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

Percentage Accurate: 68.2% → 91.1%

Time: 26.3s

Alternatives: 25

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-245}:\\ \;\;\;\;x - \frac{x \cdot \left(z - y\right) - t \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \left(\frac{y \cdot \left(x - t\right)}{z} + \frac{\left(t - x\right) \cdot a}{z}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+281}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- x t)) (- z a)))))
   (if (<= t_1 (- INFINITY))
     (+ x (* (- z y) (/ (- x t) (- a z))))
     (if (<= t_1 -1e-245)
       (- x (/ (- (* x (- z y)) (* t (- z y))) (- z a)))
       (if (<= t_1 0.0)
         (+ t (+ (/ (* y (- x t)) z) (/ (* (- t x) a) z)))
         (if (<= t_1 5e+281) t_1 (fma (- y z) (/ (- t x) (- a z)) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (x - t)) / (z - a));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((z - y) * ((x - t) / (a - z)));
	} else if (t_1 <= -1e-245) {
		tmp = x - (((x * (z - y)) - (t * (z - y))) / (z - a));
	} else if (t_1 <= 0.0) {
		tmp = t + (((y * (x - t)) / z) + (((t - x) * a) / z));
	} else if (t_1 <= 5e+281) {
		tmp = t_1;
	} else {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(z - a)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))));
	elseif (t_1 <= -1e-245)
		tmp = Float64(x - Float64(Float64(Float64(x * Float64(z - y)) - Float64(t * Float64(z - y))) / Float64(z - a)));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(y * Float64(x - t)) / z) + Float64(Float64(Float64(t - x) * a) / z)));
	elseif (t_1 <= 5e+281)
		tmp = t_1;
	else
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-245], N[(x - N[(N[(N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+281], t$95$1, N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 40.3%

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

      1. associate-/l* 84.3%

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

   3. Simplified 84.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.9999999999999993e-246

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-lft-in 99.8%

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

   4. Applied egg-rr 99.8%

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

   if -9.9999999999999993e-246 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.4%

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

      1. associate-/l* 3.3%

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

   3. Simplified 3.3%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. mul-1-neg 99.5%

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

      4. associate-*r/ 99.5%

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

      5. mul-1-neg 99.5%

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

   7. Simplified 99.5%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.00000000000000016e281

   1. Initial program 97.0%

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

   if 5.00000000000000016e281 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 42.1%

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

      1. +-commutative 42.1%

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

      2. associate-/l* 78.9%

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

      3. fma-define 79.0%

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

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]
   4. Add Preprocessing
3. Recombined 5 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq -1 \cdot 10^{-245}:\\ \;\;\;\;x - \frac{x \cdot \left(z - y\right) - t \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq 0:\\ \;\;\;\;t + \left(\frac{y \cdot \left(x - t\right)}{z} + \frac{\left(t - x\right) \cdot a}{z}\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-245}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+281}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z)))))
        (t_2 (+ x (/ (* (- y z) (- x t)) (- z a)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-245)
       t_2
       (if (<= t_2 0.0)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_2 5e+281) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double t_2 = x + (((y - z) * (x - t)) / (z - a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-245) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 5e+281) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double t_2 = x + (((y - z) * (x - t)) / (z - a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-245) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 5e+281) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	t_2 = x + (((y - z) * (x - t)) / (z - a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-245:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 5e+281:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(z - a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-245)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 5e+281)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	t_2 = x + (((y - z) * (x - t)) / (z - a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-245)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 5e+281)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-245], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+281], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 5.00000000000000016e281 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 41.2%

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

      1. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.9999999999999993e-246 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.00000000000000016e281

   1. Initial program 98.2%

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

   if -9.9999999999999993e-246 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.4%

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

      1. associate-/l* 3.3%

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

   3. Simplified 3.3%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. associate-*r/ 99.5%

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

      4. div-sub 99.4%

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

      5. distribute-lft-out-- 99.4%

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

      6. associate-*r/ 99.4%

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

      7. mul-1-neg 99.4%

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

      8. unsub-neg 99.4%

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

      9. distribute-rgt-out-- 99.4%

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

   7. Simplified 99.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq -1 \cdot 10^{-245}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-245}:\\ \;\;\;\;x - \frac{x \cdot \left(z - y\right) - t \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+281}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z)))))
        (t_2 (+ x (/ (* (- y z) (- x t)) (- z a)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-245)
       (- x (/ (- (* x (- z y)) (* t (- z y))) (- z a)))
       (if (<= t_2 0.0)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_2 5e+281) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double t_2 = x + (((y - z) * (x - t)) / (z - a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-245) {
		tmp = x - (((x * (z - y)) - (t * (z - y))) / (z - a));
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 5e+281) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double t_2 = x + (((y - z) * (x - t)) / (z - a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-245) {
		tmp = x - (((x * (z - y)) - (t * (z - y))) / (z - a));
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 5e+281) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	t_2 = x + (((y - z) * (x - t)) / (z - a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-245:
		tmp = x - (((x * (z - y)) - (t * (z - y))) / (z - a))
	elif t_2 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 5e+281:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(z - a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-245)
		tmp = Float64(x - Float64(Float64(Float64(x * Float64(z - y)) - Float64(t * Float64(z - y))) / Float64(z - a)));
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 5e+281)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	t_2 = x + (((y - z) * (x - t)) / (z - a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-245)
		tmp = x - (((x * (z - y)) - (t * (z - y))) / (z - a));
	elseif (t_2 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 5e+281)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-245], N[(x - N[(N[(N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+281], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 5.00000000000000016e281 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 41.2%

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

      1. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.9999999999999993e-246

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-lft-in 99.8%

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

   4. Applied egg-rr 99.8%

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

   if -9.9999999999999993e-246 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.4%

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

      1. associate-/l* 3.3%

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

   3. Simplified 3.3%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. associate-*r/ 99.5%

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

      4. div-sub 99.4%

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

      5. distribute-lft-out-- 99.4%

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

      6. associate-*r/ 99.4%

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

      7. mul-1-neg 99.4%

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

      8. unsub-neg 99.4%

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

      9. distribute-rgt-out-- 99.4%

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

   7. Simplified 99.4%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.00000000000000016e281

   1. Initial program 97.0%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq -1 \cdot 10^{-245}:\\ \;\;\;\;x - \frac{x \cdot \left(z - y\right) - t \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-245}:\\ \;\;\;\;x - \frac{x \cdot \left(z - y\right) - t \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \left(\frac{y \cdot \left(x - t\right)}{z} + \frac{\left(t - x\right) \cdot a}{z}\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+281}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z)))))
        (t_2 (+ x (/ (* (- y z) (- x t)) (- z a)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-245)
       (- x (/ (- (* x (- z y)) (* t (- z y))) (- z a)))
       (if (<= t_2 0.0)
         (+ t (+ (/ (* y (- x t)) z) (/ (* (- t x) a) z)))
         (if (<= t_2 5e+281) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double t_2 = x + (((y - z) * (x - t)) / (z - a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-245) {
		tmp = x - (((x * (z - y)) - (t * (z - y))) / (z - a));
	} else if (t_2 <= 0.0) {
		tmp = t + (((y * (x - t)) / z) + (((t - x) * a) / z));
	} else if (t_2 <= 5e+281) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double t_2 = x + (((y - z) * (x - t)) / (z - a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-245) {
		tmp = x - (((x * (z - y)) - (t * (z - y))) / (z - a));
	} else if (t_2 <= 0.0) {
		tmp = t + (((y * (x - t)) / z) + (((t - x) * a) / z));
	} else if (t_2 <= 5e+281) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	t_2 = x + (((y - z) * (x - t)) / (z - a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-245:
		tmp = x - (((x * (z - y)) - (t * (z - y))) / (z - a))
	elif t_2 <= 0.0:
		tmp = t + (((y * (x - t)) / z) + (((t - x) * a) / z))
	elif t_2 <= 5e+281:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(z - a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-245)
		tmp = Float64(x - Float64(Float64(Float64(x * Float64(z - y)) - Float64(t * Float64(z - y))) / Float64(z - a)));
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(y * Float64(x - t)) / z) + Float64(Float64(Float64(t - x) * a) / z)));
	elseif (t_2 <= 5e+281)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	t_2 = x + (((y - z) * (x - t)) / (z - a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-245)
		tmp = x - (((x * (z - y)) - (t * (z - y))) / (z - a));
	elseif (t_2 <= 0.0)
		tmp = t + (((y * (x - t)) / z) + (((t - x) * a) / z));
	elseif (t_2 <= 5e+281)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-245], N[(x - N[(N[(N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+281], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 5.00000000000000016e281 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 41.2%

