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

Percentage Accurate: 67.6% → 88.8%

Time: 14.9s

Alternatives: 25

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - x) * (z - t)) / (a - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.6% 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: 88.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \left(z - t\right)\\ t_2 := x + \frac{t\_1}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-281}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;x + t\_1 \cdot \frac{-1}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y x) (- z t))) (t_2 (+ x (/ t_1 (- a t)))))
   (if (<= t_2 (- INFINITY))
     (+ y (* (/ (- y x) t) (- a z)))
     (if (<= t_2 -5e-281)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (+ (* (- y x) a) (* z (- x y))) t))
         (if (<= t_2 4e+307)
           (+ x (* t_1 (/ -1.0 (- t a))))
           (- x (* (/ (- y x) (- a t)) (- t z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z - t);
	double t_2 = x + (t_1 / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t_2 <= -5e-281) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	} else if (t_2 <= 4e+307) {
		tmp = x + (t_1 * (-1.0 / (t - a)));
	} else {
		tmp = x - (((y - x) / (a - t)) * (t - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z - t);
	double t_2 = x + (t_1 / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t_2 <= -5e-281) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	} else if (t_2 <= 4e+307) {
		tmp = x + (t_1 * (-1.0 / (t - a)));
	} else {
		tmp = x - (((y - x) / (a - t)) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - x) * (z - t)
	t_2 = x + (t_1 / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = y + (((y - x) / t) * (a - z))
	elif t_2 <= -5e-281:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t)
	elif t_2 <= 4e+307:
		tmp = x + (t_1 * (-1.0 / (t - a)))
	else:
		tmp = x - (((y - x) / (a - t)) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) * Float64(z - t))
	t_2 = Float64(x + Float64(t_1 / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (t_2 <= -5e-281)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(Float64(y - x) * a) + Float64(z * Float64(x - y))) / t));
	elseif (t_2 <= 4e+307)
		tmp = Float64(x + Float64(t_1 * Float64(-1.0 / Float64(t - a))));
	else
		tmp = Float64(x - Float64(Float64(Float64(y - x) / Float64(a - t)) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - x) * (z - t);
	t_2 = x + (t_1 / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = y + (((y - x) / t) * (a - z));
	elseif (t_2 <= -5e-281)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	elseif (t_2 <= 4e+307)
		tmp = x + (t_1 * (-1.0 / (t - a)));
	else
		tmp = x - (((y - x) / (a - t)) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t$95$1 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-281], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(N[(y - x), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+307], N[(x + N[(t$95$1 * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 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. Add Preprocessing

   3. Taylor expanded in t around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. distribute-lft-out-- 55.0%

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

      3. div-sub 55.0%

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

      4. mul-1-neg 55.0%

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

      5. unsub-neg 55.0%

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

      6. div-sub 55.0%

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

      7. associate-/l* 69.1%

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

      8. associate-/l* 79.6%

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

      9. distribute-rgt-out-- 83.3%

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

   5. Simplified 83.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.9999999999999998e-281

   1. Initial program 94.9%

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

   if -4.9999999999999998e-281 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.1%

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

   3. Taylor expanded in t around -inf 99.8%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 3.99999999999999994e307

   1. Initial program 97.8%

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

      1. clear-num 97.7%

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

      2. associate-/r/ 97.9%

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

   4. Applied egg-rr 97.9%

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

   if 3.99999999999999994e307 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 35.9%

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

   3. Taylor expanded in y around 0 59.2%

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

      1. +-commutative 59.2%

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

      2. div-sub 59.2%

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

      3. mul-1-neg 59.2%

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

      4. associate-/l* 81.0%

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

      5. distribute-lft-neg-in 81.0%

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

      6. distribute-rgt-in 89.5%

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

      7. sub-neg 89.5%

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

      8. associate-*l/ 35.9%

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

      9. associate-*r/ 89.7%

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

   5. Simplified 89.7%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-281}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 4 \cdot 10^{+307}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{-1}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-281}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ y (* (/ (- y x) t) (- a z)))
     (if (<= t_1 -5e-281)
       t_1
       (if (<= t_1 0.0)
         (+ y (/ (+ (* (- y x) a) (* z (- x y))) t))
         (fma (- y x) (/ (- z t) (- a t)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t_1 <= -5e-281) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	} else {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (t_1 <= -5e-281)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(Float64(y - x) * a) + Float64(z * Float64(x - y))) / t));
	else
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-281], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(N[(y - x), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $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. Add Preprocessing

   3. Taylor expanded in t around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. distribute-lft-out-- 55.0%

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

      3. div-sub 55.0%

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

      4. mul-1-neg 55.0%

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

      5. unsub-neg 55.0%

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

      6. div-sub 55.0%

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

      7. associate-/l* 69.1%

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

      8. associate-/l* 79.6%

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

      9. distribute-rgt-out-- 83.3%

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

   5. Simplified 83.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.9999999999999998e-281

   1. Initial program 94.9%

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

   if -4.9999999999999998e-281 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.1%

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

   3. Taylor expanded in t around -inf 99.8%

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

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

   1. Initial program 72.5%

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

      1. +-commutative 72.5%

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

      2. associate-/l* 93.9%

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

      3. fma-define 93.9%

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

   3. Simplified 93.9%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-281}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \left(z - t\right)\\ t_2 := x + \frac{t\_1}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-281}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;x + t\_1 \cdot \frac{-1}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y x) (- z t))) (t_2 (+ x (/ t_1 (- a t)))))
   (if (<= t_2 (- INFINITY))
     (+ y (* (/ (- y x) t) (- a z)))
     (if (<= t_2 -5e-281)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_2 4e+307)
           (+ x (* t_1 (/ -1.0 (- t a))))
           (- x (* (/ (- y x) (- a t)) (- t z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z - t);
	double t_2 = x + (t_1 / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t_2 <= -5e-281) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 4e+307) {
		tmp = x + (t_1 * (-1.0 / (t - a)));
	} else {
		tmp = x - (((y - x) / (a - t)) * (t - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (z - t);
	double t_2 = x + (t_1 / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t_2 <= -5e-281) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 4e+307) {
		tmp = x + (t_1 * (-1.0 / (t - a)));
	} else {
		tmp = x - (((y - x) / (a - t)) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - x) * (z - t)
	t_2 = x + (t_1 / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = y + (((y - x) / t) * (a - z))
	elif t_2 <= -5e-281:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_2 <= 4e+307:
		tmp = x + (t_1 * (-1.0 / (t - a)))
	else:
		tmp = x - (((y - x) / (a - t)) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) * Float64(z - t))
	t_2 = Float64(x + Float64(t_1 / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (t_2 <= -5e-281)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_2 <= 4e+307)
		tmp = Float64(x + Float64(t_1 * Float64(-1.0 / Float64(t - a))));
	else
		tmp = Float64(x - Float64(Float64(Float64(y - x) / Float64(a - t)) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - x) * (z - t);
	t_2 = x + (t_1 / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = y + (((y - x) / t) * (a - z));
	elseif (t_2 <= -5e-281)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_2 <= 4e+307)
		tmp = x + (t_1 * (-1.0 / (t - a)));
	else
		tmp = x - (((y - x) / (a - t)) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t$95$1 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-281], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+307], N[(x + N[(t$95$1 * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 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. Add Preprocessing

   3. Taylor expanded in t around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. distribute-lft-out-- 55.0%

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

      3. div-sub 55.0%

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

      4. mul-1-neg 55.0%

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

      5. unsub-neg 55.0%

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

      6. div-sub 55.0%

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

      7. associate-/l* 69.1%

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

      8. associate-/l* 79.6%

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

      9. distribute-rgt-out-- 83.3%

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

   5. Simplified 83.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.9999999999999998e-281

   1. Initial program 94.9%

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

   if -4.9999999999999998e-281 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.1%

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

   3. Taylor expanded in y around 0 4.1%

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

      1. +-commutative 4.1%

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

      2. div-sub 4.1%

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

      3. mul-1-neg 4.1%

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

      4. associate-/l* 4.1%

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

      5. distribute-lft-neg-in 4.1%

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

      6. distribute-rgt-in 4.1%

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

      7. sub-neg 4.1%

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

      8. associate-*l/ 4.1%

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

      9. associate-*r/ 3.6%

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

   5. Simplified 3.6%

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

      1. clear-num 3.7%

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

      2. un-div-inv 3.8%

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

   7. Applied egg-rr 3.8%

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

   8. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.7%

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

   10. Simplified 99.7%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 3.99999999999999994e307

   1. Initial program 97.8%

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

      1. clear-num 97.7%

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

      2. associate-/r/ 97.9%

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

   4. Applied egg-rr 97.9%

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

   if 3.99999999999999994e307 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 35.9%

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

   3. Taylor expanded in y around 0 59.2%

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

      1. +-commutative 59.2%

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

      2. div-sub 59.2%

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

      3. mul-1-neg 59.2%

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

      4. associate-/l* 81.0%

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

      5. distribute-lft-neg-in 81.0%

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

      6. distribute-rgt-in 89.5%

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

      7. sub-neg 89.5%

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

      8. associate-*l/ 35.9%

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

      9. associate-*r/ 89.7%

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

   5. Simplified 89.7%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-281}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 4 \cdot 10^{+307}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{-1}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-281}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ y (* (/ (- y x) t) (- a z)))
     (if (<= t_1 -5e-281)
       t_1
       (if (<= t_1 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_1 4e+307) t_1 (- x (* (/ (- y x) (- a t)) (- t z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t_1 <= -5e-281) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_1 <= 4e+307) {
		tmp = t_1;
	} else {
		tmp = x - (((y - x) / (a - t)) * (t - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t_1 <= -5e-281) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_1 <= 4e+307) {
		tmp = t_1;
	} else {
		tmp = x - (((y - x) / (a - t)) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y + (((y - x) / t) * (a - z))
	elif t_1 <= -5e-281:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_1 <= 4e+307:
		tmp = t_1
	else:
		tmp = x - (((y - x) / (a - t)) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (t_1 <= -5e-281)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_1 <= 4e+307)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(Float64(y - x) / Float64(a - t)) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y + (((y - x) / t) * (a - z));
	elseif (t_1 <= -5e-281)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_1 <= 4e+307)
		tmp = t_1;
	else
		tmp = x - (((y - x) / (a - t)) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-281], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+307], t$95$1, N[(x - N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $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. Add Preprocessing

   3. Taylor expanded in t around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. distribute-lft-out-- 55.0%

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

      3. div-sub 55.0%

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

      4. mul-1-neg 55.0%

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

      5. unsub-neg 55.0%

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

      6. div-sub 55.0%

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

      7. associate-/l* 69.1%

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

      8. associate-/l* 79.6%

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

      9. distribute-rgt-out-- 83.3%

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

   5. Simplified 83.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.9999999999999998e-281 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 3.99999999999999994e307

