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

      1. associate-*r/ 82.4%

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

      2. clear-num 82.4%

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

      3. associate-/r* 92.9%

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

   6. Applied egg-rr 92.9%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{y - z}}{t - x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+17} \lor \neg \left(x \leq 2.7 \cdot 10^{-86}\right):\\ \;\;\;\;x \cdot \left(\left(1 - \frac{z}{z - a}\right) + \left(t \cdot \frac{y - z}{x \cdot \left(a - z\right)} + \frac{y}{z - a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{z - a}{y - z}}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (- x (* (- t x) (/ (- z y) a)))))
   (if (<= a -2.15e+17)
     t_2
     (if (<= a -3.8e-199)
       t_1
       (if (<= a 1.1e-246)
         (* y (/ (- x t) (- z a)))
         (if (<= a 3.05e+24) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - ((t - x) * ((z - y) / a));
	double tmp;
	if (a <= -2.15e+17) {
		tmp = t_2;
	} else if (a <= -3.8e-199) {
		tmp = t_1;
	} else if (a <= 1.1e-246) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= 3.05e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x - ((t - x) * ((z - y) / a))
    if (a <= (-2.15d+17)) then
        tmp = t_2
    else if (a <= (-3.8d-199)) then
        tmp = t_1
    else if (a <= 1.1d-246) then
        tmp = y * ((x - t) / (z - a))
    else if (a <= 3.05d+24) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - ((t - x) * ((z - y) / a));
	double tmp;
	if (a <= -2.15e+17) {
		tmp = t_2;
	} else if (a <= -3.8e-199) {
		tmp = t_1;
	} else if (a <= 1.1e-246) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= 3.05e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - ((t - x) * ((z - y) / a))
	tmp = 0
	if a <= -2.15e+17:
		tmp = t_2
	elif a <= -3.8e-199:
		tmp = t_1
	elif a <= 1.1e-246:
		tmp = y * ((x - t) / (z - a))
	elif a <= 3.05e+24:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)))
	tmp = 0.0
	if (a <= -2.15e+17)
		tmp = t_2;
	elseif (a <= -3.8e-199)
		tmp = t_1;
	elseif (a <= 1.1e-246)
		tmp = Float64(y * Float64(Float64(x - t) / Float64(z - a)));
	elseif (a <= 3.05e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - ((t - x) * ((z - y) / a));
	tmp = 0.0;
	if (a <= -2.15e+17)
		tmp = t_2;
	elseif (a <= -3.8e-199)
		tmp = t_1;
	elseif (a <= 1.1e-246)
		tmp = y * ((x - t) / (z - a));
	elseif (a <= 3.05e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.15e+17], t$95$2, If[LessEqual[a, -3.8e-199], t$95$1, If[LessEqual[a, 1.1e-246], N[(y * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.05e+24], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.15e17 or 3.05000000000000003e24 < 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* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in a around inf 64.9%

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

      1. associate-/l* 78.4%

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

   7. Simplified 78.4%

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

   if -2.15e17 < a < -3.7999999999999998e-199 or 1.09999999999999999e-246 < a < 3.05000000000000003e24

   1. Initial program 67.8%

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

      1. associate-/l* 69.8%

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

   3. Simplified 69.8%

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

   5. Taylor expanded in x around 0 56.6%

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

      1. associate-/l* 66.7%

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

   7. Simplified 66.7%

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

   if -3.7999999999999998e-199 < a < 1.09999999999999999e-246

   1. Initial program 68.6%

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

      1. associate-/l* 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in y around inf 72.8%

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

      1. div-sub 72.8%

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

   7. Simplified 72.8%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+17}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-199}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -6.2e+125)
     t_2
     (if (<= a -3.8e-203)
       t_1
       (if (<= a 1.65e-248)
         (* y (/ (- x t) (- z a)))
         (if (<= a 2.9e+41) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -6.2e+125) {
		tmp = t_2;
	} else if (a <= -3.8e-203) {
		tmp = t_1;
	} else if (a <= 1.65e-248) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= 2.9e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-6.2d+125)) then
        tmp = t_2
    else if (a <= (-3.8d-203)) then
        tmp = t_1
    else if (a <= 1.65d-248) then
        tmp = y * ((x - t) / (z - a))
    else if (a <= 2.9d+41) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -6.2e+125) {
		tmp = t_2;
	} else if (a <= -3.8e-203) {
		tmp = t_1;
	} else if (a <= 1.65e-248) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= 2.9e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -6.2e+125:
		tmp = t_2
	elif a <= -3.8e-203:
		tmp = t_1
	elif a <= 1.65e-248:
		tmp = y * ((x - t) / (z - a))
	elif a <= 2.9e+41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -6.2e+125)
		tmp = t_2;
	elseif (a <= -3.8e-203)
		tmp = t_1;
	elseif (a <= 1.65e-248)
		tmp = Float64(y * Float64(Float64(x - t) / Float64(z - a)));
	elseif (a <= 2.9e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -6.2e+125)
		tmp = t_2;
	elseif (a <= -3.8e-203)
		tmp = t_1;
	elseif (a <= 1.65e-248)
		tmp = y * ((x - t) / (z - a));
	elseif (a <= 2.9e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e+125], t$95$2, If[LessEqual[a, -3.8e-203], t$95$1, If[LessEqual[a, 1.65e-248], N[(y * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+41], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.2e125 or 2.89999999999999988e41 < a

   1. Initial program 69.4%

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

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in z around 0 59.4%

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

      1. associate-/l* 71.9%

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

   7. Simplified 71.9%

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

   if -6.2e125 < a < -3.80000000000000025e-203 or 1.6500000000000001e-248 < a < 2.89999999999999988e41

   1. Initial program 71.2%

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

      1. associate-/l* 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in x around 0 55.2%

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

      1. associate-/l* 66.9%

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

   7. Simplified 66.9%

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

   if -3.80000000000000025e-203 < a < 1.6500000000000001e-248

   1. Initial program 68.6%

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

      1. associate-/l* 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in y around inf 72.8%

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

      1. div-sub 72.8%

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

   7. Simplified 72.8%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-203}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -5.6e+125)
     (+ x (* y (/ (- t x) a)))
     (if (<= a -3.1e-193)
       t_1
       (if (<= a 1.05e-246)
         (* y (/ (- x t) (- z a)))
         (if (<= a 4.1e+35) t_1 (+ x (/ (- t x) (/ a y)))))))))