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

      1. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.9999999999999993e-246

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-lft-in 99.8%

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

   4. Applied egg-rr 99.8%

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

   if -9.9999999999999993e-246 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.4%

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

      1. associate-/l* 3.3%

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

   3. Simplified 3.3%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. mul-1-neg 99.5%

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

      4. associate-*r/ 99.5%

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

      5. mul-1-neg 99.5%

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

   7. Simplified 99.5%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.00000000000000016e281

   1. Initial program 97.0%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq -1 \cdot 10^{-245}:\\ \;\;\;\;x - \frac{x \cdot \left(z - y\right) - t \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq 0:\\ \;\;\;\;t + \left(\frac{y \cdot \left(x - t\right)}{z} + \frac{\left(t - x\right) \cdot a}{z}\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a} \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+163}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -2.3e+163)
     t
     (if (<= z -2.75e+45)
       (* x (/ (- y a) z))
       (if (<= z -7.2e-104)
         t_1
         (if (<= z -1e-272)
           (* y (/ (- t x) a))
           (if (<= z 4.7e-26)
             t_1
             (if (<= z 8.5e+34)
               (* t (/ (- y z) a))
               (if (<= z 9.8e+89) (* t (/ y (- a z))) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.3e+163) {
		tmp = t;
	} else if (z <= -2.75e+45) {
		tmp = x * ((y - a) / z);
	} else if (z <= -7.2e-104) {
		tmp = t_1;
	} else if (z <= -1e-272) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.7e-26) {
		tmp = t_1;
	} else if (z <= 8.5e+34) {
		tmp = t * ((y - z) / a);
	} else if (z <= 9.8e+89) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-2.3d+163)) then
        tmp = t
    else if (z <= (-2.75d+45)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-7.2d-104)) then
        tmp = t_1
    else if (z <= (-1d-272)) then
        tmp = y * ((t - x) / a)
    else if (z <= 4.7d-26) then
        tmp = t_1
    else if (z <= 8.5d+34) then
        tmp = t * ((y - z) / a)
    else if (z <= 9.8d+89) then
        tmp = t * (y / (a - z))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.3e+163) {
		tmp = t;
	} else if (z <= -2.75e+45) {
		tmp = x * ((y - a) / z);
	} else if (z <= -7.2e-104) {
		tmp = t_1;
	} else if (z <= -1e-272) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.7e-26) {
		tmp = t_1;
	} else if (z <= 8.5e+34) {
		tmp = t * ((y - z) / a);
	} else if (z <= 9.8e+89) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -2.3e+163:
		tmp = t
	elif z <= -2.75e+45:
		tmp = x * ((y - a) / z)
	elif z <= -7.2e-104:
		tmp = t_1
	elif z <= -1e-272:
		tmp = y * ((t - x) / a)
	elif z <= 4.7e-26:
		tmp = t_1
	elif z <= 8.5e+34:
		tmp = t * ((y - z) / a)
	elif z <= 9.8e+89:
		tmp = t * (y / (a - z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -2.3e+163)
		tmp = t;
	elseif (z <= -2.75e+45)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -7.2e-104)
		tmp = t_1;
	elseif (z <= -1e-272)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 4.7e-26)
		tmp = t_1;
	elseif (z <= 8.5e+34)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 9.8e+89)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -2.3e+163)
		tmp = t;
	elseif (z <= -2.75e+45)
		tmp = x * ((y - a) / z);
	elseif (z <= -7.2e-104)
		tmp = t_1;
	elseif (z <= -1e-272)
		tmp = y * ((t - x) / a);
	elseif (z <= 4.7e-26)
		tmp = t_1;
	elseif (z <= 8.5e+34)
		tmp = t * ((y - z) / a);
	elseif (z <= 9.8e+89)
		tmp = t * (y / (a - z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+163], t, If[LessEqual[z, -2.75e+45], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.2e-104], t$95$1, If[LessEqual[z, -1e-272], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e-26], t$95$1, If[LessEqual[z, 8.5e+34], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+89], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.30000000000000002e163 or 9.79999999999999992e89 < z

   1. Initial program 35.6%

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

      1. associate-/l* 63.4%

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

   3. Simplified 63.4%

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

   5. Taylor expanded in z around inf 51.0%

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

   if -2.30000000000000002e163 < z < -2.75e45

   1. Initial program 49.3%

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

      1. associate-/l* 68.7%

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

   3. Simplified 68.7%

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

   5. Taylor expanded in x around -inf 39.3%

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

      1. associate-*r* 39.3%

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

      2. neg-mul-1 39.3%

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

   7. Simplified 39.3%

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

   8. Taylor expanded in z around -inf 34.8%

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

      1. associate-/l* 44.4%

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

   10. Simplified 44.4%

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

   if -2.75e45 < z < -7.1999999999999996e-104 or -9.9999999999999993e-273 < z < 4.69999999999999989e-26

   1. Initial program 93.2%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in x around inf 63.4%

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

      1. mul-1-neg 63.4%

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

      2. unsub-neg 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in z around 0 60.7%

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

   if -7.1999999999999996e-104 < z < -9.9999999999999993e-273

   1. Initial program 97.1%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around inf 76.1%

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

      1. div-sub 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in a around inf 64.5%

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

   if 4.69999999999999989e-26 < z < 8.5000000000000003e34

   1. Initial program 81.6%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around 0 54.1%

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

   6. Taylor expanded in a around inf 30.1%

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

      1. associate-/l* 41.7%

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

   8. Simplified 41.7%

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

   if 8.5000000000000003e34 < z < 9.79999999999999992e89

   1. Initial program 76.2%

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

      1. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in y around inf 60.6%

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

      1. div-sub 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in t around inf 38.8%

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

      1. associate-/l* 38.8%

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

   10. Simplified 38.8%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+163}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-132}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- z y) z))))
   (if (<= z -5.8e+150)
     t_2
     (if (<= z -7.2e+21)
       (* y (/ (- x t) z))
       (if (<= z -3.1e-75)
         t_1
         (if (<= z -9.2e-132)
           (/ (* y t) (- a z))
           (if (<= z -6.2e-190)
             t_1
             (if (<= z -1.16e-275)
               (* y (/ (- t x) a))
               (if (<= z 3.9e-26) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((z - y) / z);
	double tmp;
	if (z <= -5.8e+150) {
		tmp = t_2;
	} else if (z <= -7.2e+21) {
		tmp = y * ((x - t) / z);
	} else if (z <= -3.1e-75) {
		tmp = t_1;
	} else if (z <= -9.2e-132) {
		tmp = (y * t) / (a - z);
	} else if (z <= -6.2e-190) {
		tmp = t_1;
	} else if (z <= -1.16e-275) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.9e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = t * ((z - y) / z)
    if (z <= (-5.8d+150)) then
        tmp = t_2
    else if (z <= (-7.2d+21)) then
        tmp = y * ((x - t) / z)
    else if (z <= (-3.1d-75)) then
        tmp = t_1
    else if (z <= (-9.2d-132)) then
        tmp = (y * t) / (a - z)
    else if (z <= (-6.2d-190)) then
        tmp = t_1
    else if (z <= (-1.16d-275)) then
        tmp = y * ((t - x) / a)
    else if (z <= 3.9d-26) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((z - y) / z);
	double tmp;
	if (z <= -5.8e+150) {
		tmp = t_2;
	} else if (z <= -7.2e+21) {
		tmp = y * ((x - t) / z);
	} else if (z <= -3.1e-75) {
		tmp = t_1;
	} else if (z <= -9.2e-132) {
		tmp = (y * t) / (a - z);
	} else if (z <= -6.2e-190) {
		tmp = t_1;
	} else if (z <= -1.16e-275) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.9e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((z - y) / z)
	tmp = 0
	if z <= -5.8e+150:
		tmp = t_2
	elif z <= -7.2e+21:
		tmp = y * ((x - t) / z)
	elif z <= -3.1e-75:
		tmp = t_1
	elif z <= -9.2e-132:
		tmp = (y * t) / (a - z)
	elif z <= -6.2e-190:
		tmp = t_1
	elif z <= -1.16e-275:
		tmp = y * ((t - x) / a)
	elif z <= 3.9e-26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -5.8e+150)
		tmp = t_2;
	elseif (z <= -7.2e+21)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (z <= -3.1e-75)
		tmp = t_1;
	elseif (z <= -9.2e-132)
		tmp = Float64(Float64(y * t) / Float64(a - z));
	elseif (z <= -6.2e-190)
		tmp = t_1;
	elseif (z <= -1.16e-275)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 3.9e-26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((z - y) / z);
	tmp = 0.0;
	if (z <= -5.8e+150)
		tmp = t_2;
	elseif (z <= -7.2e+21)
		tmp = y * ((x - t) / z);
	elseif (z <= -3.1e-75)
		tmp = t_1;
	elseif (z <= -9.2e-132)
		tmp = (y * t) / (a - z);
	elseif (z <= -6.2e-190)
		tmp = t_1;
	elseif (z <= -1.16e-275)
		tmp = y * ((t - x) / a);
	elseif (z <= 3.9e-26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+150], t$95$2, If[LessEqual[z, -7.2e+21], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-75], t$95$1, If[LessEqual[z, -9.2e-132], N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-190], t$95$1, If[LessEqual[z, -1.16e-275], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e-26], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.80000000000000022e150 or 3.89999999999999986e-26 < z

