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

Percentage Accurate: 68.4% → 92.0%

Time: 26.6s

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: 68.4% 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: 92.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ t_3 := \frac{y \cdot \left(z - t\right)}{a - t} - x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(t_1, z - t, x\right)\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-295}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y x) (- a t)))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t))))
        (t_3
         (-
          (/ (* y (- z t)) (- a t))
          (* x (- (/ z (- a t)) (+ 1.0 (/ t (- a t))))))))
   (if (<= t_2 (- INFINITY))
     (fma t_1 (- z t) x)
     (if (<= t_2 -4e-295)
       t_3
       (if (<= t_2 0.0)
         (+ y (/ (* x (- z a)) t))
         (if (<= t_2 5e+307) t_3 (+ x (* (- z t) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) / (a - t);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double t_3 = ((y * (z - t)) / (a - t)) - (x * ((z / (a - t)) - (1.0 + (t / (a - t)))));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(t_1, (z - t), x);
	} else if (t_2 <= -4e-295) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t_2 <= 5e+307) {
		tmp = t_3;
	} else {
		tmp = x + ((z - t) * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) / Float64(a - t))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	t_3 = Float64(Float64(Float64(y * Float64(z - t)) / Float64(a - t)) - Float64(x * Float64(Float64(z / Float64(a - t)) - Float64(1.0 + Float64(t / Float64(a - t))))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(t_1, Float64(z - t), x);
	elseif (t_2 <= -4e-295)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	elseif (t_2 <= 5e+307)
		tmp = t_3;
	else
		tmp = Float64(x + Float64(Float64(z - t) * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(1.0 + N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(t$95$1 * N[(z - t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, -4e-295], t$95$3, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+307], t$95$3, N[(x + N[(N[(z - t), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 39.4%

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

      1. +-commutative 39.4%

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

      2. associate-*l/ 78.6%

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

      3. fma-def 78.7%

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

   3. Simplified 78.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.00000000000000024e-295 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5e307

   1. Initial program 96.7%

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

      1. associate-*l/ 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in x around -inf 98.6%

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

   if -4.00000000000000024e-295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.4%

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

      1. associate-*l/ 4.8%

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

   3. Simplified 4.8%

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

   4. Taylor expanded in t around inf 98.4%

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

      1. associate--l+ 98.4%

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

      2. distribute-lft-out-- 98.4%

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

      3. div-sub 98.4%

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

      4. mul-1-neg 98.4%

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

      5. unsub-neg 98.4%

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

      6. distribute-rgt-out-- 98.4%

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

   6. Simplified 98.4%

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

   7. Taylor expanded in y around 0 98.4%

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

      1. associate-*r/ 98.4%

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

      2. associate-*r* 98.4%

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

      3. neg-mul-1 98.4%

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

      4. *-commutative 98.4%

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

   9. Simplified 98.4%

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

   if 5e307 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 43.4%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-295}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t} - x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t} - x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 2: 92.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ t_3 := \frac{y \cdot \left(z - t\right)}{a - t} - x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-295}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t)))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t))))
        (t_3
         (-
          (/ (* y (- z t)) (- a t))
          (* x (- (/ z (- a t)) (+ 1.0 (/ t (- a t))))))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -4e-295)
       t_3
       (if (<= t_2 0.0)
         (+ y (/ (* x (- z a)) t))
         (if (<= t_2 5e+307) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double t_3 = ((y * (z - t)) / (a - t)) - (x * ((z / (a - t)) - (1.0 + (t / (a - t)))));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -4e-295) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t_2 <= 5e+307) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double t_3 = ((y * (z - t)) / (a - t)) - (x * ((z / (a - t)) - (1.0 + (t / (a - t)))));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -4e-295) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t_2 <= 5e+307) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / (a - t)))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	t_3 = ((y * (z - t)) / (a - t)) - (x * ((z / (a - t)) - (1.0 + (t / (a - t)))))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -4e-295:
		tmp = t_3
	elif t_2 <= 0.0:
		tmp = y + ((x * (z - a)) / t)
	elif t_2 <= 5e+307:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	t_3 = Float64(Float64(Float64(y * Float64(z - t)) / Float64(a - t)) - Float64(x * Float64(Float64(z / Float64(a - t)) - Float64(1.0 + Float64(t / Float64(a - t))))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -4e-295)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	elseif (t_2 <= 5e+307)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / (a - t)));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	t_3 = ((y * (z - t)) / (a - t)) - (x * ((z / (a - t)) - (1.0 + (t / (a - t)))));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -4e-295)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = y + ((x * (z - a)) / t);
	elseif (t_2 <= 5e+307)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(1.0 + N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -4e-295], t$95$3, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+307], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 5e307 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 41.1%

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

      1. associate-*l/ 81.7%

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

   3. Simplified 81.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.00000000000000024e-295 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5e307

   1. Initial program 96.7%

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

      1. associate-*l/ 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in x around -inf 98.6%

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

   if -4.00000000000000024e-295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.4%

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

      1. associate-*l/ 4.8%

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

   3. Simplified 4.8%

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

   4. Taylor expanded in t around inf 98.4%

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

      1. associate--l+ 98.4%

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

      2. distribute-lft-out-- 98.4%

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

      3. div-sub 98.4%

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

      4. mul-1-neg 98.4%

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

      5. unsub-neg 98.4%

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

      6. distribute-rgt-out-- 98.4%

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

   6. Simplified 98.4%

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

   7. Taylor expanded in y around 0 98.4%

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

      1. associate-*r/ 98.4%

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

      2. associate-*r* 98.4%

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

      3. neg-mul-1 98.4%

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

      4. *-commutative 98.4%

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

   9. Simplified 98.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-295}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t} - x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t} - x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 3: 91.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t)))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -4e-295)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* x (- z a)) t))
         (if (<= t_2 5e+307) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -4e-295) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t_2 <= 5e+307) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -4e-295) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t_2 <= 5e+307) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / (a - t)))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -4e-295:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + ((x * (z - a)) / t)
	elif t_2 <= 5e+307:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -4e-295)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	elseif (t_2 <= 5e+307)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / (a - t)));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -4e-295)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + ((x * (z - a)) / t);
	elseif (t_2 <= 5e+307)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -4e-295], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+307], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 5e307 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 41.1%

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

      1. associate-*l/ 81.7%

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

   3. Simplified 81.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.00000000000000024e-295 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5e307

   1. Initial program 96.7%

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

   if -4.00000000000000024e-295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.4%

