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

Percentage Accurate: 67.9% → 89.9%

Time: 25.2s

Alternatives: 24

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-249} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{x - y}{\frac{a - t}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -1e-249) (not (<= t_1 0.0)))
     (+ x (/ (- x y) (/ (- a t) (- t z))))
     (+ y (* (- y x) (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-249) || !(t_1 <= 0.0)) {
		tmp = x + ((x - y) / ((a - t) / (t - z)));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if ((t_1 <= (-1d-249)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((x - y) / ((a - t) / (t - z)))
    else
        tmp = y + ((y - x) * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-249) || !(t_1 <= 0.0)) {
		tmp = x + ((x - y) / ((a - t) / (t - z)));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if (t_1 <= -1e-249) or not (t_1 <= 0.0):
		tmp = x + ((x - y) / ((a - t) / (t - z)))
	else:
		tmp = y + ((y - x) * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-249) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(x - y) / Float64(Float64(a - t) / Float64(t - z))));
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -1e-249) || ~((t_1 <= 0.0)))
		tmp = x + ((x - y) / ((a - t) / (t - z)));
	else
		tmp = y + ((y - x) * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-249], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000005e-249 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 76.8%

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

      1. clear-num 76.7%

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

      2. inv-pow 76.7%

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

      3. *-commutative 76.7%

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

      4. associate-/r* 91.7%

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

   4. Applied egg-rr 91.7%

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

      1. unpow-1 91.7%

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

      2. clear-num 91.9%

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

      3. div-sub 89.3%

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

   6. Applied egg-rr 89.3%

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

      1. div-sub 91.9%

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

   8. Simplified 91.9%

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

   if -1.00000000000000005e-249 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.0%

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

   3. Taylor expanded in t around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. div-sub 99.7%

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

      5. distribute-lft-out-- 99.7%

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

      6. associate-*r/ 99.7%

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

      7. mul-1-neg 99.7%

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

      8. unsub-neg 99.7%

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

      9. distribute-rgt-out-- 99.7%

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

      10. associate-/l* 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-249} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{x - y}{\frac{a - t}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-249}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-263}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+298}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- z a) (/ (- x y) t))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-249)
       t_2
       (if (<= t_2 5e-263)
         (+ y (* (- y x) (/ (- a z) t)))
         (if (<= t_2 4e+298) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-249) {
		tmp = t_2;
	} else if (t_2 <= 5e-263) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t_2 <= 4e+298) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-249) {
		tmp = t_2;
	} else if (t_2 <= 5e-263) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t_2 <= 4e+298) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((z - a) * ((x - y) / t))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-249:
		tmp = t_2
	elif t_2 <= 5e-263:
		tmp = y + ((y - x) * ((a - z) / t))
	elif t_2 <= 4e+298:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-249)
		tmp = t_2;
	elseif (t_2 <= 5e-263)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	elseif (t_2 <= 4e+298)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((z - a) * ((x - y) / t));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-249)
		tmp = t_2;
	elseif (t_2 <= 5e-263)
		tmp = y + ((y - x) * ((a - z) / t));
	elseif (t_2 <= 4e+298)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-249], t$95$2, If[LessEqual[t$95$2, 5e-263], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+298], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 3.9999999999999998e298 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 41.1%

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

      1. clear-num 41.1%

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

      2. inv-pow 41.1%

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

      3. *-commutative 41.1%

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

      4. associate-/r* 80.0%

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

   4. Applied egg-rr 80.0%

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

      1. unpow-1 80.1%

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

      2. clear-num 80.1%

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

      3. div-sub 73.2%

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

   6. Applied egg-rr 73.2%

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

      1. div-sub 80.1%

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

   8. Simplified 80.1%

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

   9. Taylor expanded in t around inf 49.5%

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

       1. associate--l+ 49.5%

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

       2. associate-*r/ 49.5%

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

       3. associate-*r/ 49.5%

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

       4. div-sub 50.6%

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

       5. distribute-lft-out-- 50.6%

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

       6. associate-*r/ 50.6%

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

       7. mul-1-neg 50.6%

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

       8. unsub-neg 50.6%

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

       9. div-sub 49.5%

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

       10. associate-/l* 43.9%

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

       11. associate-/l* 57.9%

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

       12. distribute-rgt-out-- 68.5%

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

   11. Simplified 68.5%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000005e-249 or 5.00000000000000006e-263 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 3.9999999999999998e298

   1. Initial program 98.7%

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

   if -1.00000000000000005e-249 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5.00000000000000006e-263

   1. Initial program 4.0%

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

   3. Taylor expanded in t around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. div-sub 99.7%

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

      5. distribute-lft-out-- 99.7%

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

      6. associate-*r/ 99.7%

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

      7. mul-1-neg 99.7%

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

      8. unsub-neg 99.7%

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

      9. distribute-rgt-out-- 99.7%

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

      10. associate-/l* 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-249}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{-263}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 4 \cdot 10^{+298}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+80}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -42000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-248}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-285}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{-235}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= t -7.5e+80)
     y
     (if (<= t -4000000000.0)
       t_2
       (if (<= t -42000.0)
         y
         (if (<= t -1.95e-150)
           t_1
           (if (<= t -2.5e-248)
             t_2
             (if (<= t 5.8e-285)
               t_1
               (if (<= t 1e-235) t_2 (if (<= t 3.2e+128) t_1 y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -7.5e+80) {
		tmp = y;
	} else if (t <= -4000000000.0) {
		tmp = t_2;
	} else if (t <= -42000.0) {
		tmp = y;
	} else if (t <= -1.95e-150) {
		tmp = t_1;
	} else if (t <= -2.5e-248) {
		tmp = t_2;
	} else if (t <= 5.8e-285) {
		tmp = t_1;
	} else if (t <= 1e-235) {
		tmp = t_2;
	} else if (t <= 3.2e+128) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    t_2 = x * (1.0d0 - (z / a))
    if (t <= (-7.5d+80)) then
        tmp = y
    else if (t <= (-4000000000.0d0)) then
        tmp = t_2
    else if (t <= (-42000.0d0)) then
        tmp = y
    else if (t <= (-1.95d-150)) then
        tmp = t_1
    else if (t <= (-2.5d-248)) then
        tmp = t_2
    else if (t <= 5.8d-285) then
        tmp = t_1
    else if (t <= 1d-235) then
        tmp = t_2
    else if (t <= 3.2d+128) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -7.5e+80) {
		tmp = y;
	} else if (t <= -4000000000.0) {
		tmp = t_2;
	} else if (t <= -42000.0) {
		tmp = y;
	} else if (t <= -1.95e-150) {
		tmp = t_1;
	} else if (t <= -2.5e-248) {
		tmp = t_2;
	} else if (t <= 5.8e-285) {
		tmp = t_1;
	} else if (t <= 1e-235) {
		tmp = t_2;
	} else if (t <= 3.2e+128) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -7.5e+80:
		tmp = y
	elif t <= -4000000000.0:
		tmp = t_2
	elif t <= -42000.0:
		tmp = y
	elif t <= -1.95e-150:
		tmp = t_1
	elif t <= -2.5e-248:
		tmp = t_2
	elif t <= 5.8e-285:
		tmp = t_1
	elif t <= 1e-235:
		tmp = t_2
	elif t <= 3.2e+128:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -7.5e+80)
		tmp = y;
	elseif (t <= -4000000000.0)
		tmp = t_2;
	elseif (t <= -42000.0)
		tmp = y;
	elseif (t <= -1.95e-150)
		tmp = t_1;
	elseif (t <= -2.5e-248)
		tmp = t_2;
	elseif (t <= 5.8e-285)
		tmp = t_1;
	elseif (t <= 1e-235)
		tmp = t_2;
	elseif (t <= 3.2e+128)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -7.5e+80)
		tmp = y;
	elseif (t <= -4000000000.0)
		tmp = t_2;
	elseif (t <= -42000.0)
		tmp = y;
	elseif (t <= -1.95e-150)
		tmp = t_1;
	elseif (t <= -2.5e-248)
		tmp = t_2;
	elseif (t <= 5.8e-285)
		tmp = t_1;
	elseif (t <= 1e-235)
		tmp = t_2;
	elseif (t <= 3.2e+128)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+80], y, If[LessEqual[t, -4000000000.0], t$95$2, If[LessEqual[t, -42000.0], y, If[LessEqual[t, -1.95e-150], t$95$1, If[LessEqual[t, -2.5e-248], t$95$2, If[LessEqual[t, 5.8e-285], t$95$1, If[LessEqual[t, 1e-235], t$95$2, If[LessEqual[t, 3.2e+128], t$95$1, y]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.49999999999999994e80 or -4e9 < t < -42000 or 3.19999999999999986e128 < t

   1. Initial program 43.5%

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

   3. Taylor expanded in t around inf 47.1%

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

   if -7.49999999999999994e80 < t < -4e9 or -1.9500000000000001e-150 < t < -2.5e-248 or 5.7999999999999999e-285 < t < 9.9999999999999996e-236