   1. Initial program 96.4%

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

   if -4.9999999999999998e-281 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.1%

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

   3. Taylor expanded in y around 0 4.1%

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

      1. +-commutative 4.1%

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

      2. div-sub 4.1%

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

      3. mul-1-neg 4.1%

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

      4. associate-/l* 4.1%

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

      5. distribute-lft-neg-in 4.1%

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

      6. distribute-rgt-in 4.1%

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

      7. sub-neg 4.1%

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

      8. associate-*l/ 4.1%

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

      9. associate-*r/ 3.6%

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

   5. Simplified 3.6%

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

      1. clear-num 3.7%

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

      2. un-div-inv 3.8%

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

   7. Applied egg-rr 3.8%

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

   8. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-lft-out-- 99.8%

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

      8. associate-*r/ 99.8%

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

      9. mul-1-neg 99.8%

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

      10. unsub-neg 99.8%

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

      11. distribute-rgt-out-- 99.7%

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

   10. Simplified 99.7%

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

   if 3.99999999999999994e307 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 35.9%

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

   3. Taylor expanded in y around 0 59.2%

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

      1. +-commutative 59.2%

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

      2. div-sub 59.2%

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

      3. mul-1-neg 59.2%

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

      4. associate-/l* 81.0%

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

      5. distribute-lft-neg-in 81.0%

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

      6. distribute-rgt-in 89.5%

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

      7. sub-neg 89.5%

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

      8. associate-*l/ 35.9%

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

      9. associate-*r/ 89.7%

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

   5. Simplified 89.7%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-281}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 4 \cdot 10^{+307}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-84}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-131}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-297}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-93} \lor \neg \left(a \leq 8 \cdot 10^{-43}\right) \land a \leq 1.25 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* y (- 1.0 (/ z t)))))
   (if (<= a -1.6e+29)
     t_1
     (if (<= a -4.8e-9)
       (* y (/ z a))
       (if (<= a -6.4e-84)
         y
         (if (<= a -1.8e-131)
           (/ (* y z) a)
           (if (<= a -1.25e-297)
             t_2
             (if (<= a 5.2e-278)
               (* x (/ z t))
               (if (or (<= a 8.6e-93) (and (not (<= a 8e-43)) (<= a 1.25e+14)))
                 t_2
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (a <= -1.6e+29) {
		tmp = t_1;
	} else if (a <= -4.8e-9) {
		tmp = y * (z / a);
	} else if (a <= -6.4e-84) {
		tmp = y;
	} else if (a <= -1.8e-131) {
		tmp = (y * z) / a;
	} else if (a <= -1.25e-297) {
		tmp = t_2;
	} else if (a <= 5.2e-278) {
		tmp = x * (z / t);
	} else if ((a <= 8.6e-93) || (!(a <= 8e-43) && (a <= 1.25e+14))) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = y * (1.0d0 - (z / t))
    if (a <= (-1.6d+29)) then
        tmp = t_1
    else if (a <= (-4.8d-9)) then
        tmp = y * (z / a)
    else if (a <= (-6.4d-84)) then
        tmp = y
    else if (a <= (-1.8d-131)) then
        tmp = (y * z) / a
    else if (a <= (-1.25d-297)) then
        tmp = t_2
    else if (a <= 5.2d-278) then
        tmp = x * (z / t)
    else if ((a <= 8.6d-93) .or. (.not. (a <= 8d-43)) .and. (a <= 1.25d+14)) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (a <= -1.6e+29) {
		tmp = t_1;
	} else if (a <= -4.8e-9) {
		tmp = y * (z / a);
	} else if (a <= -6.4e-84) {
		tmp = y;
	} else if (a <= -1.8e-131) {
		tmp = (y * z) / a;
	} else if (a <= -1.25e-297) {
		tmp = t_2;
	} else if (a <= 5.2e-278) {
		tmp = x * (z / t);
	} else if ((a <= 8.6e-93) || (!(a <= 8e-43) && (a <= 1.25e+14))) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y * (1.0 - (z / t))
	tmp = 0
	if a <= -1.6e+29:
		tmp = t_1
	elif a <= -4.8e-9:
		tmp = y * (z / a)
	elif a <= -6.4e-84:
		tmp = y
	elif a <= -1.8e-131:
		tmp = (y * z) / a
	elif a <= -1.25e-297:
		tmp = t_2
	elif a <= 5.2e-278:
		tmp = x * (z / t)
	elif (a <= 8.6e-93) or (not (a <= 8e-43) and (a <= 1.25e+14)):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (a <= -1.6e+29)
		tmp = t_1;
	elseif (a <= -4.8e-9)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= -6.4e-84)
		tmp = y;
	elseif (a <= -1.8e-131)
		tmp = Float64(Float64(y * z) / a);
	elseif (a <= -1.25e-297)
		tmp = t_2;
	elseif (a <= 5.2e-278)
		tmp = Float64(x * Float64(z / t));
	elseif ((a <= 8.6e-93) || (!(a <= 8e-43) && (a <= 1.25e+14)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (a <= -1.6e+29)
		tmp = t_1;
	elseif (a <= -4.8e-9)
		tmp = y * (z / a);
	elseif (a <= -6.4e-84)
		tmp = y;
	elseif (a <= -1.8e-131)
		tmp = (y * z) / a;
	elseif (a <= -1.25e-297)
		tmp = t_2;
	elseif (a <= 5.2e-278)
		tmp = x * (z / t);
	elseif ((a <= 8.6e-93) || (~((a <= 8e-43)) && (a <= 1.25e+14)))
		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[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+29], t$95$1, If[LessEqual[a, -4.8e-9], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.4e-84], y, If[LessEqual[a, -1.8e-131], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -1.25e-297], t$95$2, If[LessEqual[a, 5.2e-278], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 8.6e-93], And[N[Not[LessEqual[a, 8e-43]], $MachinePrecision], LessEqual[a, 1.25e+14]]], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.59999999999999993e29 or 8.59999999999999925e-93 < a < 8.00000000000000062e-43 or 1.25e14 < a

   1. Initial program 66.3%

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

   3. Taylor expanded in x around inf 53.3%

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

      1. mul-1-neg 53.3%

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

      2. unsub-neg 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in t around 0 52.3%

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

   if -1.59999999999999993e29 < a < -4.8e-9

   1. Initial program 79.1%

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

   3. Taylor expanded in y around 0 97.2%

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

      1. +-commutative 97.2%

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

      2. div-sub 97.2%

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

      3. mul-1-neg 97.2%

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

      4. associate-/l* 97.8%

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

      5. distribute-lft-neg-in 97.8%

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

      6. distribute-rgt-in 97.8%

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

      7. sub-neg 97.8%

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

      8. associate-*l/ 79.1%

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

      9. associate-*r/ 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in x around 0 62.1%

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

      1. associate-/l* 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in t around 0 51.8%

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

       1. associate-/l* 51.9%

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

   11. Simplified 51.9%

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

   if -4.8e-9 < a < -6.3999999999999999e-84

   1. Initial program 54.4%

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

   3. Taylor expanded in t around inf 37.5%

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

   if -6.3999999999999999e-84 < a < -1.8e-131

   1. Initial program 86.3%

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

   3. Taylor expanded in y around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. div-sub 86.0%

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

      3. mul-1-neg 86.0%

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

      4. associate-/l* 86.0%

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

      5. distribute-lft-neg-in 86.0%

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

      6. distribute-rgt-in 86.0%

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

      7. sub-neg 86.0%

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

      8. associate-*l/ 86.3%

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

      9. associate-*r/ 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in x around 0 72.4%

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

      1. associate-/l* 72.1%

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

   8. Simplified 72.1%

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

   9. Taylor expanded in t around 0 73.1%

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

   if -1.8e-131 < a < -1.25e-297 or 5.1999999999999997e-278 < a < 8.59999999999999925e-93 or 8.00000000000000062e-43 < a < 1.25e14

   1. Initial program 65.4%

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

   3. Taylor expanded in a around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. unsub-neg 56.9%

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

      3. associate-/l* 63.7%

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

      4. div-sub 63.7%

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

      5. sub-neg 63.7%

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

      6. *-inverses 63.7%

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

      7. metadata-eval 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in y around inf 62.0%

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

   if -1.25e-297 < a < 5.1999999999999997e-278

   1. Initial program 48.2%

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

   3. Taylor expanded in x around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. unsub-neg 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in a around 0 85.2%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-84}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-131}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-93} \lor \neg \left(a \leq 8 \cdot 10^{-43}\right) \land a \leq 1.25 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq -0.22:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.1e+41)
   (* z (/ (- y x) (- a t)))
   (if (<= x -0.22)
     (+ x y)
     (if (<= x 7.2e+21)
       (* y (/ (- z t) (- a t)))
       (if (<= x 4.2e+90)
         (* x (- 1.0 (/ z a)))
         (if (<= x 1.1e+119) (* y (- 1.0 (/ z t))) (* x (/ (- z a) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.1e+41) {
		tmp = z * ((y - x) / (a - t));
	} else if (x <= -0.22) {
		tmp = x + y;
	} else if (x <= 7.2e+21) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 4.2e+90) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 1.1e+119) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x * ((z - 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 (x <= (-2.1d+41)) then
        tmp = z * ((y - x) / (a - t))
    else if (x <= (-0.22d0)) then
        tmp = x + y
    else if (x <= 7.2d+21) then
        tmp = y * ((z - t) / (a - t))
    else if (x <= 4.2d+90) then
        tmp = x * (1.0d0 - (z / a))
    else if (x <= 1.1d+119) then
        tmp = y * (1.0d0 - (z / t))
    else
        tmp = x * ((z - 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 (x <= -2.1e+41) {
		tmp = z * ((y - x) / (a - t));
	} else if (x <= -0.22) {
		tmp = x + y;
	} else if (x <= 7.2e+21) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 4.2e+90) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 1.1e+119) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.1e+41:
		tmp = z * ((y - x) / (a - t))
	elif x <= -0.22:
		tmp = x + y
	elif x <= 7.2e+21:
		tmp = y * ((z - t) / (a - t))
	elif x <= 4.2e+90:
		tmp = x * (1.0 - (z / a))
	elif x <= 1.1e+119:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x * ((z - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.1e+41)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (x <= -0.22)
		tmp = Float64(x + y);
	elseif (x <= 7.2e+21)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (x <= 4.2e+90)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (x <= 1.1e+119)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x * Float64(Float64(z - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.1e+41)
		tmp = z * ((y - x) / (a - t));
	elseif (x <= -0.22)
		tmp = x + y;
	elseif (x <= 7.2e+21)
		tmp = y * ((z - t) / (a - t));
	elseif (x <= 4.2e+90)
		tmp = x * (1.0 - (z / a));
	elseif (x <= 1.1e+119)
		tmp = y * (1.0 - (z / t));
	else
		tmp = x * ((z - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.1e+41], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -0.22], N[(x + y), $MachinePrecision], If[LessEqual[x, 7.2e+21], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+90], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+119], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.1e41

