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

Percentage Accurate: 68.9% → 90.9%

Time: 25.5s

Alternatives: 22

Speedup: 1.0×

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: 68.9% 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: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -9.4 \cdot 10^{+82} \lor \neg \left(t \leq 1.12 \cdot 10^{+151}\right):\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{z}{a - t} + \frac{a}{t}, y \cdot t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_1, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (or (<= t -9.4e+82) (not (<= t 1.12e+151)))
     (fma (- x) (+ (/ z (- a t)) (/ a t)) (* y t_1))
     (fma t_1 (- y x) x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if ((t <= -9.4e+82) || !(t <= 1.12e+151)) {
		tmp = fma(-x, ((z / (a - t)) + (a / t)), (y * t_1));
	} else {
		tmp = fma(t_1, (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if ((t <= -9.4e+82) || !(t <= 1.12e+151))
		tmp = fma(Float64(-x), Float64(Float64(z / Float64(a - t)) + Float64(a / t)), Float64(y * t_1));
	else
		tmp = fma(t_1, Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -9.4e+82], N[Not[LessEqual[t, 1.12e+151]], $MachinePrecision]], N[((-x) * N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(a / t), $MachinePrecision]), $MachinePrecision] + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.4e82 or 1.12000000000000004e151 < t

   1. Initial program 38.3%

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

      1. +-commutative 38.3%

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

      2. *-commutative 38.3%

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

      3. associate-/l* 60.4%

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

      4. associate-/r/ 72.8%

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

      5. fma-def 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in x around -inf 58.4%

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

      1. associate-*r* 58.4%

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

      2. neg-mul-1 58.4%

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

      3. associate-*r/ 91.2%

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

      4. fma-def 91.3%

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

   6. Simplified 91.3%

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

   7. Taylor expanded in t around inf 93.6%

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

      1. mul-1-neg 93.6%

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

      2. distribute-neg-frac 93.6%

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

   9. Simplified 93.6%

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

   if -9.4e82 < t < 1.12000000000000004e151

   1. Initial program 86.2%

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

      1. +-commutative 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-/l* 91.8%

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

      4. associate-/r/ 93.1%

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

      5. fma-def 93.1%

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

   3. Simplified 93.1%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+82} \lor \neg \left(t \leq 1.12 \cdot 10^{+151}\right):\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{z}{a - t} + \frac{a}{t}, y \cdot \frac{z - t}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \]

Alternative 2: 91.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-x, \frac{z}{a - t} + \left(-1 - \frac{t}{a - t}\right), y \cdot \frac{z - t}{a - t}\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma
  (- x)
  (+ (/ z (- a t)) (- -1.0 (/ t (- a t))))
  (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	return fma(-x, ((z / (a - t)) + (-1.0 - (t / (a - t)))), (y * ((z - t) / (a - t))));
}

Julia

function code(x, y, z, t, a)
	return fma(Float64(-x), Float64(Float64(z / Float64(a - t)) + Float64(-1.0 - Float64(t / Float64(a - t)))), Float64(y * Float64(Float64(z - t) / Float64(a - t))))
end

Wolfram

code[x_, y_, z_, t_, a_] := N[((-x) * N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.8%

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

   1. +-commutative 71.8%

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

   2. *-commutative 71.8%

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

   3. associate-/l* 82.3%

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

   4. associate-/r/ 87.0%

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

   5. fma-def 87.0%

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

3. Simplified 87.0%

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

4. Taylor expanded in x around -inf 77.2%

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

   1. associate-*r* 77.2%

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

   2. neg-mul-1 77.2%

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

   3. associate-*r/ 91.8%

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

   4. fma-def 92.2%

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

6. Simplified 92.2%

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

7. Final simplification 92.2%

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

Alternative 3: 90.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+39} \lor \neg \left(y \leq 4.1 \cdot 10^{+79}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.7e+39) (not (<= y 4.1e+79)))
   (+ x (/ (- y x) (/ (- a t) (- z t))))
   (+
    (* x (- (+ 1.0 (/ t (- a t))) (/ z (- a t))))
    (/ (* y (- z t)) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.7e+39) || !(y <= 4.1e+79)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = (x * ((1.0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (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 ((y <= (-1.7d+39)) .or. (.not. (y <= 4.1d+79))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = (x * ((1.0d0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (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 ((y <= -1.7e+39) || !(y <= 4.1e+79)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = (x * ((1.0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.7e+39) or not (y <= 4.1e+79):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = (x * ((1.0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.7e+39) || !(y <= 4.1e+79))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(Float64(x * Float64(Float64(1.0 + Float64(t / Float64(a - t))) - Float64(z / Float64(a - t)))) + Float64(Float64(y * Float64(z - t)) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.7e+39) || ~((y <= 4.1e+79)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = (x * ((1.0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.7e+39], N[Not[LessEqual[y, 4.1e+79]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(1.0 + N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6999999999999999e39 or 4.1e79 < y

   1. Initial program 59.2%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   if -1.6999999999999999e39 < y < 4.1e79

   1. Initial program 80.0%

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

      1. +-commutative 80.0%

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

      2. *-commutative 80.0%

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

      3. associate-/l* 74.7%

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

      4. associate-/r/ 81.6%

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

      5. fma-def 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in x around -inf 90.3%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+39} \lor \neg \left(y \leq 4.1 \cdot 10^{+79}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \]