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

      1. associate-*l/ 4.8%

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

   3. Simplified 4.8%

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

   4. Taylor expanded in t around inf 98.4%

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

      1. associate--l+ 98.4%

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

      2. distribute-lft-out-- 98.4%

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

      3. div-sub 98.4%

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

      4. mul-1-neg 98.4%

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

      5. unsub-neg 98.4%

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

      6. distribute-rgt-out-- 98.4%

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

   6. Simplified 98.4%

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

   7. Taylor expanded in y around 0 98.4%

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

      1. associate-*r/ 98.4%

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

      2. associate-*r* 98.4%

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

      3. neg-mul-1 98.4%

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

      4. *-commutative 98.4%

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

   9. Simplified 98.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-295}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+307}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 4: 56.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{z - a}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-210}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-92}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ t (- z a)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= y -2.9e-21)
     t_2
     (if (<= y -1.4e-143)
       t_1
       (if (<= y -2.05e-210)
         (- x (/ x (/ a z)))
         (if (<= y 1.25e-141)
           (* x (/ (- z) (- a t)))
           (if (<= y 6.6e-92) (+ x y) (if (<= y 1.42e-83) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / (z - a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -2.9e-21) {
		tmp = t_2;
	} else if (y <= -1.4e-143) {
		tmp = t_1;
	} else if (y <= -2.05e-210) {
		tmp = x - (x / (a / z));
	} else if (y <= 1.25e-141) {
		tmp = x * (-z / (a - t));
	} else if (y <= 6.6e-92) {
		tmp = x + y;
	} else if (y <= 1.42e-83) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (t / (z - a))
    t_2 = y * ((z - t) / (a - t))
    if (y <= (-2.9d-21)) then
        tmp = t_2
    else if (y <= (-1.4d-143)) then
        tmp = t_1
    else if (y <= (-2.05d-210)) then
        tmp = x - (x / (a / z))
    else if (y <= 1.25d-141) then
        tmp = x * (-z / (a - t))
    else if (y <= 6.6d-92) then
        tmp = x + y
    else if (y <= 1.42d-83) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / (z - a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -2.9e-21) {
		tmp = t_2;
	} else if (y <= -1.4e-143) {
		tmp = t_1;
	} else if (y <= -2.05e-210) {
		tmp = x - (x / (a / z));
	} else if (y <= 1.25e-141) {
		tmp = x * (-z / (a - t));
	} else if (y <= 6.6e-92) {
		tmp = x + y;
	} else if (y <= 1.42e-83) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t / (z - a))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -2.9e-21:
		tmp = t_2
	elif y <= -1.4e-143:
		tmp = t_1
	elif y <= -2.05e-210:
		tmp = x - (x / (a / z))
	elif y <= 1.25e-141:
		tmp = x * (-z / (a - t))
	elif y <= 6.6e-92:
		tmp = x + y
	elif y <= 1.42e-83:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t / Float64(z - a)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -2.9e-21)
		tmp = t_2;
	elseif (y <= -1.4e-143)
		tmp = t_1;
	elseif (y <= -2.05e-210)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	elseif (y <= 1.25e-141)
		tmp = Float64(x * Float64(Float64(-z) / Float64(a - t)));
	elseif (y <= 6.6e-92)
		tmp = Float64(x + y);
	elseif (y <= 1.42e-83)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t / (z - a));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -2.9e-21)
		tmp = t_2;
	elseif (y <= -1.4e-143)
		tmp = t_1;
	elseif (y <= -2.05e-210)
		tmp = x - (x / (a / z));
	elseif (y <= 1.25e-141)
		tmp = x * (-z / (a - t));
	elseif (y <= 6.6e-92)
		tmp = x + y;
	elseif (y <= 1.42e-83)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e-21], t$95$2, If[LessEqual[y, -1.4e-143], t$95$1, If[LessEqual[y, -2.05e-210], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-141], N[(x * N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e-92], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.42e-83], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.9e-21 or 1.4199999999999999e-83 < y

   1. Initial program 72.7%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around inf 77.0%

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

      1. div-sub 77.0%

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

   6. Simplified 77.0%

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

   if -2.9e-21 < y < -1.3999999999999999e-143 or 6.59999999999999996e-92 < y < 1.4199999999999999e-83

   1. Initial program 53.7%

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

      1. associate-*l/ 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in x around -inf 50.2%

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

      1. associate-*r* 50.2%

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

      2. neg-mul-1 50.2%

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

   6. Simplified 50.2%

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

   7. Taylor expanded in t around -inf 40.1%

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

      1. associate-/l* 62.8%

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

   9. Simplified 62.8%

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

   if -1.3999999999999999e-143 < y < -2.04999999999999995e-210

   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/ 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in y around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. unsub-neg 64.1%

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

      3. associate-/l* 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in t around 0 67.9%

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

      1. associate-/l* 67.9%

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

   9. Simplified 67.9%

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

   if -2.04999999999999995e-210 < y < 1.25e-141

   1. Initial program 58.4%

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

      1. associate-*l/ 62.6%

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

   3. Simplified 62.6%

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

   4. Taylor expanded in x around -inf 77.8%

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

      1. associate-*r* 77.8%

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

      2. neg-mul-1 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in z around inf 57.5%

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

   if 1.25e-141 < y < 6.59999999999999996e-92

   1. Initial program 84.5%

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

      1. clear-num 84.5%

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

      2. associate-/r/ 84.0%

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

   3. Applied egg-rr 84.0%

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

   4. Taylor expanded in y around inf 92.0%

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

   5. Taylor expanded in t around inf 92.5%

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

      1. +-commutative 92.5%

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

   7. Simplified 92.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-143}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-210}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-92}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 5: 58.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-130}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* z (/ (- y x) (- a t)))))
   (if (<= z -8.6e+45)
     t_2
     (if (<= z 3.6e-271)
       t_1
       (if (<= z 3.8e-130)
         (+ x y)
         (if (<= z 2.5e-105)
           t_1
           (if (<= z 1.15e+69) (+ x (/ z (/ a (- y x)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -8.6e+45) {
		tmp = t_2;
	} else if (z <= 3.6e-271) {
		tmp = t_1;
	} else if (z <= 3.8e-130) {
		tmp = x + y;
	} else if (z <= 2.5e-105) {
		tmp = t_1;
	} else if (z <= 1.15e+69) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = z * ((y - x) / (a - t))
    if (z <= (-8.6d+45)) then
        tmp = t_2
    else if (z <= 3.6d-271) then
        tmp = t_1
    else if (z <= 3.8d-130) then
        tmp = x + y
    else if (z <= 2.5d-105) then
        tmp = t_1
    else if (z <= 1.15d+69) then
        tmp = x + (z / (a / (y - x)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -8.6e+45) {
		tmp = t_2;
	} else if (z <= 3.6e-271) {
		tmp = t_1;
	} else if (z <= 3.8e-130) {
		tmp = x + y;
	} else if (z <= 2.5e-105) {
		tmp = t_1;
	} else if (z <= 1.15e+69) {
		tmp = x + (z / (a / (y - x)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = z * ((y - x) / (a - t))
	tmp = 0
	if z <= -8.6e+45:
		tmp = t_2
	elif z <= 3.6e-271:
		tmp = t_1
	elif z <= 3.8e-130:
		tmp = x + y
	elif z <= 2.5e-105:
		tmp = t_1
	elif z <= 1.15e+69:
		tmp = x + (z / (a / (y - x)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (z <= -8.6e+45)
		tmp = t_2;
	elseif (z <= 3.6e-271)
		tmp = t_1;
	elseif (z <= 3.8e-130)
		tmp = Float64(x + y);
	elseif (z <= 2.5e-105)
		tmp = t_1;
	elseif (z <= 1.15e+69)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (z <= -8.6e+45)
		tmp = t_2;
	elseif (z <= 3.6e-271)
		tmp = t_1;
	elseif (z <= 3.8e-130)
		tmp = x + y;
	elseif (z <= 2.5e-105)
		tmp = t_1;
	elseif (z <= 1.15e+69)
		tmp = x + (z / (a / (y - x)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.6e+45], t$95$2, If[LessEqual[z, 3.6e-271], t$95$1, If[LessEqual[z, 3.8e-130], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.5e-105], t$95$1, If[LessEqual[z, 1.15e+69], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.6000000000000006e45 or 1.15000000000000008e69 < z

   1. Initial program 63.4%

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

      1. associate-*l/ 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in z around inf 79.3%

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

      1. div-sub 81.3%

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

   6. Simplified 81.3%

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

   if -8.6000000000000006e45 < z < 3.5999999999999998e-271 or 3.7999999999999998e-130 < z < 2.49999999999999982e-105

   1. Initial program 70.9%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in y around inf 65.8%

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

      1. div-sub 65.8%

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

   6. Simplified 65.8%

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

   if 3.5999999999999998e-271 < z < 3.7999999999999998e-130

   1. Initial program 65.3%

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

      1. clear-num 65.0%

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

      2. associate-/r/ 65.3%

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

   3. Applied egg-rr 65.3%

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

   4. Taylor expanded in y around inf 62.3%

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

   5. Taylor expanded in t around inf 61.9%

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

      1. +-commutative 61.9%

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

   7. Simplified 61.9%

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

   if 2.49999999999999982e-105 < z < 1.15000000000000008e69

   1. Initial program 79.3%

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

      1. associate-*l/ 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in t around 0 62.4%