   1. Initial program 64.8%

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

   3. Taylor expanded in y around 0 64.6%

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

      1. +-commutative 64.6%

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

      2. div-sub 64.6%

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

      3. mul-1-neg 64.6%

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

      4. associate-/l* 73.0%

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

      5. distribute-lft-neg-in 73.0%

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

      6. distribute-rgt-in 78.5%

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

      7. sub-neg 78.5%

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

      8. associate-*l/ 64.8%

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

      9. associate-*r/ 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in z around inf 60.4%

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

      1. div-sub 60.3%

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

   8. Simplified 60.3%

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

   if -2.1e41 < x < -0.220000000000000001

   1. Initial program 90.5%

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

   3. Taylor expanded in y around 0 90.5%

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

      1. +-commutative 90.5%

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

      2. div-sub 90.5%

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

      3. mul-1-neg 90.5%

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

      4. associate-/l* 90.5%

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

      5. distribute-lft-neg-in 90.5%

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

      6. distribute-rgt-in 90.5%

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

      7. sub-neg 90.5%

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

      8. associate-*l/ 90.5%

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

      9. associate-*r/ 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in y around inf 81.1%

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

   7. Taylor expanded in t around inf 71.7%

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

      1. +-commutative 71.7%

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

   9. Simplified 71.7%

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

   if -0.220000000000000001 < x < 7.2e21

   1. Initial program 75.7%

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

   3. Taylor expanded in y around 0 89.1%

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

      1. +-commutative 89.1%

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

      2. div-sub 89.1%

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

      3. mul-1-neg 89.1%

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

      4. associate-/l* 89.1%

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

      5. distribute-lft-neg-in 89.1%

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

      6. distribute-rgt-in 90.8%

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

      7. sub-neg 90.8%

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

      8. associate-*l/ 75.7%

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

      9. associate-*r/ 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in x around 0 60.6%

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

      1. associate-/l* 76.2%

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

   8. Simplified 76.2%

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

   if 7.2e21 < x < 4.19999999999999961e90

   1. Initial program 56.0%

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

   3. Taylor expanded in x around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. unsub-neg 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in t around 0 56.1%

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

   if 4.19999999999999961e90 < x < 1.1000000000000001e119

   1. Initial program 35.3%

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

   3. Taylor expanded in a around 0 35.3%

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

      1. mul-1-neg 35.3%

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

      2. unsub-neg 35.3%

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

      3. associate-/l* 36.7%

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

      4. div-sub 36.7%

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

      5. sub-neg 36.7%

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

      6. *-inverses 36.7%

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

      7. metadata-eval 36.7%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in y around inf 100.0%

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

   if 1.1000000000000001e119 < x

   1. Initial program 38.4%

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

   3. Taylor expanded in x around inf 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in t around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. sub-neg 50.1%

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

      3. mul-1-neg 50.1%

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

   8. Simplified 50.1%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x \leq -0.22:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;x \leq -0.0035:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.4e+41)
   (* x (/ z (- t a)))
   (if (<= x -0.0035)
     (+ x y)
     (if (<= x 1.6e+23)
       (* y (/ (- z t) (- a t)))
       (if (<= x 6.2e+90)
         (* x (- 1.0 (/ z a)))
         (if (<= x 8.2e+120) (* y (- 1.0 (/ z t))) (* x (/ (- z a) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.4e+41) {
		tmp = x * (z / (t - a));
	} else if (x <= -0.0035) {
		tmp = x + y;
	} else if (x <= 1.6e+23) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 6.2e+90) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 8.2e+120) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x * ((z - 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 (x <= (-4.4d+41)) then
        tmp = x * (z / (t - a))
    else if (x <= (-0.0035d0)) then
        tmp = x + y
    else if (x <= 1.6d+23) then
        tmp = y * ((z - t) / (a - t))
    else if (x <= 6.2d+90) then
        tmp = x * (1.0d0 - (z / a))
    else if (x <= 8.2d+120) then
        tmp = y * (1.0d0 - (z / t))
    else
        tmp = x * ((z - 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 (x <= -4.4e+41) {
		tmp = x * (z / (t - a));
	} else if (x <= -0.0035) {
		tmp = x + y;
	} else if (x <= 1.6e+23) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 6.2e+90) {
		tmp = x * (1.0 - (z / a));
	} else if (x <= 8.2e+120) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.4e+41:
		tmp = x * (z / (t - a))
	elif x <= -0.0035:
		tmp = x + y
	elif x <= 1.6e+23:
		tmp = y * ((z - t) / (a - t))
	elif x <= 6.2e+90:
		tmp = x * (1.0 - (z / a))
	elif x <= 8.2e+120:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x * ((z - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.4e+41)
		tmp = Float64(x * Float64(z / Float64(t - a)));
	elseif (x <= -0.0035)
		tmp = Float64(x + y);
	elseif (x <= 1.6e+23)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (x <= 6.2e+90)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (x <= 8.2e+120)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x * Float64(Float64(z - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.4e+41)
		tmp = x * (z / (t - a));
	elseif (x <= -0.0035)
		tmp = x + y;
	elseif (x <= 1.6e+23)
		tmp = y * ((z - t) / (a - t));
	elseif (x <= 6.2e+90)
		tmp = x * (1.0 - (z / a));
	elseif (x <= 8.2e+120)
		tmp = y * (1.0 - (z / t));
	else
		tmp = x * ((z - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.4e+41], N[(x * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -0.0035], N[(x + y), $MachinePrecision], If[LessEqual[x, 1.6e+23], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+90], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e+120], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -4.3999999999999998e41

   1. Initial program 64.8%

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

   3. Taylor expanded in x around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in z around inf 54.1%

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

      1. associate-*r/ 54.1%

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

      2. mul-1-neg 54.1%

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

   8. Simplified 54.1%

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

   if -4.3999999999999998e41 < x < -0.00350000000000000007

   1. Initial program 90.5%

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

   3. Taylor expanded in y around 0 90.5%

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

      1. +-commutative 90.5%

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

      2. div-sub 90.5%

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

      3. mul-1-neg 90.5%

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

      4. associate-/l* 90.5%

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

      5. distribute-lft-neg-in 90.5%

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

      6. distribute-rgt-in 90.5%

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

      7. sub-neg 90.5%

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

      8. associate-*l/ 90.5%

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

      9. associate-*r/ 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in y around inf 81.1%

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

   7. Taylor expanded in t around inf 71.7%

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

      1. +-commutative 71.7%

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

   9. Simplified 71.7%

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

   if -0.00350000000000000007 < x < 1.6e23

   1. Initial program 75.7%

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

   3. Taylor expanded in y around 0 89.1%

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

      1. +-commutative 89.1%

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

      2. div-sub 89.1%

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

      3. mul-1-neg 89.1%

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

      4. associate-/l* 89.1%

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

      5. distribute-lft-neg-in 89.1%

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

      6. distribute-rgt-in 90.8%

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

      7. sub-neg 90.8%

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

      8. associate-*l/ 75.7%

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

      9. associate-*r/ 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in x around 0 60.6%

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

      1. associate-/l* 76.2%

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

   8. Simplified 76.2%

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

   if 1.6e23 < x < 6.19999999999999977e90

   1. Initial program 56.0%

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

   3. Taylor expanded in x around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. unsub-neg 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in t around 0 56.1%

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

   if 6.19999999999999977e90 < x < 8.2e120

   1. Initial program 35.3%

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

   3. Taylor expanded in a around 0 35.3%

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

      1. mul-1-neg 35.3%

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

      2. unsub-neg 35.3%

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

      3. associate-/l* 36.7%

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

      4. div-sub 36.7%

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

      5. sub-neg 36.7%

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

      6. *-inverses 36.7%

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

      7. metadata-eval 36.7%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in y around inf 100.0%

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

   if 8.2e120 < x

   1. Initial program 38.4%

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

   3. Taylor expanded in x around inf 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in t around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. sub-neg 50.1%

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

      3. mul-1-neg 50.1%

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

   8. Simplified 50.1%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;x \leq -0.0035:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-109}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+86}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.9e+41)
   (* x (/ z (- t a)))
   (if (<= x -2.8e-70)
     (+ x y)
     (if (<= x 6e-109)
       (* y (- 1.0 (/ z t)))
       (if (<= x 1.95e-82)
         (* y (/ (- z t) a))
         (if (<= x 5.8e+86) (+ x y) (* x (/ (- z a) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.9e+41) {
		tmp = x * (z / (t - a));
	} else if (x <= -2.8e-70) {
		tmp = x + y;
	} else if (x <= 6e-109) {
		tmp = y * (1.0 - (z / t));
	} else if (x <= 1.95e-82) {
		tmp = y * ((z - t) / a);
	} else if (x <= 5.8e+86) {
		tmp = x + y;
	} else {
		tmp = x * ((z - 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 (x <= (-2.9d+41)) then
        tmp = x * (z / (t - a))
    else if (x <= (-2.8d-70)) then
        tmp = x + y
    else if (x <= 6d-109) then
        tmp = y * (1.0d0 - (z / t))
    else if (x <= 1.95d-82) then
        tmp = y * ((z - t) / a)
    else if (x <= 5.8d+86) then
        tmp = x + y
    else
        tmp = x * ((z - 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 (x <= -2.9e+41) {
		tmp = x * (z / (t - a));
	} else if (x <= -2.8e-70) {
		tmp = x + y;
	} else if (x <= 6e-109) {
		tmp = y * (1.0 - (z / t));
	} else if (x <= 1.95e-82) {
		tmp = y * ((z - t) / a);
	} else if (x <= 5.8e+86) {
		tmp = x + y;
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.9e+41:
		tmp = x * (z / (t - a))
	elif x <= -2.8e-70:
		tmp = x + y
	elif x <= 6e-109:
		tmp = y * (1.0 - (z / t))
	elif x <= 1.95e-82:
		tmp = y * ((z - t) / a)
	elif x <= 5.8e+86:
		tmp = x + y
	else:
		tmp = x * ((z - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.9e+41)
		tmp = Float64(x * Float64(z / Float64(t - a)));
	elseif (x <= -2.8e-70)
		tmp = Float64(x + y);
	elseif (x <= 6e-109)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (x <= 1.95e-82)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (x <= 5.8e+86)
		tmp = Float64(x + y);
	else
		tmp = Float64(x * Float64(Float64(z - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.9e+41)
		tmp = x * (z / (t - a));
	elseif (x <= -2.8e-70)
		tmp = x + y;
	elseif (x <= 6e-109)
		tmp = y * (1.0 - (z / t));
	elseif (x <= 1.95e-82)
		tmp = y * ((z - t) / a);
	elseif (x <= 5.8e+86)
		tmp = x + y;
	else
		tmp = x * ((z - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.9e+41], N[(x * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.8e-70], N[(x + y), $MachinePrecision], If[LessEqual[x, 6e-109], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e-82], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+86], N[(x + y), $MachinePrecision], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.89999999999999988e41