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+125) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -3.1e-193) {
		tmp = t_1;
	} else if (a <= 1.05e-246) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= 4.1e+35) {
		tmp = t_1;
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-5.6d+125)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= (-3.1d-193)) then
        tmp = t_1
    else if (a <= 1.05d-246) then
        tmp = y * ((x - t) / (z - a))
    else if (a <= 4.1d+35) then
        tmp = t_1
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -5.6e+125) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -3.1e-193) {
		tmp = t_1;
	} else if (a <= 1.05e-246) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= 4.1e+35) {
		tmp = t_1;
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -5.6e+125:
		tmp = x + (y * ((t - x) / a))
	elif a <= -3.1e-193:
		tmp = t_1
	elif a <= 1.05e-246:
		tmp = y * ((x - t) / (z - a))
	elif a <= 4.1e+35:
		tmp = t_1
	else:
		tmp = x + ((t - x) / (a / y))
	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+125)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= -3.1e-193)
		tmp = t_1;
	elseif (a <= 1.05e-246)
		tmp = Float64(y * Float64(Float64(x - t) / Float64(z - a)));
	elseif (a <= 4.1e+35)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	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+125)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= -3.1e-193)
		tmp = t_1;
	elseif (a <= 1.05e-246)
		tmp = y * ((x - t) / (z - a));
	elseif (a <= 4.1e+35)
		tmp = t_1;
	else
		tmp = x + ((t - x) / (a / y));
	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+125], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.1e-193], t$95$1, If[LessEqual[a, 1.05e-246], N[(y * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e+35], t$95$1, N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.6000000000000002e125

   1. Initial program 71.1%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in z around 0 63.2%

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

      1. associate-/l* 83.1%

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

   7. Simplified 83.1%

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

   if -5.6000000000000002e125 < a < -3.1000000000000002e-193 or 1.04999999999999997e-246 < a < 4.0999999999999998e35

   1. Initial program 70.7%

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

      1. associate-/l* 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in x around 0 54.4%

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

      1. associate-/l* 66.3%

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

   7. Simplified 66.3%

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

   if -3.1000000000000002e-193 < a < 1.04999999999999997e-246

   1. Initial program 68.6%

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

      1. associate-/l* 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in y around inf 72.8%

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

      1. div-sub 72.8%

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

   7. Simplified 72.8%

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

   if 4.0999999999999998e35 < a

   1. Initial program 69.2%

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

      1. associate-/l* 86.8%

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

   3. Simplified 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-*l/ 69.2%

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

      3. associate-*r/ 88.9%

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

      4. clear-num 88.8%

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

      5. un-div-inv 89.0%

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

   6. Applied egg-rr 89.0%

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

   7. Taylor expanded in z around 0 66.7%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-193}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+172}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{a - z} \cdot t\\ \mathbf{elif}\;z \leq -195000000:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.26e+172)
   t
   (if (<= z -2.8e+41)
     (* (/ y (- a z)) t)
     (if (<= z -195000000.0)
       (* x (/ y z))
       (if (<= z 3.8e+87) (* x (- 1.0 (/ y a))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.26e+172) {
		tmp = t;
	} else if (z <= -2.8e+41) {
		tmp = (y / (a - z)) * t;
	} else if (z <= -195000000.0) {
		tmp = x * (y / z);
	} else if (z <= 3.8e+87) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.26d+172)) then
        tmp = t
    else if (z <= (-2.8d+41)) then
        tmp = (y / (a - z)) * t
    else if (z <= (-195000000.0d0)) then
        tmp = x * (y / z)
    else if (z <= 3.8d+87) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.26e+172) {
		tmp = t;
	} else if (z <= -2.8e+41) {
		tmp = (y / (a - z)) * t;
	} else if (z <= -195000000.0) {
		tmp = x * (y / z);
	} else if (z <= 3.8e+87) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.26e+172:
		tmp = t
	elif z <= -2.8e+41:
		tmp = (y / (a - z)) * t
	elif z <= -195000000.0:
		tmp = x * (y / z)
	elif z <= 3.8e+87:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.26e+172)
		tmp = t;
	elseif (z <= -2.8e+41)
		tmp = Float64(Float64(y / Float64(a - z)) * t);
	elseif (z <= -195000000.0)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 3.8e+87)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.26e+172)
		tmp = t;
	elseif (z <= -2.8e+41)
		tmp = (y / (a - z)) * t;
	elseif (z <= -195000000.0)
		tmp = x * (y / z);
	elseif (z <= 3.8e+87)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.26e+172], t, If[LessEqual[z, -2.8e+41], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, -195000000.0], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+87], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2600000000000001e172 or 3.80000000000000011e87 < z

   1. Initial program 36.5%

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

      1. associate-/l* 64.1%

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

   3. Simplified 64.1%

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

   5. Taylor expanded in z around inf 51.2%

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

   if -1.2600000000000001e172 < z < -2.7999999999999999e41

   1. Initial program 66.6%

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

      1. associate-/l* 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in x around 0 40.9%