Alternative 4: 45.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+27}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-265}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-307}:\\ \;\;\;\;x - z \cdot \frac{x}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{z \cdot y}{a - t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+117}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+122}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -3.3e+27)
     y
     (if (<= t -1.25e-222)
       t_1
       (if (<= t -1.35e-265)
         (* z (/ y (- a t)))
         (if (<= t -3e-307)
           (- x (* z (/ x a)))
           (if (<= t 1.7e-100)
             (* z (/ (- y x) a))
             (if (<= t 1.8e+21)
               t_1
               (if (<= t 5.5e+67)
                 (/ (* z y) (- a t))
                 (if (<= t 3e+117)
                   (- x (/ t (/ a y)))
                   (if (<= t 7e+122) (* z (/ x t)) 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 <= -3.3e+27) {
		tmp = y;
	} else if (t <= -1.25e-222) {
		tmp = t_1;
	} else if (t <= -1.35e-265) {
		tmp = z * (y / (a - t));
	} else if (t <= -3e-307) {
		tmp = x - (z * (x / a));
	} else if (t <= 1.7e-100) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.8e+21) {
		tmp = t_1;
	} else if (t <= 5.5e+67) {
		tmp = (z * y) / (a - t);
	} else if (t <= 3e+117) {
		tmp = x - (t / (a / y));
	} else if (t <= 7e+122) {
		tmp = z * (x / t);
	} 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 <= (-3.3d+27)) then
        tmp = y
    else if (t <= (-1.25d-222)) then
        tmp = t_1
    else if (t <= (-1.35d-265)) then
        tmp = z * (y / (a - t))
    else if (t <= (-3d-307)) then
        tmp = x - (z * (x / a))
    else if (t <= 1.7d-100) then
        tmp = z * ((y - x) / a)
    else if (t <= 1.8d+21) then
        tmp = t_1
    else if (t <= 5.5d+67) then
        tmp = (z * y) / (a - t)
    else if (t <= 3d+117) then
        tmp = x - (t / (a / y))
    else if (t <= 7d+122) then
        tmp = z * (x / t)
    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 <= -3.3e+27) {
		tmp = y;
	} else if (t <= -1.25e-222) {
		tmp = t_1;
	} else if (t <= -1.35e-265) {
		tmp = z * (y / (a - t));
	} else if (t <= -3e-307) {
		tmp = x - (z * (x / a));
	} else if (t <= 1.7e-100) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.8e+21) {
		tmp = t_1;
	} else if (t <= 5.5e+67) {
		tmp = (z * y) / (a - t);
	} else if (t <= 3e+117) {
		tmp = x - (t / (a / y));
	} else if (t <= 7e+122) {
		tmp = z * (x / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -3.3e+27:
		tmp = y
	elif t <= -1.25e-222:
		tmp = t_1
	elif t <= -1.35e-265:
		tmp = z * (y / (a - t))
	elif t <= -3e-307:
		tmp = x - (z * (x / a))
	elif t <= 1.7e-100:
		tmp = z * ((y - x) / a)
	elif t <= 1.8e+21:
		tmp = t_1
	elif t <= 5.5e+67:
		tmp = (z * y) / (a - t)
	elif t <= 3e+117:
		tmp = x - (t / (a / y))
	elif t <= 7e+122:
		tmp = z * (x / t)
	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 <= -3.3e+27)
		tmp = y;
	elseif (t <= -1.25e-222)
		tmp = t_1;
	elseif (t <= -1.35e-265)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t <= -3e-307)
		tmp = Float64(x - Float64(z * Float64(x / a)));
	elseif (t <= 1.7e-100)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 1.8e+21)
		tmp = t_1;
	elseif (t <= 5.5e+67)
		tmp = Float64(Float64(z * y) / Float64(a - t));
	elseif (t <= 3e+117)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	elseif (t <= 7e+122)
		tmp = Float64(z * Float64(x / t));
	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 <= -3.3e+27)
		tmp = y;
	elseif (t <= -1.25e-222)
		tmp = t_1;
	elseif (t <= -1.35e-265)
		tmp = z * (y / (a - t));
	elseif (t <= -3e-307)
		tmp = x - (z * (x / a));
	elseif (t <= 1.7e-100)
		tmp = z * ((y - x) / a);
	elseif (t <= 1.8e+21)
		tmp = t_1;
	elseif (t <= 5.5e+67)
		tmp = (z * y) / (a - t);
	elseif (t <= 3e+117)
		tmp = x - (t / (a / y));
	elseif (t <= 7e+122)
		tmp = z * (x / t);
	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, -3.3e+27], y, If[LessEqual[t, -1.25e-222], t$95$1, If[LessEqual[t, -1.35e-265], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3e-307], N[(x - N[(z * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-100], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+21], t$95$1, If[LessEqual[t, 5.5e+67], N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+117], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+122], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], y]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -3.2999999999999998e27 or 7.00000000000000028e122 < t

   1. Initial program 46.6%

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

      1. +-commutative 46.6%

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

      2. *-commutative 46.6%

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

      3. associate-/l* 66.5%

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

      4. associate-/r/ 76.7%

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

      5. fma-def 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in t around inf 51.4%

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

   if -3.2999999999999998e27 < t < -1.25000000000000002e-222 or 1.69999999999999988e-100 < t < 1.8e21

   1. Initial program 85.9%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around 0 65.3%

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

   5. Taylor expanded in x around inf 51.6%

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

      1. mul-1-neg 51.6%

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

      2. unsub-neg 51.6%

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

   7. Simplified 51.6%

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

   if -1.25000000000000002e-222 < t < -1.3500000000000001e-265

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. *-commutative 92.6%

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

      3. associate-/l* 92.5%

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

      4. associate-/r/ 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 77.9%

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

      1. div-sub 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in y around inf 70.6%

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

   if -1.3500000000000001e-265 < t < -2.9999999999999999e-307

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

   5. Taylor expanded in y around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. unsub-neg 85.8%

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

      3. associate-/l* 85.7%

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

      4. associate-/r/ 85.8%

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

   7. Simplified 85.8%

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

   if -2.9999999999999999e-307 < t < 1.69999999999999988e-100

   1. Initial program 90.3%

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

      1. +-commutative 90.3%

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

      2. *-commutative 90.3%

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

      3. associate-/l* 91.5%

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

      4. associate-/r/ 90.5%

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

      5. fma-def 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in z around inf 70.0%

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

      1. div-sub 70.0%

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

   6. Simplified 70.0%

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

   7. Taylor expanded in a around inf 61.9%

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

   if 1.8e21 < t < 5.49999999999999968e67

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-/l* 99.7%

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

      4. associate-/r/ 99.9%

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

      5. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 54.1%

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

      1. div-sub 54.1%

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

   6. Simplified 54.1%

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

   7. Taylor expanded in y around inf 53.9%

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

   if 5.49999999999999968e67 < t < 3e117

   1. Initial program 65.4%

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

      1. +-commutative 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-/l* 90.3%

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

      4. associate-/r/ 90.6%

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

      5. fma-def 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in a around inf 51.6%

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

      1. associate-/l* 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in z around 0 43.6%

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

      1. mul-1-neg 43.6%

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

      2. associate-/l* 59.0%

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

      3. distribute-neg-frac 59.0%

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

   9. Simplified 59.0%

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

   10. Taylor expanded in y around inf 43.4%

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

       1. mul-1-neg 43.4%

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

       2. associate-/l* 51.2%

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

       3. distribute-neg-frac 51.2%

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

   12. Simplified 51.2%

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

   if 3e117 < t < 7.00000000000000028e122

   1. Initial program 43.8%

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

      1. +-commutative 43.8%

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

      2. *-commutative 43.8%

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

      3. associate-/l* 100.0%

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

      4. associate-/r/ 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around -inf 43.8%

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

   5. Taylor expanded in y around 0 23.2%

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

      1. associate-/l* 42.8%

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

   7. Simplified 42.8%

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

   8. Taylor expanded in z around inf 23.2%

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

      1. associate-*l/ 42.8%

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

      2. *-commutative 42.8%

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

   10. Simplified 42.8%

       \[\leadsto \color{blue}{z \cdot \frac{x}{t}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+27}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-265}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-307}:\\ \;\;\;\;x - z \cdot \frac{x}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{z \cdot y}{a - t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+117}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+122}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5: 45.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.05 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a t)))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= t -3.1e+29)
     y
     (if (<= t -9.5e-223)
       t_2
       (if (<= t -1.2e-263)
         t_1
         (if (<= t 2.6e-308)
           t_2
           (if (<= t 2.35e-164) t_1 (if (<= t 4.05e+40) t_2 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.1e+29) {
		tmp = y;
	} else if (t <= -9.5e-223) {
		tmp = t_2;
	} else if (t <= -1.2e-263) {
		tmp = t_1;
	} else if (t <= 2.6e-308) {
		tmp = t_2;
	} else if (t <= 2.35e-164) {
		tmp = t_1;
	} else if (t <= 4.05e+40) {
		tmp = t_2;
	} 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 = z * (y / (a - t))
    t_2 = x * (1.0d0 - (z / a))
    if (t <= (-3.1d+29)) then
        tmp = y
    else if (t <= (-9.5d-223)) then
        tmp = t_2
    else if (t <= (-1.2d-263)) then
        tmp = t_1
    else if (t <= 2.6d-308) then
        tmp = t_2
    else if (t <= 2.35d-164) then
        tmp = t_1
    else if (t <= 4.05d+40) then
        tmp = t_2
    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 = z * (y / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -3.1e+29) {
		tmp = y;
	} else if (t <= -9.5e-223) {
		tmp = t_2;
	} else if (t <= -1.2e-263) {
		tmp = t_1;
	} else if (t <= 2.6e-308) {
		tmp = t_2;
	} else if (t <= 2.35e-164) {
		tmp = t_1;
	} else if (t <= 4.05e+40) {
		tmp = t_2;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / (a - t))
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -3.1e+29:
		tmp = y
	elif t <= -9.5e-223:
		tmp = t_2
	elif t <= -1.2e-263:
		tmp = t_1
	elif t <= 2.6e-308:
		tmp = t_2
	elif t <= 2.35e-164:
		tmp = t_1
	elif t <= 4.05e+40:
		tmp = t_2
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(a - t)))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -3.1e+29)
		tmp = y;
	elseif (t <= -9.5e-223)
		tmp = t_2;
	elseif (t <= -1.2e-263)
		tmp = t_1;
	elseif (t <= 2.6e-308)
		tmp = t_2;
	elseif (t <= 2.35e-164)
		tmp = t_1;
	elseif (t <= 4.05e+40)
		tmp = t_2;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / (a - t));
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -3.1e+29)
		tmp = y;
	elseif (t <= -9.5e-223)
		tmp = t_2;
	elseif (t <= -1.2e-263)
		tmp = t_1;
	elseif (t <= 2.6e-308)
		tmp = t_2;
	elseif (t <= 2.35e-164)
		tmp = t_1;
	elseif (t <= 4.05e+40)
		tmp = t_2;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+29], y, If[LessEqual[t, -9.5e-223], t$95$2, If[LessEqual[t, -1.2e-263], t$95$1, If[LessEqual[t, 2.6e-308], t$95$2, If[LessEqual[t, 2.35e-164], t$95$1, If[LessEqual[t, 4.05e+40], t$95$2, y]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.0999999999999999e29 or 4.0499999999999999e40 < t