   1. Initial program 82.7%

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

   3. Taylor expanded in t around 0 68.7%

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

      1. associate-/l* 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in x around inf 64.0%

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

      1. mul-1-neg 64.0%

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

      2. unsub-neg 64.0%

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

   8. Simplified 64.0%

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

   if -42000 < t < -1.9500000000000001e-150 or -2.5e-248 < t < 5.7999999999999999e-285 or 9.9999999999999996e-236 < t < 3.19999999999999986e128

   1. Initial program 83.3%

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

   3. Taylor expanded in t around 0 64.6%

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

      1. associate-/l* 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in y around inf 56.1%

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

      1. associate-/l* 62.2%

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

   8. Simplified 62.2%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+80}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -42000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-285}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 10^{-235}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+128}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := y \cdot t\_1\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -15500000000:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(1 - t\_1\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+48}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+78}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* y t_1)))
   (if (<= t -2.5e+80)
     t_2
     (if (<= t -15500000000.0)
       (- x (/ (* z (- x y)) a))
       (if (<= t -3.7e-41)
         t_2
         (if (<= t -3.4e-76)
           (* x (- 1.0 t_1))
           (if (<= t 7e-24)
             (+ x (/ (- y x) (/ a z)))
             (if (<= t 1.1e+48)
               (+ x (* z (/ (- x y) t)))
               (if (<= t 9e+78) (* (- y x) (/ z (- a t))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = y * t_1;
	double tmp;
	if (t <= -2.5e+80) {
		tmp = t_2;
	} else if (t <= -15500000000.0) {
		tmp = x - ((z * (x - y)) / a);
	} else if (t <= -3.7e-41) {
		tmp = t_2;
	} else if (t <= -3.4e-76) {
		tmp = x * (1.0 - t_1);
	} else if (t <= 7e-24) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.1e+48) {
		tmp = x + (z * ((x - y) / t));
	} else if (t <= 9e+78) {
		tmp = (y - x) * (z / (a - t));
	} 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 = (z - t) / (a - t)
    t_2 = y * t_1
    if (t <= (-2.5d+80)) then
        tmp = t_2
    else if (t <= (-15500000000.0d0)) then
        tmp = x - ((z * (x - y)) / a)
    else if (t <= (-3.7d-41)) then
        tmp = t_2
    else if (t <= (-3.4d-76)) then
        tmp = x * (1.0d0 - t_1)
    else if (t <= 7d-24) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 1.1d+48) then
        tmp = x + (z * ((x - y) / t))
    else if (t <= 9d+78) then
        tmp = (y - x) * (z / (a - t))
    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 = (z - t) / (a - t);
	double t_2 = y * t_1;
	double tmp;
	if (t <= -2.5e+80) {
		tmp = t_2;
	} else if (t <= -15500000000.0) {
		tmp = x - ((z * (x - y)) / a);
	} else if (t <= -3.7e-41) {
		tmp = t_2;
	} else if (t <= -3.4e-76) {
		tmp = x * (1.0 - t_1);
	} else if (t <= 7e-24) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.1e+48) {
		tmp = x + (z * ((x - y) / t));
	} else if (t <= 9e+78) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	t_2 = y * t_1
	tmp = 0
	if t <= -2.5e+80:
		tmp = t_2
	elif t <= -15500000000.0:
		tmp = x - ((z * (x - y)) / a)
	elif t <= -3.7e-41:
		tmp = t_2
	elif t <= -3.4e-76:
		tmp = x * (1.0 - t_1)
	elif t <= 7e-24:
		tmp = x + ((y - x) / (a / z))
	elif t <= 1.1e+48:
		tmp = x + (z * ((x - y) / t))
	elif t <= 9e+78:
		tmp = (y - x) * (z / (a - t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(y * t_1)
	tmp = 0.0
	if (t <= -2.5e+80)
		tmp = t_2;
	elseif (t <= -15500000000.0)
		tmp = Float64(x - Float64(Float64(z * Float64(x - y)) / a));
	elseif (t <= -3.7e-41)
		tmp = t_2;
	elseif (t <= -3.4e-76)
		tmp = Float64(x * Float64(1.0 - t_1));
	elseif (t <= 7e-24)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 1.1e+48)
		tmp = Float64(x + Float64(z * Float64(Float64(x - y) / t)));
	elseif (t <= 9e+78)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	t_2 = y * t_1;
	tmp = 0.0;
	if (t <= -2.5e+80)
		tmp = t_2;
	elseif (t <= -15500000000.0)
		tmp = x - ((z * (x - y)) / a);
	elseif (t <= -3.7e-41)
		tmp = t_2;
	elseif (t <= -3.4e-76)
		tmp = x * (1.0 - t_1);
	elseif (t <= 7e-24)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 1.1e+48)
		tmp = x + (z * ((x - y) / t));
	elseif (t <= 9e+78)
		tmp = (y - x) * (z / (a - t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * t$95$1), $MachinePrecision]}, If[LessEqual[t, -2.5e+80], t$95$2, If[LessEqual[t, -15500000000.0], N[(x - N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.7e-41], t$95$2, If[LessEqual[t, -3.4e-76], N[(x * N[(1.0 - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-24], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+48], N[(x + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+78], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.4999999999999998e80 or -1.55e10 < t < -3.7000000000000002e-41 or 8.9999999999999999e78 < t

   1. Initial program 47.3%

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

      1. clear-num 47.3%

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

      2. inv-pow 47.3%

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

      3. *-commutative 47.3%

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

      4. associate-/r* 71.1%

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

   4. Applied egg-rr 71.1%

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

   5. Taylor expanded in x around 0 42.6%

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

      1. associate-/l* 63.6%

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

   7. Simplified 63.6%

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

   if -2.4999999999999998e80 < t < -1.55e10

   1. Initial program 72.9%

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

   3. Taylor expanded in t around 0 54.9%

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

   if -3.7000000000000002e-41 < t < -3.3999999999999999e-76

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. unsub-neg 88.2%

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

   5. Simplified 88.2%

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

   if -3.3999999999999999e-76 < t < 6.9999999999999993e-24

   1. Initial program 89.5%

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

      1. clear-num 89.5%

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

      2. inv-pow 89.5%

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

      3. *-commutative 89.5%

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

      4. associate-/r* 96.5%

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

   4. Applied egg-rr 96.5%

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

      1. unpow-1 96.5%

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

      2. clear-num 96.7%

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

      3. div-sub 91.1%

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

   6. Applied egg-rr 91.1%

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

      1. div-sub 96.7%

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

   8. Simplified 96.7%

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

   9. Taylor expanded in t around 0 84.7%

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

   if 6.9999999999999993e-24 < t < 1.1e48

   1. Initial program 91.9%

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

   3. Taylor expanded in z around inf 83.7%

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

      1. associate-/l* 91.6%

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

   5. Simplified 91.6%

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

   6. Taylor expanded in a around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

      3. associate-/l* 83.8%

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

   8. Simplified 83.8%

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

   if 1.1e48 < t < 8.9999999999999999e78

   1. Initial program 42.3%

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

      1. clear-num 42.3%

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

      2. inv-pow 42.3%

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

      3. *-commutative 42.3%

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

      4. associate-/r* 60.8%

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

   4. Applied egg-rr 60.8%

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

   5. Taylor expanded in z around inf 81.0%

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

      1. div-sub 81.0%

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

      2. associate-*r/ 62.1%

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

      3. *-commutative 62.1%

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

      4. associate-*r/ 81.3%

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

      5. *-commutative 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -15500000000:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(1 - \frac{z - t}{a - t}\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+48}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+78}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= y -5.5e+87)
     t_2
     (if (<= y -6.5e+47)
       t_1
       (if (<= y -3.6e-48)
         t_2
         (if (<= y -3.9e-232)
           t_1
           (if (<= y 7.6e-259) (* x (/ z t)) (if (<= y 8.5e-63) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -5.5e+87) {
		tmp = t_2;
	} else if (y <= -6.5e+47) {
		tmp = t_1;
	} else if (y <= -3.6e-48) {
		tmp = t_2;
	} else if (y <= -3.9e-232) {
		tmp = t_1;
	} else if (y <= 7.6e-259) {
		tmp = x * (z / t);
	} else if (y <= 8.5e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = y * ((z - t) / (a - t))
    if (y <= (-5.5d+87)) then
        tmp = t_2
    else if (y <= (-6.5d+47)) then
        tmp = t_1
    else if (y <= (-3.6d-48)) then
        tmp = t_2
    else if (y <= (-3.9d-232)) then
        tmp = t_1
    else if (y <= 7.6d-259) then
        tmp = x * (z / t)
    else if (y <= 8.5d-63) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -5.5e+87) {
		tmp = t_2;
	} else if (y <= -6.5e+47) {
		tmp = t_1;
	} else if (y <= -3.6e-48) {
		tmp = t_2;
	} else if (y <= -3.9e-232) {
		tmp = t_1;
	} else if (y <= 7.6e-259) {
		tmp = x * (z / t);
	} else if (y <= 8.5e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -5.5e+87:
		tmp = t_2
	elif y <= -6.5e+47:
		tmp = t_1
	elif y <= -3.6e-48:
		tmp = t_2
	elif y <= -3.9e-232:
		tmp = t_1
	elif y <= 7.6e-259:
		tmp = x * (z / t)
	elif y <= 8.5e-63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -5.5e+87)
		tmp = t_2;
	elseif (y <= -6.5e+47)
		tmp = t_1;
	elseif (y <= -3.6e-48)
		tmp = t_2;
	elseif (y <= -3.9e-232)
		tmp = t_1;
	elseif (y <= 7.6e-259)
		tmp = Float64(x * Float64(z / t));
	elseif (y <= 8.5e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -5.5e+87)
		tmp = t_2;
	elseif (y <= -6.5e+47)
		tmp = t_1;
	elseif (y <= -3.6e-48)
		tmp = t_2;
	elseif (y <= -3.9e-232)
		tmp = t_1;
	elseif (y <= 7.6e-259)
		tmp = x * (z / t);
	elseif (y <= 8.5e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+87], t$95$2, If[LessEqual[y, -6.5e+47], t$95$1, If[LessEqual[y, -3.6e-48], t$95$2, If[LessEqual[y, -3.9e-232], t$95$1, If[LessEqual[y, 7.6e-259], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-63], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.50000000000000022e87 or -6.49999999999999988e47 < y < -3.6000000000000002e-48 or 8.49999999999999969e-63 < y