   1. Initial program 64.8%

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

   3. Taylor expanded in x around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in z around inf 54.1%

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

      1. associate-*r/ 54.1%

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

      2. mul-1-neg 54.1%

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

   8. Simplified 54.1%

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

   if -2.89999999999999988e41 < x < -2.7999999999999999e-70 or 1.94999999999999987e-82 < x < 5.79999999999999981e86

   1. Initial program 67.6%

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

   3. Taylor expanded in y around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. div-sub 77.4%

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

      3. mul-1-neg 77.4%

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

      4. associate-/l* 81.4%

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

      5. distribute-lft-neg-in 81.4%

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

      6. distribute-rgt-in 83.6%

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

      7. sub-neg 83.6%

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

      8. associate-*l/ 67.6%

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

      9. associate-*r/ 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in y around inf 76.9%

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

   7. Taylor expanded in t around inf 50.9%

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

      1. +-commutative 50.9%

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

   9. Simplified 50.9%

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

   if -2.7999999999999999e-70 < x < 6.00000000000000043e-109

   1. Initial program 78.8%

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

   3. Taylor expanded in a around 0 46.6%

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

      1. mul-1-neg 46.6%

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

      2. unsub-neg 46.6%

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

      3. associate-/l* 52.8%

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

      4. div-sub 52.8%

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

      5. sub-neg 52.8%

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

      6. *-inverses 52.8%

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

      7. metadata-eval 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around inf 52.9%

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

   if 6.00000000000000043e-109 < x < 1.94999999999999987e-82

   1. Initial program 83.9%

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

   3. Taylor expanded in y around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. div-sub 83.9%

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

      3. mul-1-neg 83.9%

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

      4. associate-/l* 83.9%

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

      5. distribute-lft-neg-in 83.9%

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

      6. distribute-rgt-in 83.9%

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

      7. sub-neg 83.9%

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

      8. associate-*l/ 83.9%

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

      9. associate-*r/ 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in x around 0 84.4%

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

      1. associate-/l* 84.4%

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

   8. Simplified 84.4%

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

   9. Taylor expanded in a around inf 83.6%

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

       1. associate-/l* 83.6%

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

   11. Simplified 83.6%

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

   if 5.79999999999999981e86 < x

   1. Initial program 39.7%

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

   3. Taylor expanded in x around inf 45.9%

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

      1. mul-1-neg 45.9%

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

      2. unsub-neg 45.9%

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

   5. Simplified 45.9%

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

   6. Taylor expanded in t around inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. sub-neg 48.6%

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

      3. mul-1-neg 48.6%

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

   8. Simplified 48.6%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-109}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+86}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - a}{t}\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-69}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+86}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- z a) t))))
   (if (<= x -5.5e+40)
     t_1
     (if (<= x -1.5e-69)
       (+ x y)
       (if (<= x 4.5e-105)
         (* y (- 1.0 (/ z t)))
         (if (<= x 3.3e-79)
           (* y (/ (- z t) a))
           (if (<= x 1.2e+86) (+ x y) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (x <= -5.5e+40) {
		tmp = t_1;
	} else if (x <= -1.5e-69) {
		tmp = x + y;
	} else if (x <= 4.5e-105) {
		tmp = y * (1.0 - (z / t));
	} else if (x <= 3.3e-79) {
		tmp = y * ((z - t) / a);
	} else if (x <= 1.2e+86) {
		tmp = x + y;
	} 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 * ((z - a) / t)
    if (x <= (-5.5d+40)) then
        tmp = t_1
    else if (x <= (-1.5d-69)) then
        tmp = x + y
    else if (x <= 4.5d-105) then
        tmp = y * (1.0d0 - (z / t))
    else if (x <= 3.3d-79) then
        tmp = y * ((z - t) / a)
    else if (x <= 1.2d+86) then
        tmp = x + y
    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 * ((z - a) / t);
	double tmp;
	if (x <= -5.5e+40) {
		tmp = t_1;
	} else if (x <= -1.5e-69) {
		tmp = x + y;
	} else if (x <= 4.5e-105) {
		tmp = y * (1.0 - (z / t));
	} else if (x <= 3.3e-79) {
		tmp = y * ((z - t) / a);
	} else if (x <= 1.2e+86) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((z - a) / t)
	tmp = 0
	if x <= -5.5e+40:
		tmp = t_1
	elif x <= -1.5e-69:
		tmp = x + y
	elif x <= 4.5e-105:
		tmp = y * (1.0 - (z / t))
	elif x <= 3.3e-79:
		tmp = y * ((z - t) / a)
	elif x <= 1.2e+86:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(z - a) / t))
	tmp = 0.0
	if (x <= -5.5e+40)
		tmp = t_1;
	elseif (x <= -1.5e-69)
		tmp = Float64(x + y);
	elseif (x <= 4.5e-105)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (x <= 3.3e-79)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (x <= 1.2e+86)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((z - a) / t);
	tmp = 0.0;
	if (x <= -5.5e+40)
		tmp = t_1;
	elseif (x <= -1.5e-69)
		tmp = x + y;
	elseif (x <= 4.5e-105)
		tmp = y * (1.0 - (z / t));
	elseif (x <= 3.3e-79)
		tmp = y * ((z - t) / a);
	elseif (x <= 1.2e+86)
		tmp = x + y;
	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 - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e+40], t$95$1, If[LessEqual[x, -1.5e-69], N[(x + y), $MachinePrecision], If[LessEqual[x, 4.5e-105], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e-79], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+86], N[(x + y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.49999999999999974e40 or 1.2e86 < x

   1. Initial program 52.2%

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

   3. Taylor expanded in x around inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. unsub-neg 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in t around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. sub-neg 48.7%

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

      3. mul-1-neg 48.7%

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

   8. Simplified 48.7%

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

   if -5.49999999999999974e40 < x < -1.49999999999999995e-69 or 3.2999999999999998e-79 < x < 1.2e86

   1. Initial program 67.6%

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

   3. Taylor expanded in y around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. div-sub 77.4%

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

      3. mul-1-neg 77.4%

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

      4. associate-/l* 81.4%

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

      5. distribute-lft-neg-in 81.4%

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

      6. distribute-rgt-in 83.6%

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

      7. sub-neg 83.6%

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

      8. associate-*l/ 67.6%

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

      9. associate-*r/ 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in y around inf 76.9%

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

   7. Taylor expanded in t around inf 50.9%

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

      1. +-commutative 50.9%

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

   9. Simplified 50.9%

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

   if -1.49999999999999995e-69 < x < 4.4999999999999997e-105

   1. Initial program 78.8%

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

   3. Taylor expanded in a around 0 46.6%

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

      1. mul-1-neg 46.6%

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

      2. unsub-neg 46.6%

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

      3. associate-/l* 52.8%

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

      4. div-sub 52.8%

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

      5. sub-neg 52.8%

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

      6. *-inverses 52.8%

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

      7. metadata-eval 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around inf 52.9%

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

   if 4.4999999999999997e-105 < x < 3.2999999999999998e-79

   1. Initial program 83.9%

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

   3. Taylor expanded in y around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. div-sub 83.9%

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

      3. mul-1-neg 83.9%

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

      4. associate-/l* 83.9%

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

      5. distribute-lft-neg-in 83.9%

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

      6. distribute-rgt-in 83.9%

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

      7. sub-neg 83.9%

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

      8. associate-*l/ 83.9%

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

      9. associate-*r/ 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in x around 0 84.4%

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

      1. associate-/l* 84.4%

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

   8. Simplified 84.4%

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

   9. Taylor expanded in a around inf 83.6%

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

       1. associate-/l* 83.6%

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

   11. Simplified 83.6%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-69}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+86}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 45.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* y (- 1.0 (/ z t)))))
   (if (<= t -5.2e+66)
     t_2
     (if (<= t -3.1e-169)
       t_1
       (if (<= t 7.8e-206)
         (* y (/ z a))
         (if (<= t 2.25e-123)
           t_1
           (if (<= t 2.3e-48) (/ (* x (- z a)) t) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -5.2e+66) {
		tmp = t_2;
	} else if (t <= -3.1e-169) {
		tmp = t_1;
	} else if (t <= 7.8e-206) {
		tmp = y * (z / a);
	} else if (t <= 2.25e-123) {
		tmp = t_1;
	} else if (t <= 2.3e-48) {
		tmp = (x * (z - a)) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = y * (1.0d0 - (z / t))
    if (t <= (-5.2d+66)) then
        tmp = t_2
    else if (t <= (-3.1d-169)) then
        tmp = t_1
    else if (t <= 7.8d-206) then
        tmp = y * (z / a)
    else if (t <= 2.25d-123) then
        tmp = t_1
    else if (t <= 2.3d-48) then
        tmp = (x * (z - a)) / t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -5.2e+66) {
		tmp = t_2;
	} else if (t <= -3.1e-169) {
		tmp = t_1;
	} else if (t <= 7.8e-206) {
		tmp = y * (z / a);
	} else if (t <= 2.25e-123) {
		tmp = t_1;
	} else if (t <= 2.3e-48) {
		tmp = (x * (z - a)) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y * (1.0 - (z / t))
	tmp = 0
	if t <= -5.2e+66:
		tmp = t_2
	elif t <= -3.1e-169:
		tmp = t_1
	elif t <= 7.8e-206:
		tmp = y * (z / a)
	elif t <= 2.25e-123:
		tmp = t_1
	elif t <= 2.3e-48:
		tmp = (x * (z - a)) / t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -5.2e+66)
		tmp = t_2;
	elseif (t <= -3.1e-169)
		tmp = t_1;
	elseif (t <= 7.8e-206)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 2.25e-123)
		tmp = t_1;
	elseif (t <= 2.3e-48)
		tmp = Float64(Float64(x * Float64(z - a)) / t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (t <= -5.2e+66)
		tmp = t_2;
	elseif (t <= -3.1e-169)
		tmp = t_1;
	elseif (t <= 7.8e-206)
		tmp = y * (z / a);
	elseif (t <= 2.25e-123)
		tmp = t_1;
	elseif (t <= 2.3e-48)
		tmp = (x * (z - a)) / t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+66], t$95$2, If[LessEqual[t, -3.1e-169], t$95$1, If[LessEqual[t, 7.8e-206], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e-123], t$95$1, If[LessEqual[t, 2.3e-48], N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.20000000000000024e66 or 2.3000000000000001e-48 < t