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

      1. associate-/l* 53.1%

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

   7. Simplified 53.1%

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

   8. Taylor expanded in y around inf 24.7%

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

      1. associate-/l* 36.9%

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

   10. Simplified 36.9%

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

   if -2.7999999999999999e41 < z < -1.95e8

   1. Initial program 58.7%

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

      1. associate-/l* 68.7%

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

   3. Simplified 68.7%

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

   5. Taylor expanded in y around -inf 27.2%

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

   6. Taylor expanded in t around 0 26.9%

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

      1. associate-*r* 26.9%

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

      2. mul-1-neg 26.9%

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

   8. Simplified 26.9%

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

   9. Taylor expanded in a around 0 26.9%

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

       1. associate-/l* 35.5%

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

   11. Simplified 35.5%

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

   if -1.95e8 < z < 3.80000000000000011e87

   1. Initial program 87.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 61.7%

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

   6. Taylor expanded in x around inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

   8. Simplified 53.0%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+172}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{a - z} \cdot t\\ \mathbf{elif}\;z \leq -195000000:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+172}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+40}:\\ \;\;\;\;\frac{y}{a - z} \cdot t\\ \mathbf{elif}\;z \leq -225000000:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.26e+172)
   t
   (if (<= z -7.6e+40)
     (* (/ y (- a z)) t)
     (if (<= z -225000000.0)
       (* x (/ y z))
       (if (<= z 9.5e+84) (* x (- 1.0 (/ y a))) (+ t (* a (/ t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.26e+172) {
		tmp = t;
	} else if (z <= -7.6e+40) {
		tmp = (y / (a - z)) * t;
	} else if (z <= -225000000.0) {
		tmp = x * (y / z);
	} else if (z <= 9.5e+84) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t + (a * (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 <= (-1.26d+172)) then
        tmp = t
    else if (z <= (-7.6d+40)) then
        tmp = (y / (a - z)) * t
    else if (z <= (-225000000.0d0)) then
        tmp = x * (y / z)
    else if (z <= 9.5d+84) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t + (a * (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 <= -1.26e+172) {
		tmp = t;
	} else if (z <= -7.6e+40) {
		tmp = (y / (a - z)) * t;
	} else if (z <= -225000000.0) {
		tmp = x * (y / z);
	} else if (z <= 9.5e+84) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t + (a * (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.26e+172:
		tmp = t
	elif z <= -7.6e+40:
		tmp = (y / (a - z)) * t
	elif z <= -225000000.0:
		tmp = x * (y / z)
	elif z <= 9.5e+84:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t + (a * (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.26e+172)
		tmp = t;
	elseif (z <= -7.6e+40)
		tmp = Float64(Float64(y / Float64(a - z)) * t);
	elseif (z <= -225000000.0)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 9.5e+84)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t + Float64(a * Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.26e+172)
		tmp = t;
	elseif (z <= -7.6e+40)
		tmp = (y / (a - z)) * t;
	elseif (z <= -225000000.0)
		tmp = x * (y / z);
	elseif (z <= 9.5e+84)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t + (a * (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.26e+172], t, If[LessEqual[z, -7.6e+40], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, -225000000.0], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+84], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.2600000000000001e172

   1. Initial program 29.7%

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

      1. associate-/l* 59.1%

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

   3. Simplified 59.1%

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

   5. Taylor expanded in z around inf 53.2%

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

   if -1.2600000000000001e172 < z < -7.60000000000000009e40

   1. Initial program 66.6%

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

      1. associate-/l* 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in x around 0 40.9%

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

      1. associate-/l* 53.1%

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

   7. Simplified 53.1%

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

   8. Taylor expanded in y around inf 24.7%

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

      1. associate-/l* 36.9%

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

   10. Simplified 36.9%

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

   if -7.60000000000000009e40 < z < -2.25e8

   1. Initial program 58.7%

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

      1. associate-/l* 68.7%

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

   3. Simplified 68.7%

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

   5. Taylor expanded in y around -inf 27.2%

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

   6. Taylor expanded in t around 0 26.9%

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

      1. associate-*r* 26.9%

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

      2. mul-1-neg 26.9%

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

   8. Simplified 26.9%

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

   9. Taylor expanded in a around 0 26.9%

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

       1. associate-/l* 35.5%

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

   11. Simplified 35.5%

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

   if -2.25e8 < z < 9.49999999999999979e84

   1. Initial program 87.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 61.5%

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

   6. Taylor expanded in x around inf 53.3%

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

      1. mul-1-neg 53.3%

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

      2. unsub-neg 53.3%

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

   8. Simplified 53.3%

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

   if 9.49999999999999979e84 < z

   1. Initial program 41.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 y around 0 33.0%

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

      1. mul-1-neg 33.0%

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

      2. unsub-neg 33.0%

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

      3. associate-/l* 54.7%

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

   7. Simplified 54.7%

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

   8. Taylor expanded in z around inf 47.7%

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

      1. mul-1-neg 47.7%

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

      2. associate-+r+ 47.7%

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

      3. mul-1-neg 47.7%

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

      4. distribute-rgt1-in 47.7%

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

      5. metadata-eval 47.7%

         \[\leadsto \left(\color{blue}{0} \cdot x + \frac{a \cdot t}{z}\right) - \left(-1 \cdot t + \frac{a \cdot x}{z}\right) \]

      6. mul0-lft 47.7%

         \[\leadsto \left(\color{blue}{0} + \frac{a \cdot t}{z}\right) - \left(-1 \cdot t + \frac{a \cdot x}{z}\right) \]

      7. associate-/l* 55.7%

         \[\leadsto \left(0 + \color{blue}{a \cdot \frac{t}{z}}\right) - \left(-1 \cdot t + \frac{a \cdot x}{z}\right) \]

      8. +-commutative 55.7%

         \[\leadsto \left(0 + a \cdot \frac{t}{z}\right) - \color{blue}{\left(\frac{a \cdot x}{z} + -1 \cdot t\right)} \]

      9. mul-1-neg 55.7%

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

      10. unsub-neg 55.7%

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

      11. associate-/l* 57.1%

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

   10. Simplified 57.1%

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

   11. Taylor expanded in x around 0 43.3%

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

       1. associate-/l* 51.4%

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

   13. Simplified 51.4%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+172}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+40}:\\ \;\;\;\;\frac{y}{a - z} \cdot t\\ \mathbf{elif}\;z \leq -225000000:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+134}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -7.8e+134)
     t
     (if (<= z 1.65e-223)
       t_1
       (if (<= z 6.2e-114)
         (* x (- 1.0 (/ y a)))
         (if (<= z 3.2e+98) t_1 (+ t (* a (/ t z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -7.8e+134) {
		tmp = t;
	} else if (z <= 1.65e-223) {
		tmp = t_1;
	} else if (z <= 6.2e-114) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.2e+98) {
		tmp = t_1;
	} else {
		tmp = t + (a * (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) :: tmp
    t_1 = x + (t * (y / a))
    if (z <= (-7.8d+134)) then
        tmp = t
    else if (z <= 1.65d-223) then
        tmp = t_1
    else if (z <= 6.2d-114) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 3.2d+98) then
        tmp = t_1
    else
        tmp = t + (a * (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 + (t * (y / a));
	double tmp;
	if (z <= -7.8e+134) {
		tmp = t;
	} else if (z <= 1.65e-223) {
		tmp = t_1;
	} else if (z <= 6.2e-114) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.2e+98) {
		tmp = t_1;
	} else {
		tmp = t + (a * (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -7.8e+134:
		tmp = t
	elif z <= 1.65e-223:
		tmp = t_1
	elif z <= 6.2e-114:
		tmp = x * (1.0 - (y / a))
	elif z <= 3.2e+98:
		tmp = t_1
	else:
		tmp = t + (a * (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -7.8e+134)
		tmp = t;
	elseif (z <= 1.65e-223)
		tmp = t_1;
	elseif (z <= 6.2e-114)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 3.2e+98)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(a * Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -7.8e+134)
		tmp = t;
	elseif (z <= 1.65e-223)
		tmp = t_1;
	elseif (z <= 6.2e-114)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 3.2e+98)
		tmp = t_1;
	else
		tmp = t + (a * (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+134], t, If[LessEqual[z, 1.65e-223], t$95$1, If[LessEqual[z, 6.2e-114], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+98], t$95$1, N[(t + N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.79999999999999967e134