   1. Initial program 71.4%

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

      1. clear-num 71.3%

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

      2. inv-pow 71.3%

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

      3. *-commutative 71.3%

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

      4. associate-/r* 92.0%

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

   4. Applied egg-rr 92.0%

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

   5. Taylor expanded in x around 0 54.6%

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

      1. associate-/l* 74.0%

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

   7. Simplified 74.0%

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

   if -5.50000000000000022e87 < y < -6.49999999999999988e47 or -3.6000000000000002e-48 < y < -3.8999999999999998e-232 or 7.6000000000000001e-259 < y < 8.49999999999999969e-63

   1. Initial program 75.8%

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

   3. Taylor expanded in t around 0 61.1%

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

      1. associate-/l* 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in x around inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. unsub-neg 61.0%

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

   8. Simplified 61.0%

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

   if -3.8999999999999998e-232 < y < 7.6000000000000001e-259

   1. Initial program 41.3%

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

      1. clear-num 41.2%

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

      2. inv-pow 41.2%

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

      3. *-commutative 41.2%

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

      4. associate-/r* 46.1%

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

   4. Applied egg-rr 46.1%

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

   5. Taylor expanded in z around -inf 55.2%

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

   6. Taylor expanded in y around 0 50.9%

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

      1. mul-1-neg 50.9%

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

      2. *-commutative 50.9%

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

      3. distribute-lft-neg-in 50.9%

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

   8. Simplified 50.9%

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

   9. Taylor expanded in a around 0 41.5%

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

       1. associate-/l* 53.9%

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

   11. Simplified 53.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.46 \cdot 10^{-46}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 10^{-258}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= y -5.5e+87)
     t_2
     (if (<= y -6.4e+47)
       t_1
       (if (<= y -1.46e-46)
         (* (- z t) (/ y (- a t)))
         (if (<= y -3.4e-232)
           t_1
           (if (<= y 1e-258) (* x (/ z t)) (if (<= y 3.5e-61) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -5.5e+87) {
		tmp = t_2;
	} else if (y <= -6.4e+47) {
		tmp = t_1;
	} else if (y <= -1.46e-46) {
		tmp = (z - t) * (y / (a - t));
	} else if (y <= -3.4e-232) {
		tmp = t_1;
	} else if (y <= 1e-258) {
		tmp = x * (z / t);
	} else if (y <= 3.5e-61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = y * ((z - t) / (a - t))
    if (y <= (-5.5d+87)) then
        tmp = t_2
    else if (y <= (-6.4d+47)) then
        tmp = t_1
    else if (y <= (-1.46d-46)) then
        tmp = (z - t) * (y / (a - t))
    else if (y <= (-3.4d-232)) then
        tmp = t_1
    else if (y <= 1d-258) then
        tmp = x * (z / t)
    else if (y <= 3.5d-61) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -5.5e+87) {
		tmp = t_2;
	} else if (y <= -6.4e+47) {
		tmp = t_1;
	} else if (y <= -1.46e-46) {
		tmp = (z - t) * (y / (a - t));
	} else if (y <= -3.4e-232) {
		tmp = t_1;
	} else if (y <= 1e-258) {
		tmp = x * (z / t);
	} else if (y <= 3.5e-61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -5.5e+87:
		tmp = t_2
	elif y <= -6.4e+47:
		tmp = t_1
	elif y <= -1.46e-46:
		tmp = (z - t) * (y / (a - t))
	elif y <= -3.4e-232:
		tmp = t_1
	elif y <= 1e-258:
		tmp = x * (z / t)
	elif y <= 3.5e-61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -5.5e+87)
		tmp = t_2;
	elseif (y <= -6.4e+47)
		tmp = t_1;
	elseif (y <= -1.46e-46)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (y <= -3.4e-232)
		tmp = t_1;
	elseif (y <= 1e-258)
		tmp = Float64(x * Float64(z / t));
	elseif (y <= 3.5e-61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -5.5e+87)
		tmp = t_2;
	elseif (y <= -6.4e+47)
		tmp = t_1;
	elseif (y <= -1.46e-46)
		tmp = (z - t) * (y / (a - t));
	elseif (y <= -3.4e-232)
		tmp = t_1;
	elseif (y <= 1e-258)
		tmp = x * (z / t);
	elseif (y <= 3.5e-61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+87], t$95$2, If[LessEqual[y, -6.4e+47], t$95$1, If[LessEqual[y, -1.46e-46], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.4e-232], t$95$1, If[LessEqual[y, 1e-258], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-61], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.50000000000000022e87 or 3.5000000000000003e-61 < y

   1. Initial program 69.5%

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

      1. clear-num 69.5%

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

      2. inv-pow 69.5%

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

      3. *-commutative 69.5%

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

      4. associate-/r* 93.6%

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

   4. Applied egg-rr 93.6%

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

   5. Taylor expanded in x around 0 52.0%

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

      1. associate-/l* 74.6%

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

   7. Simplified 74.6%

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

   if -5.50000000000000022e87 < y < -6.4e47 or -1.46000000000000008e-46 < y < -3.4000000000000002e-232 or 9.99999999999999954e-259 < y < 3.5000000000000003e-61

   1. Initial program 75.8%

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

   3. Taylor expanded in t around 0 61.1%

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

      1. associate-/l* 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in x around inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. unsub-neg 61.0%

