Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.3% → 91.9%

Time: 16.1s

Alternatives: 19

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 80.3% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 91.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;x + \frac{-1}{\frac{a - z}{\left(y - z\right) \cdot \left(x - t\right)}}\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-185}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t\_1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 (- INFINITY))
     (+ x (/ -1.0 (/ (- a z) (* (- y z) (- x t)))))
     (if (<= t_2 -2e-185)
       t_2
       (if (<= t_2 0.0)
         (- t (* (- t x) (/ (- y a) z)))
         (fma (- y z) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = x + (-1.0 / ((a - z) / ((y - z) * (x - t))));
	} else if (t_2 <= -2e-185) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t - ((t - x) * ((y - a) / z));
	} else {
		tmp = fma((y - z), t_1, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(a - z) / Float64(Float64(y - z) * Float64(x - t)))));
	elseif (t_2 <= -2e-185)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(Float64(t - x) * Float64(Float64(y - a) / z)));
	else
		tmp = fma(Float64(y - z), t_1, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(x + N[(-1.0 / N[(N[(a - z), $MachinePrecision] / N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-185], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t - N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 76.5%

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

      1. associate-*r/ 96.3%

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

      2. clear-num 96.4%

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

   4. Applied egg-rr 96.4%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-185

   1. Initial program 95.5%

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

   if -2e-185 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 7.1%

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

   3. Taylor expanded in z around inf 81.1%

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

      1. associate--l+ 81.1%

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

      2. distribute-lft-out-- 81.1%

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

      3. div-sub 81.1%

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

      4. mul-1-neg 81.1%

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

      5. unsub-neg 81.1%

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

      6. distribute-rgt-out-- 81.3%

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

      7. associate-/l* 95.0%

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

   5. Simplified 95.0%

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

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

   1. Initial program 90.1%

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

      1. +-commutative 90.1%

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

      2. fma-define 90.2%

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

   3. Simplified 90.2%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{-1}{\frac{a - z}{\left(y - z\right) \cdot \left(x - t\right)}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-185}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{-1}{\frac{a - z}{\left(y - z\right) \cdot \left(x - t\right)}}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-185} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ -1.0 (/ (- a z) (* (- y z) (- x t)))))
     (if (or (<= t_1 -2e-185) (not (<= t_1 0.0)))
       t_1
       (- t (* (- t x) (/ (- y a) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (-1.0 / ((a - z) / ((y - z) * (x - t))));
	} else if ((t_1 <= -2e-185) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) * ((y - a) / z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (-1.0 / ((a - z) / ((y - z) * (x - t))));
	} else if ((t_1 <= -2e-185) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) * ((y - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (-1.0 / ((a - z) / ((y - z) * (x - t))))
	elif (t_1 <= -2e-185) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t - ((t - x) * ((y - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(a - z) / Float64(Float64(y - z) * Float64(x - t)))));
	elseif ((t_1 <= -2e-185) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(t - x) * Float64(Float64(y - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (-1.0 / ((a - z) / ((y - z) * (x - t))));
	elseif ((t_1 <= -2e-185) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t - ((t - x) * ((y - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(-1.0 / N[(N[(a - z), $MachinePrecision] / N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-185], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t - N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 76.5%

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

      1. associate-*r/ 96.3%

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

      2. clear-num 96.4%

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

   4. Applied egg-rr 96.4%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-185 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.6%