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

      1. associate-/l* 62.3%

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

   6. Simplified 62.3%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+45}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-130}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 6: 58.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-131}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* z (/ (- y x) (- a t)))))
   (if (<= z -6.2e+45)
     t_2
     (if (<= z 7e-269)
       t_1
       (if (<= z 2.5e-131)
         (+ x y)
         (if (<= z 1.32e-105)
           t_1
           (if (<= z 5e+69) (+ x (/ (* (- y x) z) a)) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -6.2e+45) {
		tmp = t_2;
	} else if (z <= 7e-269) {
		tmp = t_1;
	} else if (z <= 2.5e-131) {
		tmp = x + y;
	} else if (z <= 1.32e-105) {
		tmp = t_1;
	} else if (z <= 5e+69) {
		tmp = x + (((y - x) * z) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = z * ((y - x) / (a - t))
    if (z <= (-6.2d+45)) then
        tmp = t_2
    else if (z <= 7d-269) then
        tmp = t_1
    else if (z <= 2.5d-131) then
        tmp = x + y
    else if (z <= 1.32d-105) then
        tmp = t_1
    else if (z <= 5d+69) then
        tmp = x + (((y - x) * z) / a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -6.2e+45) {
		tmp = t_2;
	} else if (z <= 7e-269) {
		tmp = t_1;
	} else if (z <= 2.5e-131) {
		tmp = x + y;
	} else if (z <= 1.32e-105) {
		tmp = t_1;
	} else if (z <= 5e+69) {
		tmp = x + (((y - x) * z) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = z * ((y - x) / (a - t))
	tmp = 0
	if z <= -6.2e+45:
		tmp = t_2
	elif z <= 7e-269:
		tmp = t_1
	elif z <= 2.5e-131:
		tmp = x + y
	elif z <= 1.32e-105:
		tmp = t_1
	elif z <= 5e+69:
		tmp = x + (((y - x) * z) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (z <= -6.2e+45)
		tmp = t_2;
	elseif (z <= 7e-269)
		tmp = t_1;
	elseif (z <= 2.5e-131)
		tmp = Float64(x + y);
	elseif (z <= 1.32e-105)
		tmp = t_1;
	elseif (z <= 5e+69)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (z <= -6.2e+45)
		tmp = t_2;
	elseif (z <= 7e-269)
		tmp = t_1;
	elseif (z <= 2.5e-131)
		tmp = x + y;
	elseif (z <= 1.32e-105)
		tmp = t_1;
	elseif (z <= 5e+69)
		tmp = x + (((y - x) * z) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+45], t$95$2, If[LessEqual[z, 7e-269], t$95$1, If[LessEqual[z, 2.5e-131], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.32e-105], t$95$1, If[LessEqual[z, 5e+69], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.19999999999999975e45 or 5.00000000000000036e69 < z

   1. Initial program 63.4%

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

      1. associate-*l/ 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in z around inf 79.3%

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

      1. div-sub 81.3%

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

   6. Simplified 81.3%

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

   if -6.19999999999999975e45 < z < 7.00000000000000038e-269 or 2.5000000000000002e-131 < z < 1.32000000000000006e-105

   1. Initial program 70.9%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in y around inf 65.8%

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

      1. div-sub 65.8%

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

   6. Simplified 65.8%

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

   if 7.00000000000000038e-269 < z < 2.5000000000000002e-131

   1. Initial program 65.3%

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

      1. clear-num 65.0%

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

      2. associate-/r/ 65.3%

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

   3. Applied egg-rr 65.3%

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

   4. Taylor expanded in y around inf 62.3%

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

   5. Taylor expanded in t around inf 61.9%

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

      1. +-commutative 61.9%

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

   7. Simplified 61.9%

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

   if 1.32000000000000006e-105 < z < 5.00000000000000036e69

   1. Initial program 79.3%

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

      1. associate-*l/ 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in t around 0 62.4%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-131}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 7: 58.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-133}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* z (/ (- y x) (- a t)))))
   (if (<= z -8.5e+45)
     t_2
     (if (<= z 4.3e-267)
       t_1
       (if (<= z 4.2e-133)
         (+ x y)
         (if (<= z 2.4e-106)
           t_1
           (if (<= z 2.7e+49) (+ x (/ y (/ a (- z t)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -8.5e+45) {
		tmp = t_2;
	} else if (z <= 4.3e-267) {
		tmp = t_1;
	} else if (z <= 4.2e-133) {
		tmp = x + y;
	} else if (z <= 2.4e-106) {
		tmp = t_1;
	} else if (z <= 2.7e+49) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = z * ((y - x) / (a - t))
    if (z <= (-8.5d+45)) then
        tmp = t_2
    else if (z <= 4.3d-267) then
        tmp = t_1
    else if (z <= 4.2d-133) then
        tmp = x + y
    else if (z <= 2.4d-106) then
        tmp = t_1
    else if (z <= 2.7d+49) then
        tmp = x + (y / (a / (z - t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -8.5e+45) {
		tmp = t_2;
	} else if (z <= 4.3e-267) {
		tmp = t_1;
	} else if (z <= 4.2e-133) {
		tmp = x + y;
	} else if (z <= 2.4e-106) {
		tmp = t_1;
	} else if (z <= 2.7e+49) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = z * ((y - x) / (a - t))
	tmp = 0
	if z <= -8.5e+45:
		tmp = t_2
	elif z <= 4.3e-267:
		tmp = t_1
	elif z <= 4.2e-133:
		tmp = x + y
	elif z <= 2.4e-106:
		tmp = t_1
	elif z <= 2.7e+49:
		tmp = x + (y / (a / (z - t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (z <= -8.5e+45)
		tmp = t_2;
	elseif (z <= 4.3e-267)
		tmp = t_1;
	elseif (z <= 4.2e-133)
		tmp = Float64(x + y);
	elseif (z <= 2.4e-106)
		tmp = t_1;
	elseif (z <= 2.7e+49)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (z <= -8.5e+45)
		tmp = t_2;
	elseif (z <= 4.3e-267)
		tmp = t_1;
	elseif (z <= 4.2e-133)
		tmp = x + y;
	elseif (z <= 2.4e-106)
		tmp = t_1;
	elseif (z <= 2.7e+49)
		tmp = x + (y / (a / (z - t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+45], t$95$2, If[LessEqual[z, 4.3e-267], t$95$1, If[LessEqual[z, 4.2e-133], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.4e-106], t$95$1, If[LessEqual[z, 2.7e+49], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.4999999999999996e45 or 2.7000000000000001e49 < z

   1. Initial program 65.1%

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

      1. associate-*l/ 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in z around inf 78.5%

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

      1. div-sub 80.4%

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

   6. Simplified 80.4%

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

   if -8.4999999999999996e45 < z < 4.2999999999999996e-267 or 4.2000000000000002e-133 < z < 2.3999999999999998e-106