   1. Initial program 46.0%

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

   3. Taylor expanded in a around 0 29.9%

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

      1. mul-1-neg 29.9%

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

      2. unsub-neg 29.9%

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

      3. associate-/l* 43.9%

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

      4. div-sub 43.9%

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

      5. sub-neg 43.9%

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

      6. *-inverses 43.9%

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

      7. metadata-eval 43.9%

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

   5. Simplified 43.9%

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

   6. Taylor expanded in y around inf 46.9%

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

   if -5.20000000000000024e66 < t < -3.1000000000000002e-169 or 7.80000000000000014e-206 < t < 2.24999999999999997e-123

   1. Initial program 86.3%

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

   3. Taylor expanded in x around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in t around 0 52.7%

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

   if -3.1000000000000002e-169 < t < 7.80000000000000014e-206

   1. Initial program 91.6%

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

   3. Taylor expanded in y around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. div-sub 79.6%

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

      3. mul-1-neg 79.6%

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

      4. associate-/l* 82.2%

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

      5. distribute-lft-neg-in 82.2%

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

      6. distribute-rgt-in 97.1%

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

      7. sub-neg 97.1%

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

      8. associate-*l/ 91.6%

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

      9. associate-*r/ 94.8%

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

   5. Simplified 94.8%

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

   6. Taylor expanded in x around 0 55.1%

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

      1. associate-/l* 57.8%

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

   8. Simplified 57.8%

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

   9. Taylor expanded in t around 0 52.1%

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

       1. associate-/l* 57.6%

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

   11. Simplified 57.6%

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

   if 2.24999999999999997e-123 < t < 2.3000000000000001e-48

   1. Initial program 73.6%

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

   3. Taylor expanded in t around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. distribute-lft-out-- 77.5%

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

      3. div-sub 77.5%

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

      4. mul-1-neg 77.5%

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

      5. unsub-neg 77.5%

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

      6. div-sub 77.5%

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

      7. associate-/l* 77.6%

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

      8. associate-/l* 72.1%

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

      9. distribute-rgt-out-- 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in y around 0 62.4%

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

Alternative 11: 37.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{+246}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= z -2.75e+246)
     (* x (/ z (- a)))
     (if (<= z -7e+119)
       t_1
       (if (<= z -9e+22) (* x (/ z t)) (if (<= z 1.9e+38) (+ x y) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (z <= -2.75e+246) {
		tmp = x * (z / -a);
	} else if (z <= -7e+119) {
		tmp = t_1;
	} else if (z <= -9e+22) {
		tmp = x * (z / t);
	} else if (z <= 1.9e+38) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / a)
    if (z <= (-2.75d+246)) then
        tmp = x * (z / -a)
    else if (z <= (-7d+119)) then
        tmp = t_1
    else if (z <= (-9d+22)) then
        tmp = x * (z / t)
    else if (z <= 1.9d+38) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (z <= -2.75e+246) {
		tmp = x * (z / -a);
	} else if (z <= -7e+119) {
		tmp = t_1;
	} else if (z <= -9e+22) {
		tmp = x * (z / t);
	} else if (z <= 1.9e+38) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if z <= -2.75e+246:
		tmp = x * (z / -a)
	elif z <= -7e+119:
		tmp = t_1
	elif z <= -9e+22:
		tmp = x * (z / t)
	elif z <= 1.9e+38:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (z <= -2.75e+246)
		tmp = Float64(x * Float64(z / Float64(-a)));
	elseif (z <= -7e+119)
		tmp = t_1;
	elseif (z <= -9e+22)
		tmp = Float64(x * Float64(z / t));
	elseif (z <= 1.9e+38)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (z <= -2.75e+246)
		tmp = x * (z / -a);
	elseif (z <= -7e+119)
		tmp = t_1;
	elseif (z <= -9e+22)
		tmp = x * (z / t);
	elseif (z <= 1.9e+38)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.75e+246], N[(x * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e+119], t$95$1, If[LessEqual[z, -9e+22], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+38], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.75000000000000014e246

   1. Initial program 68.7%

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

   3. Taylor expanded in x around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in t around 0 62.4%

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

   7. Taylor expanded in z around inf 31.0%

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

      1. mul-1-neg 31.0%

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

      2. associate-/l* 47.2%

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

      3. distribute-lft-neg-out 47.2%

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

      4. *-commutative 47.2%

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

   9. Simplified 47.2%

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

   if -2.75000000000000014e246 < z < -7.0000000000000001e119 or 1.8999999999999999e38 < z

   1. Initial program 69.6%

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

   3. Taylor expanded in y around 0 71.8%

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

      1. +-commutative 71.8%

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

      2. div-sub 71.8%

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

      3. mul-1-neg 71.8%

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

      4. associate-/l* 79.4%

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

      5. distribute-lft-neg-in 79.4%

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

      6. distribute-rgt-in 89.0%

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

      7. sub-neg 89.0%

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

      8. associate-*l/ 69.6%

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

      9. associate-*r/ 86.7%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in x around 0 44.5%

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

      1. associate-/l* 60.0%

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

   8. Simplified 60.0%

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

   9. Taylor expanded in t around 0 37.9%

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

       1. associate-/l* 47.0%

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

   11. Simplified 47.0%

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

   if -7.0000000000000001e119 < z < -8.9999999999999996e22

   1. Initial program 59.5%

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

   3. Taylor expanded in x around inf 36.4%

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

      1. mul-1-neg 36.4%

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

      2. unsub-neg 36.4%

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

   5. Simplified 36.4%

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

   6. Taylor expanded in a around 0 40.7%

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

   if -8.9999999999999996e22 < z < 1.8999999999999999e38

   1. Initial program 63.6%

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

   3. Taylor expanded in y around 0 70.2%

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

      1. +-commutative 70.2%

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

      2. div-sub 70.2%

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

      3. mul-1-neg 70.2%

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

      4. associate-/l* 73.4%

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

      5. distribute-lft-neg-in 73.4%

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

      6. distribute-rgt-in 73.4%

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

      7. sub-neg 73.4%

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

      8. associate-*l/ 63.6%

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

      9. associate-*r/ 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in y around inf 62.5%

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

   7. Taylor expanded in t around inf 46.9%

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

      1. +-commutative 46.9%

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

   9. Simplified 46.9%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+246}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -5.4e+19)
     t_1
     (if (<= t 2.25e-123)
       (+ x (/ (- y x) (/ a z)))
       (if (<= t 5.8e+52) (* z (/ (- y x) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -5.4e+19) {
		tmp = t_1;
	} else if (t <= 2.25e-123) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 5.8e+52) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-5.4d+19)) then
        tmp = t_1
    else if (t <= 2.25d-123) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 5.8d+52) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -5.4e+19) {
		tmp = t_1;
	} else if (t <= 2.25e-123) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 5.8e+52) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -5.4e+19:
		tmp = t_1
	elif t <= 2.25e-123:
		tmp = x + ((y - x) / (a / z))
	elif t <= 5.8e+52:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -5.4e+19)
		tmp = t_1;
	elseif (t <= 2.25e-123)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 5.8e+52)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -5.4e+19)
		tmp = t_1;
	elseif (t <= 2.25e-123)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 5.8e+52)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e+19], t$95$1, If[LessEqual[t, 2.25e-123], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+52], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.4e19 or 5.8e52 < t

   1. Initial program 41.0%

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

   3. Taylor expanded in y around 0 57.5%

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

      1. +-commutative 57.5%

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

      2. div-sub 57.5%

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

      3. mul-1-neg 57.5%

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

      4. associate-/l* 65.5%

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

      5. distribute-lft-neg-in 65.5%

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

      6. distribute-rgt-in 65.5%

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

      7. sub-neg 65.5%

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

      8. associate-*l/ 41.0%

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

      9. associate-*r/ 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in x around 0 36.1%

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

      1. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

   if -5.4e19 < t < 2.24999999999999997e-123

   1. Initial program 89.8%

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

      1. clear-num 89.8%

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

      2. inv-pow 89.8%

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

      3. *-commutative 89.8%

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

      4. associate-/r* 94.0%

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

   4. Applied egg-rr 94.0%

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

      1. unpow-1 94.0%

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

      2. associate-/l/ 89.8%

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

      3. *-commutative 89.8%

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

   6. Simplified 89.8%

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

   7. Taylor expanded in t around 0 71.4%

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

      1. associate-/r* 77.7%

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

   9. Simplified 77.7%

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

       1. clear-num 77.7%

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

       2. add-cube-cbrt 77.1%

          \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}{\frac{a}{z}} \]

       3. associate-/l* 77.1%

          \[\leadsto x + \color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]

       4. pow2 77.1%

          \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

   11. Applied egg-rr 77.1%

       \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]
   12. Step-by-step derivation

       1. associate-*r/ 77.1%

          \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \sqrt[3]{y - x}}{\frac{a}{z}}} \]

       2. unpow2 77.1%

          \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)} \cdot \sqrt[3]{y - x}}{\frac{a}{z}} \]

       3. rem-3cbrt-lft 77.7%

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

   13. Simplified 77.7%

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

   if 2.24999999999999997e-123 < t < 5.8e52

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. div-sub 76.3%

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

      3. mul-1-neg 76.3%

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

      4. associate-/l* 80.7%

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

      5. distribute-lft-neg-in 80.7%

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

      6. distribute-rgt-in 85.6%

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

      7. sub-neg 85.6%

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

      8. associate-*l/ 78.8%

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

      9. associate-*r/ 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in z around inf 70.1%

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

      1. div-sub 70.0%

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

   8. Simplified 70.0%

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

Alternative 13: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -7 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-131}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -7e+20)
     t_1
     (if (<= t 1.7e-131)
       (+ x (* (- y x) (/ z a)))
       (if (<= t 3e+55) (* z (/ (- y x) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7e+20) {
		tmp = t_1;
	} else if (t <= 1.7e-131) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 3e+55) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-7d+20)) then
        tmp = t_1
    else if (t <= 1.7d-131) then
        tmp = x + ((y - x) * (z / a))
    else if (t <= 3d+55) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7e+20) {
		tmp = t_1;
	} else if (t <= 1.7e-131) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 3e+55) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -7e+20:
		tmp = t_1
	elif t <= 1.7e-131:
		tmp = x + ((y - x) * (z / a))
	elif t <= 3e+55:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -7e+20)
		tmp = t_1;
	elseif (t <= 1.7e-131)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	elseif (t <= 3e+55)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -7e+20)
		tmp = t_1;
	elseif (t <= 1.7e-131)
		tmp = x + ((y - x) * (z / a));
	elseif (t <= 3e+55)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+20], t$95$1, If[LessEqual[t, 1.7e-131], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+55], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7e20 or 3.00000000000000017e55 < t