   1. Initial program 51.5%

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

      1. +-commutative 51.5%

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

      2. *-commutative 51.5%

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

      3. associate-/l* 72.3%

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

      4. associate-/r/ 80.5%

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

      5. fma-def 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in t around inf 48.5%

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

   if -3.0999999999999999e29 < t < -9.49999999999999992e-223 or -1.2e-263 < t < 2.6e-308 or 2.3499999999999998e-164 < t < 4.0499999999999999e40

   1. Initial program 87.4%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around 0 66.7%

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

   5. Taylor expanded in x around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. unsub-neg 51.8%

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

   7. Simplified 51.8%

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

   if -9.49999999999999992e-223 < t < -1.2e-263 or 2.6e-308 < t < 2.3499999999999998e-164

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. *-commutative 93.0%

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

      3. associate-/l* 95.2%

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

      4. associate-/r/ 95.3%

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

      5. fma-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around inf 76.5%

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

      1. div-sub 76.5%

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

   6. Simplified 76.5%

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

   7. Taylor expanded in y around inf 64.9%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-263}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-164}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 4.05 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6: 45.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{+28}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-265}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -3e+28)
     y
     (if (<= t -9e-223)
       t_1
       (if (<= t -1.8e-265)
         (* z (/ y (- a t)))
         (if (<= t -8e-307)
           t_1
           (if (<= t 3.5e-100)
             (* z (/ (- y x) a))
             (if (<= t 2.1e+40) 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 <= -3e+28) {
		tmp = y;
	} else if (t <= -9e-223) {
		tmp = t_1;
	} else if (t <= -1.8e-265) {
		tmp = z * (y / (a - t));
	} else if (t <= -8e-307) {
		tmp = t_1;
	} else if (t <= 3.5e-100) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.1e+40) {
		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 <= (-3d+28)) then
        tmp = y
    else if (t <= (-9d-223)) then
        tmp = t_1
    else if (t <= (-1.8d-265)) then
        tmp = z * (y / (a - t))
    else if (t <= (-8d-307)) then
        tmp = t_1
    else if (t <= 3.5d-100) then
        tmp = z * ((y - x) / a)
    else if (t <= 2.1d+40) 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 <= -3e+28) {
		tmp = y;
	} else if (t <= -9e-223) {
		tmp = t_1;
	} else if (t <= -1.8e-265) {
		tmp = z * (y / (a - t));
	} else if (t <= -8e-307) {
		tmp = t_1;
	} else if (t <= 3.5e-100) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.1e+40) {
		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 <= -3e+28:
		tmp = y
	elif t <= -9e-223:
		tmp = t_1
	elif t <= -1.8e-265:
		tmp = z * (y / (a - t))
	elif t <= -8e-307:
		tmp = t_1
	elif t <= 3.5e-100:
		tmp = z * ((y - x) / a)
	elif t <= 2.1e+40:
		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 <= -3e+28)
		tmp = y;
	elseif (t <= -9e-223)
		tmp = t_1;
	elseif (t <= -1.8e-265)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t <= -8e-307)
		tmp = t_1;
	elseif (t <= 3.5e-100)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 2.1e+40)
		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 <= -3e+28)
		tmp = y;
	elseif (t <= -9e-223)
		tmp = t_1;
	elseif (t <= -1.8e-265)
		tmp = z * (y / (a - t));
	elseif (t <= -8e-307)
		tmp = t_1;
	elseif (t <= 3.5e-100)
		tmp = z * ((y - x) / a);
	elseif (t <= 2.1e+40)
		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, -3e+28], y, If[LessEqual[t, -9e-223], t$95$1, If[LessEqual[t, -1.8e-265], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8e-307], t$95$1, If[LessEqual[t, 3.5e-100], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e+40], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.0000000000000001e28 or 2.1000000000000001e40 < t

   1. Initial program 51.5%

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

      1. +-commutative 51.5%

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

      2. *-commutative 51.5%

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

      3. associate-/l* 72.3%

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

      4. associate-/r/ 80.5%

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

      5. fma-def 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in t around inf 48.5%

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

   if -3.0000000000000001e28 < t < -8.99999999999999935e-223 or -1.8000000000000001e-265 < t < -7.99999999999999927e-307 or 3.5000000000000001e-100 < t < 2.1000000000000001e40

   1. Initial program 87.9%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in t around 0 66.5%

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

   5. Taylor expanded in x around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

   7. Simplified 53.4%

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

   if -8.99999999999999935e-223 < t < -1.8000000000000001e-265

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. *-commutative 92.6%

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

      3. associate-/l* 92.5%

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

      4. associate-/r/ 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 77.9%

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

      1. div-sub 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in y around inf 70.6%

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

   if -7.99999999999999927e-307 < t < 3.5000000000000001e-100

   1. Initial program 90.3%

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

      1. +-commutative 90.3%

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

      2. *-commutative 90.3%

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

      3. associate-/l* 91.5%

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

      4. associate-/r/ 90.5%

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

      5. fma-def 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in z around inf 70.0%