   1. Initial program 70.9%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in y around inf 65.8%

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

      1. div-sub 65.8%

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

   6. Simplified 65.8%

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

   if 4.2999999999999996e-267 < z < 4.2000000000000002e-133

   1. Initial program 65.3%

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

      1. clear-num 65.0%

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

      2. associate-/r/ 65.3%

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

   3. Applied egg-rr 65.3%

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

   4. Taylor expanded in y around inf 62.3%

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

   5. Taylor expanded in t around inf 61.9%

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

      1. +-commutative 61.9%

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

   7. Simplified 61.9%

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

   if 2.3999999999999998e-106 < z < 2.7000000000000001e49

   1. Initial program 76.9%

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

      1. clear-num 76.9%

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

      2. associate-/r/ 76.7%

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

   3. Applied egg-rr 76.7%

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

   4. Taylor expanded in y around inf 71.3%

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

   5. Taylor expanded in a around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. associate-/l* 64.6%

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

   7. Simplified 64.6%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+45}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-267}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-133}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 8: 40.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.0018:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a t)))))
   (if (<= z -2.2e+54)
     t_1
     (if (<= z 0.0018)
       (+ x y)
       (if (<= z 2.35e+28)
         (* x (/ (- z a) t))
         (if (<= z 1.8e+31)
           x
           (if (<= z 4e+46)
             t_1
             (if (<= z 3.3e+76) (+ x y) (/ x (/ t z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (a - t));
	double tmp;
	if (z <= -2.2e+54) {
		tmp = t_1;
	} else if (z <= 0.0018) {
		tmp = x + y;
	} else if (z <= 2.35e+28) {
		tmp = x * ((z - a) / t);
	} else if (z <= 1.8e+31) {
		tmp = x;
	} else if (z <= 4e+46) {
		tmp = t_1;
	} else if (z <= 3.3e+76) {
		tmp = x + y;
	} else {
		tmp = x / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y / (a - t))
    if (z <= (-2.2d+54)) then
        tmp = t_1
    else if (z <= 0.0018d0) then
        tmp = x + y
    else if (z <= 2.35d+28) then
        tmp = x * ((z - a) / t)
    else if (z <= 1.8d+31) then
        tmp = x
    else if (z <= 4d+46) then
        tmp = t_1
    else if (z <= 3.3d+76) then
        tmp = x + y
    else
        tmp = x / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (a - t));
	double tmp;
	if (z <= -2.2e+54) {
		tmp = t_1;
	} else if (z <= 0.0018) {
		tmp = x + y;
	} else if (z <= 2.35e+28) {
		tmp = x * ((z - a) / t);
	} else if (z <= 1.8e+31) {
		tmp = x;
	} else if (z <= 4e+46) {
		tmp = t_1;
	} else if (z <= 3.3e+76) {
		tmp = x + y;
	} else {
		tmp = x / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / (a - t))
	tmp = 0
	if z <= -2.2e+54:
		tmp = t_1
	elif z <= 0.0018:
		tmp = x + y
	elif z <= 2.35e+28:
		tmp = x * ((z - a) / t)
	elif z <= 1.8e+31:
		tmp = x
	elif z <= 4e+46:
		tmp = t_1
	elif z <= 3.3e+76:
		tmp = x + y
	else:
		tmp = x / (t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (z <= -2.2e+54)
		tmp = t_1;
	elseif (z <= 0.0018)
		tmp = Float64(x + y);
	elseif (z <= 2.35e+28)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (z <= 1.8e+31)
		tmp = x;
	elseif (z <= 4e+46)
		tmp = t_1;
	elseif (z <= 3.3e+76)
		tmp = Float64(x + y);
	else
		tmp = Float64(x / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / (a - t));
	tmp = 0.0;
	if (z <= -2.2e+54)
		tmp = t_1;
	elseif (z <= 0.0018)
		tmp = x + y;
	elseif (z <= 2.35e+28)
		tmp = x * ((z - a) / t);
	elseif (z <= 1.8e+31)
		tmp = x;
	elseif (z <= 4e+46)
		tmp = t_1;
	elseif (z <= 3.3e+76)
		tmp = x + y;
	else
		tmp = x / (t / z);
	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]}, If[LessEqual[z, -2.2e+54], t$95$1, If[LessEqual[z, 0.0018], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.35e+28], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+31], x, If[LessEqual[z, 4e+46], t$95$1, If[LessEqual[z, 3.3e+76], N[(x + y), $MachinePrecision], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.1999999999999999e54 or 1.79999999999999998e31 < z < 4e46

   1. Initial program 63.3%

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

      1. associate-*l/ 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in z around inf 77.8%

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

      1. div-sub 79.7%

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

   6. Simplified 79.7%

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

   7. Taylor expanded in y around inf 51.2%

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

   if -2.1999999999999999e54 < z < 0.0018 or 4e46 < z < 3.3000000000000001e76

   1. Initial program 73.0%

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

      1. clear-num 72.9%

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

      2. associate-/r/ 72.9%

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

   3. Applied egg-rr 72.9%

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

   4. Taylor expanded in y around inf 67.2%

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

   5. Taylor expanded in t around inf 50.1%

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

      1. +-commutative 50.1%

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

   7. Simplified 50.1%

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

   if 0.0018 < z < 2.34999999999999983e28

   1. Initial program 42.0%

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

      1. associate-*l/ 47.6%

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

   3. Simplified 47.6%

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

   4. Taylor expanded in x around -inf 41.2%

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

      1. associate-*r* 41.2%

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

      2. neg-mul-1 41.2%

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

   6. Simplified 41.2%

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

   7. Taylor expanded in t around -inf 55.1%

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

      1. associate-/l* 55.2%

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

   9. Simplified 55.2%

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

       1. div-inv 55.2%

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

       2. clear-num 55.2%

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

   11. Applied egg-rr 55.2%

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

   if 2.34999999999999983e28 < z < 1.79999999999999998e31

   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%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around inf 56.6%

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

   if 3.3000000000000001e76 < z

   1. Initial program 67.3%

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

      1. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in x around -inf 63.4%

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

      1. associate-*r* 63.4%

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

      2. neg-mul-1 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in a around 0 28.7%

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

      1. associate-/l* 45.2%

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

   9. Simplified 45.2%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 0.0018:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+46}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \end{array} \]

Alternative 9: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+197} \lor \neg \left(t \leq 2.55 \cdot 10^{+107}\right):\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.6e+197) (not (<= t 2.55e+107)))
   (- y (* (/ x t) (- a z)))
   (+ x (* (- z t) (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e+197) || !(t <= 2.55e+107)) {
		tmp = y - ((x / t) * (a - z));
	} 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 <= (-2.6d+197)) .or. (.not. (t <= 2.55d+107))) then
        tmp = y - ((x / t) * (a - z))
    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 <= -2.6e+197) || !(t <= 2.55e+107)) {
		tmp = y - ((x / t) * (a - z));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.6e+197) or not (t <= 2.55e+107):
		tmp = y - ((x / t) * (a - z))
	else:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.6e+197) || !(t <= 2.55e+107))
		tmp = Float64(y - Float64(Float64(x / t) * Float64(a - z)));
	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 <= -2.6e+197) || ~((t <= 2.55e+107)))
		tmp = y - ((x / t) * (a - z));
	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, -2.6e+197], N[Not[LessEqual[t, 2.55e+107]], $MachinePrecision]], N[(y - N[(N[(x / t), $MachinePrecision] * N[(a - z), $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 < -2.59999999999999987e197 or 2.5500000000000001e107 < t

   1. Initial program 31.1%

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

      1. associate-*l/ 55.7%

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

   3. Simplified 55.7%

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

   4. Taylor expanded in t around inf 62.3%

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

      1. associate--l+ 62.3%

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

      2. distribute-lft-out-- 62.3%

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

      3. div-sub 62.3%

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

      4. mul-1-neg 62.3%

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

      5. unsub-neg 62.3%

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

      6. distribute-rgt-out-- 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in y around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. associate-*l/ 83.4%