   1. Initial program 34.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 z around inf 46.9%

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

   if -7.79999999999999967e134 < z < 1.64999999999999997e-223 or 6.2e-114 < z < 3.2000000000000002e98

   1. Initial program 82.8%

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

      1. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in z around 0 53.9%

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

   6. Taylor expanded in t around inf 47.8%

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

      1. associate-/l* 52.7%

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

   8. Simplified 52.7%

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

   if 1.64999999999999997e-223 < z < 6.2e-114

   1. Initial program 92.6%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in z around 0 67.1%

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

   6. Taylor expanded in x around inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. unsub-neg 69.9%

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

   8. Simplified 69.9%

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

   if 3.2000000000000002e98 < z

   1. Initial program 39.7%

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

      1. associate-/l* 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in y around 0 32.8%

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

      1. mul-1-neg 32.8%

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

      2. unsub-neg 32.8%

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

      3. associate-/l* 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in z around inf 46.4%

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

      1. mul-1-neg 46.4%

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

      2. associate-+r+ 46.4%

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

      3. mul-1-neg 46.4%

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

      4. distribute-rgt1-in 46.4%

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

      5. metadata-eval 46.4%

         \[\leadsto \left(\color{blue}{0} \cdot x + \frac{a \cdot t}{z}\right) - \left(-1 \cdot t + \frac{a \cdot x}{z}\right) \]

      6. mul0-lft 46.4%

         \[\leadsto \left(\color{blue}{0} + \frac{a \cdot t}{z}\right) - \left(-1 \cdot t + \frac{a \cdot x}{z}\right) \]

      7. associate-/l* 55.0%

         \[\leadsto \left(0 + \color{blue}{a \cdot \frac{t}{z}}\right) - \left(-1 \cdot t + \frac{a \cdot x}{z}\right) \]

      8. +-commutative 55.0%

         \[\leadsto \left(0 + a \cdot \frac{t}{z}\right) - \color{blue}{\left(\frac{a \cdot x}{z} + -1 \cdot t\right)} \]

      9. mul-1-neg 55.0%

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

      10. unsub-neg 55.0%

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

      11. associate-/l* 56.4%

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

   10. Simplified 56.4%

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

   11. Taylor expanded in x around 0 41.8%

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

       1. associate-/l* 50.4%

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

   13. Simplified 50.4%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+134}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-223}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+98}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))) (t_2 (* t (/ z (- z a)))))
   (if (<= z -4.9e+100)
     t_2
     (if (<= z 3.4e-224)
       t_1
       (if (<= z 5.3e-114)
         (* x (- 1.0 (/ y a)))
         (if (<= z 2.6e+95) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -4.9e+100) {
		tmp = t_2;
	} else if (z <= 3.4e-224) {
		tmp = t_1;
	} else if (z <= 5.3e-114) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.6e+95) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    t_2 = t * (z / (z - a))
    if (z <= (-4.9d+100)) then
        tmp = t_2
    else if (z <= 3.4d-224) then
        tmp = t_1
    else if (z <= 5.3d-114) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 2.6d+95) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -4.9e+100) {
		tmp = t_2;
	} else if (z <= 3.4e-224) {
		tmp = t_1;
	} else if (z <= 5.3e-114) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.6e+95) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = t * (z / (z - a))
	tmp = 0
	if z <= -4.9e+100:
		tmp = t_2
	elif z <= 3.4e-224:
		tmp = t_1
	elif z <= 5.3e-114:
		tmp = x * (1.0 - (y / a))
	elif z <= 2.6e+95:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -4.9e+100)
		tmp = t_2;
	elseif (z <= 3.4e-224)
		tmp = t_1;
	elseif (z <= 5.3e-114)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 2.6e+95)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	t_2 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -4.9e+100)
		tmp = t_2;
	elseif (z <= 3.4e-224)
		tmp = t_1;
	elseif (z <= 5.3e-114)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 2.6e+95)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.9e+100], t$95$2, If[LessEqual[z, 3.4e-224], t$95$1, If[LessEqual[z, 5.3e-114], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+95], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.89999999999999967e100 or 2.5999999999999999e95 < z

   1. Initial program 41.6%

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

      1. associate-/l* 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in y around 0 32.7%

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

      1. mul-1-neg 32.7%

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

      2. unsub-neg 32.7%

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

      3. associate-/l* 52.6%

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

   7. Simplified 52.6%

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

   8. Taylor expanded in x around 0 31.6%

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

      1. mul-1-neg 31.6%

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

      2. associate-/l* 52.4%

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

      3. distribute-rgt-neg-in 52.4%

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

      4. mul-1-neg 52.4%

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

      5. associate-*r/ 52.4%

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

      6. neg-mul-1 52.4%

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

   10. Simplified 52.4%

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

   if -4.89999999999999967e100 < z < 3.39999999999999992e-224 or 5.29999999999999973e-114 < z < 2.5999999999999999e95

   1. Initial program 83.1%

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

      1. associate-/l* 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in z around 0 55.7%