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

      1. div-sub 70.0%

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

   6. Simplified 70.0%

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

   7. Taylor expanded in a around inf 61.9%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+28}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-265}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-307}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7: 45.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-263}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-306}:\\ \;\;\;\;x - z \cdot \frac{x}{a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-99}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -3.6e+29)
     y
     (if (<= t -9e-223)
       t_1
       (if (<= t -5.5e-263)
         (* z (/ y (- a t)))
         (if (<= t -1.35e-306)
           (- x (* z (/ x a)))
           (if (<= t 2.2e-99)
             (* z (/ (- y x) a))
             (if (<= t 4.3e+38) 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 <= -3.6e+29) {
		tmp = y;
	} else if (t <= -9e-223) {
		tmp = t_1;
	} else if (t <= -5.5e-263) {
		tmp = z * (y / (a - t));
	} else if (t <= -1.35e-306) {
		tmp = x - (z * (x / a));
	} else if (t <= 2.2e-99) {
		tmp = z * ((y - x) / a);
	} else if (t <= 4.3e+38) {
		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 <= (-3.6d+29)) then
        tmp = y
    else if (t <= (-9d-223)) then
        tmp = t_1
    else if (t <= (-5.5d-263)) then
        tmp = z * (y / (a - t))
    else if (t <= (-1.35d-306)) then
        tmp = x - (z * (x / a))
    else if (t <= 2.2d-99) then
        tmp = z * ((y - x) / a)
    else if (t <= 4.3d+38) 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 <= -3.6e+29) {
		tmp = y;
	} else if (t <= -9e-223) {
		tmp = t_1;
	} else if (t <= -5.5e-263) {
		tmp = z * (y / (a - t));
	} else if (t <= -1.35e-306) {
		tmp = x - (z * (x / a));
	} else if (t <= 2.2e-99) {
		tmp = z * ((y - x) / a);
	} else if (t <= 4.3e+38) {
		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 <= -3.6e+29:
		tmp = y
	elif t <= -9e-223:
		tmp = t_1
	elif t <= -5.5e-263:
		tmp = z * (y / (a - t))
	elif t <= -1.35e-306:
		tmp = x - (z * (x / a))
	elif t <= 2.2e-99:
		tmp = z * ((y - x) / a)
	elif t <= 4.3e+38:
		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 <= -3.6e+29)
		tmp = y;
	elseif (t <= -9e-223)
		tmp = t_1;
	elseif (t <= -5.5e-263)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t <= -1.35e-306)
		tmp = Float64(x - Float64(z * Float64(x / a)));
	elseif (t <= 2.2e-99)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 4.3e+38)
		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 <= -3.6e+29)
		tmp = y;
	elseif (t <= -9e-223)
		tmp = t_1;
	elseif (t <= -5.5e-263)
		tmp = z * (y / (a - t));
	elseif (t <= -1.35e-306)
		tmp = x - (z * (x / a));
	elseif (t <= 2.2e-99)
		tmp = z * ((y - x) / a);
	elseif (t <= 4.3e+38)
		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, -3.6e+29], y, If[LessEqual[t, -9e-223], t$95$1, If[LessEqual[t, -5.5e-263], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e-306], N[(x - N[(z * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-99], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e+38], t$95$1, y]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.59999999999999976e29 or 4.2999999999999997e38 < t

   1. Initial program 51.5%

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

      1. +-commutative 51.5%

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

      2. *-commutative 51.5%

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

      3. associate-/l* 72.3%

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

      4. associate-/r/ 80.5%

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

      5. fma-def 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in t around inf 48.5%

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

   if -3.59999999999999976e29 < t < -8.99999999999999935e-223 or 2.20000000000000004e-99 < t < 4.2999999999999997e38

   1. Initial program 86.7%

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

      1. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in t around 0 63.3%

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

   5. Taylor expanded in x around inf 50.3%

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

      1. mul-1-neg 50.3%

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

      2. unsub-neg 50.3%

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

   7. Simplified 50.3%

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

   if -8.99999999999999935e-223 < t < -5.49999999999999971e-263

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. *-commutative 92.6%

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

      3. associate-/l* 92.5%

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

      4. associate-/r/ 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 77.9%

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

      1. div-sub 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in y around inf 70.6%

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

   if -5.49999999999999971e-263 < t < -1.35000000000000005e-306

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

   5. Taylor expanded in y around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. unsub-neg 85.8%

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

      3. associate-/l* 85.7%

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

      4. associate-/r/ 85.8%

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

   7. Simplified 85.8%

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

   if -1.35000000000000005e-306 < t < 2.20000000000000004e-99

   1. Initial program 90.3%

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

      1. +-commutative 90.3%

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

      2. *-commutative 90.3%

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

      3. associate-/l* 91.5%

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

      4. associate-/r/ 90.5%

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

      5. fma-def 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in z around inf 70.0%

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

      1. div-sub 70.0%

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

   6. Simplified 70.0%

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

   7. Taylor expanded in a around inf 61.9%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-263}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-306}:\\ \;\;\;\;x - z \cdot \frac{x}{a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-99}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 70.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+110}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-48} \lor \neg \left(t \leq 2 \cdot 10^{-13}\right):\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.2e+110)
   (+ y (* (- z a) (/ x t)))
   (if (<= t -2.6e+91)
     (* y (/ (- z t) (- a t)))
     (if (or (<= t -1.15e-48) (not (<= t 2e-13)))
       (- y (/ z (/ t (- y x))))
       (- x (/ (- x y) (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+110) {
		tmp = y + ((z - a) * (x / t));
	} else if (t <= -2.6e+91) {
		tmp = y * ((z - t) / (a - t));
	} else if ((t <= -1.15e-48) || !(t <= 2e-13)) {
		tmp = y - (z / (t / (y - x)));
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.2d+110)) then
        tmp = y + ((z - a) * (x / t))
    else if (t <= (-2.6d+91)) then
        tmp = y * ((z - t) / (a - t))
    else if ((t <= (-1.15d-48)) .or. (.not. (t <= 2d-13))) then
        tmp = y - (z / (t / (y - x)))
    else
        tmp = x - ((x - y) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+110) {
		tmp = y + ((z - a) * (x / t));
	} else if (t <= -2.6e+91) {
		tmp = y * ((z - t) / (a - t));
	} else if ((t <= -1.15e-48) || !(t <= 2e-13)) {
		tmp = y - (z / (t / (y - x)));
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.2e+110:
		tmp = y + ((z - a) * (x / t))
	elif t <= -2.6e+91:
		tmp = y * ((z - t) / (a - t))
	elif (t <= -1.15e-48) or not (t <= 2e-13):
		tmp = y - (z / (t / (y - x)))
	else:
		tmp = x - ((x - y) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.2e+110)
		tmp = Float64(y + Float64(Float64(z - a) * Float64(x / t)));
	elseif (t <= -2.6e+91)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif ((t <= -1.15e-48) || !(t <= 2e-13))
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.2e+110)
		tmp = y + ((z - a) * (x / t));
	elseif (t <= -2.6e+91)
		tmp = y * ((z - t) / (a - t));
	elseif ((t <= -1.15e-48) || ~((t <= 2e-13)))
		tmp = y - (z / (t / (y - x)));
	else
		tmp = x - ((x - y) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.2e+110], N[(y + N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6e+91], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.15e-48], N[Not[LessEqual[t, 2e-13]], $MachinePrecision]], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.1999999999999994e110

   1. Initial program 36.6%

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

      1. +-commutative 36.6%

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

      2. *-commutative 36.6%

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

      3. associate-/l* 59.3%

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

      4. associate-/r/ 72.1%

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

      5. fma-def 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in t around inf 58.7%

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

      1. cancel-sign-sub-inv 58.7%

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

      2. metadata-eval 58.7%

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

      3. *-lft-identity 58.7%

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

      4. distribute-lft-in 58.3%

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

      5. mul-1-neg 58.3%

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

      6. distribute-rgt-neg-in 58.3%

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

      7. *-commutative 58.3%

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

      8. mul-1-neg 58.3%

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

      9. *-commutative 58.3%

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

      10. cancel-sign-sub 58.3%

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

      11. mul-1-neg 58.3%

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

      12. associate-*r* 58.3%

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

      13. distribute-lft-out-- 58.3%

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

      14. associate-*r/ 58.3%

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

   6. Simplified 85.5%

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

   7. Taylor expanded in y around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. associate-*l/ 80.8%

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

      3. distribute-lft-neg-out 80.8%

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

      4. *-commutative 80.8%

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

      5. distribute-neg-frac 80.8%

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

   9. Simplified 80.8%

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

   if -7.1999999999999994e110 < t < -2.6e91

   1. Initial program 44.6%

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

      1. +-commutative 44.6%

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

      2. *-commutative 44.6%

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

      3. associate-/l* 99.7%

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

      4. associate-/r/ 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 99.7%

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

      1. div-sub 99.7%

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

   6. Simplified 99.7%

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

   if -2.6e91 < t < -1.15e-48 or 2.0000000000000001e-13 < t

   1. Initial program 66.4%

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

      1. +-commutative 66.4%

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

      2. *-commutative 66.4%

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

      3. associate-/l* 80.0%

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

      4. associate-/r/ 84.4%

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

      5. fma-def 84.4%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in t around -inf 67.4%