   1. Initial program 47.5%

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

      1. associate-/l* 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in x around 0 40.4%

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

   6. Taylor expanded in a around 0 31.0%

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

      1. mul-1-neg 31.0%

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

      2. associate-/l* 52.5%

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

      3. distribute-rgt-neg-in 52.5%

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

   8. Simplified 52.5%

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

   if -5.80000000000000022e150 < z < -7.2e21

   1. Initial program 54.4%

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

      1. associate-/l* 76.3%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in y around inf 48.3%

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

      1. div-sub 48.3%

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

   7. Simplified 48.3%

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

   8. Taylor expanded in a around 0 48.2%

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

      1. mul-1-neg 48.2%

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

      2. distribute-neg-frac2 48.2%

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

   10. Simplified 48.2%

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

   if -7.2e21 < z < -3.10000000000000007e-75 or -9.20000000000000012e-132 < z < -6.19999999999999987e-190 or -1.15999999999999995e-275 < z < 3.89999999999999986e-26

   1. Initial program 93.4%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in z around 0 62.8%

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

   if -3.10000000000000007e-75 < z < -9.20000000000000012e-132

   1. Initial program 100.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 48.4%

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

      1. div-sub 57.5%

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

   7. Simplified 57.5%

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

   8. Taylor expanded in t around inf 56.8%

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

   if -6.19999999999999987e-190 < z < -1.15999999999999995e-275

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 79.5%

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

      1. div-sub 79.5%

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

   7. Simplified 79.5%

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

   8. Taylor expanded in a around inf 72.8%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-132}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 34.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-154}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-244}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-276}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-300}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.9e-55)
   (* t (/ y (- a z)))
   (if (<= y -4.4e-154)
     x
     (if (<= y -8.5e-244)
       t
       (if (<= y -2.35e-276)
         x
         (if (<= y -5e-300)
           t
           (if (<= y 8e-188) x (if (<= y 1.12e+66) t (* x (/ y z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.9e-55) {
		tmp = t * (y / (a - z));
	} else if (y <= -4.4e-154) {
		tmp = x;
	} else if (y <= -8.5e-244) {
		tmp = t;
	} else if (y <= -2.35e-276) {
		tmp = x;
	} else if (y <= -5e-300) {
		tmp = t;
	} else if (y <= 8e-188) {
		tmp = x;
	} else if (y <= 1.12e+66) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-5.9d-55)) then
        tmp = t * (y / (a - z))
    else if (y <= (-4.4d-154)) then
        tmp = x
    else if (y <= (-8.5d-244)) then
        tmp = t
    else if (y <= (-2.35d-276)) then
        tmp = x
    else if (y <= (-5d-300)) then
        tmp = t
    else if (y <= 8d-188) then
        tmp = x
    else if (y <= 1.12d+66) then
        tmp = t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.9e-55) {
		tmp = t * (y / (a - z));
	} else if (y <= -4.4e-154) {
		tmp = x;
	} else if (y <= -8.5e-244) {
		tmp = t;
	} else if (y <= -2.35e-276) {
		tmp = x;
	} else if (y <= -5e-300) {
		tmp = t;
	} else if (y <= 8e-188) {
		tmp = x;
	} else if (y <= 1.12e+66) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.9e-55:
		tmp = t * (y / (a - z))
	elif y <= -4.4e-154:
		tmp = x
	elif y <= -8.5e-244:
		tmp = t
	elif y <= -2.35e-276:
		tmp = x
	elif y <= -5e-300:
		tmp = t
	elif y <= 8e-188:
		tmp = x
	elif y <= 1.12e+66:
		tmp = t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.9e-55)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (y <= -4.4e-154)
		tmp = x;
	elseif (y <= -8.5e-244)
		tmp = t;
	elseif (y <= -2.35e-276)
		tmp = x;
	elseif (y <= -5e-300)
		tmp = t;
	elseif (y <= 8e-188)
		tmp = x;
	elseif (y <= 1.12e+66)
		tmp = t;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.9e-55)
		tmp = t * (y / (a - z));
	elseif (y <= -4.4e-154)
		tmp = x;
	elseif (y <= -8.5e-244)
		tmp = t;
	elseif (y <= -2.35e-276)
		tmp = x;
	elseif (y <= -5e-300)
		tmp = t;
	elseif (y <= 8e-188)
		tmp = x;
	elseif (y <= 1.12e+66)
		tmp = t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.9e-55], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.4e-154], x, If[LessEqual[y, -8.5e-244], t, If[LessEqual[y, -2.35e-276], x, If[LessEqual[y, -5e-300], t, If[LessEqual[y, 8e-188], x, If[LessEqual[y, 1.12e+66], t, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.8999999999999998e-55

   1. Initial program 69.9%

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

      1. associate-/l* 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in y around inf 67.8%

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

      1. div-sub 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in t around inf 39.0%

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

      1. associate-/l* 49.5%

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

   10. Simplified 49.5%

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

   if -5.8999999999999998e-55 < y < -4.40000000000000015e-154 or -8.4999999999999999e-244 < y < -2.34999999999999982e-276 or -4.99999999999999996e-300 < y < 7.9999999999999996e-188

   1. Initial program 81.8%

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

      1. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in a around inf 51.5%

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

   if -4.40000000000000015e-154 < y < -8.4999999999999999e-244 or -2.34999999999999982e-276 < y < -4.99999999999999996e-300 or 7.9999999999999996e-188 < y < 1.12e66

   1. Initial program 72.8%

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

      1. associate-/l* 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in z around inf 43.2%

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

   if 1.12e66 < y

   1. Initial program 63.0%

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

      1. associate-/l* 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in x around inf 48.0%