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

   6. Taylor expanded in t around inf 49.2%

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

      1. associate-/l* 54.4%

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

   8. Simplified 54.4%

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

   if 3.39999999999999992e-224 < z < 5.29999999999999973e-114

   1. Initial program 92.6%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in z around 0 67.1%

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

   6. Taylor expanded in x around inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. unsub-neg 69.9%

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

   8. Simplified 69.9%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-224}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+95}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -7.8e+29)
     t_2
     (if (<= a -7e-208)
       t_1
       (if (<= a 1.15e-261)
         (* x (/ y (- z a)))
         (if (<= a 1.6e+35) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -7.8e+29) {
		tmp = t_2;
	} else if (a <= -7e-208) {
		tmp = t_1;
	} else if (a <= 1.15e-261) {
		tmp = x * (y / (z - a));
	} else if (a <= 1.6e+35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    t_2 = x + (t * (y / a))
    if (a <= (-7.8d+29)) then
        tmp = t_2
    else if (a <= (-7d-208)) then
        tmp = t_1
    else if (a <= 1.15d-261) then
        tmp = x * (y / (z - a))
    else if (a <= 1.6d+35) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -7.8e+29) {
		tmp = t_2;
	} else if (a <= -7e-208) {
		tmp = t_1;
	} else if (a <= 1.15e-261) {
		tmp = x * (y / (z - a));
	} else if (a <= 1.6e+35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	t_2 = x + (t * (y / a))
	tmp = 0
	if a <= -7.8e+29:
		tmp = t_2
	elif a <= -7e-208:
		tmp = t_1
	elif a <= 1.15e-261:
		tmp = x * (y / (z - a))
	elif a <= 1.6e+35:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -7.8e+29)
		tmp = t_2;
	elseif (a <= -7e-208)
		tmp = t_1;
	elseif (a <= 1.15e-261)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (a <= 1.6e+35)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -7.8e+29)
		tmp = t_2;
	elseif (a <= -7e-208)
		tmp = t_1;
	elseif (a <= 1.15e-261)
		tmp = x * (y / (z - a));
	elseif (a <= 1.6e+35)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.8e+29], t$95$2, If[LessEqual[a, -7e-208], t$95$1, If[LessEqual[a, 1.15e-261], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+35], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.79999999999999937e29 or 1.59999999999999991e35 < a

   1. Initial program 70.7%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around 0 59.9%

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

   6. Taylor expanded in t around inf 57.8%

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

      1. associate-/l* 63.1%

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

   8. Simplified 63.1%

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

   if -7.79999999999999937e29 < a < -6.99999999999999982e-208 or 1.15e-261 < a < 1.59999999999999991e35

   1. Initial program 70.8%

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

      1. associate-/l* 71.6%

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

   3. Simplified 71.6%

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

   5. Taylor expanded in x around 0 55.7%

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

      1. associate-/l* 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in a around 0 52.5%

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

      1. associate-*r/ 52.5%

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

      2. neg-mul-1 52.5%

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

   10. Simplified 52.5%

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

   if -6.99999999999999982e-208 < a < 1.15e-261

   1. Initial program 65.8%

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

      1. associate-/l* 69.0%

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

   3. Simplified 69.0%

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

   5. Taylor expanded in y around -inf 62.3%

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

   6. Taylor expanded in t around 0 47.5%

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

      1. mul-1-neg 47.5%

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

      2. associate-/l* 61.5%

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

   8. Simplified 61.5%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+29}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-208}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-251}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -1.35e+30)
     t_2
     (if (<= a -2.45e-236)
       t_1
       (if (<= a 3.1e-251) (/ (* y (- x t)) z) (if (<= a 1.2e+35) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -1.35e+30) {
		tmp = t_2;
	} else if (a <= -2.45e-236) {
		tmp = t_1;
	} else if (a <= 3.1e-251) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.2e+35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    t_2 = x + (t * (y / a))
    if (a <= (-1.35d+30)) then
        tmp = t_2
    else if (a <= (-2.45d-236)) then
        tmp = t_1
    else if (a <= 3.1d-251) then
        tmp = (y * (x - t)) / z
    else if (a <= 1.2d+35) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -1.35e+30) {
		tmp = t_2;
	} else if (a <= -2.45e-236) {
		tmp = t_1;
	} else if (a <= 3.1e-251) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.2e+35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	t_2 = x + (t * (y / a))
	tmp = 0
	if a <= -1.35e+30:
		tmp = t_2
	elif a <= -2.45e-236:
		tmp = t_1
	elif a <= 3.1e-251:
		tmp = (y * (x - t)) / z
	elif a <= 1.2e+35:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.35e+30)
		tmp = t_2;
	elseif (a <= -2.45e-236)
		tmp = t_1;
	elseif (a <= 3.1e-251)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 1.2e+35)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -1.35e+30)
		tmp = t_2;
	elseif (a <= -2.45e-236)
		tmp = t_1;
	elseif (a <= 3.1e-251)
		tmp = (y * (x - t)) / z;
	elseif (a <= 1.2e+35)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.35e+30], t$95$2, If[LessEqual[a, -2.45e-236], t$95$1, If[LessEqual[a, 3.1e-251], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.2e+35], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3499999999999999e30 or 1.20000000000000007e35 < a

   1. Initial program 70.7%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around 0 59.9%

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

   6. Taylor expanded in t around inf 57.8%

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

      1. associate-/l* 63.1%

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

   8. Simplified 63.1%

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

   if -1.3499999999999999e30 < a < -2.4499999999999998e-236 or 3.10000000000000003e-251 < a < 1.20000000000000007e35

   1. Initial program 68.5%

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

      1. associate-/l* 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in x around 0 55.6%

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

      1. associate-/l* 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in a around 0 52.5%

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

      1. associate-*r/ 52.5%

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

      2. neg-mul-1 52.5%

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

   10. Simplified 52.5%

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

   if -2.4499999999999998e-236 < a < 3.10000000000000003e-251

   1. Initial program 72.6%

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

      1. associate-/l* 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in y around -inf 71.7%