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

   5. Taylor expanded in a around 0 66.3%

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

      1. mul-1-neg 66.3%

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

      2. unsub-neg 66.3%

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

      3. associate-/l* 75.1%

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

   7. Simplified 75.1%

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

   if -1.15e-48 < t < 2.0000000000000001e-13

   1. Initial program 89.9%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in t around 0 77.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+110}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-48} \lor \neg \left(t \leq 2 \cdot 10^{-13}\right):\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+199} \lor \neg \left(t \leq 2.55 \cdot 10^{+161}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e+199) (not (<= t 2.55e+161)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (* (- z t) (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e+199) || !(t <= 2.55e+161)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((z - t) * ((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 <= (-1.2d+199)) .or. (.not. (t <= 2.55d+161))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((z - t) * ((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 <= -1.2e+199) || !(t <= 2.55e+161)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e+199) or not (t <= 2.55e+161):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e+199) || !(t <= 2.55e+161))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * 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 <= -1.2e+199) || ~((t <= 2.55e+161)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e+199], N[Not[LessEqual[t, 2.55e+161]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.20000000000000007e199 or 2.54999999999999982e161 < t

   1. Initial program 34.2%

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

      1. +-commutative 34.2%

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

      2. *-commutative 34.2%

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

      3. associate-/l* 53.4%

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

      4. associate-/r/ 70.8%

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

      5. fma-def 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in t around inf 59.6%

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

      1. cancel-sign-sub-inv 59.6%

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

      2. metadata-eval 59.6%

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

      3. *-lft-identity 59.6%

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

      4. distribute-lft-in 59.2%

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

      5. mul-1-neg 59.2%

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

      6. distribute-rgt-neg-in 59.2%

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

      7. *-commutative 59.2%

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

      8. mul-1-neg 59.2%

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

      9. *-commutative 59.2%

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

      10. cancel-sign-sub 59.2%

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

      11. mul-1-neg 59.2%

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

      12. associate-*r* 59.2%

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

      13. distribute-lft-out-- 59.2%

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

      14. associate-*r/ 59.2%

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

   6. Simplified 90.2%

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

   if -1.20000000000000007e199 < t < 2.54999999999999982e161

   1. Initial program 82.0%

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

      1. associate-*l/ 89.8%

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

   3. Simplified 89.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+199} \lor \neg \left(t \leq 2.55 \cdot 10^{+161}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 10: 88.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+223} \lor \neg \left(t \leq 7.2 \cdot 10^{+157}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.3e+223) (not (<= t 7.2e+157)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (/ (- y x) (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e+223) || !(t <= 7.2e+157)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) / ((a - t) / (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 <= (-2.3d+223)) .or. (.not. (t <= 7.2d+157))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((y - x) / ((a - t) / (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 <= -2.3e+223) || !(t <= 7.2e+157)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.3e+223) or not (t <= 7.2e+157):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.3e+223) || !(t <= 7.2e+157))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.3e+223) || ~((t <= 7.2e+157)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.3e+223], N[Not[LessEqual[t, 7.2e+157]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.30000000000000004e223 or 7.20000000000000049e157 < t

   1. Initial program 32.2%

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

      1. +-commutative 32.2%

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

      2. *-commutative 32.2%

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

      3. associate-/l* 52.6%

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

      4. associate-/r/ 69.2%

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

      5. fma-def 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in t around inf 59.5%

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

      1. cancel-sign-sub-inv 59.5%

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

      2. metadata-eval 59.5%

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

      3. *-lft-identity 59.5%

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

      4. distribute-lft-in 59.1%

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

      5. mul-1-neg 59.1%

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

      6. distribute-rgt-neg-in 59.1%

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

      7. *-commutative 59.1%

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

      8. mul-1-neg 59.1%

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

      9. *-commutative 59.1%

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

      10. cancel-sign-sub 59.1%

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

      11. mul-1-neg 59.1%

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

      12. associate-*r* 59.1%

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

      13. distribute-lft-out-- 59.1%

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

      14. associate-*r/ 59.1%

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

   6. Simplified 90.0%

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

   if -2.30000000000000004e223 < t < 7.20000000000000049e157

   1. Initial program 81.9%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+223} \lor \neg \left(t \leq 7.2 \cdot 10^{+157}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 11: 39.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+172}:\\ \;\;\;\;\frac{-z}{\frac{t}{y - x}}\\ \mathbf{elif}\;z \leq -0.49:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-272}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+78}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e+172)
   (/ (- z) (/ t (- y x)))
   (if (<= z -0.49)
     (* z (/ y (- a t)))
     (if (<= z -4.7e-272)
       y
       (if (<= z 5.2e+78) (- x (/ t (/ a y))) (/ y (/ (- a t) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e+172) {
		tmp = -z / (t / (y - x));
	} else if (z <= -0.49) {
		tmp = z * (y / (a - t));
	} else if (z <= -4.7e-272) {
		tmp = y;
	} else if (z <= 5.2e+78) {
		tmp = x - (t / (a / y));
	} else {
		tmp = 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 (z <= (-1.65d+172)) then
        tmp = -z / (t / (y - x))
    else if (z <= (-0.49d0)) then
        tmp = z * (y / (a - t))
    else if (z <= (-4.7d-272)) then
        tmp = y
    else if (z <= 5.2d+78) then
        tmp = x - (t / (a / y))
    else
        tmp = 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 (z <= -1.65e+172) {
		tmp = -z / (t / (y - x));
	} else if (z <= -0.49) {
		tmp = z * (y / (a - t));
	} else if (z <= -4.7e-272) {
		tmp = y;
	} else if (z <= 5.2e+78) {
		tmp = x - (t / (a / y));
	} else {
		tmp = y / ((a - t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.65e+172:
		tmp = -z / (t / (y - x))
	elif z <= -0.49:
		tmp = z * (y / (a - t))
	elif z <= -4.7e-272:
		tmp = y
	elif z <= 5.2e+78:
		tmp = x - (t / (a / y))
	else:
		tmp = y / ((a - t) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.65e+172)
		tmp = Float64(Float64(-z) / Float64(t / Float64(y - x)));
	elseif (z <= -0.49)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (z <= -4.7e-272)
		tmp = y;
	elseif (z <= 5.2e+78)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	else
		tmp = Float64(y / Float64(Float64(a - t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.65e+172)
		tmp = -z / (t / (y - x));
	elseif (z <= -0.49)
		tmp = z * (y / (a - t));
	elseif (z <= -4.7e-272)
		tmp = y;
	elseif (z <= 5.2e+78)
		tmp = x - (t / (a / y));
	else
		tmp = y / ((a - t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.65e+172], N[((-z) / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.49], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.7e-272], y, If[LessEqual[z, 5.2e+78], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.64999999999999991e172