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

      1. mul-1-neg 48.0%

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

      2. unsub-neg 48.0%

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

   7. Simplified 48.0%

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

   8. Taylor expanded in a around 0 34.8%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-154}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-244}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-276}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-300}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.000225:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-45}:\\ \;\;\;\;\frac{z \cdot t}{z - a}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.9e+152)
     t_1
     (if (<= z -0.000225)
       (* y (/ (- x t) z))
       (if (<= z -7e-45)
         (/ (* z t) (- z a))
         (if (<= z -8.6e-104)
           t_2
           (if (<= z -2.4e-273)
             (* y (/ (- t x) a))
             (if (<= z 2.7e-26) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.9e+152) {
		tmp = t_1;
	} else if (z <= -0.000225) {
		tmp = y * ((x - t) / z);
	} else if (z <= -7e-45) {
		tmp = (z * t) / (z - a);
	} else if (z <= -8.6e-104) {
		tmp = t_2;
	} else if (z <= -2.4e-273) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.7e-26) {
		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 = t * ((z - y) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-1.9d+152)) then
        tmp = t_1
    else if (z <= (-0.000225d0)) then
        tmp = y * ((x - t) / z)
    else if (z <= (-7d-45)) then
        tmp = (z * t) / (z - a)
    else if (z <= (-8.6d-104)) then
        tmp = t_2
    else if (z <= (-2.4d-273)) then
        tmp = y * ((t - x) / a)
    else if (z <= 2.7d-26) 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 = t * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.9e+152) {
		tmp = t_1;
	} else if (z <= -0.000225) {
		tmp = y * ((x - t) / z);
	} else if (z <= -7e-45) {
		tmp = (z * t) / (z - a);
	} else if (z <= -8.6e-104) {
		tmp = t_2;
	} else if (z <= -2.4e-273) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.7e-26) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -1.9e+152:
		tmp = t_1
	elif z <= -0.000225:
		tmp = y * ((x - t) / z)
	elif z <= -7e-45:
		tmp = (z * t) / (z - a)
	elif z <= -8.6e-104:
		tmp = t_2
	elif z <= -2.4e-273:
		tmp = y * ((t - x) / a)
	elif z <= 2.7e-26:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -1.9e+152)
		tmp = t_1;
	elseif (z <= -0.000225)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (z <= -7e-45)
		tmp = Float64(Float64(z * t) / Float64(z - a));
	elseif (z <= -8.6e-104)
		tmp = t_2;
	elseif (z <= -2.4e-273)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 2.7e-26)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -1.9e+152)
		tmp = t_1;
	elseif (z <= -0.000225)
		tmp = y * ((x - t) / z);
	elseif (z <= -7e-45)
		tmp = (z * t) / (z - a);
	elseif (z <= -8.6e-104)
		tmp = t_2;
	elseif (z <= -2.4e-273)
		tmp = y * ((t - x) / a);
	elseif (z <= 2.7e-26)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+152], t$95$1, If[LessEqual[z, -0.000225], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e-45], N[(N[(z * t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.6e-104], t$95$2, If[LessEqual[z, -2.4e-273], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-26], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.9e152 or 2.69999999999999982e-26 < z

   1. Initial program 47.5%

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

      1. associate-/l* 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in x around 0 40.4%

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

   6. Taylor expanded in a around 0 31.0%

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

      1. mul-1-neg 31.0%

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

      2. associate-/l* 52.5%

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

      3. distribute-rgt-neg-in 52.5%

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

   8. Simplified 52.5%

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

   if -1.9e152 < z < -2.2499999999999999e-4

   1. Initial program 60.8%

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

      1. associate-/l* 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in y around inf 45.2%

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

      1. div-sub 45.2%

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

   7. Simplified 45.2%

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

   8. Taylor expanded in a around 0 42.1%

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

      1. mul-1-neg 42.1%

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

      2. distribute-neg-frac2 42.1%

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

   10. Simplified 42.1%

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

   if -2.2499999999999999e-4 < z < -7e-45

   1. Initial program 83.3%

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

      1. associate-/l* 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in x around 0 66.9%

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

   6. Taylor expanded in y around 0 66.9%

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

      1. associate-*r/ 66.9%

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

      2. associate-*r* 66.9%

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

      3. neg-mul-1 66.9%

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

   8. Simplified 66.9%

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

   if -7e-45 < z < -8.6000000000000002e-104 or -2.39999999999999982e-273 < z < 2.69999999999999982e-26

   1. Initial program 95.4%

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

      1. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in x around inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. unsub-neg 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in z around 0 65.8%

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

   if -8.6000000000000002e-104 < z < -2.39999999999999982e-273

   1. Initial program 97.1%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around inf 76.1%

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

      1. div-sub 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in a around inf 64.5%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -0.000225:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-45}:\\ \;\;\;\;\frac{z \cdot t}{z - a}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{t \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-76}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+87}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (* (- t x) (- a y)) z))))
   (if (<= z -1.35e+47)
     t_1
     (if (<= z -2.3e-125)
       (+ x (/ (* t (- z y)) (- z a)))
       (if (<= z 3.2e-76)
         (+ x (* (- t x) (/ (- y z) a)))
         (if (<= z 3.5e+87)
           (+ x (/ (- y z) (/ (- a z) t)))
           (if (<= z 4.4e+152) t_1 (* t (/ (- y z) (- a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) * (a - y)) / z);
	double tmp;
	if (z <= -1.35e+47) {
		tmp = t_1;
	} else if (z <= -2.3e-125) {
		tmp = x + ((t * (z - y)) / (z - a));
	} else if (z <= 3.2e-76) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else if (z <= 3.5e+87) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (z <= 4.4e+152) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (((t - x) * (a - y)) / z)
    if (z <= (-1.35d+47)) then
        tmp = t_1
    else if (z <= (-2.3d-125)) then
        tmp = x + ((t * (z - y)) / (z - a))
    else if (z <= 3.2d-76) then
        tmp = x + ((t - x) * ((y - z) / a))
    else if (z <= 3.5d+87) then
        tmp = x + ((y - z) / ((a - z) / t))
    else if (z <= 4.4d+152) then
        tmp = t_1
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) * (a - y)) / z);
	double tmp;
	if (z <= -1.35e+47) {
		tmp = t_1;
	} else if (z <= -2.3e-125) {
		tmp = x + ((t * (z - y)) / (z - a));
	} else if (z <= 3.2e-76) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else if (z <= 3.5e+87) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (z <= 4.4e+152) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) * (a - y)) / z)
	tmp = 0
	if z <= -1.35e+47:
		tmp = t_1
	elif z <= -2.3e-125:
		tmp = x + ((t * (z - y)) / (z - a))
	elif z <= 3.2e-76:
		tmp = x + ((t - x) * ((y - z) / a))
	elif z <= 3.5e+87:
		tmp = x + ((y - z) / ((a - z) / t))
	elif z <= 4.4e+152:
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z))
	tmp = 0.0
	if (z <= -1.35e+47)
		tmp = t_1;
	elseif (z <= -2.3e-125)
		tmp = Float64(x + Float64(Float64(t * Float64(z - y)) / Float64(z - a)));
	elseif (z <= 3.2e-76)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	elseif (z <= 3.5e+87)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	elseif (z <= 4.4e+152)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) * (a - y)) / z);
	tmp = 0.0;
	if (z <= -1.35e+47)
		tmp = t_1;
	elseif (z <= -2.3e-125)
		tmp = x + ((t * (z - y)) / (z - a));
	elseif (z <= 3.2e-76)
		tmp = x + ((t - x) * ((y - z) / a));
	elseif (z <= 3.5e+87)
		tmp = x + ((y - z) / ((a - z) / t));
	elseif (z <= 4.4e+152)
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+47], t$95$1, If[LessEqual[z, -2.3e-125], N[(x + N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-76], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+87], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+152], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.34999999999999998e47 or 3.49999999999999986e87 < z < 4.3999999999999996e152

   1. Initial program 33.8%

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

      1. associate-/l* 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in z around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. associate-*r/ 64.9%