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

   6. Taylor expanded in a around 0 65.0%

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

      1. associate-*r/ 65.0%

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

      2. mul-1-neg 65.0%

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

   8. Simplified 65.0%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+30}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-236}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-251}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{if}\;a \leq -18000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-151}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- t x) (/ (- z y) a)))))
   (if (<= a -18000000000000.0)
     t_1
     (if (<= a 2.75e-151)
       (+ t (/ (* (- t x) (- a y)) z))
       (if (<= a 3.1e+19) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t - x) * ((z - y) / a));
	double tmp;
	if (a <= -18000000000000.0) {
		tmp = t_1;
	} else if (a <= 2.75e-151) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (a <= 3.1e+19) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((t - x) * ((z - y) / a))
    if (a <= (-18000000000000.0d0)) then
        tmp = t_1
    else if (a <= 2.75d-151) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (a <= 3.1d+19) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t - x) * ((z - y) / a));
	double tmp;
	if (a <= -18000000000000.0) {
		tmp = t_1;
	} else if (a <= 2.75e-151) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (a <= 3.1e+19) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((t - x) * ((z - y) / a))
	tmp = 0
	if a <= -18000000000000.0:
		tmp = t_1
	elif a <= 2.75e-151:
		tmp = t + (((t - x) * (a - y)) / z)
	elif a <= 3.1e+19:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)))
	tmp = 0.0
	if (a <= -18000000000000.0)
		tmp = t_1;
	elseif (a <= 2.75e-151)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (a <= 3.1e+19)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((t - x) * ((z - y) / a));
	tmp = 0.0;
	if (a <= -18000000000000.0)
		tmp = t_1;
	elseif (a <= 2.75e-151)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (a <= 3.1e+19)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -18000000000000.0], t$95$1, If[LessEqual[a, 2.75e-151], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e+19], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8e13 or 3.1e19 < 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* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in a around inf 64.9%

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

      1. associate-/l* 78.4%

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

   7. Simplified 78.4%

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

   if -1.8e13 < a < 2.7499999999999999e-151

   1. Initial program 65.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 76.8%

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

      1. associate--l+ 76.8%

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

      2. associate-*r/ 76.8%

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

      3. associate-*r/ 76.8%

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

      4. mul-1-neg 76.8%

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

      5. div-sub 76.8%

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

      6. mul-1-neg 76.8%

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

      7. distribute-lft-out-- 76.8%

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

      8. associate-*r/ 76.8%

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

      9. mul-1-neg 76.8%

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

      10. unsub-neg 76.8%

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

      11. distribute-rgt-out-- 76.8%

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

   7. Simplified 76.8%

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

   if 2.7499999999999999e-151 < a < 3.1e19

   1. Initial program 75.5%

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

      1. associate-/l* 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in x around 0 60.0%

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

      1. associate-/l* 74.9%

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

   7. Simplified 74.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -18000000000000:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-151}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-71} \lor \neg \left(x \leq 2.35 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -9e+186)
   (* x (/ y (- z a)))
   (if (or (<= x -7e-71) (not (<= x 2.35e-23)))
     (* x (- 1.0 (/ y a)))
     (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9e+186) {
		tmp = x * (y / (z - a));
	} else if ((x <= -7e-71) || !(x <= 2.35e-23)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-9d+186)) then
        tmp = x * (y / (z - a))
    else if ((x <= (-7d-71)) .or. (.not. (x <= 2.35d-23))) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9e+186) {
		tmp = x * (y / (z - a));
	} else if ((x <= -7e-71) || !(x <= 2.35e-23)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -9e+186:
		tmp = x * (y / (z - a))
	elif (x <= -7e-71) or not (x <= 2.35e-23):
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -9e+186)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif ((x <= -7e-71) || !(x <= 2.35e-23))
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -9e+186)
		tmp = x * (y / (z - a));
	elseif ((x <= -7e-71) || ~((x <= 2.35e-23)))
		tmp = x * (1.0 - (y / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -9e+186], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -7e-71], N[Not[LessEqual[x, 2.35e-23]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.0000000000000009e186

   1. Initial program 44.0%

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

      1. associate-/l* 62.3%

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

   3. Simplified 62.3%

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

   5. Taylor expanded in y around -inf 44.8%

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

   6. Taylor expanded in t around 0 40.7%

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

      1. mul-1-neg 40.7%

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

      2. associate-/l* 55.5%

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

   8. Simplified 55.5%

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

   if -9.0000000000000009e186 < x < -6.9999999999999998e-71 or 2.35e-23 < x

   1. Initial program 67.7%

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

      1. associate-/l* 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in z around 0 49.2%

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

   6. Taylor expanded in x around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. unsub-neg 55.4%

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

   8. Simplified 55.4%

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

   if -6.9999999999999998e-71 < x < 2.35e-23

   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* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in x around 0 65.4%

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

      1. associate-/l* 77.3%

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

   7. Simplified 77.3%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-71} \lor \neg \left(x \leq 2.35 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 57.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+187}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-65} \lor \neg \left(x \leq 2.35 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.75e+187)
   (* y (/ (- x t) (- z a)))
   (if (or (<= x -1.56e-65) (not (<= x 2.35e-23)))
     (* x (- 1.0 (/ y a)))
     (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.75e+187) {
		tmp = y * ((x - t) / (z - a));
	} else if ((x <= -1.56e-65) || !(x <= 2.35e-23)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.75d+187)) then
        tmp = y * ((x - t) / (z - a))
    else if ((x <= (-1.56d-65)) .or. (.not. (x <= 2.35d-23))) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.75e+187) {
		tmp = y * ((x - t) / (z - a));
	} else if ((x <= -1.56e-65) || !(x <= 2.35e-23)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.75e+187:
		tmp = y * ((x - t) / (z - a))
	elif (x <= -1.56e-65) or not (x <= 2.35e-23):
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.75e+187)
		tmp = Float64(y * Float64(Float64(x - t) / Float64(z - a)));
	elseif ((x <= -1.56e-65) || !(x <= 2.35e-23))
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.75e+187)
		tmp = y * ((x - t) / (z - a));
	elseif ((x <= -1.56e-65) || ~((x <= 2.35e-23)))
		tmp = x * (1.0 - (y / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.75e+187], N[(y * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.56e-65], N[Not[LessEqual[x, 2.35e-23]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7499999999999999e187

   1. Initial program 44.0%

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

      1. associate-/l* 62.3%

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

   3. Simplified 62.3%

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

   5. Taylor expanded in y around inf 66.8%

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

      1. div-sub 66.8%

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

   7. Simplified 66.8%

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

   if -1.7499999999999999e187 < x < -1.55999999999999993e-65 or 2.35e-23 < x

   1. Initial program 67.7%

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

      1. associate-/l* 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in z around 0 49.2%

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

   6. Taylor expanded in x around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. unsub-neg 55.4%

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

   8. Simplified 55.4%

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

   if -1.55999999999999993e-65 < x < 2.35e-23

   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* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in x around 0 65.4%