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

   8. Simplified 61.0%

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

   if -6.4e47 < y < -1.46000000000000008e-46

   1. Initial program 82.5%

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

      1. clear-num 82.4%

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

      2. inv-pow 82.4%

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

      3. *-commutative 82.4%

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

      4. associate-/r* 82.4%

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

   4. Applied egg-rr 82.4%

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

      1. unpow-1 82.4%

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

      2. clear-num 82.5%

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

      3. div-sub 72.6%

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

   6. Applied egg-rr 72.6%

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

      1. div-sub 82.5%

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

   8. Simplified 82.5%

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

   9. Taylor expanded in x around 0 70.1%

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

       1. associate-*l/ 70.4%

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

   11. Simplified 70.4%

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

   if -3.4000000000000002e-232 < y < 9.99999999999999954e-259

   1. Initial program 41.3%

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

      1. clear-num 41.2%

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

      2. inv-pow 41.2%

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

      3. *-commutative 41.2%

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

      4. associate-/r* 46.1%

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

   4. Applied egg-rr 46.1%

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

   5. Taylor expanded in z around -inf 55.2%

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

   6. Taylor expanded in y around 0 50.9%

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

      1. mul-1-neg 50.9%

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

      2. *-commutative 50.9%

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

      3. distribute-lft-neg-in 50.9%

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

   8. Simplified 50.9%

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

   9. Taylor expanded in a around 0 41.5%

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

       1. associate-/l* 53.9%

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

   11. Simplified 53.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq -1.46 \cdot 10^{-46}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq 10^{-258}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -6 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-39}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-64}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= y -6e+87)
     t_2
     (if (<= y -6.4e+47)
       t_1
       (if (<= y -2.5e-39)
         (* (- z t) (/ y (- a t)))
         (if (<= y -1.9e-231)
           t_1
           (if (<= y 4.4e-64) (* (- y x) (/ z (- a t))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -6e+87) {
		tmp = t_2;
	} else if (y <= -6.4e+47) {
		tmp = t_1;
	} else if (y <= -2.5e-39) {
		tmp = (z - t) * (y / (a - t));
	} else if (y <= -1.9e-231) {
		tmp = t_1;
	} else if (y <= 4.4e-64) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = y * ((z - t) / (a - t))
    if (y <= (-6d+87)) then
        tmp = t_2
    else if (y <= (-6.4d+47)) then
        tmp = t_1
    else if (y <= (-2.5d-39)) then
        tmp = (z - t) * (y / (a - t))
    else if (y <= (-1.9d-231)) then
        tmp = t_1
    else if (y <= 4.4d-64) then
        tmp = (y - x) * (z / (a - t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -6e+87) {
		tmp = t_2;
	} else if (y <= -6.4e+47) {
		tmp = t_1;
	} else if (y <= -2.5e-39) {
		tmp = (z - t) * (y / (a - t));
	} else if (y <= -1.9e-231) {
		tmp = t_1;
	} else if (y <= 4.4e-64) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -6e+87:
		tmp = t_2
	elif y <= -6.4e+47:
		tmp = t_1
	elif y <= -2.5e-39:
		tmp = (z - t) * (y / (a - t))
	elif y <= -1.9e-231:
		tmp = t_1
	elif y <= 4.4e-64:
		tmp = (y - x) * (z / (a - t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -6e+87)
		tmp = t_2;
	elseif (y <= -6.4e+47)
		tmp = t_1;
	elseif (y <= -2.5e-39)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (y <= -1.9e-231)
		tmp = t_1;
	elseif (y <= 4.4e-64)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -6e+87)
		tmp = t_2;
	elseif (y <= -6.4e+47)
		tmp = t_1;
	elseif (y <= -2.5e-39)
		tmp = (z - t) * (y / (a - t));
	elseif (y <= -1.9e-231)
		tmp = t_1;
	elseif (y <= 4.4e-64)
		tmp = (y - x) * (z / (a - t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+87], t$95$2, If[LessEqual[y, -6.4e+47], t$95$1, If[LessEqual[y, -2.5e-39], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-231], t$95$1, If[LessEqual[y, 4.4e-64], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.9999999999999998e87 or 4.3999999999999999e-64 < y

   1. Initial program 69.8%

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

      1. clear-num 69.7%

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

      2. inv-pow 69.7%

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

      3. *-commutative 69.7%

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

      4. associate-/r* 93.7%

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

   4. Applied egg-rr 93.7%

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

   5. Taylor expanded in x around 0 51.6%

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

      1. associate-/l* 74.0%

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

   7. Simplified 74.0%

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

   if -5.9999999999999998e87 < y < -6.4e47 or -2.4999999999999999e-39 < y < -1.90000000000000007e-231

   1. Initial program 70.9%

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

   3. Taylor expanded in t around 0 62.6%

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

      1. associate-/l* 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in x around inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. unsub-neg 66.8%

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

   8. Simplified 66.8%

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

   if -6.4e47 < y < -2.4999999999999999e-39

   1. Initial program 82.5%

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

      1. clear-num 82.4%

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

      2. inv-pow 82.4%

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

      3. *-commutative 82.4%

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

      4. associate-/r* 82.4%

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

   4. Applied egg-rr 82.4%

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

      1. unpow-1 82.4%

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

      2. clear-num 82.5%

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

      3. div-sub 72.6%

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

   6. Applied egg-rr 72.6%

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

      1. div-sub 82.5%

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

   8. Simplified 82.5%

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

   9. Taylor expanded in x around 0 70.1%

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

       1. associate-*l/ 70.4%

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

   11. Simplified 70.4%

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

   if -1.90000000000000007e-231 < y < 4.3999999999999999e-64

   1. Initial program 67.2%

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

      1. clear-num 67.1%

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

      2. inv-pow 67.1%

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

      3. *-commutative 67.1%

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

      4. associate-/r* 68.8%

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

   4. Applied egg-rr 68.8%

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

   5. Taylor expanded in z around inf 57.1%

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

      1. div-sub 57.1%

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

      2. associate-*r/ 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*r/ 64.3%

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

      5. *-commutative 64.3%

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

   7. Simplified 64.3%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-39}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-64}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -6600:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(-\frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a z))))
   (if (<= t -6600.0)
     y
     (if (<= t -1.05e-248)
       x
       (if (<= t 1.8e-287)
         t_1
         (if (<= t 1.1e-236)
           (* x (- (/ z a)))
           (if (<= t 2.9e-151) t_1 (if (<= t 9e+122) x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (t <= -6600.0) {
		tmp = y;
	} else if (t <= -1.05e-248) {
		tmp = x;
	} else if (t <= 1.8e-287) {
		tmp = t_1;
	} else if (t <= 1.1e-236) {
		tmp = x * -(z / a);
	} else if (t <= 2.9e-151) {
		tmp = t_1;
	} else if (t <= 9e+122) {
		tmp = x;
	} else {
		tmp = 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 = y / (a / z)
    if (t <= (-6600.0d0)) then
        tmp = y
    else if (t <= (-1.05d-248)) then
        tmp = x
    else if (t <= 1.8d-287) then
        tmp = t_1
    else if (t <= 1.1d-236) then
        tmp = x * -(z / a)
    else if (t <= 2.9d-151) then
        tmp = t_1
    else if (t <= 9d+122) then
        tmp = x
    else
        tmp = 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 = y / (a / z);
	double tmp;
	if (t <= -6600.0) {
		tmp = y;
	} else if (t <= -1.05e-248) {
		tmp = x;
	} else if (t <= 1.8e-287) {
		tmp = t_1;
	} else if (t <= 1.1e-236) {
		tmp = x * -(z / a);
	} else if (t <= 2.9e-151) {
		tmp = t_1;
	} else if (t <= 9e+122) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / z)
	tmp = 0
	if t <= -6600.0:
		tmp = y
	elif t <= -1.05e-248:
		tmp = x
	elif t <= 1.8e-287:
		tmp = t_1
	elif t <= 1.1e-236:
		tmp = x * -(z / a)
	elif t <= 2.9e-151:
		tmp = t_1
	elif t <= 9e+122:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / z))
	tmp = 0.0
	if (t <= -6600.0)
		tmp = y;
	elseif (t <= -1.05e-248)
		tmp = x;
	elseif (t <= 1.8e-287)
		tmp = t_1;
	elseif (t <= 1.1e-236)
		tmp = Float64(x * Float64(-Float64(z / a)));
	elseif (t <= 2.9e-151)
		tmp = t_1;
	elseif (t <= 9e+122)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / z);
	tmp = 0.0;
	if (t <= -6600.0)
		tmp = y;
	elseif (t <= -1.05e-248)
		tmp = x;
	elseif (t <= 1.8e-287)
		tmp = t_1;
	elseif (t <= 1.1e-236)
		tmp = x * -(z / a);
	elseif (t <= 2.9e-151)
		tmp = t_1;
	elseif (t <= 9e+122)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6600.0], y, If[LessEqual[t, -1.05e-248], x, If[LessEqual[t, 1.8e-287], t$95$1, If[LessEqual[t, 1.1e-236], N[(x * (-N[(z / a), $MachinePrecision])), $MachinePrecision], If[LessEqual[t, 2.9e-151], t$95$1, If[LessEqual[t, 9e+122], x, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6600 or 8.99999999999999995e122 < t

   1. Initial program 48.5%

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

   3. Taylor expanded in t around inf 42.6%

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

   if -6600 < t < -1.05e-248 or 2.90000000000000013e-151 < t < 8.99999999999999995e122

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 38.1%

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

   if -1.05e-248 < t < 1.8000000000000001e-287 or 1.09999999999999996e-236 < t < 2.90000000000000013e-151

   1. Initial program 89.1%

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

   3. Taylor expanded in t around 0 89.1%

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

      1. associate-/l* 89.3%

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

   5. Simplified 89.3%

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

   6. Taylor expanded in y around inf 70.1%

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

   7. Taylor expanded in x around 0 48.1%

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

      1. associate-*r/ 58.7%

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

   9. Simplified 58.7%

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

       1. clear-num 58.8%

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

       2. div-inv 58.9%

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

   11. Applied egg-rr 58.9%

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

   if 1.8000000000000001e-287 < t < 1.09999999999999996e-236

   1. Initial program 95.9%

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

   3. Taylor expanded in t around 0 86.2%

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

      1. associate-/l* 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in z around inf 50.7%