   1. Initial program 41.0%

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

   3. Taylor expanded in y around 0 57.5%

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

      1. +-commutative 57.5%

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

      2. div-sub 57.5%

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

      3. mul-1-neg 57.5%

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

      4. associate-/l* 65.5%

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

      5. distribute-lft-neg-in 65.5%

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

      6. distribute-rgt-in 65.5%

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

      7. sub-neg 65.5%

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

      8. associate-*l/ 41.0%

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

      9. associate-*r/ 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in x around 0 36.1%

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

      1. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

   if -7e20 < t < 1.69999999999999998e-131

   1. Initial program 89.8%

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

      1. clear-num 89.8%

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

      2. inv-pow 89.8%

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

      3. *-commutative 89.8%

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

      4. associate-/r* 94.0%

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

   4. Applied egg-rr 94.0%

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

      1. unpow-1 94.0%

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

      2. associate-/l/ 89.8%

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

      3. *-commutative 89.8%

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

   6. Simplified 89.8%

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

   7. Taylor expanded in t around 0 71.4%

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

      1. associate-/r* 77.7%

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

   9. Simplified 77.7%

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

       1. associate-/r/ 77.3%

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

       2. clear-num 77.3%

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

   11. Applied egg-rr 77.3%

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

   if 1.69999999999999998e-131 < t < 3.00000000000000017e55

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. div-sub 76.3%

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

      3. mul-1-neg 76.3%

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

      4. associate-/l* 80.7%

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

      5. distribute-lft-neg-in 80.7%

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

      6. distribute-rgt-in 85.6%

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

      7. sub-neg 85.6%

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

      8. associate-*l/ 78.8%

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

      9. associate-*r/ 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in z around inf 70.1%

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

      1. div-sub 70.0%

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

   8. Simplified 70.0%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-131}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-123}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -7.4e+15)
     t_1
     (if (<= t 1.45e-123)
       (+ x (* z (/ (- y x) a)))
       (if (<= t 1.18e+51) (* z (/ (- y x) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7.4e+15) {
		tmp = t_1;
	} else if (t <= 1.45e-123) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 1.18e+51) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-7.4d+15)) then
        tmp = t_1
    else if (t <= 1.45d-123) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 1.18d+51) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7.4e+15) {
		tmp = t_1;
	} else if (t <= 1.45e-123) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 1.18e+51) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -7.4e+15:
		tmp = t_1
	elif t <= 1.45e-123:
		tmp = x + (z * ((y - x) / a))
	elif t <= 1.18e+51:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -7.4e+15)
		tmp = t_1;
	elseif (t <= 1.45e-123)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 1.18e+51)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -7.4e+15)
		tmp = t_1;
	elseif (t <= 1.45e-123)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 1.18e+51)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.4e+15], t$95$1, If[LessEqual[t, 1.45e-123], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.18e+51], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.4e15 or 1.18e51 < t

   1. Initial program 41.0%

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

   3. Taylor expanded in y around 0 57.5%

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

      1. +-commutative 57.5%

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

      2. div-sub 57.5%

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

      3. mul-1-neg 57.5%

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

      4. associate-/l* 65.5%

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

      5. distribute-lft-neg-in 65.5%

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

      6. distribute-rgt-in 65.5%

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

      7. sub-neg 65.5%

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

      8. associate-*l/ 41.0%

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

      9. associate-*r/ 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in x around 0 36.1%

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

      1. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

   if -7.4e15 < t < 1.45000000000000002e-123

   1. Initial program 89.8%

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

   3. Taylor expanded in t around 0 71.4%

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

      1. associate-/l* 75.4%

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

   5. Simplified 75.4%

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

   if 1.45000000000000002e-123 < t < 1.18e51

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. div-sub 76.3%

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

      3. mul-1-neg 76.3%

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

      4. associate-/l* 80.7%

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

      5. distribute-lft-neg-in 80.7%

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

      6. distribute-rgt-in 85.6%

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

      7. sub-neg 85.6%

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

      8. associate-*l/ 78.8%

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

      9. associate-*r/ 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in z around inf 70.1%

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

      1. div-sub 70.0%

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

   8. Simplified 70.0%

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

Alternative 15: 38.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-252}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-93}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.42e+29)
   x
   (if (<= a -8e-252)
     y
     (if (<= a 1.8e-275) (* x (/ z t)) (if (<= a 3.5e-93) y (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.42e+29) {
		tmp = x;
	} else if (a <= -8e-252) {
		tmp = y;
	} else if (a <= 1.8e-275) {
		tmp = x * (z / t);
	} else if (a <= 3.5e-93) {
		tmp = 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 (a <= (-1.42d+29)) then
        tmp = x
    else if (a <= (-8d-252)) then
        tmp = y
    else if (a <= 1.8d-275) then
        tmp = x * (z / t)
    else if (a <= 3.5d-93) then
        tmp = 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 (a <= -1.42e+29) {
		tmp = x;
	} else if (a <= -8e-252) {
		tmp = y;
	} else if (a <= 1.8e-275) {
		tmp = x * (z / t);
	} else if (a <= 3.5e-93) {
		tmp = y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.42e+29:
		tmp = x
	elif a <= -8e-252:
		tmp = y
	elif a <= 1.8e-275:
		tmp = x * (z / t)
	elif a <= 3.5e-93:
		tmp = y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.42e+29)
		tmp = x;
	elseif (a <= -8e-252)
		tmp = y;
	elseif (a <= 1.8e-275)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 3.5e-93)
		tmp = y;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.42e+29)
		tmp = x;
	elseif (a <= -8e-252)
		tmp = y;
	elseif (a <= 1.8e-275)
		tmp = x * (z / t);
	elseif (a <= 3.5e-93)
		tmp = y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.42e+29], x, If[LessEqual[a, -8e-252], y, If[LessEqual[a, 1.8e-275], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-93], y, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.42e29

   1. Initial program 66.1%

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

   3. Taylor expanded in a around inf 44.2%

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

   if -1.42e29 < a < -7.99999999999999954e-252 or 1.79999999999999985e-275 < a < 3.5e-93

   1. Initial program 63.9%

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

   3. Taylor expanded in t around inf 41.0%

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

   if -7.99999999999999954e-252 < a < 1.79999999999999985e-275

   1. Initial program 66.2%

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

   3. Taylor expanded in x around inf 41.8%

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

      1. mul-1-neg 41.8%

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

      2. unsub-neg 41.8%

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

   5. Simplified 41.8%

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

   6. Taylor expanded in a around 0 62.2%

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

   if 3.5e-93 < a

   1. Initial program 66.2%

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

   3. Taylor expanded in y around 0 78.2%

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

      1. +-commutative 78.2%

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

      2. div-sub 78.2%

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

      3. mul-1-neg 78.2%

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

      4. associate-/l* 86.5%

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

      5. distribute-lft-neg-in 86.5%

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

      6. distribute-rgt-in 86.5%

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

      7. sub-neg 86.5%

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

      8. associate-*l/ 66.2%

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

      9. associate-*r/ 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in y around inf 69.5%

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

   7. Taylor expanded in t around inf 45.9%

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

      1. +-commutative 45.9%

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

   9. Simplified 45.9%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-252}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-93}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+166}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+187}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e+166)
   (+ y (/ (- z a) (/ t (- x y))))
   (if (<= t 2.05e+187)
     (- x (* (/ (- y x) (- a t)) (- t z)))
     (+ y (* (/ (- y x) t) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+166) {
		tmp = y + ((z - a) / (t / (x - y)));
	} else if (t <= 2.05e+187) {
		tmp = x - (((y - x) / (a - t)) * (t - z));
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.5d+166)) then
        tmp = y + ((z - a) / (t / (x - y)))
    else if (t <= 2.05d+187) then
        tmp = x - (((y - x) / (a - t)) * (t - z))
    else
        tmp = y + (((y - x) / t) * (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+166) {
		tmp = y + ((z - a) / (t / (x - y)));
	} else if (t <= 2.05e+187) {
		tmp = x - (((y - x) / (a - t)) * (t - z));
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.5e+166:
		tmp = y + ((z - a) / (t / (x - y)))
	elif t <= 2.05e+187:
		tmp = x - (((y - x) / (a - t)) * (t - z))
	else:
		tmp = y + (((y - x) / t) * (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e+166)
		tmp = Float64(y + Float64(Float64(z - a) / Float64(t / Float64(x - y))));
	elseif (t <= 2.05e+187)
		tmp = Float64(x - Float64(Float64(Float64(y - x) / Float64(a - t)) * Float64(t - z)));
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.5e+166)
		tmp = y + ((z - a) / (t / (x - y)));
	elseif (t <= 2.05e+187)
		tmp = x - (((y - x) / (a - t)) * (t - z));
	else
		tmp = y + (((y - x) / t) * (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e+166], N[(y + N[(N[(z - a), $MachinePrecision] / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e+187], N[(x - N[(N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5000000000000003e166