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

      1. associate-/l* 77.3%

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

   7. Simplified 77.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+187}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-65} \lor \neg \left(x \leq 2.35 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-78} \lor \neg \left(a \leq 1.75 \cdot 10^{-116}\right):\\ \;\;\;\;x - \frac{x - t}{z - a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.75e-78) (not (<= a 1.75e-116)))
   (- x (* (/ (- x t) (- z a)) (- z y)))
   (+ t (/ (* (- t x) (- a y)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.75e-78) || !(a <= 1.75e-116)) {
		tmp = x - (((x - t) / (z - a)) * (z - y));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.75d-78)) .or. (.not. (a <= 1.75d-116))) then
        tmp = x - (((x - t) / (z - a)) * (z - y))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.75e-78) || !(a <= 1.75e-116)) {
		tmp = x - (((x - t) / (z - a)) * (z - y));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.75e-78) or not (a <= 1.75e-116):
		tmp = x - (((x - t) / (z - a)) * (z - y))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.75e-78) || !(a <= 1.75e-116))
		tmp = Float64(x - Float64(Float64(Float64(x - t) / Float64(z - a)) * Float64(z - y)));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.75e-78) || ~((a <= 1.75e-116)))
		tmp = x - (((x - t) / (z - a)) * (z - y));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.75e-78], N[Not[LessEqual[a, 1.75e-116]], $MachinePrecision]], N[(x - N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.75e-78 or 1.74999999999999992e-116 < a

   1. Initial program 72.2%

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

      1. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   if -1.75e-78 < a < 1.74999999999999992e-116

   1. Initial program 66.1%

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

      1. associate-/l* 66.2%

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

   3. Simplified 66.2%

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

   5. Taylor expanded in z around inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. associate-*r/ 78.2%

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

      3. associate-*r/ 78.2%

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

      4. mul-1-neg 78.2%

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

      5. div-sub 78.2%

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

      6. mul-1-neg 78.2%

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

      7. distribute-lft-out-- 78.2%

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

      8. associate-*r/ 78.2%

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

      9. mul-1-neg 78.2%

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

      10. unsub-neg 78.2%

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

      11. distribute-rgt-out-- 78.2%

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

   7. Simplified 78.2%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-78} \lor \neg \left(a \leq 1.75 \cdot 10^{-116}\right):\\ \;\;\;\;x - \frac{x - t}{z - a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 47.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -7.1 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+36}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= a -7.1e-90)
     t_1
     (if (<= a 1.65e-184)
       (* x (/ y (- z a)))
       (if (<= a 8e+36) (+ t (* a (/ t z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (a <= -7.1e-90) {
		tmp = t_1;
	} else if (a <= 1.65e-184) {
		tmp = x * (y / (z - a));
	} else if (a <= 8e+36) {
		tmp = t + (a * (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 + (t * (y / a))
    if (a <= (-7.1d-90)) then
        tmp = t_1
    else if (a <= 1.65d-184) then
        tmp = x * (y / (z - a))
    else if (a <= 8d+36) then
        tmp = t + (a * (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 + (t * (y / a));
	double tmp;
	if (a <= -7.1e-90) {
		tmp = t_1;
	} else if (a <= 1.65e-184) {
		tmp = x * (y / (z - a));
	} else if (a <= 8e+36) {
		tmp = t + (a * (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if a <= -7.1e-90:
		tmp = t_1
	elif a <= 1.65e-184:
		tmp = x * (y / (z - a))
	elif a <= 8e+36:
		tmp = t + (a * (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -7.1e-90)
		tmp = t_1;
	elseif (a <= 1.65e-184)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (a <= 8e+36)
		tmp = Float64(t + Float64(a * Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -7.1e-90)
		tmp = t_1;
	elseif (a <= 1.65e-184)
		tmp = x * (y / (z - a));
	elseif (a <= 8e+36)
		tmp = t + (a * (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[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.1e-90], t$95$1, If[LessEqual[a, 1.65e-184], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+36], N[(t + N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.1000000000000001e-90 or 8.00000000000000034e36 < a

   1. Initial program 69.8%

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

      1. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in z around 0 55.0%

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

   6. Taylor expanded in t around inf 52.6%

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

      1. associate-/l* 57.2%

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

   8. Simplified 57.2%

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

   if -7.1000000000000001e-90 < a < 1.6499999999999999e-184

   1. Initial program 67.4%

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

      1. associate-/l* 66.2%

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

   3. Simplified 66.2%

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

   5. Taylor expanded in y around -inf 57.4%

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

   6. Taylor expanded in t around 0 41.5%

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

      1. mul-1-neg 41.5%

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

      2. associate-/l* 48.0%

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

   8. Simplified 48.0%

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

   if 1.6499999999999999e-184 < a < 8.00000000000000034e36

   1. Initial program 76.3%

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

      1. associate-/l* 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in y around 0 40.4%

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

      1. mul-1-neg 40.4%

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

      2. unsub-neg 40.4%

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

      3. associate-/l* 47.2%

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

   7. Simplified 47.2%

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

   8. Taylor expanded in z around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. associate-+r+ 53.4%

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

      3. mul-1-neg 53.4%

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

      4. distribute-rgt1-in 53.4%

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

      5. metadata-eval 53.4%

         \[\leadsto \left(\color{blue}{0} \cdot x + \frac{a \cdot t}{z}\right) - \left(-1 \cdot t + \frac{a \cdot x}{z}\right) \]

      6. mul0-lft 53.4%

         \[\leadsto \left(\color{blue}{0} + \frac{a \cdot t}{z}\right) - \left(-1 \cdot t + \frac{a \cdot x}{z}\right) \]

      7. associate-/l* 55.7%

         \[\leadsto \left(0 + \color{blue}{a \cdot \frac{t}{z}}\right) - \left(-1 \cdot t + \frac{a \cdot x}{z}\right) \]

      8. +-commutative 55.7%

         \[\leadsto \left(0 + a \cdot \frac{t}{z}\right) - \color{blue}{\left(\frac{a \cdot x}{z} + -1 \cdot t\right)} \]