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

   7. Taylor expanded in y around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. associate-/l* 50.7%

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

      3. distribute-rgt-neg-in 50.7%

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

      4. distribute-frac-neg2 50.7%

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

   9. Simplified 50.7%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6600:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-287}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(-\frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-151}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -26500000000:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-18} \lor \neg \left(t \leq 6.6 \cdot 10^{+16}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.5e+80)
     t_1
     (if (<= t -26500000000.0)
       (- x (/ (* z (- x y)) a))
       (if (or (<= t -1.05e-18) (not (<= t 6.6e+16)))
         t_1
         (- x (/ z (/ a (- x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.5e+80) {
		tmp = t_1;
	} else if (t <= -26500000000.0) {
		tmp = x - ((z * (x - y)) / a);
	} else if ((t <= -1.05e-18) || !(t <= 6.6e+16)) {
		tmp = t_1;
	} else {
		tmp = x - (z / (a / (x - 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 = y * ((z - t) / (a - t))
    if (t <= (-2.5d+80)) then
        tmp = t_1
    else if (t <= (-26500000000.0d0)) then
        tmp = x - ((z * (x - y)) / a)
    else if ((t <= (-1.05d-18)) .or. (.not. (t <= 6.6d+16))) then
        tmp = t_1
    else
        tmp = x - (z / (a / (x - 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 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.5e+80) {
		tmp = t_1;
	} else if (t <= -26500000000.0) {
		tmp = x - ((z * (x - y)) / a);
	} else if ((t <= -1.05e-18) || !(t <= 6.6e+16)) {
		tmp = t_1;
	} else {
		tmp = x - (z / (a / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.5e+80:
		tmp = t_1
	elif t <= -26500000000.0:
		tmp = x - ((z * (x - y)) / a)
	elif (t <= -1.05e-18) or not (t <= 6.6e+16):
		tmp = t_1
	else:
		tmp = x - (z / (a / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.5e+80)
		tmp = t_1;
	elseif (t <= -26500000000.0)
		tmp = Float64(x - Float64(Float64(z * Float64(x - y)) / a));
	elseif ((t <= -1.05e-18) || !(t <= 6.6e+16))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(z / Float64(a / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.5e+80)
		tmp = t_1;
	elseif (t <= -26500000000.0)
		tmp = x - ((z * (x - y)) / a);
	elseif ((t <= -1.05e-18) || ~((t <= 6.6e+16)))
		tmp = t_1;
	else
		tmp = x - (z / (a / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+80], t$95$1, If[LessEqual[t, -26500000000.0], N[(x - N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.05e-18], N[Not[LessEqual[t, 6.6e+16]], $MachinePrecision]], t$95$1, N[(x - N[(z / N[(a / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4999999999999998e80 or -2.65e10 < t < -1.05e-18 or 6.6e16 < t

   1. Initial program 47.8%

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

      1. clear-num 47.9%

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

      2. inv-pow 47.9%

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

      3. *-commutative 47.9%

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

      4. associate-/r* 71.0%

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

   4. Applied egg-rr 71.0%

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

   5. Taylor expanded in x around 0 42.4%

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

      1. associate-/l* 63.8%

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

   7. Simplified 63.8%

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

   if -2.4999999999999998e80 < t < -2.65e10

   1. Initial program 72.9%

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

   3. Taylor expanded in t around 0 54.9%

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

   if -1.05e-18 < t < 6.6e16

   1. Initial program 89.1%

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

   3. Taylor expanded in t around 0 73.0%

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

      1. associate-/l* 73.7%

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

   5. Simplified 73.7%

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

      1. clear-num 73.7%

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

      2. un-div-inv 75.0%

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

   7. Applied egg-rr 75.0%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -26500000000:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-18} \lor \neg \left(t \leq 6.6 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+48}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+78}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.5e+80)
     t_1
     (if (<= t 1.2e-20)
       (+ x (/ (- y x) (/ a z)))
       (if (<= t 1.4e+48)
         (+ x (* z (/ (- x y) t)))
         (if (<= t 1.35e+78) (* (- y x) (/ z (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.5e+80) {
		tmp = t_1;
	} else if (t <= 1.2e-20) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.4e+48) {
		tmp = x + (z * ((x - y) / t));
	} else if (t <= 1.35e+78) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-2.5d+80)) then
        tmp = t_1
    else if (t <= 1.2d-20) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 1.4d+48) then
        tmp = x + (z * ((x - y) / t))
    else if (t <= 1.35d+78) then
        tmp = (y - x) * (z / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.5e+80) {
		tmp = t_1;
	} else if (t <= 1.2e-20) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.4e+48) {
		tmp = x + (z * ((x - y) / t));
	} else if (t <= 1.35e+78) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.5e+80:
		tmp = t_1
	elif t <= 1.2e-20:
		tmp = x + ((y - x) / (a / z))
	elif t <= 1.4e+48:
		tmp = x + (z * ((x - y) / t))
	elif t <= 1.35e+78:
		tmp = (y - x) * (z / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.5e+80)
		tmp = t_1;
	elseif (t <= 1.2e-20)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 1.4e+48)
		tmp = Float64(x + Float64(z * Float64(Float64(x - y) / t)));
	elseif (t <= 1.35e+78)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.5e+80)
		tmp = t_1;
	elseif (t <= 1.2e-20)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 1.4e+48)
		tmp = x + (z * ((x - y) / t));
	elseif (t <= 1.35e+78)
		tmp = (y - x) * (z / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+80], t$95$1, If[LessEqual[t, 1.2e-20], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+48], N[(x + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+78], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.4999999999999998e80 or 1.35000000000000002e78 < t

   1. Initial program 42.9%

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

      1. clear-num 42.9%

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

      2. inv-pow 42.9%

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

      3. *-commutative 42.9%

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

      4. associate-/r* 68.6%

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

   4. Applied egg-rr 68.6%

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

   5. Taylor expanded in x around 0 40.5%

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

      1. associate-/l* 64.0%

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

   7. Simplified 64.0%

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

   if -2.4999999999999998e80 < t < 1.19999999999999996e-20

   1. Initial program 86.6%

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

      1. clear-num 86.5%

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

      2. inv-pow 86.5%

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

      3. *-commutative 86.5%

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

      4. associate-/r* 93.0%

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

   4. Applied egg-rr 93.0%

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

      1. unpow-1 93.0%

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

      2. clear-num 93.1%

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

      3. div-sub 89.0%

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

   6. Applied egg-rr 89.0%

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

      1. div-sub 93.1%

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

   8. Simplified 93.1%

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

   9. Taylor expanded in t around 0 76.3%

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

   if 1.19999999999999996e-20 < t < 1.40000000000000006e48

   1. Initial program 91.9%

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

   3. Taylor expanded in z around inf 83.7%

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

      1. associate-/l* 91.6%

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

   5. Simplified 91.6%

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

   6. Taylor expanded in a around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

      3. associate-/l* 83.8%

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

   8. Simplified 83.8%

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

   if 1.40000000000000006e48 < t < 1.35000000000000002e78

   1. Initial program 42.3%

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

      1. clear-num 42.3%

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

      2. inv-pow 42.3%

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

      3. *-commutative 42.3%

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

      4. associate-/r* 60.8%

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

   4. Applied egg-rr 60.8%

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

   5. Taylor expanded in z around inf 81.0%

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

      1. div-sub 81.0%

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

      2. associate-*r/ 62.1%

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

      3. *-commutative 62.1%

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

      4. associate-*r/ 81.3%

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

      5. *-commutative 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+48}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+78}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{+80}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-277}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -7.4e+80)
     y
     (if (<= t -2.45e-248)
       t_1
       (if (<= t -1.5e-277) (/ y (/ a z)) (if (<= t 6.6e+128) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -7.4e+80) {
		tmp = y;
	} else if (t <= -2.45e-248) {
		tmp = t_1;
	} else if (t <= -1.5e-277) {
		tmp = y / (a / z);
	} else if (t <= 6.6e+128) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-7.4d+80)) then
        tmp = y
    else if (t <= (-2.45d-248)) then
        tmp = t_1
    else if (t <= (-1.5d-277)) then
        tmp = y / (a / z)
    else if (t <= 6.6d+128) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -7.4e+80) {
		tmp = y;
	} else if (t <= -2.45e-248) {
		tmp = t_1;
	} else if (t <= -1.5e-277) {
		tmp = y / (a / z);
	} else if (t <= 6.6e+128) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -7.4e+80:
		tmp = y
	elif t <= -2.45e-248:
		tmp = t_1
	elif t <= -1.5e-277:
		tmp = y / (a / z)
	elif t <= 6.6e+128:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -7.4e+80)
		tmp = y;
	elseif (t <= -2.45e-248)
		tmp = t_1;
	elseif (t <= -1.5e-277)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 6.6e+128)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -7.4e+80)
		tmp = y;
	elseif (t <= -2.45e-248)
		tmp = t_1;
	elseif (t <= -1.5e-277)
		tmp = y / (a / z);
	elseif (t <= 6.6e+128)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.4e+80], y, If[LessEqual[t, -2.45e-248], t$95$1, If[LessEqual[t, -1.5e-277], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+128], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.39999999999999992e80 or 6.6000000000000001e128 < t

   1. Initial program 41.4%

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

   3. Taylor expanded in t around inf 46.3%

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

   if -7.39999999999999992e80 < t < -2.4499999999999998e-248 or -1.49999999999999989e-277 < t < 6.6000000000000001e128

   1. Initial program 82.9%

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

   3. Taylor expanded in t around 0 63.1%

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

      1. associate-/l* 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in x around inf 52.8%

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

      1. mul-1-neg 52.8%

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

      2. unsub-neg 52.8%

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

   8. Simplified 52.8%

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

   if -2.4499999999999998e-248 < t < -1.49999999999999989e-277

   1. Initial program 91.2%

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

   3. Taylor expanded in t around 0 91.2%

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

      1. associate-/l* 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in y around inf 82.8%