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. *-commutative 76.4%

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

      3. associate-/l* 90.7%

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

      4. associate-/r/ 97.7%

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

      5. fma-def 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in t around -inf 65.7%

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

   5. Taylor expanded in z around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. associate-/l* 72.0%

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

      3. distribute-neg-frac 72.0%

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

   7. Simplified 72.0%

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

   if -1.64999999999999991e172 < z < -0.48999999999999999

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. *-commutative 71.4%

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

      3. associate-/l* 90.7%

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

      4. associate-/r/ 90.8%

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

      5. fma-def 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in z around inf 56.6%

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

      1. div-sub 56.6%

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

   6. Simplified 56.6%

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

   7. Taylor expanded in y around inf 45.1%

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

   if -0.48999999999999999 < z < -4.6999999999999998e-272

   1. Initial program 68.7%

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

      1. +-commutative 68.7%

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

      2. *-commutative 68.7%

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

      3. associate-/l* 75.6%

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

      4. associate-/r/ 82.4%

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

      5. fma-def 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in t around inf 46.4%

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

   if -4.6999999999999998e-272 < z < 5.2e78

   1. Initial program 73.3%

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

      1. +-commutative 73.3%

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

      2. *-commutative 73.3%

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

      3. associate-/l* 73.7%

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

      4. associate-/r/ 82.1%

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

      5. fma-def 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in a around inf 50.6%

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

      1. associate-/l* 54.6%

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

   6. Simplified 54.6%

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

   7. Taylor expanded in z around 0 40.8%

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

      1. mul-1-neg 40.8%

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

      2. associate-/l* 46.2%

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

      3. distribute-neg-frac 46.2%

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

   9. Simplified 46.2%

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

   10. Taylor expanded in y around inf 43.7%

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

       1. mul-1-neg 43.7%

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

       2. associate-/l* 46.4%

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

       3. distribute-neg-frac 46.4%

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

   12. Simplified 46.4%

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

   if 5.2e78 < z

   1. Initial program 71.1%

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

      1. +-commutative 71.1%

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

      2. *-commutative 71.1%

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

      3. associate-/l* 89.6%

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

      4. associate-/r/ 89.7%

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

      5. fma-def 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in z around inf 84.1%

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

      1. div-sub 84.2%

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

   6. Simplified 84.2%

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

   7. Taylor expanded in y around inf 45.3%

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

      1. associate-/l* 55.6%

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

   9. Simplified 55.6%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+172}:\\ \;\;\;\;\frac{-z}{\frac{t}{y - x}}\\ \mathbf{elif}\;z \leq -0.49:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-272}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+78}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 12: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+171} \lor \neg \left(z \leq 2.65 \cdot 10^{+132}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1e+171) (not (<= z 2.65e+132)))
   (* z (/ (- y x) (- a t)))
   (+ x (/ y (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e+171) || !(z <= 2.65e+132)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + (y / ((a - t) / (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 ((z <= (-1d+171)) .or. (.not. (z <= 2.65d+132))) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = x + (y / ((a - t) / (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 ((z <= -1e+171) || !(z <= 2.65e+132)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + (y / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1e+171) or not (z <= 2.65e+132):
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = x + (y / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1e+171) || !(z <= 2.65e+132))
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1e+171) || ~((z <= 2.65e+132)))
		tmp = z * ((y - x) / (a - t));
	else
		tmp = x + (y / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1e+171], N[Not[LessEqual[z, 2.65e+132]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999954e170 or 2.65e132 < z

   1. Initial program 74.6%

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

      1. +-commutative 74.6%

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

      2. *-commutative 74.6%

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

      3. associate-/l* 90.8%

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

      4. associate-/r/ 92.3%

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

      5. fma-def 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around inf 89.7%

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

      1. div-sub 89.7%

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

   6. Simplified 89.7%

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

   if -9.99999999999999954e170 < z < 2.65e132

   1. Initial program 70.7%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

      1. *-commutative 78.6%

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

      2. clear-num 78.5%

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

      3. un-div-inv 79.1%

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

   5. Applied egg-rr 79.1%

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

      1. *-un-lft-identity 79.1%

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

      2. div-inv 79.0%

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

      3. times-frac 70.4%

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

   7. Applied egg-rr 70.4%

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

   8. Taylor expanded in y around inf 65.3%

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

      1. associate-/l* 77.2%

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

   10. Simplified 77.2%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+171} \lor \neg \left(z \leq 2.65 \cdot 10^{+132}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 13: 78.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+31} \lor \neg \left(a \leq 35000\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.8e+31) (not (<= a 35000.0)))
   (+ x (/ y (/ (- a t) (- z t))))
   (+ y (/ (- x y) (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.8e+31) || !(a <= 35000.0)) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else {
		tmp = y + ((x - y) / (t / (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 ((a <= (-3.8d+31)) .or. (.not. (a <= 35000.0d0))) then
        tmp = x + (y / ((a - t) / (z - t)))
    else
        tmp = y + ((x - y) / (t / (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 ((a <= -3.8e+31) || !(a <= 35000.0)) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.8e+31) or not (a <= 35000.0):
		tmp = x + (y / ((a - t) / (z - t)))
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.8e+31) || !(a <= 35000.0))
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.8e+31) || ~((a <= 35000.0)))
		tmp = x + (y / ((a - t) / (z - t)));
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.8e+31], N[Not[LessEqual[a, 35000.0]], $MachinePrecision]], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.8000000000000001e31 or 35000 < a

   1. Initial program 68.5%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

      1. *-commutative 90.2%

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

      2. clear-num 90.2%

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

      3. un-div-inv 90.2%

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

   5. Applied egg-rr 90.2%

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

      1. *-un-lft-identity 90.2%

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

      2. div-inv 90.2%

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

      3. times-frac 68.5%

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

   7. Applied egg-rr 68.5%

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

   8. Taylor expanded in y around inf 65.5%

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

      1. associate-/l* 85.9%

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

   10. Simplified 85.9%

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

   if -3.8000000000000001e31 < a < 35000

   1. Initial program 74.5%

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

      1. +-commutative 74.5%

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

      2. *-commutative 74.5%

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

      3. associate-/l* 75.7%

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

      4. associate-/r/ 80.1%

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

      5. fma-def 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in t around inf 74.0%

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

      1. cancel-sign-sub-inv 74.0%

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

      2. metadata-eval 74.0%

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

      3. *-lft-identity 74.0%

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

      4. distribute-lft-in 74.0%

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

      5. mul-1-neg 74.0%

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

      6. distribute-rgt-neg-in 74.0%

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

      7. *-commutative 74.0%

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

      8. mul-1-neg 74.0%

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

      9. *-commutative 74.0%

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

      10. cancel-sign-sub 74.0%

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

      11. mul-1-neg 74.0%

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

      12. associate-*r* 74.0%

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

      13. distribute-lft-out-- 74.0%

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

      14. associate-*r/ 74.0%

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

   6. Simplified 80.0%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+31} \lor \neg \left(a \leq 35000\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 14: 66.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8000000000 \lor \neg \left(t \leq 80000000000000\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8000000000.0) (not (<= t 80000000000000.0)))
   (* y (/ (- z t) (- a t)))
   (+ x (/ z (/ a (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8000000000.0) || !(t <= 80000000000000.0)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z / (a / (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 <= (-8000000000.0d0)) .or. (.not. (t <= 80000000000000.0d0))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z / (a / (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 <= -8000000000.0) || !(t <= 80000000000000.0)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8000000000.0) or not (t <= 80000000000000.0):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z / (a / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8000000000.0) || !(t <= 80000000000000.0))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8000000000.0) || ~((t <= 80000000000000.0)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z / (a / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8000000000.0], N[Not[LessEqual[t, 80000000000000.0]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8e9 or 8e13 < t