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

   if -2e-185 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 7.1%

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

   3. Taylor expanded in z around inf 81.1%

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

      1. associate--l+ 81.1%

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

      2. distribute-lft-out-- 81.1%

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

      3. div-sub 81.1%

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

      4. mul-1-neg 81.1%

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

      5. unsub-neg 81.1%

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

      6. distribute-rgt-out-- 81.3%

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

      7. associate-/l* 95.0%

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

   5. Simplified 95.0%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{-1}{\frac{a - z}{\left(y - z\right) \cdot \left(x - t\right)}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-185} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := t - a \cdot \frac{x}{z}\\ t_3 := x - y \cdot \frac{x - t}{a}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+42}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-216}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-236}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 5800000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+136} \lor \neg \left(a \leq 7.1 \cdot 10^{+152}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z))))
        (t_2 (- t (* a (/ x z))))
        (t_3 (- x (* y (/ (- x t) a)))))
   (if (<= a -5.2e+42)
     t_3
     (if (<= a -2.5e-216)
       (* (- y z) (/ t (- a z)))
       (if (<= a -4.9e-236)
         (/ (* x y) z)
         (if (<= a 3.8e-104)
           t_1
           (if (<= a 5.2e-31)
             t_2
             (if (<= a 5800000.0)
               t_1
               (if (or (<= a 4.3e+136) (not (<= a 7.1e+152))) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = t - (a * (x / z));
	double t_3 = x - (y * ((x - t) / a));
	double tmp;
	if (a <= -5.2e+42) {
		tmp = t_3;
	} else if (a <= -2.5e-216) {
		tmp = (y - z) * (t / (a - z));
	} else if (a <= -4.9e-236) {
		tmp = (x * y) / z;
	} else if (a <= 3.8e-104) {
		tmp = t_1;
	} else if (a <= 5.2e-31) {
		tmp = t_2;
	} else if (a <= 5800000.0) {
		tmp = t_1;
	} else if ((a <= 4.3e+136) || !(a <= 7.1e+152)) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    t_2 = t - (a * (x / z))
    t_3 = x - (y * ((x - t) / a))
    if (a <= (-5.2d+42)) then
        tmp = t_3
    else if (a <= (-2.5d-216)) then
        tmp = (y - z) * (t / (a - z))
    else if (a <= (-4.9d-236)) then
        tmp = (x * y) / z
    else if (a <= 3.8d-104) then
        tmp = t_1
    else if (a <= 5.2d-31) then
        tmp = t_2
    else if (a <= 5800000.0d0) then
        tmp = t_1
    else if ((a <= 4.3d+136) .or. (.not. (a <= 7.1d+152))) then
        tmp = t_3
    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 = (t - x) * (y / (a - z));
	double t_2 = t - (a * (x / z));
	double t_3 = x - (y * ((x - t) / a));
	double tmp;
	if (a <= -5.2e+42) {
		tmp = t_3;
	} else if (a <= -2.5e-216) {
		tmp = (y - z) * (t / (a - z));
	} else if (a <= -4.9e-236) {
		tmp = (x * y) / z;
	} else if (a <= 3.8e-104) {
		tmp = t_1;
	} else if (a <= 5.2e-31) {
		tmp = t_2;
	} else if (a <= 5800000.0) {
		tmp = t_1;
	} else if ((a <= 4.3e+136) || !(a <= 7.1e+152)) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	t_2 = t - (a * (x / z))
	t_3 = x - (y * ((x - t) / a))
	tmp = 0
	if a <= -5.2e+42:
		tmp = t_3
	elif a <= -2.5e-216:
		tmp = (y - z) * (t / (a - z))
	elif a <= -4.9e-236:
		tmp = (x * y) / z
	elif a <= 3.8e-104:
		tmp = t_1
	elif a <= 5.2e-31:
		tmp = t_2
	elif a <= 5800000.0:
		tmp = t_1
	elif (a <= 4.3e+136) or not (a <= 7.1e+152):
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_2 = Float64(t - Float64(a * Float64(x / z)))
	t_3 = Float64(x - Float64(y * Float64(Float64(x - t) / a)))
	tmp = 0.0
	if (a <= -5.2e+42)
		tmp = t_3;
	elseif (a <= -2.5e-216)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (a <= -4.9e-236)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 3.8e-104)
		tmp = t_1;
	elseif (a <= 5.2e-31)
		tmp = t_2;
	elseif (a <= 5800000.0)
		tmp = t_1;
	elseif ((a <= 4.3e+136) || !(a <= 7.1e+152))
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	t_2 = t - (a * (x / z));
	t_3 = x - (y * ((x - t) / a));
	tmp = 0.0;
	if (a <= -5.2e+42)
		tmp = t_3;
	elseif (a <= -2.5e-216)
		tmp = (y - z) * (t / (a - z));
	elseif (a <= -4.9e-236)
		tmp = (x * y) / z;
	elseif (a <= 3.8e-104)
		tmp = t_1;
	elseif (a <= 5.2e-31)
		tmp = t_2;
	elseif (a <= 5800000.0)
		tmp = t_1;
	elseif ((a <= 4.3e+136) || ~((a <= 7.1e+152)))
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e+42], t$95$3, If[LessEqual[a, -2.5e-216], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.9e-236], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 3.8e-104], t$95$1, If[LessEqual[a, 5.2e-31], t$95$2, If[LessEqual[a, 5800000.0], t$95$1, If[Or[LessEqual[a, 4.3e+136], N[Not[LessEqual[a, 7.1e+152]], $MachinePrecision]], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.1999999999999998e42 or 5.8e6 < a < 4.2999999999999999e136 or 7.10000000000000017e152 < a