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

   7. Taylor expanded in x around 0 74.2%

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

      1. associate-*r/ 82.7%

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

   9. Simplified 82.7%

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

       1. clear-num 82.9%

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

       2. div-inv 82.9%

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

   11. Applied egg-rr 82.9%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+80}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-277}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-73}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot z}{t - a}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+129}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5.8e-56)
   (* x (- 1.0 (/ z a)))
   (if (<= x 3.1e-73)
     (+ x (* y (/ z a)))
     (if (<= x 5e-10)
       (/ (* x z) (- t a))
       (if (<= x 2.6e+129) y (- x (* x (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.8e-56) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 3.1e-73) {
		tmp = x + (y * (z / a));
	} else if (x <= 5e-10) {
		tmp = (x * z) / (t - a);
	} else if (x <= 2.6e+129) {
		tmp = y;
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-5.8d-56)) then
        tmp = x * (1.0d0 - (z / a))
    else if (x <= 3.1d-73) then
        tmp = x + (y * (z / a))
    else if (x <= 5d-10) then
        tmp = (x * z) / (t - a)
    else if (x <= 2.6d+129) then
        tmp = y
    else
        tmp = x - (x * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.8e-56) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 3.1e-73) {
		tmp = x + (y * (z / a));
	} else if (x <= 5e-10) {
		tmp = (x * z) / (t - a);
	} else if (x <= 2.6e+129) {
		tmp = y;
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5.8e-56:
		tmp = x * (1.0 - (z / a))
	elif x <= 3.1e-73:
		tmp = x + (y * (z / a))
	elif x <= 5e-10:
		tmp = (x * z) / (t - a)
	elif x <= 2.6e+129:
		tmp = y
	else:
		tmp = x - (x * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5.8e-56)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (x <= 3.1e-73)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (x <= 5e-10)
		tmp = Float64(Float64(x * z) / Float64(t - a));
	elseif (x <= 2.6e+129)
		tmp = y;
	else
		tmp = Float64(x - Float64(x * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5.8e-56)
		tmp = x * (1.0 - (z / a));
	elseif (x <= 3.1e-73)
		tmp = x + (y * (z / a));
	elseif (x <= 5e-10)
		tmp = (x * z) / (t - a);
	elseif (x <= 2.6e+129)
		tmp = y;
	else
		tmp = x - (x * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5.8e-56], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e-73], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e-10], N[(N[(x * z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+129], y, N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.79999999999999982e-56

   1. Initial program 63.1%

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

   3. Taylor expanded in t around 0 47.7%

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

      1. associate-/l* 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in x around inf 49.5%

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

      1. mul-1-neg 49.5%

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

      2. unsub-neg 49.5%

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

   8. Simplified 49.5%

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

   if -5.79999999999999982e-56 < x < 3.09999999999999969e-73

   1. Initial program 84.3%

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

   3. Taylor expanded in t around 0 52.9%

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

      1. associate-/l* 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in y around inf 46.6%

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

      1. associate-/l* 51.1%

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

   8. Simplified 51.1%

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

   if 3.09999999999999969e-73 < x < 5.00000000000000031e-10

   1. Initial program 80.8%

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

      1. clear-num 81.0%

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

      2. inv-pow 81.0%

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

      3. *-commutative 81.0%

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

      4. associate-/r* 81.2%

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

   4. Applied egg-rr 81.2%

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

   5. Taylor expanded in z around -inf 67.9%

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

   6. Taylor expanded in y around 0 67.5%

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

      1. mul-1-neg 67.5%

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

      2. *-commutative 67.5%

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

      3. distribute-lft-neg-in 67.5%

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

   8. Simplified 67.5%

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

   if 5.00000000000000031e-10 < x < 2.60000000000000012e129

   1. Initial program 48.8%

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

   3. Taylor expanded in t around inf 52.0%

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

   if 2.60000000000000012e129 < x

   1. Initial program 55.3%

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

   3. Taylor expanded in t around 0 47.1%

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

      1. associate-/l* 49.4%

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

   5. Simplified 49.4%

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

   6. Taylor expanded in y around 0 46.8%

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

      1. mul-1-neg 46.8%

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

      2. unsub-neg 46.8%

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

      3. associate-/l* 53.7%

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

   8. Simplified 53.7%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-73}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot z}{t - a}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+129}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 81.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+125}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- y x) (/ (- a z) t)))))
   (if (<= t -1.8e+34)
     t_1
     (if (<= t 1.08e+24)
       (- x (/ (- x y) (/ (- a t) z)))
       (if (<= t 2.5e+125) (- x (* (/ y (- a t)) (- t z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -1.8e+34) {
		tmp = t_1;
	} else if (t <= 1.08e+24) {
		tmp = x - ((x - y) / ((a - t) / z));
	} else if (t <= 2.5e+125) {
		tmp = x - ((y / (a - t)) * (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 = y + ((y - x) * ((a - z) / t))
    if (t <= (-1.8d+34)) then
        tmp = t_1
    else if (t <= 1.08d+24) then
        tmp = x - ((x - y) / ((a - t) / z))
    else if (t <= 2.5d+125) then
        tmp = x - ((y / (a - t)) * (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 = y + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -1.8e+34) {
		tmp = t_1;
	} else if (t <= 1.08e+24) {
		tmp = x - ((x - y) / ((a - t) / z));
	} else if (t <= 2.5e+125) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((y - x) * ((a - z) / t))
	tmp = 0
	if t <= -1.8e+34:
		tmp = t_1
	elif t <= 1.08e+24:
		tmp = x - ((x - y) / ((a - t) / z))
	elif t <= 2.5e+125:
		tmp = x - ((y / (a - t)) * (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -1.8e+34)
		tmp = t_1;
	elseif (t <= 1.08e+24)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / z)));
	elseif (t <= 2.5e+125)
		tmp = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((y - x) * ((a - z) / t));
	tmp = 0.0;
	if (t <= -1.8e+34)
		tmp = t_1;
	elseif (t <= 1.08e+24)
		tmp = x - ((x - y) / ((a - t) / z));
	elseif (t <= 2.5e+125)
		tmp = x - ((y / (a - t)) * (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e+34], t$95$1, If[LessEqual[t, 1.08e+24], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+125], N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8e34 or 2.49999999999999981e125 < t

   1. Initial program 43.9%

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

   3. Taylor expanded in t around inf 68.9%

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

      1. associate--l+ 68.9%

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

      2. associate-*r/ 68.9%

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

      3. associate-*r/ 68.9%

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

      4. div-sub 68.9%

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

      5. distribute-lft-out-- 68.9%

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

      6. associate-*r/ 68.9%

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

      7. mul-1-neg 68.9%

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

      8. unsub-neg 68.9%

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

      9. distribute-rgt-out-- 70.1%

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

      10. associate-/l* 82.7%

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

   5. Simplified 82.7%

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

   if -1.8e34 < t < 1.0799999999999999e24

   1. Initial program 88.4%

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

      1. clear-num 88.4%

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

      2. inv-pow 88.4%

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

      3. *-commutative 88.4%

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

      4. associate-/r* 95.4%

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

   4. Applied egg-rr 95.4%

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

      1. unpow-1 95.4%

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

      2. clear-num 95.5%

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

      3. div-sub 91.5%

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

   6. Applied egg-rr 91.5%

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

      1. div-sub 95.5%

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

   8. Simplified 95.5%

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

   9. Taylor expanded in z around inf 88.7%

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

   if 1.0799999999999999e24 < t < 2.49999999999999981e125

   1. Initial program 55.1%

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

   3. Taylor expanded in y around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+34}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+125}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 81.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+34}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+35}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+123}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+34)
   (+ y (* (- z a) (/ (- x y) t)))
   (if (<= t 6.4e+35)
     (- x (/ (- x y) (/ (- a t) z)))
     (if (<= t 3e+123)
       (- x (* (/ y (- a t)) (- t z)))
       (+ y (* (- y x) (/ (- a z) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+34) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else if (t <= 6.4e+35) {
		tmp = x - ((x - y) / ((a - t) / z));
	} else if (t <= 3e+123) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else {
		tmp = y + ((y - x) * ((a - z) / 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 (t <= (-2.8d+34)) then
        tmp = y + ((z - a) * ((x - y) / t))
    else if (t <= 6.4d+35) then
        tmp = x - ((x - y) / ((a - t) / z))
    else if (t <= 3d+123) then
        tmp = x - ((y / (a - t)) * (t - z))
    else
        tmp = y + ((y - x) * ((a - z) / 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 (t <= -2.8e+34) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else if (t <= 6.4e+35) {
		tmp = x - ((x - y) / ((a - t) / z));
	} else if (t <= 3e+123) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+34:
		tmp = y + ((z - a) * ((x - y) / t))
	elif t <= 6.4e+35:
		tmp = x - ((x - y) / ((a - t) / z))
	elif t <= 3e+123:
		tmp = x - ((y / (a - t)) * (t - z))
	else:
		tmp = y + ((y - x) * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+34)
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	elseif (t <= 6.4e+35)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / z)));
	elseif (t <= 3e+123)
		tmp = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)));
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+34)
		tmp = y + ((z - a) * ((x - y) / t));
	elseif (t <= 6.4e+35)
		tmp = x - ((x - y) / ((a - t) / z));
	elseif (t <= 3e+123)
		tmp = x - ((y / (a - t)) * (t - z));
	else
		tmp = y + ((y - x) * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+34], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e+35], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+123], N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.80000000000000008e34