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

      3. *-commutative 83.4%

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

      4. distribute-rgt-neg-in 83.4%

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

      5. distribute-neg-frac 83.4%

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

   9. Simplified 83.4%

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

   if -2.59999999999999987e197 < t < 2.5500000000000001e107

   1. Initial program 80.6%

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

      1. associate-*l/ 84.2%

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

   3. Simplified 84.2%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+197} \lor \neg \left(t \leq 2.55 \cdot 10^{+107}\right):\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 10: 49.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - a}{t}\\ \mathbf{if}\;t \leq -8 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{+35}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+60}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+228}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- z a) t))))
   (if (<= t -8e+244)
     t_1
     (if (<= t -6.1e+35)
       y
       (if (<= t 1.9e+60)
         (+ x (* y (/ z a)))
         (if (<= t 3.7e+228) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (t <= -8e+244) {
		tmp = t_1;
	} else if (t <= -6.1e+35) {
		tmp = y;
	} else if (t <= 1.9e+60) {
		tmp = x + (y * (z / a));
	} else if (t <= 3.7e+228) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - a) / t)
    if (t <= (-8d+244)) then
        tmp = t_1
    else if (t <= (-6.1d+35)) then
        tmp = y
    else if (t <= 1.9d+60) then
        tmp = x + (y * (z / a))
    else if (t <= 3.7d+228) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (t <= -8e+244) {
		tmp = t_1;
	} else if (t <= -6.1e+35) {
		tmp = y;
	} else if (t <= 1.9e+60) {
		tmp = x + (y * (z / a));
	} else if (t <= 3.7e+228) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((z - a) / t)
	tmp = 0
	if t <= -8e+244:
		tmp = t_1
	elif t <= -6.1e+35:
		tmp = y
	elif t <= 1.9e+60:
		tmp = x + (y * (z / a))
	elif t <= 3.7e+228:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(z - a) / t))
	tmp = 0.0
	if (t <= -8e+244)
		tmp = t_1;
	elseif (t <= -6.1e+35)
		tmp = y;
	elseif (t <= 1.9e+60)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 3.7e+228)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((z - a) / t);
	tmp = 0.0;
	if (t <= -8e+244)
		tmp = t_1;
	elseif (t <= -6.1e+35)
		tmp = y;
	elseif (t <= 1.9e+60)
		tmp = x + (y * (z / a));
	elseif (t <= 3.7e+228)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+244], t$95$1, If[LessEqual[t, -6.1e+35], y, If[LessEqual[t, 1.9e+60], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e+228], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.0000000000000006e244 or 1.90000000000000005e60 < t < 3.6999999999999998e228

   1. Initial program 34.9%

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

      1. associate-*l/ 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in x around -inf 48.4%

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

      1. associate-*r* 48.4%

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

      2. neg-mul-1 48.4%

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

   6. Simplified 48.4%

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

   7. Taylor expanded in t around -inf 36.7%

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

      1. associate-/l* 52.8%

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

   9. Simplified 52.8%

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

       1. div-inv 52.7%

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

       2. clear-num 52.7%

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

   11. Applied egg-rr 52.7%

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

   if -8.0000000000000006e244 < t < -6.09999999999999977e35

   1. Initial program 57.5%

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

      1. associate-*l/ 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in t around inf 55.7%

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

   if -6.09999999999999977e35 < t < 1.90000000000000005e60

   1. Initial program 87.6%

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

      1. clear-num 87.5%

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

      2. associate-/r/ 87.5%

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

   3. Applied egg-rr 87.5%

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

   4. Taylor expanded in y around inf 69.2%

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

   5. Taylor expanded in t around 0 49.7%

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

      1. associate-*r/ 55.7%

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

   7. Simplified 55.7%

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

   if 3.6999999999999998e228 < t

   1. Initial program 18.3%

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

      1. clear-num 18.3%

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

      2. associate-/r/ 18.2%

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

   3. Applied egg-rr 18.2%

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

   4. Taylor expanded in y around inf 18.8%

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

   5. Taylor expanded in t around inf 65.7%

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

      1. +-commutative 65.7%

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

   7. Simplified 65.7%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+244}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{+35}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+60}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 49.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -8 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{+35}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+59}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ t (- z a)))))
   (if (<= t -8e+244)
     t_1
     (if (<= t -6.1e+35)
       y
       (if (<= t 7.5e+59)
         (+ x (* y (/ z a)))
         (if (<= t 5.5e+229) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / (z - a));
	double tmp;
	if (t <= -8e+244) {
		tmp = t_1;
	} else if (t <= -6.1e+35) {
		tmp = y;
	} else if (t <= 7.5e+59) {
		tmp = x + (y * (z / a));
	} else if (t <= 5.5e+229) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t / (z - a))
    if (t <= (-8d+244)) then
        tmp = t_1
    else if (t <= (-6.1d+35)) then
        tmp = y
    else if (t <= 7.5d+59) then
        tmp = x + (y * (z / a))
    else if (t <= 5.5d+229) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / (z - a));
	double tmp;
	if (t <= -8e+244) {
		tmp = t_1;
	} else if (t <= -6.1e+35) {
		tmp = y;
	} else if (t <= 7.5e+59) {
		tmp = x + (y * (z / a));
	} else if (t <= 5.5e+229) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t / (z - a))
	tmp = 0
	if t <= -8e+244:
		tmp = t_1
	elif t <= -6.1e+35:
		tmp = y
	elif t <= 7.5e+59:
		tmp = x + (y * (z / a))
	elif t <= 5.5e+229:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t / Float64(z - a)))
	tmp = 0.0
	if (t <= -8e+244)
		tmp = t_1;
	elseif (t <= -6.1e+35)
		tmp = y;
	elseif (t <= 7.5e+59)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 5.5e+229)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t / (z - a));
	tmp = 0.0;
	if (t <= -8e+244)
		tmp = t_1;
	elseif (t <= -6.1e+35)
		tmp = y;
	elseif (t <= 7.5e+59)
		tmp = x + (y * (z / a));
	elseif (t <= 5.5e+229)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+244], t$95$1, If[LessEqual[t, -6.1e+35], y, If[LessEqual[t, 7.5e+59], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+229], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.0000000000000006e244 or 7.4999999999999996e59 < t < 5.5000000000000002e229

   1. Initial program 34.9%

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

      1. associate-*l/ 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in x around -inf 48.4%

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

      1. associate-*r* 48.4%

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

      2. neg-mul-1 48.4%

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

   6. Simplified 48.4%

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

   7. Taylor expanded in t around -inf 36.7%

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

      1. associate-/l* 52.8%

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

   9. Simplified 52.8%

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

   if -8.0000000000000006e244 < t < -6.09999999999999977e35

   1. Initial program 57.5%

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

      1. associate-*l/ 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in t around inf 55.7%