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

      3. associate-*r/ 64.9%

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

      4. div-sub 64.9%

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

      5. distribute-lft-out-- 64.9%

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

      6. associate-*r/ 64.9%

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

      7. mul-1-neg 64.9%

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

      8. unsub-neg 64.9%

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

      9. distribute-rgt-out-- 65.1%

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

   7. Simplified 65.1%

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

   if -1.34999999999999998e47 < z < -2.2999999999999999e-125

   1. Initial program 91.1%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

      1. clear-num 94.0%

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

      2. un-div-inv 96.1%

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

   6. Applied egg-rr 96.1%

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

      1. add-sqr-sqrt 60.4%

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

      2. div-inv 60.3%

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

      3. times-frac 60.2%

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

      4. sub-neg 60.2%

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

      5. add-sqr-sqrt 30.1%

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

      6. sqrt-unprod 45.7%

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

      7. sqr-neg 45.7%

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

      8. sqrt-unprod 24.3%

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

      9. add-sqr-sqrt 51.4%

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

   8. Applied egg-rr 51.4%

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

      1. associate-*r/ 51.4%

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

      2. *-commutative 51.4%

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

      3. associate-*r/ 51.4%

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

      4. rem-square-sqrt 79.9%

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

   10. Simplified 79.9%

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

   11. Taylor expanded in t around inf 83.5%

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

   if -2.2999999999999999e-125 < z < 3.1999999999999998e-76

   1. Initial program 95.7%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around inf 89.2%

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

      1. associate-/l* 91.3%

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

   7. Simplified 91.3%

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

   if 3.1999999999999998e-76 < z < 3.49999999999999986e87

   1. Initial program 84.4%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

      1. clear-num 94.3%

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

      2. un-div-inv 94.6%

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

   6. Applied egg-rr 94.6%

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

   7. Taylor expanded in t around inf 79.1%

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

   if 4.3999999999999996e152 < z

   1. Initial program 44.9%

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

      1. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in x around 0 37.1%

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

      1. associate-/l* 73.3%

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

   7. Simplified 73.3%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+47}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{t \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-76}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+87}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+152}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1620000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -1620000.0)
     t_2
     (if (<= t -8.4e-119)
       t_1
       (if (<= t -3.8e-178)
         t_2
         (if (<= t -8.5e-302)
           (* y (/ x (- z a)))
           (if (<= t 2.2e-81) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1620000.0) {
		tmp = t_2;
	} else if (t <= -8.4e-119) {
		tmp = t_1;
	} else if (t <= -3.8e-178) {
		tmp = t_2;
	} else if (t <= -8.5e-302) {
		tmp = y * (x / (z - a));
	} else if (t <= 2.2e-81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-1620000.0d0)) then
        tmp = t_2
    else if (t <= (-8.4d-119)) then
        tmp = t_1
    else if (t <= (-3.8d-178)) then
        tmp = t_2
    else if (t <= (-8.5d-302)) then
        tmp = y * (x / (z - a))
    else if (t <= 2.2d-81) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1620000.0) {
		tmp = t_2;
	} else if (t <= -8.4e-119) {
		tmp = t_1;
	} else if (t <= -3.8e-178) {
		tmp = t_2;
	} else if (t <= -8.5e-302) {
		tmp = y * (x / (z - a));
	} else if (t <= 2.2e-81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -1620000.0:
		tmp = t_2
	elif t <= -8.4e-119:
		tmp = t_1
	elif t <= -3.8e-178:
		tmp = t_2
	elif t <= -8.5e-302:
		tmp = y * (x / (z - a))
	elif t <= 2.2e-81:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -1620000.0)
		tmp = t_2;
	elseif (t <= -8.4e-119)
		tmp = t_1;
	elseif (t <= -3.8e-178)
		tmp = t_2;
	elseif (t <= -8.5e-302)
		tmp = Float64(y * Float64(x / Float64(z - a)));
	elseif (t <= 2.2e-81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -1620000.0)
		tmp = t_2;
	elseif (t <= -8.4e-119)
		tmp = t_1;
	elseif (t <= -3.8e-178)
		tmp = t_2;
	elseif (t <= -8.5e-302)
		tmp = y * (x / (z - a));
	elseif (t <= 2.2e-81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1620000.0], t$95$2, If[LessEqual[t, -8.4e-119], t$95$1, If[LessEqual[t, -3.8e-178], t$95$2, If[LessEqual[t, -8.5e-302], N[(y * N[(x / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-81], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.62e6 or -8.4e-119 < t < -3.80000000000000015e-178 or 2.1999999999999999e-81 < t

   1. Initial program 71.4%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in x around 0 56.0%

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

      1. associate-/l* 74.1%

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

   7. Simplified 74.1%

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

   if -1.62e6 < t < -8.4e-119 or -8.5000000000000005e-302 < t < 2.1999999999999999e-81

   1. Initial program 75.9%

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

      1. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in x around inf 69.5%

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

      1. mul-1-neg 69.5%

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

      2. unsub-neg 69.5%

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

   7. Simplified 69.5%

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

   8. Taylor expanded in z around 0 61.6%

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

   if -3.80000000000000015e-178 < t < -8.5000000000000005e-302

   1. Initial program 59.7%

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

      1. associate-/l* 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in y around inf 80.7%

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

      1. div-sub 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in t around 0 80.7%

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

      1. neg-mul-1 80.7%

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

      2. distribute-neg-frac2 80.7%

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

   10. Simplified 80.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1620000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-178}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -205000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-179}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -205000.0)
     t_2
     (if (<= t -1.1e-119)
       t_1
       (if (<= t -8.2e-179)
         t_2
         (if (<= t -2.95e-297)
           (* y (/ (- t x) (- a z)))
           (if (<= t 6.2e-82) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -205000.0) {
		tmp = t_2;
	} else if (t <= -1.1e-119) {
		tmp = t_1;
	} else if (t <= -8.2e-179) {
		tmp = t_2;
	} else if (t <= -2.95e-297) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 6.2e-82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-205000.0d0)) then
        tmp = t_2
    else if (t <= (-1.1d-119)) then
        tmp = t_1
    else if (t <= (-8.2d-179)) then
        tmp = t_2
    else if (t <= (-2.95d-297)) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= 6.2d-82) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -205000.0) {
		tmp = t_2;
	} else if (t <= -1.1e-119) {
		tmp = t_1;
	} else if (t <= -8.2e-179) {
		tmp = t_2;
	} else if (t <= -2.95e-297) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 6.2e-82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -205000.0:
		tmp = t_2
	elif t <= -1.1e-119:
		tmp = t_1
	elif t <= -8.2e-179:
		tmp = t_2
	elif t <= -2.95e-297:
		tmp = y * ((t - x) / (a - z))
	elif t <= 6.2e-82:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -205000.0)
		tmp = t_2;
	elseif (t <= -1.1e-119)
		tmp = t_1;
	elseif (t <= -8.2e-179)
		tmp = t_2;
	elseif (t <= -2.95e-297)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= 6.2e-82)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -205000.0)
		tmp = t_2;
	elseif (t <= -1.1e-119)
		tmp = t_1;
	elseif (t <= -8.2e-179)
		tmp = t_2;
	elseif (t <= -2.95e-297)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= 6.2e-82)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -205000.0], t$95$2, If[LessEqual[t, -1.1e-119], t$95$1, If[LessEqual[t, -8.2e-179], t$95$2, If[LessEqual[t, -2.95e-297], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-82], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -205000 or -1.1e-119 < t < -8.2e-179 or 6.19999999999999999e-82 < t

   1. Initial program 71.4%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in x around 0 56.0%

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

      1. associate-/l* 74.1%

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

   7. Simplified 74.1%

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

   if -205000 < t < -1.1e-119 or -2.9499999999999999e-297 < t < 6.19999999999999999e-82

   1. Initial program 75.9%

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

      1. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in x around inf 69.5%

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

      1. mul-1-neg 69.5%

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

      2. unsub-neg 69.5%

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

   7. Simplified 69.5%

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

   8. Taylor expanded in z around 0 61.6%

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

   if -8.2e-179 < t < -2.9499999999999999e-297

   1. Initial program 59.7%

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

      1. associate-/l* 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in y around inf 80.7%