   1. Initial program 53.8%

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

      1. +-commutative 53.8%

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

      2. *-commutative 53.8%

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

      3. associate-/l* 73.3%

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

      4. associate-/r/ 80.9%

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

      5. fma-def 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in y around inf 67.9%

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

      1. div-sub 67.9%

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

   6. Simplified 67.9%

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

   if -8e9 < t < 8e13

   1. Initial program 89.2%

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

      1. +-commutative 89.2%

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

      2. *-commutative 89.2%

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

      3. associate-/l* 91.1%

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

      4. associate-/r/ 92.9%

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

      5. fma-def 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in t around 0 70.1%

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

      1. associate-/l* 73.7%

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

   6. Simplified 73.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8000000000 \lor \neg \left(t \leq 80000000000000\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 15: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+14} \lor \neg \left(t \leq 65000000000000\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e+14) (not (<= t 65000000000000.0)))
   (* y (/ (- z t) (- a t)))
   (- x (/ (- x y) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+14) || !(t <= 65000000000000.0)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.15d+14)) .or. (.not. (t <= 65000000000000.0d0))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x - ((x - y) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+14) || !(t <= 65000000000000.0)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.15e+14) or not (t <= 65000000000000.0):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x - ((x - y) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.15e+14) || !(t <= 65000000000000.0))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.15e+14) || ~((t <= 65000000000000.0)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x - ((x - y) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.15e+14], N[Not[LessEqual[t, 65000000000000.0]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15e14 or 6.5e13 < t

   1. Initial program 53.8%

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

      1. +-commutative 53.8%

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

      2. *-commutative 53.8%

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

      3. associate-/l* 73.3%

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

      4. associate-/r/ 80.9%

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

      5. fma-def 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in y around inf 67.9%

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

      1. div-sub 67.9%

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

   6. Simplified 67.9%

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

   if -1.15e14 < t < 6.5e13

   1. Initial program 89.2%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around 0 75.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+14} \lor \neg \left(t \leq 65000000000000\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \]

Alternative 16: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-36} \lor \neg \left(t \leq 2.8 \cdot 10^{-13}\right):\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e-36) (not (<= t 2.8e-13)))
   (- y (/ z (/ t (- y x))))
   (- x (/ (- x y) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e-36) || !(t <= 2.8e-13)) {
		tmp = y - (z / (t / (y - x)));
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.4d-36)) .or. (.not. (t <= 2.8d-13))) then
        tmp = y - (z / (t / (y - x)))
    else
        tmp = x - ((x - y) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e-36) || !(t <= 2.8e-13)) {
		tmp = y - (z / (t / (y - x)));
	} else {
		tmp = x - ((x - y) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e-36) or not (t <= 2.8e-13):
		tmp = y - (z / (t / (y - x)))
	else:
		tmp = x - ((x - y) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e-36) || !(t <= 2.8e-13))
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.4e-36) || ~((t <= 2.8e-13)))
		tmp = y - (z / (t / (y - x)));
	else
		tmp = x - ((x - y) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e-36], N[Not[LessEqual[t, 2.8e-13]], $MachinePrecision]], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4e-36 or 2.8000000000000002e-13 < t

   1. Initial program 55.8%

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

      1. +-commutative 55.8%

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

      2. *-commutative 55.8%

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

      3. associate-/l* 73.8%

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

      4. associate-/r/ 80.9%

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

      5. fma-def 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in t around -inf 62.9%

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

   5. Taylor expanded in a around 0 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

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

      3. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   if -2.4e-36 < t < 2.8000000000000002e-13

   1. Initial program 89.9%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in t around 0 77.8%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-36} \lor \neg \left(t \leq 2.8 \cdot 10^{-13}\right):\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \end{array} \]

Alternative 17: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+109}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.2e+85)
   (* x (- 1.0 (/ z a)))
   (if (<= x 1.3e+109) (* y (/ (- z t) (- a t))) (- x (* z (/ x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.2e+85) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 1.3e+109) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (z * (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 (x <= (-2.2d+85)) then
        tmp = x * (1.0d0 - (z / a))
    else if (x <= 1.3d+109) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x - (z * (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 (x <= -2.2e+85) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 1.3e+109) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (z * (x / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.2e+85:
		tmp = x * (1.0 - (z / a))
	elif x <= 1.3e+109:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x - (z * (x / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.2e+85)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (x <= 1.3e+109)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(z * Float64(x / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.2e+85)
		tmp = x * (1.0 - (z / a));
	elseif (x <= 1.3e+109)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x - (z * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.2e+85], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+109], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2000000000000002e85

   1. Initial program 62.1%

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

      1. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in t around 0 52.9%

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

   5. Taylor expanded in x around inf 47.8%

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

      1. mul-1-neg 47.8%

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

      2. unsub-neg 47.8%

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

   7. Simplified 47.8%

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

   if -2.2000000000000002e85 < x < 1.2999999999999999e109

   1. Initial program 76.7%

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

      1. +-commutative 76.7%

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

      2. *-commutative 76.7%

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

      3. associate-/l* 86.1%

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

      4. associate-/r/ 91.6%

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

      5. fma-def 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in y around inf 72.4%

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

      1. div-sub 72.4%

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

   6. Simplified 72.4%

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

   if 1.2999999999999999e109 < x

   1. Initial program 59.3%

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

      1. associate-/l* 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in t around 0 62.2%

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

   5. Taylor expanded in y around 0 48.5%

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

      1. mul-1-neg 48.5%

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

      2. unsub-neg 48.5%

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

      3. associate-/l* 53.0%

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

      4. associate-/r/ 54.6%

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

   7. Simplified 54.6%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+109}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{a}\\ \end{array} \]

Alternative 18: 39.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-307}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.6e+96)
   x
   (if (<= a 2.6e-307)
     y
     (if (<= a 1.85e-259) (/ x (/ t z)) (if (<= a 1.45e+32) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.6e+96) {
		tmp = x;
	} else if (a <= 2.6e-307) {
		tmp = y;
	} else if (a <= 1.85e-259) {
		tmp = x / (t / z);
	} else if (a <= 1.45e+32) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.6d+96)) then
        tmp = x
    else if (a <= 2.6d-307) then
        tmp = y
    else if (a <= 1.85d-259) then
        tmp = x / (t / z)
    else if (a <= 1.45d+32) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.6e+96) {
		tmp = x;
	} else if (a <= 2.6e-307) {
		tmp = y;
	} else if (a <= 1.85e-259) {
		tmp = x / (t / z);
	} else if (a <= 1.45e+32) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.6e+96:
		tmp = x
	elif a <= 2.6e-307:
		tmp = y
	elif a <= 1.85e-259:
		tmp = x / (t / z)
	elif a <= 1.45e+32:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.6e+96)
		tmp = x;
	elseif (a <= 2.6e-307)
		tmp = y;
	elseif (a <= 1.85e-259)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 1.45e+32)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.6e+96)
		tmp = x;
	elseif (a <= 2.6e-307)
		tmp = y;
	elseif (a <= 1.85e-259)
		tmp = x / (t / z);
	elseif (a <= 1.45e+32)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.6e+96], x, If[LessEqual[a, 2.6e-307], y, If[LessEqual[a, 1.85e-259], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+32], y, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.6000000000000003e96 or 1.45000000000000001e32 < a