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

   if -6.09999999999999977e35 < t < 7.4999999999999996e59

   1. Initial program 87.6%

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

      1. clear-num 87.5%

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

      2. associate-/r/ 87.5%

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

   3. Applied egg-rr 87.5%

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

   4. Taylor expanded in y around inf 69.2%

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

   5. Taylor expanded in t around 0 49.7%

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

      1. associate-*r/ 55.7%

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

   7. Simplified 55.7%

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

   if 5.5000000000000002e229 < t

   1. Initial program 18.3%

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

      1. clear-num 18.3%

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

      2. associate-/r/ 18.2%

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

   3. Applied egg-rr 18.2%

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

   4. Taylor expanded in y around inf 18.8%

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

   5. Taylor expanded in t around inf 65.7%

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

      1. +-commutative 65.7%

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

   7. Simplified 65.7%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{+35}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+59}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+229}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 50.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+35}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+109}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8e+244)
   (/ x (/ t (- z a)))
   (if (<= t -5.8e+35)
     y
     (if (<= t 1.3e+41)
       (+ x (* y (/ z a)))
       (if (<= t 1.6e+109) (/ z (/ t (- x y))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8e+244) {
		tmp = x / (t / (z - a));
	} else if (t <= -5.8e+35) {
		tmp = y;
	} else if (t <= 1.3e+41) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.6e+109) {
		tmp = z / (t / (x - y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-8d+244)) then
        tmp = x / (t / (z - a))
    else if (t <= (-5.8d+35)) then
        tmp = y
    else if (t <= 1.3d+41) then
        tmp = x + (y * (z / a))
    else if (t <= 1.6d+109) then
        tmp = z / (t / (x - y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8e+244) {
		tmp = x / (t / (z - a));
	} else if (t <= -5.8e+35) {
		tmp = y;
	} else if (t <= 1.3e+41) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.6e+109) {
		tmp = z / (t / (x - y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8e+244:
		tmp = x / (t / (z - a))
	elif t <= -5.8e+35:
		tmp = y
	elif t <= 1.3e+41:
		tmp = x + (y * (z / a))
	elif t <= 1.6e+109:
		tmp = z / (t / (x - y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8e+244)
		tmp = Float64(x / Float64(t / Float64(z - a)));
	elseif (t <= -5.8e+35)
		tmp = y;
	elseif (t <= 1.3e+41)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 1.6e+109)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8e+244)
		tmp = x / (t / (z - a));
	elseif (t <= -5.8e+35)
		tmp = y;
	elseif (t <= 1.3e+41)
		tmp = x + (y * (z / a));
	elseif (t <= 1.6e+109)
		tmp = z / (t / (x - y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8e+244], N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.8e+35], y, If[LessEqual[t, 1.3e+41], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+109], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.0000000000000006e244

   1. Initial program 23.9%

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

      1. associate-*l/ 37.7%

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

   3. Simplified 37.7%

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

   4. Taylor expanded in x around -inf 58.2%

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

      1. associate-*r* 58.2%

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

      2. neg-mul-1 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in t around -inf 39.1%

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

      1. associate-/l* 59.8%

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

   9. Simplified 59.8%

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

   if -8.0000000000000006e244 < t < -5.79999999999999989e35

   1. Initial program 57.5%

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

      1. associate-*l/ 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in t around inf 55.7%

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

   if -5.79999999999999989e35 < t < 1.3e41

   1. Initial program 87.8%

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

      1. clear-num 87.7%

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

      2. associate-/r/ 87.8%

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

   3. Applied egg-rr 87.8%

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

   4. Taylor expanded in y around inf 68.8%

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

   5. Taylor expanded in t around 0 50.6%

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

      1. associate-*r/ 56.8%

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

   7. Simplified 56.8%

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

   if 1.3e41 < t < 1.6000000000000001e109

   1. Initial program 66.0%

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

      1. associate-*l/ 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in z around inf 61.2%

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

      1. div-sub 61.2%

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

   6. Simplified 61.2%

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

   7. Taylor expanded in a around 0 45.2%

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

      1. associate-*r/ 45.2%

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

      2. neg-mul-1 45.2%

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

      3. distribute-rgt-neg-in 45.2%

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

   9. Simplified 45.2%

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

   10. Taylor expanded in z around 0 45.2%

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

       1. associate-/l* 55.9%

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

   12. Simplified 55.9%

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

   if 1.6000000000000001e109 < t

   1. Initial program 24.1%

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

      1. clear-num 24.2%

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

      2. associate-/r/ 24.2%

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

   3. Applied egg-rr 24.2%

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

   4. Taylor expanded in y around inf 24.2%

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

   5. Taylor expanded in t around inf 50.8%

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

      1. +-commutative 50.8%

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

   7. Simplified 50.8%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+35}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+109}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13: 72.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-6} \lor \neg \left(a \leq 1.46 \cdot 10^{+29}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.3e-6) (not (<= a 1.46e+29)))
   (+ x (/ (- y x) (/ a (- z t))))
   (- y (/ z (/ t (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.3e-6) || !(a <= 1.46e+29)) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else {
		tmp = y - (z / (t / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.3d-6)) .or. (.not. (a <= 1.46d+29))) then
        tmp = x + ((y - x) / (a / (z - t)))
    else
        tmp = y - (z / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.3e-6) || !(a <= 1.46e+29)) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else {
		tmp = y - (z / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.3e-6) or not (a <= 1.46e+29):
		tmp = x + ((y - x) / (a / (z - t)))
	else:
		tmp = y - (z / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.3e-6) || !(a <= 1.46e+29))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))));
	else
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.3e-6) || ~((a <= 1.46e+29)))
		tmp = x + ((y - x) / (a / (z - t)));
	else
		tmp = y - (z / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.3e-6], N[Not[LessEqual[a, 1.46e+29]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.30000000000000005e-6 or 1.46e29 < a

   1. Initial program 71.5%

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

      1. associate-*l/ 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in a around inf 64.9%

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

      1. associate-/l* 76.9%

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

   6. Simplified 76.9%

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

   if -1.30000000000000005e-6 < a < 1.46e29

   1. Initial program 66.6%

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

      1. associate-*l/ 69.0%

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

   3. Simplified 69.0%

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

   4. Taylor expanded in t around inf 68.5%

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

      1. associate--l+ 68.5%

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

      2. distribute-lft-out-- 68.5%

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

      3. div-sub 68.6%

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

      4. mul-1-neg 68.6%

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

      5. unsub-neg 68.6%

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

      6. distribute-rgt-out-- 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in z around inf 64.5%

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

      1. associate-/l* 75.3%

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

   9. Simplified 75.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-6} \lor \neg \left(a \leq 1.46 \cdot 10^{+29}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 14: 37.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+175}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 0.0007:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;z \leq 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+175)
   (/ (* y (- z)) t)
   (if (<= z 0.0007)
     (+ x y)
     (if (<= z 3.2e+27)
       (* x (/ (- z a) t))
       (if (<= z 1e+77) (+ x y) (/ x (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+175) {
		tmp = (y * -z) / t;
	} else if (z <= 0.0007) {
		tmp = x + y;
	} else if (z <= 3.2e+27) {
		tmp = x * ((z - a) / t);
	} else if (z <= 1e+77) {
		tmp = x + y;
	} else {
		tmp = x / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.25d+175)) then
        tmp = (y * -z) / t
    else if (z <= 0.0007d0) then
        tmp = x + y
    else if (z <= 3.2d+27) then
        tmp = x * ((z - a) / t)
    else if (z <= 1d+77) then
        tmp = x + y
    else
        tmp = x / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+175) {
		tmp = (y * -z) / t;
	} else if (z <= 0.0007) {
		tmp = x + y;
	} else if (z <= 3.2e+27) {
		tmp = x * ((z - a) / t);
	} else if (z <= 1e+77) {
		tmp = x + y;
	} else {
		tmp = x / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e+175:
		tmp = (y * -z) / t
	elif z <= 0.0007:
		tmp = x + y
	elif z <= 3.2e+27:
		tmp = x * ((z - a) / t)
	elif z <= 1e+77:
		tmp = x + y
	else:
		tmp = x / (t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+175)
		tmp = Float64(Float64(y * Float64(-z)) / t);
	elseif (z <= 0.0007)
		tmp = Float64(x + y);
	elseif (z <= 3.2e+27)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (z <= 1e+77)
		tmp = Float64(x + y);
	else
		tmp = Float64(x / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.25e+175)
		tmp = (y * -z) / t;
	elseif (z <= 0.0007)
		tmp = x + y;
	elseif (z <= 3.2e+27)
		tmp = x * ((z - a) / t);
	elseif (z <= 1e+77)
		tmp = x + y;
	else
		tmp = x / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+175], N[(N[(y * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 0.0007], N[(x + y), $MachinePrecision], If[LessEqual[z, 3.2e+27], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+77], N[(x + y), $MachinePrecision], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.25e175