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

      1. div-sub 80.7%

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

   7. Simplified 80.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -205000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-179}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+160}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.96 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.6e+160)
   t
   (if (<= z -1.96e+43)
     (* x (/ (- y a) z))
     (if (<= z 4.1e-26)
       (* x (- 1.0 (/ y a)))
       (if (<= z 1.75e+34)
         (* t (/ (- y z) a))
         (if (<= z 8.2e+89) (* t (/ y (- a z))) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.6e+160) {
		tmp = t;
	} else if (z <= -1.96e+43) {
		tmp = x * ((y - a) / z);
	} else if (z <= 4.1e-26) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.75e+34) {
		tmp = t * ((y - z) / a);
	} else if (z <= 8.2e+89) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.6d+160)) then
        tmp = t
    else if (z <= (-1.96d+43)) then
        tmp = x * ((y - a) / z)
    else if (z <= 4.1d-26) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.75d+34) then
        tmp = t * ((y - z) / a)
    else if (z <= 8.2d+89) then
        tmp = t * (y / (a - z))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.6e+160) {
		tmp = t;
	} else if (z <= -1.96e+43) {
		tmp = x * ((y - a) / z);
	} else if (z <= 4.1e-26) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.75e+34) {
		tmp = t * ((y - z) / a);
	} else if (z <= 8.2e+89) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.6e+160:
		tmp = t
	elif z <= -1.96e+43:
		tmp = x * ((y - a) / z)
	elif z <= 4.1e-26:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.75e+34:
		tmp = t * ((y - z) / a)
	elif z <= 8.2e+89:
		tmp = t * (y / (a - z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.6e+160)
		tmp = t;
	elseif (z <= -1.96e+43)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= 4.1e-26)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.75e+34)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 8.2e+89)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.6e+160)
		tmp = t;
	elseif (z <= -1.96e+43)
		tmp = x * ((y - a) / z);
	elseif (z <= 4.1e-26)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.75e+34)
		tmp = t * ((y - z) / a);
	elseif (z <= 8.2e+89)
		tmp = t * (y / (a - z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.6e+160], t, If[LessEqual[z, -1.96e+43], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e-26], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+34], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+89], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.59999999999999978e160 or 8.1999999999999997e89 < z

   1. Initial program 35.6%

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

      1. associate-/l* 63.4%

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

   3. Simplified 63.4%

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

   5. Taylor expanded in z around inf 51.0%

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

   if -8.59999999999999978e160 < z < -1.9600000000000001e43

   1. Initial program 49.3%

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

      1. associate-/l* 68.7%

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

   3. Simplified 68.7%

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

   5. Taylor expanded in x around -inf 39.3%

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

      1. associate-*r* 39.3%

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

      2. neg-mul-1 39.3%

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

   7. Simplified 39.3%

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

   8. Taylor expanded in z around -inf 34.8%

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

      1. associate-/l* 44.4%

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

   10. Simplified 44.4%

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

   if -1.9600000000000001e43 < z < 4.0999999999999999e-26

   1. Initial program 94.2%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

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

   7. Simplified 61.5%

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

   8. Taylor expanded in z around 0 57.9%

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

   if 4.0999999999999999e-26 < z < 1.74999999999999999e34

   1. Initial program 81.6%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around 0 54.1%

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

   6. Taylor expanded in a around inf 30.1%

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

      1. associate-/l* 41.7%

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

   8. Simplified 41.7%

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

   if 1.74999999999999999e34 < z < 8.1999999999999997e89

   1. Initial program 76.2%

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

      1. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in y around inf 60.6%

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

      1. div-sub 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in t around inf 38.8%

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

      1. associate-/l* 38.8%

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

   10. Simplified 38.8%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+160}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.96 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+34}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+34)
   t
   (if (<= z 4.1e-26)
     (* x (- 1.0 (/ y a)))
     (if (<= z 4.5e+35)
       (* t (/ (- y z) a))
       (if (<= z 6.8e+89) (* t (/ y (- a z))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+34) {
		tmp = t;
	} else if (z <= 4.1e-26) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.5e+35) {
		tmp = t * ((y - z) / a);
	} else if (z <= 6.8e+89) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7d+34)) then
        tmp = t
    else if (z <= 4.1d-26) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 4.5d+35) then
        tmp = t * ((y - z) / a)
    else if (z <= 6.8d+89) then
        tmp = t * (y / (a - z))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+34) {
		tmp = t;
	} else if (z <= 4.1e-26) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.5e+35) {
		tmp = t * ((y - z) / a);
	} else if (z <= 6.8e+89) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+34:
		tmp = t
	elif z <= 4.1e-26:
		tmp = x * (1.0 - (y / a))
	elif z <= 4.5e+35:
		tmp = t * ((y - z) / a)
	elif z <= 6.8e+89:
		tmp = t * (y / (a - z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+34)
		tmp = t;
	elseif (z <= 4.1e-26)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 4.5e+35)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 6.8e+89)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7e+34)
		tmp = t;
	elseif (z <= 4.1e-26)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 4.5e+35)
		tmp = t * ((y - z) / a);
	elseif (z <= 6.8e+89)
		tmp = t * (y / (a - z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+34], t, If[LessEqual[z, 4.1e-26], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+35], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+89], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.99999999999999996e34 or 6.8000000000000004e89 < z

   1. Initial program 39.0%

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

      1. associate-/l* 64.9%

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

   3. Simplified 64.9%

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

   5. Taylor expanded in z around inf 44.1%

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

   if -6.99999999999999996e34 < z < 4.0999999999999999e-26

   1. Initial program 94.1%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in x around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. unsub-neg 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in z around 0 58.3%

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

   if 4.0999999999999999e-26 < z < 4.4999999999999997e35

   1. Initial program 81.6%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around 0 54.1%

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

   6. Taylor expanded in a around inf 30.1%

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

      1. associate-/l* 41.7%

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

   8. Simplified 41.7%

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

   if 4.4999999999999997e35 < z < 6.8000000000000004e89

   1. Initial program 76.2%

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

      1. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in y around inf 60.6%

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

      1. div-sub 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in t around inf 38.8%

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

      1. associate-/l* 38.8%

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

   10. Simplified 38.8%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+34}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -1.58 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-278}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- z y) z))))
   (if (<= z -1.58e+38)
     t_2
     (if (<= z -9.5e-104)
       t_1
       (if (<= z -1.8e-278)
         (* y (/ (- t x) a))
         (if (<= z 4.7e-26) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((z - y) / z);
	double tmp;
	if (z <= -1.58e+38) {
		tmp = t_2;
	} else if (z <= -9.5e-104) {
		tmp = t_1;
	} else if (z <= -1.8e-278) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.7e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = t * ((z - y) / z)
    if (z <= (-1.58d+38)) then
        tmp = t_2
    else if (z <= (-9.5d-104)) then
        tmp = t_1
    else if (z <= (-1.8d-278)) then
        tmp = y * ((t - x) / a)
    else if (z <= 4.7d-26) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((z - y) / z);
	double tmp;
	if (z <= -1.58e+38) {
		tmp = t_2;
	} else if (z <= -9.5e-104) {
		tmp = t_1;
	} else if (z <= -1.8e-278) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.7e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((z - y) / z)
	tmp = 0
	if z <= -1.58e+38:
		tmp = t_2
	elif z <= -9.5e-104:
		tmp = t_1
	elif z <= -1.8e-278:
		tmp = y * ((t - x) / a)
	elif z <= 4.7e-26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -1.58e+38)
		tmp = t_2;
	elseif (z <= -9.5e-104)
		tmp = t_1;
	elseif (z <= -1.8e-278)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 4.7e-26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((z - y) / z);
	tmp = 0.0;
	if (z <= -1.58e+38)
		tmp = t_2;
	elseif (z <= -9.5e-104)
		tmp = t_1;
	elseif (z <= -1.8e-278)
		tmp = y * ((t - x) / a);
	elseif (z <= 4.7e-26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.58e+38], t$95$2, If[LessEqual[z, -9.5e-104], t$95$1, If[LessEqual[z, -1.8e-278], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e-26], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.58e38 or 4.69999999999999989e-26 < z

   1. Initial program 48.1%

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

      1. associate-/l* 70.4%

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

   3. Simplified 70.4%

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

   5. Taylor expanded in x around 0 39.6%

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

   6. Taylor expanded in a around 0 29.4%

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

      1. mul-1-neg 29.4%

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

      2. associate-/l* 49.2%

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

      3. distribute-rgt-neg-in 49.2%

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

   8. Simplified 49.2%

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

   if -1.58e38 < z < -9.5000000000000002e-104 or -1.79999999999999998e-278 < z < 4.69999999999999989e-26

   1. Initial program 93.2%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in x around inf 64.0%

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

      1. mul-1-neg 64.0%

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

      2. unsub-neg 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in z around 0 61.2%