   1. Initial program 33.8%

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

   3. Taylor expanded in t around inf 74.2%

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

      1. associate--l+ 74.2%

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

      2. distribute-lft-out-- 74.2%

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

      3. div-sub 74.2%

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

      4. mul-1-neg 74.2%

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

      5. unsub-neg 74.2%

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

      6. div-sub 74.2%

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

      7. associate-/l* 74.1%

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

      8. associate-/l* 87.1%

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

      9. distribute-rgt-out-- 87.1%

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

   5. Simplified 87.1%

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

      1. *-commutative 87.1%

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

      2. clear-num 87.1%

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

      3. un-div-inv 87.2%

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

   7. Applied egg-rr 87.2%

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

   if -4.5000000000000003e166 < t < 2.05e187

   1. Initial program 75.3%

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

   3. Taylor expanded in y around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. div-sub 76.6%

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

      3. mul-1-neg 76.6%

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

      4. associate-/l* 82.6%

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

      5. distribute-lft-neg-in 82.6%

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

      6. distribute-rgt-in 86.7%

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

      7. sub-neg 86.7%

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

      8. associate-*l/ 75.3%

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

      9. associate-*r/ 84.3%

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

   5. Simplified 84.3%

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

   if 2.05e187 < t

   1. Initial program 25.3%

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

   3. Taylor expanded in t around inf 60.7%

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

      1. associate--l+ 60.7%

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

      2. distribute-lft-out-- 60.7%

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

      3. div-sub 60.7%

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

      4. mul-1-neg 60.7%

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

      5. unsub-neg 60.7%

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

      6. div-sub 60.7%

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

      7. associate-/l* 78.2%

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

      8. associate-/l* 98.0%

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

      9. distribute-rgt-out-- 98.0%

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

   5. Simplified 98.0%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+166}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+187}:\\ \;\;\;\;x - \frac{y - x}{a - t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 77.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-9} \lor \neg \left(a \leq 1200000\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.9e-9) (not (<= a 1200000.0)))
   (+ x (* y (/ (- z t) (- a t))))
   (+ y (/ (- z a) (/ t (- x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.9e-9) || !(a <= 1200000.0)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + ((z - a) / (t / (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 ((a <= (-2.9d-9)) .or. (.not. (a <= 1200000.0d0))) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = y + ((z - a) / (t / (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 ((a <= -2.9e-9) || !(a <= 1200000.0)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + ((z - a) / (t / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.9e-9) or not (a <= 1200000.0):
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = y + ((z - a) / (t / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.9e-9) || !(a <= 1200000.0))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(z - a) / Float64(t / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.9e-9) || ~((a <= 1200000.0)))
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = y + ((z - a) / (t / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.9e-9], N[Not[LessEqual[a, 1200000.0]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(z - a), $MachinePrecision] / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.89999999999999991e-9 or 1.2e6 < a

   1. Initial program 65.8%

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

   3. Taylor expanded in y around inf 63.7%

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

      1. associate-/l* 79.0%

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

   5. Simplified 79.0%

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

   if -2.89999999999999991e-9 < a < 1.2e6

   1. Initial program 64.9%

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

   3. Taylor expanded in t around inf 76.6%

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

      1. associate--l+ 76.6%

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

      2. distribute-lft-out-- 76.6%

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

      3. div-sub 76.6%

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

      4. mul-1-neg 76.6%

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

      5. unsub-neg 76.6%

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

      6. div-sub 76.6%

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

      7. associate-/l* 79.6%

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

      8. associate-/l* 77.2%

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

      9. distribute-rgt-out-- 79.7%

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

   5. Simplified 79.7%

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

      1. *-commutative 79.7%

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

      2. clear-num 79.6%

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

      3. un-div-inv 80.3%

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

   7. Applied egg-rr 80.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-9} \lor \neg \left(a \leq 1200000\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-14} \lor \neg \left(a \leq 19000000\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8e-14) (not (<= a 19000000.0)))
   (+ x (* y (/ (- z t) (- a t))))
   (+ y (* (/ (- y x) t) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8e-14) || !(a <= 19000000.0)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + (((y - x) / t) * (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 ((a <= (-8d-14)) .or. (.not. (a <= 19000000.0d0))) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = y + (((y - x) / t) * (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 ((a <= -8e-14) || !(a <= 19000000.0)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + (((y - x) / t) * (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8e-14) or not (a <= 19000000.0):
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = y + (((y - x) / t) * (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8e-14) || !(a <= 19000000.0))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8e-14) || ~((a <= 19000000.0)))
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = y + (((y - x) / t) * (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8e-14], N[Not[LessEqual[a, 19000000.0]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.99999999999999999e-14 or 1.9e7 < a

   1. Initial program 65.8%

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

   3. Taylor expanded in y around inf 63.7%

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

      1. associate-/l* 79.0%

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

   5. Simplified 79.0%

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

   if -7.99999999999999999e-14 < a < 1.9e7

   1. Initial program 64.9%

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

   3. Taylor expanded in t around inf 76.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 76.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 76.6%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 76.6%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 76.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 76.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 76.6%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 79.6%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 77.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 79.7%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 79.7%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-14} \lor \neg \left(a \leq 19000000\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-14} \lor \neg \left(a \leq 7.5 \cdot 10^{-91}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.8e-14) (not (<= a 7.5e-91)))
   (+ x (* y (/ (- z t) (- a t))))
   (+ y (* z (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e-14) || !(a <= 7.5e-91)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + (z * ((x - y) / 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 <= (-1.8d-14)) .or. (.not. (a <= 7.5d-91))) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = y + (z * ((x - y) / 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 <= -1.8e-14) || !(a <= 7.5e-91)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.8e-14) or not (a <= 7.5e-91):
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.8e-14) || !(a <= 7.5e-91))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.8e-14) || ~((a <= 7.5e-91)))
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.8e-14], N[Not[LessEqual[a, 7.5e-91]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.7999999999999999e-14 or 7.50000000000000051e-91 < a

   1. Initial program 66.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.5%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 74.3%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 74.3%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.7999999999999999e-14 < a < 7.50000000000000051e-91

   1. Initial program 63.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 82.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 82.2%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 82.2%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 82.2%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 82.2%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 82.2%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 82.2%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 85.2%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 82.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 85.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 85.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 76.4%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 79.4%

         \[\leadsto y - \color{blue}{z \cdot \frac{y - x}{t}} \]

   8. Simplified 79.4%

      \[\leadsto y - \color{blue}{z \cdot \frac{y - x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-14} \lor \neg \left(a \leq 7.5 \cdot 10^{-91}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 38.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+75} \lor \neg \left(z \leq 1.62 \cdot 10^{+38}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.15e+245)
   (* x (- 1.0 (/ z a)))
   (if (or (<= z -5.2e+75) (not (<= z 1.62e+38))) (* y (/ z a)) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.15e+245) {
		tmp = x * (1.0 - (z / a));
	} else if ((z <= -5.2e+75) || !(z <= 1.62e+38)) {
		tmp = y * (z / a);
	} 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 <= (-2.15d+245)) then
        tmp = x * (1.0d0 - (z / a))
    else if ((z <= (-5.2d+75)) .or. (.not. (z <= 1.62d+38))) then
        tmp = y * (z / a)
    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 <= -2.15e+245) {
		tmp = x * (1.0 - (z / a));
	} else if ((z <= -5.2e+75) || !(z <= 1.62e+38)) {
		tmp = y * (z / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.15e+245:
		tmp = x * (1.0 - (z / a))
	elif (z <= -5.2e+75) or not (z <= 1.62e+38):
		tmp = y * (z / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.15e+245)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif ((z <= -5.2e+75) || !(z <= 1.62e+38))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.15e+245)
		tmp = x * (1.0 - (z / a));
	elseif ((z <= -5.2e+75) || ~((z <= 1.62e+38)))
		tmp = y * (z / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.15e+245], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -5.2e+75], N[Not[LessEqual[z, 1.62e+38]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1499999999999999e245

   1. Initial program 68.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 67.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 67.2%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z - t}{a - t}\right)}\right) \]

      2. unsub-neg 67.2%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z - t}{a - t}\right)} \]

   5. Simplified 67.2%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z - t}{a - t}\right)} \]

   6. Taylor expanded in t around 0 62.4%

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   if -2.1499999999999999e245 < z < -5.1999999999999997e75 or 1.62000000000000001e38 < z

   1. Initial program 70.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 72.2%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 72.2%

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right) + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right)} \]

      2. div-sub 72.2%

         \[\leadsto x + \left(y \cdot \color{blue}{\frac{z - t}{a - t}} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) \]

      3. mul-1-neg 72.2%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \color{blue}{\left(-\frac{x \cdot \left(z - t\right)}{a - t}\right)}\right) \]

      4. associate-/l* 79.0%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \left(-\color{blue}{x \cdot \frac{z - t}{a - t}}\right)\right) \]

      5. distribute-lft-neg-in 79.0%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \color{blue}{\left(-x\right) \cdot \frac{z - t}{a - t}}\right) \]

      6. distribute-rgt-in 87.7%

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y + \left(-x\right)\right)} \]

      7. sub-neg 87.7%

         \[\leadsto x + \frac{z - t}{a - t} \cdot \color{blue}{\left(y - x\right)} \]

      8. associate-*l/ 70.2%

         \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}} \]

      9. associate-*r/ 85.6%

         \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} \]

   5. Simplified 85.6%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} \]

   6. Taylor expanded in x around 0 45.0%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   7. Step-by-step derivation

      1. associate-/l* 59.1%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   8. Simplified 59.1%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in t around 0 37.8%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   10. Step-by-step derivation

       1. associate-/l* 46.1%

          \[\leadsto \color{blue}{y \cdot \frac{z}{a}} \]

   11. Simplified 46.1%

       \[\leadsto \color{blue}{y \cdot \frac{z}{a}} \]

   if -5.1999999999999997e75 < z < 1.62000000000000001e38

   1. Initial program 62.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 69.8%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 69.8%

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right) + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right)} \]

      2. div-sub 69.8%

         \[\leadsto x + \left(y \cdot \color{blue}{\frac{z - t}{a - t}} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) \]

      3. mul-1-neg 69.8%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \color{blue}{\left(-\frac{x \cdot \left(z - t\right)}{a - t}\right)}\right) \]

      4. associate-/l* 72.8%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \left(-\color{blue}{x \cdot \frac{z - t}{a - t}}\right)\right) \]

      5. distribute-lft-neg-in 72.8%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \color{blue}{\left(-x\right) \cdot \frac{z - t}{a - t}}\right) \]

      6. distribute-rgt-in 72.8%

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y + \left(-x\right)\right)} \]

      7. sub-neg 72.8%

         \[\leadsto x + \frac{z - t}{a - t} \cdot \color{blue}{\left(y - x\right)} \]

      8. associate-*l/ 62.4%

         \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}} \]

      9. associate-*r/ 66.2%

         \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} \]

   5. Simplified 66.2%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} \]

   6. Taylor expanded in y around inf 61.5%

      \[\leadsto x + \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

   7. Taylor expanded in t around inf 45.1%

      \[\leadsto \color{blue}{x + y} \]
   8. Step-by-step derivation

      1. +-commutative 45.1%

         \[\leadsto \color{blue}{y + x} \]

   9. Simplified 45.1%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+75} \lor \neg \left(z \leq 1.62 \cdot 10^{+38}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 69.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-9} \lor \neg \left(a \leq 3550000000\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.5e-9) (not (<= a 3550000000.0)))
   (+ x (* (- y x) (/ z a)))
   (+ y (* z (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.5e-9) || !(a <= 3550000000.0)) {
		tmp = x + ((y - x) * (z / a));
	} else {
		tmp = y + (z * ((x - y) / 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-9)) .or. (.not. (a <= 3550000000.0d0))) then
        tmp = x + ((y - x) * (z / a))
    else
        tmp = y + (z * ((x - y) / 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-9) || !(a <= 3550000000.0)) {
		tmp = x + ((y - x) * (z / a));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.5e-9) or not (a <= 3550000000.0):
		tmp = x + ((y - x) * (z / a))
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.5e-9) || !(a <= 3550000000.0))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.5e-9) || ~((a <= 3550000000.0)))
		tmp = x + ((y - x) * (z / a));
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.5e-9], N[Not[LessEqual[a, 3550000000.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.49999999999999933e-9 or 3.55e9 < a