   1. Initial program 49.0%

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

      1. clear-num 48.8%

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

      2. inv-pow 48.8%

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

      3. *-commutative 48.8%

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

      4. associate-/r* 66.8%

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

   4. Applied egg-rr 66.8%

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

      1. unpow-1 66.9%

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

      2. clear-num 67.0%

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

      3. div-sub 67.0%

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

   6. Applied egg-rr 67.0%

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

      1. div-sub 67.0%

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

   8. Simplified 67.0%

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

   9. Taylor expanded in t around inf 70.1%

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

       1. associate--l+ 70.1%

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

       2. associate-*r/ 70.1%

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

       3. associate-*r/ 70.1%

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

       4. div-sub 70.1%

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

       5. distribute-lft-out-- 70.1%

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

       6. associate-*r/ 70.1%

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

       7. mul-1-neg 70.1%

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

       8. unsub-neg 70.1%

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

       9. div-sub 70.1%

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

       10. associate-/l* 72.1%

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

       11. associate-/l* 75.7%

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

       12. distribute-rgt-out-- 75.7%

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

   11. Simplified 75.7%

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

   if -2.80000000000000008e34 < t < 6.39999999999999965e35

   1. Initial program 88.4%

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

      1. clear-num 88.4%

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

      2. inv-pow 88.4%

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

      3. *-commutative 88.4%

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

      4. associate-/r* 95.4%

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

   4. Applied egg-rr 95.4%

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

      1. unpow-1 95.4%

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

      2. clear-num 95.5%

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

      3. div-sub 91.5%

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

   6. Applied egg-rr 91.5%

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

      1. div-sub 95.5%

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

   8. Simplified 95.5%

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

   9. Taylor expanded in z around inf 88.7%

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

   if 6.39999999999999965e35 < t < 3.00000000000000008e123

   1. Initial program 55.1%

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

   3. Taylor expanded in y around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

   if 3.00000000000000008e123 < t

   1. Initial program 36.9%

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

   3. Taylor expanded in t around inf 67.2%

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

      1. associate--l+ 67.2%

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

      2. associate-*r/ 67.2%

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

      3. associate-*r/ 67.2%

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

      4. div-sub 67.2%

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

      5. distribute-lft-out-- 67.2%

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

      6. associate-*r/ 67.2%

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

      7. mul-1-neg 67.2%

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

      8. unsub-neg 67.2%

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

      9. distribute-rgt-out-- 70.0%

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

      10. associate-/l* 92.2%

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

   5. Simplified 92.2%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+34}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+35}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+123}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3200:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3200.0)
   y
   (if (<= t -8.8e-246)
     x
     (if (<= t 1.9e-153) (* y (/ z a)) (if (<= t 8.6e+122) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3200.0) {
		tmp = y;
	} else if (t <= -8.8e-246) {
		tmp = x;
	} else if (t <= 1.9e-153) {
		tmp = y * (z / a);
	} else if (t <= 8.6e+122) {
		tmp = x;
	} else {
		tmp = 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) :: tmp
    if (t <= (-3200.0d0)) then
        tmp = y
    else if (t <= (-8.8d-246)) then
        tmp = x
    else if (t <= 1.9d-153) then
        tmp = y * (z / a)
    else if (t <= 8.6d+122) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3200.0) {
		tmp = y;
	} else if (t <= -8.8e-246) {
		tmp = x;
	} else if (t <= 1.9e-153) {
		tmp = y * (z / a);
	} else if (t <= 8.6e+122) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3200.0:
		tmp = y
	elif t <= -8.8e-246:
		tmp = x
	elif t <= 1.9e-153:
		tmp = y * (z / a)
	elif t <= 8.6e+122:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3200.0)
		tmp = y;
	elseif (t <= -8.8e-246)
		tmp = x;
	elseif (t <= 1.9e-153)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 8.6e+122)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3200.0)
		tmp = y;
	elseif (t <= -8.8e-246)
		tmp = x;
	elseif (t <= 1.9e-153)
		tmp = y * (z / a);
	elseif (t <= 8.6e+122)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3200.0], y, If[LessEqual[t, -8.8e-246], x, If[LessEqual[t, 1.9e-153], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e+122], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3200 or 8.59999999999999943e122 < t

   1. Initial program 48.5%

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

   3. Taylor expanded in t around inf 42.6%

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

   if -3200 < t < -8.79999999999999992e-246 or 1.90000000000000011e-153 < t < 8.59999999999999943e122

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 38.1%

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

   if -8.79999999999999992e-246 < t < 1.90000000000000011e-153

   1. Initial program 91.0%

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

   3. Taylor expanded in t around 0 88.3%

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

      1. associate-/l* 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in y around inf 61.2%

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

   7. Taylor expanded in x around 0 37.7%

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

      1. associate-*r/ 45.3%

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

   9. Simplified 45.3%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3200:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -245:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-154}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -245.0)
   y
   (if (<= t -7e-248)
     x
     (if (<= t 5.6e-154) (/ y (/ a z)) (if (<= t 1.05e+123) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -245.0) {
		tmp = y;
	} else if (t <= -7e-248) {
		tmp = x;
	} else if (t <= 5.6e-154) {
		tmp = y / (a / z);
	} else if (t <= 1.05e+123) {
		tmp = x;
	} else {
		tmp = 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) :: tmp
    if (t <= (-245.0d0)) then
        tmp = y
    else if (t <= (-7d-248)) then
        tmp = x
    else if (t <= 5.6d-154) then
        tmp = y / (a / z)
    else if (t <= 1.05d+123) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -245.0) {
		tmp = y;
	} else if (t <= -7e-248) {
		tmp = x;
	} else if (t <= 5.6e-154) {
		tmp = y / (a / z);
	} else if (t <= 1.05e+123) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -245.0:
		tmp = y
	elif t <= -7e-248:
		tmp = x
	elif t <= 5.6e-154:
		tmp = y / (a / z)
	elif t <= 1.05e+123:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -245.0)
		tmp = y;
	elseif (t <= -7e-248)
		tmp = x;
	elseif (t <= 5.6e-154)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 1.05e+123)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -245.0)
		tmp = y;
	elseif (t <= -7e-248)
		tmp = x;
	elseif (t <= 5.6e-154)
		tmp = y / (a / z);
	elseif (t <= 1.05e+123)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -245.0], y, If[LessEqual[t, -7e-248], x, If[LessEqual[t, 5.6e-154], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+123], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -245 or 1.04999999999999997e123 < t

   1. Initial program 48.5%

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

   3. Taylor expanded in t around inf 42.6%

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

   if -245 < t < -6.99999999999999966e-248 or 5.60000000000000025e-154 < t < 1.04999999999999997e123

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 38.1%

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

   if -6.99999999999999966e-248 < t < 5.60000000000000025e-154

   1. Initial program 91.0%

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

   3. Taylor expanded in t around 0 88.3%

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

      1. associate-/l* 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in y around inf 61.2%

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

   7. Taylor expanded in x around 0 37.7%

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

      1. associate-*r/ 45.3%

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

   9. Simplified 45.3%

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

       1. clear-num 45.3%

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

       2. div-inv 45.4%

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

   11. Applied egg-rr 45.4%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -245:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-154}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+34} \lor \neg \left(t \leq 5.8 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.6e+34) (not (<= t 5.8e+65)))
   (* y (/ (- z t) (- a t)))
   (+ x (* z (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.6e+34) || !(t <= 5.8e+65)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / (a - 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 ((t <= (-6.6d+34)) .or. (.not. (t <= 5.8d+65))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z * ((y - x) / (a - 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 ((t <= -6.6e+34) || !(t <= 5.8e+65)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.6e+34) or not (t <= 5.8e+65):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.6e+34) || !(t <= 5.8e+65))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.6e+34) || ~((t <= 5.8e+65)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.6e+34], N[Not[LessEqual[t, 5.8e+65]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.59999999999999976e34 or 5.8000000000000001e65 < t

   1. Initial program 44.5%

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

      1. clear-num 44.5%

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

      2. inv-pow 44.5%

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

      3. *-commutative 44.5%

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

      4. associate-/r* 67.4%

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

   4. Applied egg-rr 67.4%

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

   5. Taylor expanded in x around 0 39.4%

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

      1. associate-/l* 60.4%

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

   7. Simplified 60.4%

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

   if -6.59999999999999976e34 < t < 5.8000000000000001e65

   1. Initial program 87.6%

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

   3. Taylor expanded in z around inf 81.0%

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

      1. associate-/l* 82.3%

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

   5. Simplified 82.3%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+34} \lor \neg \left(t \leq 5.8 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+34} \lor \neg \left(t \leq 6.5 \cdot 10^{+72}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.5e+34) (not (<= t 6.5e+72)))
   (* y (/ (- z t) (- a t)))
   (+ x (/ z (/ (- a t) (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e+34) || !(t <= 6.5e+72)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z / ((a - t) / (y - 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 ((t <= (-4.5d+34)) .or. (.not. (t <= 6.5d+72))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z / ((a - t) / (y - 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 ((t <= -4.5e+34) || !(t <= 6.5e+72)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z / ((a - t) / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.5e+34) or not (t <= 6.5e+72):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z / ((a - t) / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.5e+34) || !(t <= 6.5e+72))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.5e+34) || ~((t <= 6.5e+72)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z / ((a - t) / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.5e+34], N[Not[LessEqual[t, 6.5e+72]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5e34 or 6.5000000000000001e72 < t