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

   if -9.5000000000000002e-104 < z < -1.79999999999999998e-278

   1. Initial program 97.1%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around inf 76.1%

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

      1. div-sub 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in a around inf 64.5%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.58 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-278}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-133} \lor \neg \left(z \leq 9.5 \cdot 10^{-72}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+138)
   (* t (/ (- y z) (- a z)))
   (if (or (<= z -1.45e-133) (not (<= z 9.5e-72)))
     (+ x (/ (- y z) (/ (- a z) t)))
     (+ x (* (- t x) (/ (- y z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+138) {
		tmp = t * ((y - z) / (a - z));
	} else if ((z <= -1.45e-133) || !(z <= 9.5e-72)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = x + ((t - x) * ((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 <= (-9.5d+138)) then
        tmp = t * ((y - z) / (a - z))
    else if ((z <= (-1.45d-133)) .or. (.not. (z <= 9.5d-72))) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = x + ((t - x) * ((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 <= -9.5e+138) {
		tmp = t * ((y - z) / (a - z));
	} else if ((z <= -1.45e-133) || !(z <= 9.5e-72)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = x + ((t - x) * ((y - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e+138:
		tmp = t * ((y - z) / (a - z))
	elif (z <= -1.45e-133) or not (z <= 9.5e-72):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = x + ((t - x) * ((y - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+138)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif ((z <= -1.45e-133) || !(z <= 9.5e-72))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e+138)
		tmp = t * ((y - z) / (a - z));
	elseif ((z <= -1.45e-133) || ~((z <= 9.5e-72)))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = x + ((t - x) * ((y - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+138], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.45e-133], N[Not[LessEqual[z, 9.5e-72]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.49999999999999998e138

   1. Initial program 26.6%

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

      1. associate-/l* 53.0%

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

   3. Simplified 53.0%

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

   5. Taylor expanded in x around 0 32.6%

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

      1. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

   if -9.49999999999999998e138 < z < -1.4499999999999999e-133 or 9.4999999999999998e-72 < z

   1. Initial program 68.1%

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

      1. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

      1. clear-num 83.3%

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

      2. un-div-inv 84.0%

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

   6. Applied egg-rr 84.0%

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

   7. Taylor expanded in t around inf 72.1%

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

   if -1.4499999999999999e-133 < z < 9.4999999999999998e-72

   1. Initial program 95.7%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around inf 89.2%

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

      1. associate-/l* 91.3%

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

   7. Simplified 91.3%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-133} \lor \neg \left(z \leq 9.5 \cdot 10^{-72}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 70.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-126}:\\ \;\;\;\;x + \frac{t \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;z \leq 0.92:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.15e+49)
     t_1
     (if (<= z -1.5e-126)
       (+ x (/ (* t (- z y)) (- z a)))
       (if (<= z 0.92) (+ x (* (- t x) (/ (- y z) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.15e+49) {
		tmp = t_1;
	} else if (z <= -1.5e-126) {
		tmp = x + ((t * (z - y)) / (z - a));
	} else if (z <= 0.92) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-2.15d+49)) then
        tmp = t_1
    else if (z <= (-1.5d-126)) then
        tmp = x + ((t * (z - y)) / (z - a))
    else if (z <= 0.92d0) then
        tmp = x + ((t - x) * ((y - z) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.15e+49) {
		tmp = t_1;
	} else if (z <= -1.5e-126) {
		tmp = x + ((t * (z - y)) / (z - a));
	} else if (z <= 0.92) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -2.15e+49:
		tmp = t_1
	elif z <= -1.5e-126:
		tmp = x + ((t * (z - y)) / (z - a))
	elif z <= 0.92:
		tmp = x + ((t - x) * ((y - z) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.15e+49)
		tmp = t_1;
	elseif (z <= -1.5e-126)
		tmp = Float64(x + Float64(Float64(t * Float64(z - y)) / Float64(z - a)));
	elseif (z <= 0.92)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -2.15e+49)
		tmp = t_1;
	elseif (z <= -1.5e-126)
		tmp = x + ((t * (z - y)) / (z - a));
	elseif (z <= 0.92)
		tmp = x + ((t - x) * ((y - z) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e+49], t$95$1, If[LessEqual[z, -1.5e-126], N[(x + N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.92], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.15e49 or 0.92000000000000004 < z

   1. Initial program 46.6%

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

      1. associate-/l* 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in x around 0 38.5%

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

      1. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

   if -2.15e49 < z < -1.5000000000000001e-126

   1. Initial program 88.7%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

      1. clear-num 94.2%

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

      2. un-div-inv 96.2%

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

   6. Applied egg-rr 96.2%

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

      1. add-sqr-sqrt 58.6%

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

      2. div-inv 58.5%

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

      3. times-frac 58.4%

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

      4. sub-neg 58.4%

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

      5. add-sqr-sqrt 29.2%

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

      6. sqrt-unprod 44.3%

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

      7. sqr-neg 44.3%

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

      8. sqrt-unprod 23.6%

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

      9. add-sqr-sqrt 49.9%

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

   8. Applied egg-rr 49.9%

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

      1. associate-*r/ 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-*r/ 49.9%

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

      4. rem-square-sqrt 77.5%

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

   10. Simplified 77.5%

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

   11. Taylor expanded in t around inf 81.3%

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

   if -1.5000000000000001e-126 < z < 0.92000000000000004

   1. Initial program 94.5%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in a around inf 86.1%

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

      1. associate-/l* 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-126}:\\ \;\;\;\;x + \frac{t \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;z \leq 0.92:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 69.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+34} \lor \neg \left(z \leq 0.92\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e+34) (not (<= z 0.92)))
   (* t (/ (- y z) (- a z)))
   (+ x (* (- t x) (/ (- y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+34) || !(z <= 0.92)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) * ((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 <= (-9d+34)) .or. (.not. (z <= 0.92d0))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - x) * ((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 <= -9e+34) || !(z <= 0.92)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) * ((y - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e+34) or not (z <= 0.92):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) * ((y - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e+34) || !(z <= 0.92))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9e+34) || ~((z <= 0.92)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) * ((y - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e+34], N[Not[LessEqual[z, 0.92]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.0000000000000001e34 or 0.92000000000000004 < z

   1. Initial program 46.7%

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

      1. associate-/l* 69.2%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in x around 0 38.7%

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

      1. associate-/l* 63.2%

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

   7. Simplified 63.2%

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

   if -9.0000000000000001e34 < z < 0.92000000000000004

   1. Initial program 93.7%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in a around inf 80.7%

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

      1. associate-/l* 84.2%

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

   7. Simplified 84.2%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+34} \lor \neg \left(z \leq 0.92\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 31.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+188}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -100000000000:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.5e+188)
   (* (- y) (/ t z))
   (if (<= y -100000000000.0)
     (/ t (/ a y))
     (if (<= y 9.2e+66) t (* x (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.5e+188) {
		tmp = -y * (t / z);
	} else if (y <= -100000000000.0) {
		tmp = t / (a / y);
	} else if (y <= 9.2e+66) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.5d+188)) then
        tmp = -y * (t / z)
    else if (y <= (-100000000000.0d0)) then
        tmp = t / (a / y)
    else if (y <= 9.2d+66) then
        tmp = t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.5e+188) {
		tmp = -y * (t / z);
	} else if (y <= -100000000000.0) {
		tmp = t / (a / y);
	} else if (y <= 9.2e+66) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.5e+188:
		tmp = -y * (t / z)
	elif y <= -100000000000.0:
		tmp = t / (a / y)
	elif y <= 9.2e+66:
		tmp = t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.5e+188)
		tmp = Float64(Float64(-y) * Float64(t / z));
	elseif (y <= -100000000000.0)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 9.2e+66)
		tmp = t;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.5e+188)
		tmp = -y * (t / z);
	elseif (y <= -100000000000.0)
		tmp = t / (a / y);
	elseif (y <= 9.2e+66)
		tmp = t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.5e+188], N[((-y) * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -100000000000.0], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e+66], t, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.5000000000000001e188

   1. Initial program 62.6%

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

      1. associate-/l* 84.7%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in y around inf 75.8%