      9. mul-1-neg 55.7%

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

      10. unsub-neg 55.7%

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

      11. associate-/l* 55.7%

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

   10. Simplified 55.7%

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

   11. Taylor expanded in x around 0 44.0%

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

       1. associate-/l* 46.3%

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

   13. Simplified 46.3%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.1 \cdot 10^{-90}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+36}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.4 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-157}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.4e+123)
   x
   (if (<= a -2.9e-157)
     t
     (if (<= a 8.2e-183) (* x (/ y z)) (if (<= a 2.2e+46) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.4e+123) {
		tmp = x;
	} else if (a <= -2.9e-157) {
		tmp = t;
	} else if (a <= 8.2e-183) {
		tmp = x * (y / z);
	} else if (a <= 2.2e+46) {
		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 <= (-9.4d+123)) then
        tmp = x
    else if (a <= (-2.9d-157)) then
        tmp = t
    else if (a <= 8.2d-183) then
        tmp = x * (y / z)
    else if (a <= 2.2d+46) 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 <= -9.4e+123) {
		tmp = x;
	} else if (a <= -2.9e-157) {
		tmp = t;
	} else if (a <= 8.2e-183) {
		tmp = x * (y / z);
	} else if (a <= 2.2e+46) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.4e+123:
		tmp = x
	elif a <= -2.9e-157:
		tmp = t
	elif a <= 8.2e-183:
		tmp = x * (y / z)
	elif a <= 2.2e+46:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.4e+123)
		tmp = x;
	elseif (a <= -2.9e-157)
		tmp = t;
	elseif (a <= 8.2e-183)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 2.2e+46)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.4e+123)
		tmp = x;
	elseif (a <= -2.9e-157)
		tmp = t;
	elseif (a <= 8.2e-183)
		tmp = x * (y / z);
	elseif (a <= 2.2e+46)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.4e+123], x, If[LessEqual[a, -2.9e-157], t, If[LessEqual[a, 8.2e-183], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+46], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.39999999999999958e123 or 2.2e46 < a

   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* 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 a around inf 50.1%

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

   if -9.39999999999999958e123 < a < -2.89999999999999988e-157 or 8.1999999999999996e-183 < a < 2.2e46

   1. Initial program 70.8%

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

      1. associate-/l* 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in z around inf 34.9%

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

   if -2.89999999999999988e-157 < a < 8.1999999999999996e-183

   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* 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 y around -inf 59.5%

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

   6. Taylor expanded in t around 0 41.8%

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

      1. associate-*r* 41.8%

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

      2. mul-1-neg 41.8%

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

   8. Simplified 41.8%

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

   9. Taylor expanded in a around 0 35.0%

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

       1. associate-/l* 44.5%

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

   11. Simplified 44.5%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.4 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-157}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-189}:\\ \;\;\;\;\frac{y}{a - z} \cdot t\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.2e+126)
   x
   (if (<= a -2.6e-189)
     (* (/ y (- a z)) t)
     (if (<= a 2.7e-185) (* x (/ y z)) (if (<= a 5e+41) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e+126) {
		tmp = x;
	} else if (a <= -2.6e-189) {
		tmp = (y / (a - z)) * t;
	} else if (a <= 2.7e-185) {
		tmp = x * (y / z);
	} else if (a <= 5e+41) {
		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 <= (-7.2d+126)) then
        tmp = x
    else if (a <= (-2.6d-189)) then
        tmp = (y / (a - z)) * t
    else if (a <= 2.7d-185) then
        tmp = x * (y / z)
    else if (a <= 5d+41) 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 <= -7.2e+126) {
		tmp = x;
	} else if (a <= -2.6e-189) {
		tmp = (y / (a - z)) * t;
	} else if (a <= 2.7e-185) {
		tmp = x * (y / z);
	} else if (a <= 5e+41) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.2e+126:
		tmp = x
	elif a <= -2.6e-189:
		tmp = (y / (a - z)) * t
	elif a <= 2.7e-185:
		tmp = x * (y / z)
	elif a <= 5e+41:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.2e+126)
		tmp = x;
	elseif (a <= -2.6e-189)
		tmp = Float64(Float64(y / Float64(a - z)) * t);
	elseif (a <= 2.7e-185)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 5e+41)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.2e+126)
		tmp = x;
	elseif (a <= -2.6e-189)
		tmp = (y / (a - z)) * t;
	elseif (a <= 2.7e-185)
		tmp = x * (y / z);
	elseif (a <= 5e+41)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.2e+126], x, If[LessEqual[a, -2.6e-189], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 2.7e-185], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+41], t, x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.2000000000000001e126 or 5.00000000000000022e41 < a

   1. Initial program 69.4%

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

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in a around inf 50.5%

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

   if -7.2000000000000001e126 < a < -2.5999999999999999e-189

   1. Initial program 66.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around 0 51.8%

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

      1. associate-/l* 65.5%

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

   7. Simplified 65.5%

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

   8. Taylor expanded in y around inf 27.0%

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

      1. associate-/l* 32.0%

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

   10. Simplified 32.0%

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

   if -2.5999999999999999e-189 < a < 2.69999999999999988e-185

   1. Initial program 69.5%

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

      1. associate-/l* 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in y around -inf 60.0%

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

   6. Taylor expanded in t around 0 42.9%

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

      1. associate-*r* 42.9%

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

      2. mul-1-neg 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in a around 0 35.6%

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

       1. associate-/l* 45.7%

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

   11. Simplified 45.7%

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

   if 2.69999999999999988e-185 < a < 5.00000000000000022e41

   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* 79.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in z around inf 39.3%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-189}:\\ \;\;\;\;\frac{y}{a - z} \cdot t\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 38.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.4 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.4e+123) x (if (<= a 7.2e+42) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.4e+123) {
		tmp = x;
	} else if (a <= 7.2e+42) {
		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 <= (-9.4d+123)) then
        tmp = x
    else if (a <= 7.2d+42) 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 <= -9.4e+123) {
		tmp = x;
	} else if (a <= 7.2e+42) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.4e+123:
		tmp = x
	elif a <= 7.2e+42:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.4e+123)
		tmp = x;
	elseif (a <= 7.2e+42)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.4e+123)
		tmp = x;
	elseif (a <= 7.2e+42)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.4e+123], x, If[LessEqual[a, 7.2e+42], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.39999999999999958e123 or 7.2000000000000002e42 < a

   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* 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 a around inf 50.1%

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

   if -9.39999999999999958e123 < a < 7.2000000000000002e42

   1. Initial program 70.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 30.0%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.4 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 24.6% 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 70.1%

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

   1. associate-/l* 80.9%

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

3. Simplified 80.9%

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

5. Taylor expanded in z around inf 21.9%

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

6. Final simplification 21.9%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 84.2% 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 2024059 
(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))))