   1. Initial program 70.1%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around inf 93.7%

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

      1. div-sub 93.7%

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

   6. Simplified 93.7%

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

   7. Taylor expanded in a around 0 69.6%

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

      1. associate-*r/ 69.6%

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

      2. neg-mul-1 69.6%

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

      3. distribute-rgt-neg-in 69.6%

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

   9. Simplified 69.6%

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

   10. Taylor expanded in y around inf 54.3%

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

       1. associate-*r/ 54.3%

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

       2. mul-1-neg 54.3%

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

       3. distribute-rgt-neg-out 54.3%

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

   12. Simplified 54.3%

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

   if -1.25e175 < z < 6.99999999999999993e-4 or 3.20000000000000015e27 < z < 9.99999999999999983e76

   1. Initial program 70.7%

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

      1. clear-num 70.5%

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

      2. associate-/r/ 70.5%

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

   3. Applied egg-rr 70.5%

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

   4. Taylor expanded in y around inf 63.0%

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

   5. Taylor expanded in t around inf 44.7%

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

      1. +-commutative 44.7%

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

   7. Simplified 44.7%

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

   if 6.99999999999999993e-4 < z < 3.20000000000000015e27

   1. Initial program 42.0%

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

      1. associate-*l/ 47.6%

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

   3. Simplified 47.6%

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

   4. Taylor expanded in x around -inf 41.2%

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

      1. associate-*r* 41.2%

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

      2. neg-mul-1 41.2%

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

   6. Simplified 41.2%

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

   7. Taylor expanded in t around -inf 55.1%

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

      1. associate-/l* 55.2%

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

   9. Simplified 55.2%

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

       1. div-inv 55.2%

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

       2. clear-num 55.2%

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

   11. Applied egg-rr 55.2%

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

   if 9.99999999999999983e76 < z

   1. Initial program 67.3%

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

      1. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in x around -inf 63.4%

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

      1. associate-*r* 63.4%

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

      2. neg-mul-1 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in a around 0 28.7%

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

      1. associate-/l* 45.2%

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

   9. Simplified 45.2%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+175}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 0.0007:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;z \leq 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \end{array} \]

Alternative 15: 56.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.9e-19)
   (* z (/ (- y x) (- a t)))
   (if (<= x 2.2e+96)
     (* y (/ (- z t) (- a t)))
     (if (<= x 3.2e+244) (/ x (/ t (- z a))) (- x (/ x (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.9e-19) {
		tmp = z * ((y - x) / (a - t));
	} else if (x <= 2.2e+96) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 3.2e+244) {
		tmp = x / (t / (z - a));
	} else {
		tmp = x - (x / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.9d-19)) then
        tmp = z * ((y - x) / (a - t))
    else if (x <= 2.2d+96) then
        tmp = y * ((z - t) / (a - t))
    else if (x <= 3.2d+244) then
        tmp = x / (t / (z - a))
    else
        tmp = x - (x / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.9e-19) {
		tmp = z * ((y - x) / (a - t));
	} else if (x <= 2.2e+96) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 3.2e+244) {
		tmp = x / (t / (z - a));
	} else {
		tmp = x - (x / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.9e-19:
		tmp = z * ((y - x) / (a - t))
	elif x <= 2.2e+96:
		tmp = y * ((z - t) / (a - t))
	elif x <= 3.2e+244:
		tmp = x / (t / (z - a))
	else:
		tmp = x - (x / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.9e-19)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (x <= 2.2e+96)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (x <= 3.2e+244)
		tmp = Float64(x / Float64(t / Float64(z - a)));
	else
		tmp = Float64(x - Float64(x / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.9e-19)
		tmp = z * ((y - x) / (a - t));
	elseif (x <= 2.2e+96)
		tmp = y * ((z - t) / (a - t));
	elseif (x <= 3.2e+244)
		tmp = x / (t / (z - a));
	else
		tmp = x - (x / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.9e-19], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+96], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+244], N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.9e-19

   1. Initial program 67.7%

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

      1. associate-*l/ 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in z around inf 52.4%

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

      1. div-sub 56.9%

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

   6. Simplified 56.9%

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

   if -1.9e-19 < x < 2.1999999999999999e96

   1. Initial program 76.4%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in y around inf 73.7%

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

      1. div-sub 73.7%

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

   6. Simplified 73.7%

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

   if 2.1999999999999999e96 < x < 3.2000000000000002e244

   1. Initial program 34.8%

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

      1. associate-*l/ 56.1%

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

   3. Simplified 56.1%

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

   4. Taylor expanded in x around -inf 59.7%

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

      1. associate-*r* 59.7%

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

      2. neg-mul-1 59.7%

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

   6. Simplified 59.7%

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

   7. Taylor expanded in t around -inf 41.1%

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

      1. associate-/l* 56.8%

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

   9. Simplified 56.8%

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

   if 3.2000000000000002e244 < x

   1. Initial program 63.5%

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

      1. associate-*l/ 62.9%

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

   3. Simplified 62.9%

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

   4. Taylor expanded in y around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

      3. associate-/l* 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in t around 0 69.3%

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

      1. associate-/l* 75.6%

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

   9. Simplified 75.6%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \end{array} \]

Alternative 16: 68.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+38}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.5e-5)
   (+ x (/ z (/ a (- y x))))
   (if (<= a 2.3e+38) (- y (/ z (/ t (- y x)))) (+ x (/ y (/ a (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.5e-5) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= 2.3e+38) {
		tmp = y - (z / (t / (y - x)));
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.5d-5)) then
        tmp = x + (z / (a / (y - x)))
    else if (a <= 2.3d+38) then
        tmp = y - (z / (t / (y - x)))
    else
        tmp = x + (y / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.5e-5) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= 2.3e+38) {
		tmp = y - (z / (t / (y - x)));
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.5e-5:
		tmp = x + (z / (a / (y - x)))
	elif a <= 2.3e+38:
		tmp = y - (z / (t / (y - x)))
	else:
		tmp = x + (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.5e-5)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (a <= 2.3e+38)
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.5e-5)
		tmp = x + (z / (a / (y - x)));
	elseif (a <= 2.3e+38)
		tmp = y - (z / (t / (y - x)));
	else
		tmp = x + (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.5e-5], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+38], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.49999999999999934e-5

   1. Initial program 71.9%

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

      1. associate-*l/ 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in t around 0 63.2%

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

      1. associate-/l* 70.4%

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

   6. Simplified 70.4%

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

   if -7.49999999999999934e-5 < a < 2.3000000000000001e38

   1. Initial program 66.4%

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

      1. associate-*l/ 68.8%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in t around inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. distribute-lft-out-- 68.2%

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

      3. div-sub 68.3%

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

      4. mul-1-neg 68.3%

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

      5. unsub-neg 68.3%

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

      6. distribute-rgt-out-- 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in z around inf 64.4%

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

      1. associate-/l* 74.9%

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

   9. Simplified 74.9%

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

   if 2.3000000000000001e38 < a

   1. Initial program 71.8%

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

      1. clear-num 71.7%

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

      2. associate-/r/ 71.7%

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

   3. Applied egg-rr 71.7%

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

   4. Taylor expanded in y around inf 67.0%

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

   5. Taylor expanded in a around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. associate-/l* 72.7%

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

   7. Simplified 72.7%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+38}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 17: 38.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+122} \lor \neg \left(z \leq 2.15 \cdot 10^{+77}\right):\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+122) (not (<= z 2.15e+77))) (* z (/ x t)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+122) || !(z <= 2.15e+77)) {
		tmp = z * (x / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.35d+122)) .or. (.not. (z <= 2.15d+77))) then
        tmp = z * (x / t)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+122) || !(z <= 2.15e+77)) {
		tmp = z * (x / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+122) or not (z <= 2.15e+77):
		tmp = z * (x / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+122) || !(z <= 2.15e+77))
		tmp = Float64(z * Float64(x / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.35e+122) || ~((z <= 2.15e+77)))
		tmp = z * (x / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+122], N[Not[LessEqual[z, 2.15e+77]], $MachinePrecision]], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3499999999999999e122 or 2.14999999999999996e77 < z