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

      1. div-sub 79.4%

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

   7. Simplified 79.4%

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

   8. Taylor expanded in a around 0 55.8%

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

      1. mul-1-neg 55.8%

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

      2. distribute-neg-frac2 55.8%

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

   10. Simplified 55.8%

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

   11. Taylor expanded in t around inf 51.7%

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

       1. associate-*r/ 51.7%

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

       2. neg-mul-1 51.7%

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

   13. Simplified 51.7%

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

   if -4.5000000000000001e188 < y < -1e11

   1. Initial program 79.9%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in x around 0 46.2%

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

   6. Taylor expanded in z around 0 34.4%

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

      1. associate-/l* 37.0%

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

   8. Simplified 37.0%

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

      1. clear-num 37.0%

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

      2. un-div-inv 37.0%

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

   10. Applied egg-rr 37.0%

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

   if -1e11 < y < 9.2e66

   1. Initial program 74.9%

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

      1. associate-/l* 80.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in z around inf 34.4%

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

   if 9.2e66 < y

   1. Initial program 63.0%

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

      1. associate-/l* 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in x around inf 48.0%

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

      1. mul-1-neg 48.0%

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

      2. unsub-neg 48.0%

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

   7. Simplified 48.0%

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

   8. Taylor expanded in a around 0 34.8%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+188}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -100000000000:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-45} \lor \neg \left(z \leq 4.4 \cdot 10^{-26}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e-45) (not (<= z 4.4e-26)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ (* y (- t x)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-45) || !(z <= 4.4e-26)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((y * (t - x)) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.7d-45)) .or. (.not. (z <= 4.4d-26))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((y * (t - x)) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-45) || !(z <= 4.4e-26)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((y * (t - x)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e-45) or not (z <= 4.4e-26):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((y * (t - x)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e-45) || !(z <= 4.4e-26))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e-45) || ~((z <= 4.4e-26)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((y * (t - x)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e-45], N[Not[LessEqual[z, 4.4e-26]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999985e-45 or 4.4000000000000002e-26 < z

   1. Initial program 51.6%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in x around 0 40.5%

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

      1. associate-/l* 62.1%

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

   7. Simplified 62.1%

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

   if -2.69999999999999985e-45 < z < 4.4000000000000002e-26

   1. Initial program 95.9%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in z around 0 81.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-45} \lor \neg \left(z \leq 4.4 \cdot 10^{-26}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9000000000000 \lor \neg \left(y \leq 2.55 \cdot 10^{+130}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -9000000000000.0) (not (<= y 2.55e+130))) (* t (/ y a)) t))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9000000000000.0) || !(y <= 2.55e+130)) {
		tmp = t * (y / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-9000000000000.0d0)) .or. (.not. (y <= 2.55d+130))) then
        tmp = t * (y / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9000000000000.0) || !(y <= 2.55e+130)) {
		tmp = t * (y / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -9000000000000.0) or not (y <= 2.55e+130):
		tmp = t * (y / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -9000000000000.0) || !(y <= 2.55e+130))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -9000000000000.0) || ~((y <= 2.55e+130)))
		tmp = t * (y / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -9000000000000.0], N[Not[LessEqual[y, 2.55e+130]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -9e12 or 2.5499999999999998e130 < y

   1. Initial program 72.0%

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

      1. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around 0 40.4%

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

   6. Taylor expanded in z around 0 30.0%

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

      1. associate-/l* 30.8%

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

   8. Simplified 30.8%

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

   if -9e12 < y < 2.5499999999999998e130

   1. Initial program 71.8%

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

      1. associate-/l* 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in z around inf 33.4%

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

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9000000000000 \lor \neg \left(y \leq 2.55 \cdot 10^{+130}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 32.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -32000000000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -32000000000.0) (* t (/ y a)) (if (<= y 8.2e+65) t (* x (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -32000000000.0) {
		tmp = t * (y / a);
	} else if (y <= 8.2e+65) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-32000000000.0d0)) then
        tmp = t * (y / a)
    else if (y <= 8.2d+65) then
        tmp = t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -32000000000.0) {
		tmp = t * (y / a);
	} else if (y <= 8.2e+65) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -32000000000.0:
		tmp = t * (y / a)
	elif y <= 8.2e+65:
		tmp = t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -32000000000.0)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 8.2e+65)
		tmp = t;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -32000000000.0)
		tmp = t * (y / a);
	elseif (y <= 8.2e+65)
		tmp = t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -32000000000.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+65], t, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2e10

   1. Initial program 72.1%

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

      1. associate-/l* 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in x around 0 45.8%

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

   6. Taylor expanded in z around 0 32.6%

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

      1. associate-/l* 35.2%

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

   8. Simplified 35.2%

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

   if -3.2e10 < y < 8.2000000000000003e65

   1. Initial program 74.9%

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

      1. associate-/l* 80.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in z around inf 34.4%

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

   if 8.2000000000000003e65 < y

   1. Initial program 63.0%

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

      1. associate-/l* 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in x around inf 48.0%

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

      1. mul-1-neg 48.0%

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

      2. unsub-neg 48.0%

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

   7. Simplified 48.0%

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

   8. Taylor expanded in a around 0 34.8%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -32000000000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 32.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -52000000000000:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+65}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -52000000000000.0)
   (/ t (/ a y))
   (if (<= y 6.5e+65) t (* x (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -52000000000000.0) {
		tmp = t / (a / y);
	} else if (y <= 6.5e+65) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-52000000000000.0d0)) then
        tmp = t / (a / y)
    else if (y <= 6.5d+65) then
        tmp = t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -52000000000000.0) {
		tmp = t / (a / y);
	} else if (y <= 6.5e+65) {
		tmp = t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -52000000000000.0:
		tmp = t / (a / y)
	elif y <= 6.5e+65:
		tmp = t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -52000000000000.0)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 6.5e+65)
		tmp = t;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -52000000000000.0)
		tmp = t / (a / y);
	elseif (y <= 6.5e+65)
		tmp = t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -52000000000000.0], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+65], t, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2e13

   1. Initial program 72.1%

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

      1. associate-/l* 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in x around 0 45.8%

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

   6. Taylor expanded in z around 0 32.6%

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

      1. associate-/l* 35.2%

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

   8. Simplified 35.2%

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

      1. clear-num 35.2%

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

      2. un-div-inv 35.2%

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

   10. Applied egg-rr 35.2%

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

   if -5.2e13 < y < 6.5000000000000003e65

   1. Initial program 74.9%

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

      1. associate-/l* 80.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in z around inf 34.4%

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

   if 6.5000000000000003e65 < y

   1. Initial program 63.0%

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

      1. associate-/l* 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in x around inf 48.0%

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

      1. mul-1-neg 48.0%

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

      2. unsub-neg 48.0%

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

   7. Simplified 48.0%

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

   8. Taylor expanded in a around 0 34.8%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -52000000000000:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+65}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 80.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.8%

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

   1. associate-/l* 81.9%

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

3. Simplified 81.9%

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

5. Final simplification 81.9%

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

Alternative 24: 32.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 105:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.9e-29) t (if (<= t 105.0) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e-29) {
		tmp = t;
	} else if (t <= 105.0) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.9d-29)) then
        tmp = t
    else if (t <= 105.0d0) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e-29) {
		tmp = t;
	} else if (t <= 105.0) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.9e-29:
		tmp = t
	elif t <= 105.0:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.9e-29)
		tmp = t;
	elseif (t <= 105.0)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.9e-29)
		tmp = t;
	elseif (t <= 105.0)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.9e-29], t, If[LessEqual[t, 105.0], x, t]]

Derivation

1. Split input into 2 regimes

2. if t < -1.89999999999999988e-29 or 105 < t

   1. Initial program 70.3%

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

      1. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in z around inf 31.4%

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

   if -1.89999999999999988e-29 < t < 105

   1. Initial program 73.7%

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

      1. associate-/l* 73.4%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in a around inf 29.5%

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

4. Final simplification 30.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 105:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 25.4% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 71.8%

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

   1. associate-/l* 81.9%

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

3. Simplified 81.9%

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

5. Taylor expanded in z around inf 22.3%

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

6. Final simplification 22.3%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024046 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))