   1. Initial program 65.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 65.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}}} \]

      2. inv-pow 65.8%

         \[\leadsto x + \color{blue}{{\left(\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}\right)}^{-1}} \]

      3. *-commutative 65.8%

         \[\leadsto x + {\left(\frac{a - t}{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}\right)}^{-1} \]

      4. associate-/r* 88.0%

         \[\leadsto x + {\color{blue}{\left(\frac{\frac{a - t}{z - t}}{y - x}\right)}}^{-1} \]

   4. Applied egg-rr 88.0%

      \[\leadsto x + \color{blue}{{\left(\frac{\frac{a - t}{z - t}}{y - x}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 88.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y - x}}} \]

      2. associate-/l/ 65.8%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}}} \]

      3. *-commutative 65.8%

         \[\leadsto x + \frac{1}{\frac{a - t}{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}} \]

   6. Simplified 65.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a - t}{\left(z - t\right) \cdot \left(y - x\right)}}} \]

   7. Taylor expanded in t around 0 55.4%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{a}{z \cdot \left(y - x\right)}}} \]
   8. Step-by-step derivation

      1. associate-/r* 65.8%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{z}}{y - x}}} \]

   9. Simplified 65.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{z}}{y - x}}} \]
   10. Step-by-step derivation

       1. associate-/r/ 65.8%

          \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z}} \cdot \left(y - x\right)} \]

       2. clear-num 65.9%

          \[\leadsto x + \color{blue}{\frac{z}{a}} \cdot \left(y - x\right) \]

   11. Applied egg-rr 65.9%

       \[\leadsto x + \color{blue}{\frac{z}{a} \cdot \left(y - x\right)} \]

   if -7.49999999999999933e-9 < a < 3.55e9

   1. Initial program 64.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 76.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 76.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 76.6%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 76.6%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 76.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 76.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 76.6%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 79.6%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 77.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 79.7%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 79.7%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 71.3%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 74.3%

         \[\leadsto y - \color{blue}{z \cdot \frac{y - x}{t}} \]

   8. Simplified 74.3%

      \[\leadsto y - \color{blue}{z \cdot \frac{y - x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-9} \lor \neg \left(a \leq 3550000000\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 37.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+23)
   (* x (/ z t))
   (if (<= z 1.15e+38) (+ x y) (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+23) {
		tmp = x * (z / t);
	} else if (z <= 1.15e+38) {
		tmp = x + y;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d+23)) then
        tmp = x * (z / t)
    else if (z <= 1.15d+38) then
        tmp = x + y
    else
        tmp = y * (z / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+23) {
		tmp = x * (z / t);
	} else if (z <= 1.15e+38) {
		tmp = x + y;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+23:
		tmp = x * (z / t)
	elif z <= 1.15e+38:
		tmp = x + y
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+23)
		tmp = Float64(x * Float64(z / t));
	elseif (z <= 1.15e+38)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+23)
		tmp = x * (z / t);
	elseif (z <= 1.15e+38)
		tmp = x + y;
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+23], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+38], N[(x + y), $MachinePrecision], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e23

   1. Initial program 64.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 46.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 46.9%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z - t}{a - t}\right)}\right) \]

      2. unsub-neg 46.9%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z - t}{a - t}\right)} \]

   5. Simplified 46.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z - t}{a - t}\right)} \]

   6. Taylor expanded in a around 0 36.5%

      \[\leadsto x \cdot \color{blue}{\frac{z}{t}} \]

   if -1.15e23 < z < 1.1500000000000001e38

   1. Initial program 63.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 70.2%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 70.2%

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right) + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right)} \]

      2. div-sub 70.2%

         \[\leadsto x + \left(y \cdot \color{blue}{\frac{z - t}{a - t}} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) \]

      3. mul-1-neg 70.2%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \color{blue}{\left(-\frac{x \cdot \left(z - t\right)}{a - t}\right)}\right) \]

      4. associate-/l* 73.4%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \left(-\color{blue}{x \cdot \frac{z - t}{a - t}}\right)\right) \]

      5. distribute-lft-neg-in 73.4%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \color{blue}{\left(-x\right) \cdot \frac{z - t}{a - t}}\right) \]

      6. distribute-rgt-in 73.4%

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y + \left(-x\right)\right)} \]

      7. sub-neg 73.4%

         \[\leadsto x + \frac{z - t}{a - t} \cdot \color{blue}{\left(y - x\right)} \]

      8. associate-*l/ 63.6%

         \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}} \]

      9. associate-*r/ 66.3%

         \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} \]

   5. Simplified 66.3%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} \]

   6. Taylor expanded in y around inf 62.5%

      \[\leadsto x + \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

   7. Taylor expanded in t around inf 46.9%

      \[\leadsto \color{blue}{x + y} \]
   8. Step-by-step derivation

      1. +-commutative 46.9%

         \[\leadsto \color{blue}{y + x} \]

   9. Simplified 46.9%

      \[\leadsto \color{blue}{y + x} \]

   if 1.1500000000000001e38 < z

   1. Initial program 71.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 69.3%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 69.3%

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right) + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right)} \]

      2. div-sub 69.3%

         \[\leadsto x + \left(y \cdot \color{blue}{\frac{z - t}{a - t}} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) \]

      3. mul-1-neg 69.3%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \color{blue}{\left(-\frac{x \cdot \left(z - t\right)}{a - t}\right)}\right) \]

      4. associate-/l* 74.3%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \left(-\color{blue}{x \cdot \frac{z - t}{a - t}}\right)\right) \]

      5. distribute-lft-neg-in 74.3%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \color{blue}{\left(-x\right) \cdot \frac{z - t}{a - t}}\right) \]

      6. distribute-rgt-in 85.5%

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y + \left(-x\right)\right)} \]

      7. sub-neg 85.5%

         \[\leadsto x + \frac{z - t}{a - t} \cdot \color{blue}{\left(y - x\right)} \]

      8. associate-*l/ 71.5%

         \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}} \]

      9. associate-*r/ 87.1%

         \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} \]

   5. Simplified 87.1%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} \]

   6. Taylor expanded in x around 0 44.4%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   7. Step-by-step derivation

      1. associate-/l* 56.8%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   8. Simplified 56.8%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in t around 0 39.2%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   10. Step-by-step derivation

       1. associate-/l* 46.3%

          \[\leadsto \color{blue}{y \cdot \frac{z}{a}} \]

   11. Simplified 46.3%

       \[\leadsto \color{blue}{y \cdot \frac{z}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 38.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.75 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-93}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.75e+30) x (if (<= a 7.2e-93) y (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.75e+30) {
		tmp = x;
	} else if (a <= 7.2e-93) {
		tmp = 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 (a <= (-3.75d+30)) then
        tmp = x
    else if (a <= 7.2d-93) then
        tmp = 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 (a <= -3.75e+30) {
		tmp = x;
	} else if (a <= 7.2e-93) {
		tmp = y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.75e+30:
		tmp = x
	elif a <= 7.2e-93:
		tmp = y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.75e+30)
		tmp = x;
	elseif (a <= 7.2e-93)
		tmp = y;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.75e+30)
		tmp = x;
	elseif (a <= 7.2e-93)
		tmp = y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.75e+30], x, If[LessEqual[a, 7.2e-93], y, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.74999999999999986e30

   1. Initial program 66.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 44.2%

      \[\leadsto \color{blue}{x} \]

   if -3.74999999999999986e30 < a < 7.2000000000000003e-93

   1. Initial program 64.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 33.7%

      \[\leadsto \color{blue}{y} \]

   if 7.2000000000000003e-93 < a

   1. Initial program 66.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 78.2%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 78.2%

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right) + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right)} \]

      2. div-sub 78.2%

         \[\leadsto x + \left(y \cdot \color{blue}{\frac{z - t}{a - t}} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) \]

      3. mul-1-neg 78.2%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \color{blue}{\left(-\frac{x \cdot \left(z - t\right)}{a - t}\right)}\right) \]

      4. associate-/l* 86.5%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \left(-\color{blue}{x \cdot \frac{z - t}{a - t}}\right)\right) \]

      5. distribute-lft-neg-in 86.5%

         \[\leadsto x + \left(y \cdot \frac{z - t}{a - t} + \color{blue}{\left(-x\right) \cdot \frac{z - t}{a - t}}\right) \]

      6. distribute-rgt-in 86.5%

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y + \left(-x\right)\right)} \]

      7. sub-neg 86.5%

         \[\leadsto x + \frac{z - t}{a - t} \cdot \color{blue}{\left(y - x\right)} \]

      8. associate-*l/ 66.2%

         \[\leadsto x + \color{blue}{\frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}} \]

      9. associate-*r/ 81.7%

         \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} \]

   5. Simplified 81.7%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \frac{y - x}{a - t}} \]

   6. Taylor expanded in y around inf 69.5%

      \[\leadsto x + \left(z - t\right) \cdot \color{blue}{\frac{y}{a - t}} \]

   7. Taylor expanded in t around inf 45.9%

      \[\leadsto \color{blue}{x + y} \]
   8. Step-by-step derivation

      1. +-commutative 45.9%

         \[\leadsto \color{blue}{y + x} \]

   9. Simplified 45.9%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.75 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-93}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6400000000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+28) x (if (<= a 6400000000.0) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+28) {
		tmp = x;
	} else if (a <= 6400000000.0) {
		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 <= (-1.9d+28)) then
        tmp = x
    else if (a <= 6400000000.0d0) 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 <= -1.9e+28) {
		tmp = x;
	} else if (a <= 6400000000.0) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+28:
		tmp = x
	elif a <= 6400000000.0:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+28)
		tmp = x;
	elseif (a <= 6400000000.0)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e+28)
		tmp = x;
	elseif (a <= 6400000000.0)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+28], x, If[LessEqual[a, 6400000000.0], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8999999999999999e28 or 6.4e9 < a

   1. Initial program 64.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 43.7%

      \[\leadsto \color{blue}{x} \]

   if -1.8999999999999999e28 < a < 6.4e9

   1. Initial program 65.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 32.7%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 24.6% 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 65.3%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in a around inf 22.6%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024108 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))