   1. Initial program 69.5%

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

      1. +-commutative 69.5%

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

      2. *-commutative 69.5%

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

      3. associate-/l* 92.4%

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

      4. associate-/r/ 97.3%

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

      5. fma-def 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in a around inf 46.2%

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

   if -4.6000000000000003e96 < a < 2.59999999999999996e-307 or 1.84999999999999996e-259 < a < 1.45000000000000001e32

   1. Initial program 72.7%

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

      1. +-commutative 72.7%

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

      2. *-commutative 72.7%

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

      3. associate-/l* 76.3%

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

      4. associate-/r/ 80.7%

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

      5. fma-def 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in t around inf 36.0%

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

   if 2.59999999999999996e-307 < a < 1.84999999999999996e-259

   1. Initial program 78.8%

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

      1. +-commutative 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-/l* 72.3%

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

      4. associate-/r/ 79.0%

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

      5. fma-def 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in t around -inf 92.8%

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

   5. Taylor expanded in y around 0 49.2%

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

      1. associate-/l* 62.6%

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

   7. Simplified 62.6%

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

   8. Taylor expanded in z around inf 49.2%

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

      1. associate-/l* 62.6%

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

   10. Simplified 62.6%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-307}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 39.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(1 + \frac{t}{a}\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-304}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.7e+112)
   (* x (+ 1.0 (/ t a)))
   (if (<= a 2.45e-304)
     y
     (if (<= a 1.7e-259) (/ x (/ t z)) (if (<= a 1.5e+32) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e+112) {
		tmp = x * (1.0 + (t / a));
	} else if (a <= 2.45e-304) {
		tmp = y;
	} else if (a <= 1.7e-259) {
		tmp = x / (t / z);
	} else if (a <= 1.5e+32) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.7d+112)) then
        tmp = x * (1.0d0 + (t / a))
    else if (a <= 2.45d-304) then
        tmp = y
    else if (a <= 1.7d-259) then
        tmp = x / (t / z)
    else if (a <= 1.5d+32) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e+112) {
		tmp = x * (1.0 + (t / a));
	} else if (a <= 2.45e-304) {
		tmp = y;
	} else if (a <= 1.7e-259) {
		tmp = x / (t / z);
	} else if (a <= 1.5e+32) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.7e+112:
		tmp = x * (1.0 + (t / a))
	elif a <= 2.45e-304:
		tmp = y
	elif a <= 1.7e-259:
		tmp = x / (t / z)
	elif a <= 1.5e+32:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.7e+112)
		tmp = Float64(x * Float64(1.0 + Float64(t / a)));
	elseif (a <= 2.45e-304)
		tmp = y;
	elseif (a <= 1.7e-259)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 1.5e+32)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.7e+112)
		tmp = x * (1.0 + (t / a));
	elseif (a <= 2.45e-304)
		tmp = y;
	elseif (a <= 1.7e-259)
		tmp = x / (t / z);
	elseif (a <= 1.5e+32)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.7e+112], N[(x * N[(1.0 + N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e-304], y, If[LessEqual[a, 1.7e-259], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+32], y, x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.69999999999999997e112

   1. Initial program 68.3%

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

      1. +-commutative 68.3%

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

      2. *-commutative 68.3%

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

      3. associate-/l* 91.8%

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

      4. associate-/r/ 97.2%

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

      5. fma-def 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in a around inf 65.4%

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

      1. associate-/l* 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in z around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. associate-/l* 62.0%

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

      3. distribute-neg-frac 62.0%

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

   9. Simplified 62.0%

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

   10. Taylor expanded in x around inf 49.0%

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

   if -1.69999999999999997e112 < a < 2.4500000000000002e-304 or 1.70000000000000006e-259 < a < 1.5e32

   1. Initial program 73.2%

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

      1. +-commutative 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-/l* 76.8%

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

      4. associate-/r/ 81.1%

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

      5. fma-def 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in t around inf 36.0%

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

   if 2.4500000000000002e-304 < a < 1.70000000000000006e-259

   1. Initial program 78.8%

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

      1. +-commutative 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-/l* 72.3%

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

      4. associate-/r/ 79.0%

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

      5. fma-def 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in t around -inf 92.8%

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

   5. Taylor expanded in y around 0 49.2%

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

      1. associate-/l* 62.6%

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

   7. Simplified 62.6%

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

   8. Taylor expanded in z around inf 49.2%

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

      1. associate-/l* 62.6%

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

   10. Simplified 62.6%

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

   if 1.5e32 < a

   1. Initial program 68.7%

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

      1. +-commutative 68.7%

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

      2. *-commutative 68.7%

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

      3. associate-/l* 92.4%

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

      4. associate-/r/ 97.2%

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

      5. fma-def 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in a around inf 45.3%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(1 + \frac{t}{a}\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-304}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 49.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+27) y (if (<= t 3.7e+39) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+27) {
		tmp = y;
	} else if (t <= 3.7e+39) {
		tmp = x * (1.0 - (z / a));
	} 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 <= (-4.2d+27)) then
        tmp = y
    else if (t <= 3.7d+39) then
        tmp = x * (1.0d0 - (z / a))
    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 <= -4.2e+27) {
		tmp = y;
	} else if (t <= 3.7e+39) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e+27:
		tmp = y
	elif t <= 3.7e+39:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+27)
		tmp = y;
	elseif (t <= 3.7e+39)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.2e+27)
		tmp = y;
	elseif (t <= 3.7e+39)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+27], y, If[LessEqual[t, 3.7e+39], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -4.19999999999999989e27 or 3.70000000000000012e39 < t

   1. Initial program 51.5%

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

      1. +-commutative 51.5%

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

      2. *-commutative 51.5%

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

      3. associate-/l* 72.3%

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

      4. associate-/r/ 80.5%

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

      5. fma-def 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in t around inf 48.5%

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

   if -4.19999999999999989e27 < t < 3.70000000000000012e39

   1. Initial program 89.1%

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

      1. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in t around 0 72.4%

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

   5. Taylor expanded in x around inf 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

   7. Simplified 47.2%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 21: 39.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.1e+95) x (if (<= a 1.3e+32) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.1e+95) {
		tmp = x;
	} else if (a <= 1.3e+32) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.1d+95)) then
        tmp = x
    else if (a <= 1.3d+32) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.1e+95) {
		tmp = x;
	} else if (a <= 1.3e+32) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.1e+95:
		tmp = x
	elif a <= 1.3e+32:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.1e+95)
		tmp = x;
	elseif (a <= 1.3e+32)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.1e+95)
		tmp = x;
	elseif (a <= 1.3e+32)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.1e+95], x, If[LessEqual[a, 1.3e+32], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.10000000000000003e95 or 1.3000000000000001e32 < a

   1. Initial program 69.5%

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

      1. +-commutative 69.5%

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

      2. *-commutative 69.5%

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

      3. associate-/l* 92.4%

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

      4. associate-/r/ 97.3%

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

      5. fma-def 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in a around inf 46.2%

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

   if -5.10000000000000003e95 < a < 1.3000000000000001e32

   1. Initial program 73.2%

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

      1. +-commutative 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-/l* 76.0%

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

      4. associate-/r/ 80.5%

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

      5. fma-def 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in t around inf 35.5%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 25.5% 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 71.8%

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

   1. +-commutative 71.8%

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

   2. *-commutative 71.8%

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

   3. associate-/l* 82.3%

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

   4. associate-/r/ 87.0%

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

   5. fma-def 87.0%

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

3. Simplified 87.0%

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

4. Taylor expanded in a around inf 22.5%

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

5. Final simplification 22.5%

   \[\leadsto x \]

Developer target: 86.8% accurate, 0.7× 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 2023333 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (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))))