   1. Initial program 66.0%

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

      1. associate-*l/ 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in x around -inf 55.8%

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

      1. associate-*r* 55.8%

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

      2. neg-mul-1 55.8%

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

   6. Simplified 55.8%

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

   7. Taylor expanded in t around -inf 30.1%

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

      1. associate-/l* 41.8%

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

   9. Simplified 41.8%

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

   10. Taylor expanded in z around inf 30.1%

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

       1. associate-*l/ 39.8%

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

       2. *-commutative 39.8%

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

   12. Simplified 39.8%

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

   if -1.3499999999999999e122 < z < 2.14999999999999996e77

   1. Initial program 70.1%

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

      1. clear-num 70.0%

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

      2. associate-/r/ 70.0%

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

   3. Applied egg-rr 70.0%

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

   4. Taylor expanded in y around inf 62.4%

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

   5. Taylor expanded in t around inf 44.1%

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

      1. +-commutative 44.1%

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

   7. Simplified 44.1%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+122} \lor \neg \left(z \leq 2.15 \cdot 10^{+77}\right):\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 18: 39.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e+113) (* z (/ x t)) (if (<= z 1.35e+76) (+ x y) (/ x (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+113) {
		tmp = z * (x / t);
	} else if (z <= 1.35e+76) {
		tmp = x + y;
	} else {
		tmp = x / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5d+113)) then
        tmp = z * (x / t)
    else if (z <= 1.35d+76) then
        tmp = x + y
    else
        tmp = x / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+113) {
		tmp = z * (x / t);
	} else if (z <= 1.35e+76) {
		tmp = x + y;
	} else {
		tmp = x / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e+113:
		tmp = z * (x / t)
	elif z <= 1.35e+76:
		tmp = x + y
	else:
		tmp = x / (t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e+113)
		tmp = Float64(z * Float64(x / t));
	elseif (z <= 1.35e+76)
		tmp = Float64(x + y);
	else
		tmp = Float64(x / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5e+113)
		tmp = z * (x / t);
	elseif (z <= 1.35e+76)
		tmp = x + y;
	else
		tmp = x / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e+113], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+76], N[(x + y), $MachinePrecision], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5e113

   1. Initial program 63.9%

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

      1. associate-*l/ 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in x around -inf 42.9%

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

      1. associate-*r* 42.9%

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

      2. neg-mul-1 42.9%

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

   6. Simplified 42.9%

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

   7. Taylor expanded in t around -inf 32.7%

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

      1. associate-/l* 36.0%

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

   9. Simplified 36.0%

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

   10. Taylor expanded in z around inf 32.7%

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

       1. associate-*l/ 36.6%

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

       2. *-commutative 36.6%

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

   12. Simplified 36.6%

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

   if -5e113 < z < 1.34999999999999995e76

   1. Initial program 70.1%

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

      1. clear-num 70.0%

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

      2. associate-/r/ 70.0%

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

   3. Applied egg-rr 70.0%

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

   4. Taylor expanded in y around inf 62.4%

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

   5. Taylor expanded in t around inf 44.1%

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

      1. +-commutative 44.1%

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

   7. Simplified 44.1%

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

   if 1.34999999999999995e76 < z

   1. Initial program 67.3%

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

      1. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in x around -inf 63.4%

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

      1. associate-*r* 63.4%

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

      2. neg-mul-1 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in a around 0 28.7%

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

      1. associate-/l* 45.2%

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

   9. Simplified 45.2%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \end{array} \]

Alternative 19: 38.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+175}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e+175)
   (/ (* y (- z)) t)
   (if (<= z 1.6e+77) (+ x y) (/ x (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+175) {
		tmp = (y * -z) / t;
	} else if (z <= 1.6e+77) {
		tmp = x + y;
	} else {
		tmp = x / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.4d+175)) then
        tmp = (y * -z) / t
    else if (z <= 1.6d+77) then
        tmp = x + y
    else
        tmp = x / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+175) {
		tmp = (y * -z) / t;
	} else if (z <= 1.6e+77) {
		tmp = x + y;
	} else {
		tmp = x / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.4e+175:
		tmp = (y * -z) / t
	elif z <= 1.6e+77:
		tmp = x + y
	else:
		tmp = x / (t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.4e+175)
		tmp = Float64(Float64(y * Float64(-z)) / t);
	elseif (z <= 1.6e+77)
		tmp = Float64(x + y);
	else
		tmp = Float64(x / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.4e+175)
		tmp = (y * -z) / t;
	elseif (z <= 1.6e+77)
		tmp = x + y;
	else
		tmp = x / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.4e+175], N[(N[(y * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.6e+77], N[(x + y), $MachinePrecision], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4000000000000001e175

   1. Initial program 70.1%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around inf 93.7%

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

      1. div-sub 93.7%

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

   6. Simplified 93.7%

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

   7. Taylor expanded in a around 0 69.6%

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

      1. associate-*r/ 69.6%

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

      2. neg-mul-1 69.6%

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

      3. distribute-rgt-neg-in 69.6%

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

   9. Simplified 69.6%

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

   10. Taylor expanded in y around inf 54.3%

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

       1. associate-*r/ 54.3%

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

       2. mul-1-neg 54.3%

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

       3. distribute-rgt-neg-out 54.3%

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

   12. Simplified 54.3%

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

   if -1.4000000000000001e175 < z < 1.6000000000000001e77

   1. Initial program 69.1%

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

      1. clear-num 69.0%

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

      2. associate-/r/ 69.0%

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

   3. Applied egg-rr 69.0%

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

   4. Taylor expanded in y around inf 61.4%

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

   5. Taylor expanded in t around inf 43.0%

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

      1. +-commutative 43.0%

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

   7. Simplified 43.0%

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

   if 1.6000000000000001e77 < z

   1. Initial program 67.3%

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

      1. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in x around -inf 63.4%

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

      1. associate-*r* 63.4%

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

      2. neg-mul-1 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in a around 0 28.7%

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

      1. associate-/l* 45.2%

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

   9. Simplified 45.2%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+175}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \end{array} \]

Alternative 20: 38.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+72}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e+64) x (if (<= a 8e+72) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+64) {
		tmp = x;
	} else if (a <= 8e+72) {
		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 <= (-1.1d+64)) then
        tmp = x
    else if (a <= 8d+72) 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 <= -1.1e+64) {
		tmp = x;
	} else if (a <= 8e+72) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e+64:
		tmp = x
	elif a <= 8e+72:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e+64)
		tmp = x;
	elseif (a <= 8e+72)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e+64)
		tmp = x;
	elseif (a <= 8e+72)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e+64], x, If[LessEqual[a, 8e+72], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.10000000000000001e64 or 7.99999999999999955e72 < a

   1. Initial program 70.1%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in a around inf 47.1%

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

   if -1.10000000000000001e64 < a < 7.99999999999999955e72

   1. Initial program 68.2%

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

      1. associate-*l/ 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in t around inf 30.8%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+72}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 33.7% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x + y \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 68.8%

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

   1. clear-num 68.7%

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

   2. associate-/r/ 68.8%

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

3. Applied egg-rr 68.8%

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

4. Taylor expanded in y around inf 56.7%

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

5. Taylor expanded in t around inf 34.1%

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

   1. +-commutative 34.1%

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

7. Simplified 34.1%

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

8. Final simplification 34.1%

   \[\leadsto x + y \]

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 68.8%

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

   1. associate-*l/ 77.5%

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

3. Simplified 77.5%

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

4. Taylor expanded in a around inf 21.0%

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

5. Final simplification 21.0%

   \[\leadsto x \]

Developer target: 86.4% 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 2023340 
(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))))