   1. Initial program 44.5%

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

      1. clear-num 44.5%

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

      2. inv-pow 44.5%

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

      3. *-commutative 44.5%

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

      4. associate-/r* 67.4%

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

   4. Applied egg-rr 67.4%

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

   5. Taylor expanded in x around 0 39.4%

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

      1. associate-/l* 60.4%

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

   7. Simplified 60.4%

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

   if -4.5e34 < t < 6.5000000000000001e72

   1. Initial program 87.6%

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

   3. Taylor expanded in z around inf 81.0%

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

      1. associate-/l* 82.3%

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

   5. Simplified 82.3%

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

      1. clear-num 82.3%

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

      2. un-div-inv 83.4%

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

   7. Applied egg-rr 83.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+34} \lor \neg \left(t \leq 6.5 \cdot 10^{+72}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+80} \lor \neg \left(t \leq 1.62 \cdot 10^{+67}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8e+80) (not (<= t 1.62e+67)))
   (* y (/ (- z t) (- a t)))
   (- x (/ (- x y) (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+80) || !(t <= 1.62e+67)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - ((x - y) / ((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 ((t <= (-8d+80)) .or. (.not. (t <= 1.62d+67))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x - ((x - y) / ((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 ((t <= -8e+80) || !(t <= 1.62e+67)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - ((x - y) / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8e+80) or not (t <= 1.62e+67):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x - ((x - y) / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8e+80) || !(t <= 1.62e+67))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8e+80) || ~((t <= 1.62e+67)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x - ((x - y) / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8e+80], N[Not[LessEqual[t, 1.62e+67]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8e80 or 1.6199999999999999e67 < t

   1. Initial program 42.5%

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

      1. clear-num 42.5%

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

      2. inv-pow 42.5%

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

      3. *-commutative 42.5%

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

      4. associate-/r* 67.9%

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

   4. Applied egg-rr 67.9%

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

   5. Taylor expanded in x around 0 40.1%

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

      1. associate-/l* 63.3%

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

   7. Simplified 63.3%

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

   if -8e80 < t < 1.6199999999999999e67

   1. Initial program 86.1%

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

      1. clear-num 86.1%

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

      2. inv-pow 86.1%

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

      3. *-commutative 86.1%

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

      4. associate-/r* 93.0%

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

   4. Applied egg-rr 93.0%

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

      1. unpow-1 93.0%

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

      2. clear-num 93.1%

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

      3. div-sub 89.5%

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

   6. Applied egg-rr 89.5%

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

      1. div-sub 93.1%

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

   8. Simplified 93.1%

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

   9. Taylor expanded in z around inf 85.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+80} \lor \neg \left(t \leq 1.62 \cdot 10^{+67}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-19} \lor \neg \left(t \leq 7 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.6e-19) (not (<= t 7e+16)))
   (* y (/ (- z t) (- a t)))
   (+ x (* z (/ (- y x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e-19) || !(t <= 7e+16)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.6d-19)) .or. (.not. (t <= 7d+16))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z * ((y - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e-19) || !(t <= 7e+16)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.6e-19) or not (t <= 7e+16):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z * ((y - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.6e-19) || !(t <= 7e+16))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.6e-19) || ~((t <= 7e+16)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z * ((y - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.6e-19], N[Not[LessEqual[t, 7e+16]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5999999999999996e-19 or 7e16 < t

   1. Initial program 51.2%

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

      1. clear-num 51.2%

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

      2. inv-pow 51.2%

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

      3. *-commutative 51.2%

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

      4. associate-/r* 71.2%

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

   4. Applied egg-rr 71.2%

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

   5. Taylor expanded in x around 0 40.2%

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

      1. associate-/l* 58.7%

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

   7. Simplified 58.7%

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

   if -4.5999999999999996e-19 < t < 7e16

   1. Initial program 89.1%

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

   3. Taylor expanded in t around 0 73.0%

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

      1. associate-/l* 73.7%

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

   5. Simplified 73.7%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-19} \lor \neg \left(t \leq 7 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 66.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+31} \lor \neg \left(t \leq 1.45 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.2e+31) (not (<= t 1.45e+17)))
   (* y (/ (- z t) (- a t)))
   (- x (/ z (/ a (- x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.2e+31) || !(t <= 1.45e+17)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (z / (a / (x - 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) :: tmp
    if ((t <= (-2.2d+31)) .or. (.not. (t <= 1.45d+17))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x - (z / (a / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.2e+31) || !(t <= 1.45e+17)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (z / (a / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.2e+31) or not (t <= 1.45e+17):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x - (z / (a / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.2e+31) || !(t <= 1.45e+17))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(z / Float64(a / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.2e+31) || ~((t <= 1.45e+17)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x - (z / (a / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.2e+31], N[Not[LessEqual[t, 1.45e+17]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(a / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2000000000000001e31 or 1.45e17 < t

   1. Initial program 46.4%

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

      1. clear-num 46.4%

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

      2. inv-pow 46.4%

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

      3. *-commutative 46.4%

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

      4. associate-/r* 69.1%

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

   4. Applied egg-rr 69.1%

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

   5. Taylor expanded in x around 0 39.1%

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

      1. associate-/l* 60.1%

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

   7. Simplified 60.1%

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

   if -2.2000000000000001e31 < t < 1.45e17

   1. Initial program 88.8%

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

   3. Taylor expanded in t around 0 71.1%

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

      1. associate-/l* 71.1%

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

   5. Simplified 71.1%

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

      1. clear-num 71.1%

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

      2. un-div-inv 72.3%

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

   7. Applied egg-rr 72.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+31} \lor \neg \left(t \leq 1.45 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+80} \lor \neg \left(t \leq 8 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.5e+80) (not (<= t 8e+16)))
   (* y (/ (- z t) (- a t)))
   (+ x (/ (- y x) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e+80) || !(t <= 8e+16)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (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 ((t <= (-2.5d+80)) .or. (.not. (t <= 8d+16))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + ((y - x) / (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 ((t <= -2.5e+80) || !(t <= 8e+16)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.5e+80) or not (t <= 8e+16):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.5e+80) || !(t <= 8e+16))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.5e+80) || ~((t <= 8e+16)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.5e+80], N[Not[LessEqual[t, 8e+16]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4999999999999998e80 or 8e16 < t

   1. Initial program 44.7%

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

      1. clear-num 44.7%

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

      2. inv-pow 44.7%

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

      3. *-commutative 44.7%

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

      4. associate-/r* 69.7%

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

   4. Applied egg-rr 69.7%

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

   5. Taylor expanded in x around 0 39.8%

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

      1. associate-/l* 62.8%

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

   7. Simplified 62.8%

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

   if -2.4999999999999998e80 < t < 8e16

   1. Initial program 87.2%

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

      1. clear-num 87.1%

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

      2. inv-pow 87.1%

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

      3. *-commutative 87.1%

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

      4. associate-/r* 93.3%

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

   4. Applied egg-rr 93.3%

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

      1. unpow-1 93.3%

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

      2. clear-num 93.4%

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

      3. div-sub 89.5%

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

   6. Applied egg-rr 89.5%

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

      1. div-sub 93.4%

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

   8. Simplified 93.4%

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

   9. Taylor expanded in t around 0 74.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+80} \lor \neg \left(t \leq 8 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 37.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3500:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3500.0) y (if (<= t 9.5e+122) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3500.0) {
		tmp = y;
	} else if (t <= 9.5e+122) {
		tmp = x;
	} else {
		tmp = 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) :: tmp
    if (t <= (-3500.0d0)) then
        tmp = y
    else if (t <= 9.5d+122) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3500.0) {
		tmp = y;
	} else if (t <= 9.5e+122) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3500.0:
		tmp = y
	elif t <= 9.5e+122:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3500.0)
		tmp = y;
	elseif (t <= 9.5e+122)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3500.0)
		tmp = y;
	elseif (t <= 9.5e+122)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3500.0], y, If[LessEqual[t, 9.5e+122], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -3500 or 9.49999999999999986e122 < t

   1. Initial program 48.5%

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

   3. Taylor expanded in t around inf 42.6%

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

   if -3500 < t < 9.49999999999999986e122

   1. Initial program 84.2%

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

   3. Taylor expanded in a around inf 34.5%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3500:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 25.0% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.3%

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

3. Taylor expanded in a around inf 24.8%

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

4. Final simplification 24.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024043 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))