   1. Initial program 87.3%

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

   3. Taylor expanded in z around 0 63.9%

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

      1. associate-/l* 73.7%

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

   5. Simplified 73.7%

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

   if -5.1999999999999998e42 < a < -2.5000000000000001e-216

   1. Initial program 78.9%

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

   3. Taylor expanded in x around 0 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-/l* 66.1%

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

   5. Simplified 66.1%

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

   if -2.5000000000000001e-216 < a < -4.8999999999999997e-236

   1. Initial program 41.5%

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

   3. Taylor expanded in y around -inf 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

      3. distribute-lft-neg-out 100.0%

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

      4. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in a around 0 100.0%

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

   if -4.8999999999999997e-236 < a < 3.8000000000000001e-104 or 5.19999999999999991e-31 < a < 5.8e6

   1. Initial program 67.3%

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

      1. clear-num 66.6%

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

      2. un-div-inv 66.5%

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

   4. Applied egg-rr 66.5%

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

   5. Taylor expanded in y around inf 59.2%

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

      1. div-sub 62.6%

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

      2. associate-*r/ 66.9%

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

      3. associate-*l/ 72.7%

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

   7. Simplified 72.7%

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

   if 3.8000000000000001e-104 < a < 5.19999999999999991e-31 or 4.2999999999999999e136 < a < 7.10000000000000017e152

   1. Initial program 52.7%

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

   3. Taylor expanded in z around -inf 62.2%

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

   4. Taylor expanded in a around inf 65.3%

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

      1. associate-/l* 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in x around inf 65.3%

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

      1. associate-/l* 66.8%

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

   9. Simplified 66.8%

      \[\leadsto t + -1 \cdot \color{blue}{\left(a \cdot \frac{x}{z}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+42}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-216}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-236}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-104}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-31}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 5800000:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+136} \lor \neg \left(a \leq 7.1 \cdot 10^{+152}\right):\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := t - a \cdot \frac{x}{z}\\ t_3 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -6.6 \cdot 10^{+42}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-216}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-236}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 150000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+136}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq 7.1 \cdot 10^{+152}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z))))
        (t_2 (- t (* a (/ x z))))
        (t_3 (+ x (* (- t x) (/ y a)))))
   (if (<= a -6.6e+42)
     t_3
     (if (<= a -2.55e-216)
       (* (- y z) (/ t (- a z)))
       (if (<= a -4.9e-236)
         (/ (* x y) z)
         (if (<= a 5e-105)
           t_1
           (if (<= a 2.55e-31)
             t_2
             (if (<= a 150000.0)
               t_1
               (if (<= a 4.3e+136)
                 (- x (* y (/ (- x t) a)))
                 (if (<= a 7.1e+152) t_2 t_3))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = t - (a * (x / z));
	double t_3 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -6.6e+42) {
		tmp = t_3;
	} else if (a <= -2.55e-216) {
		tmp = (y - z) * (t / (a - z));
	} else if (a <= -4.9e-236) {
		tmp = (x * y) / z;
	} else if (a <= 5e-105) {
		tmp = t_1;
	} else if (a <= 2.55e-31) {
		tmp = t_2;
	} else if (a <= 150000.0) {
		tmp = t_1;
	} else if (a <= 4.3e+136) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= 7.1e+152) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    t_2 = t - (a * (x / z))
    t_3 = x + ((t - x) * (y / a))
    if (a <= (-6.6d+42)) then
        tmp = t_3
    else if (a <= (-2.55d-216)) then
        tmp = (y - z) * (t / (a - z))
    else if (a <= (-4.9d-236)) then
        tmp = (x * y) / z
    else if (a <= 5d-105) then
        tmp = t_1
    else if (a <= 2.55d-31) then
        tmp = t_2
    else if (a <= 150000.0d0) then
        tmp = t_1
    else if (a <= 4.3d+136) then
        tmp = x - (y * ((x - t) / a))
    else if (a <= 7.1d+152) then
        tmp = t_2
    else
        tmp = t_3
    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 - x) * (y / (a - z));
	double t_2 = t - (a * (x / z));
	double t_3 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -6.6e+42) {
		tmp = t_3;
	} else if (a <= -2.55e-216) {
		tmp = (y - z) * (t / (a - z));
	} else if (a <= -4.9e-236) {
		tmp = (x * y) / z;
	} else if (a <= 5e-105) {
		tmp = t_1;
	} else if (a <= 2.55e-31) {
		tmp = t_2;
	} else if (a <= 150000.0) {
		tmp = t_1;
	} else if (a <= 4.3e+136) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= 7.1e+152) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	t_2 = t - (a * (x / z))
	t_3 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -6.6e+42:
		tmp = t_3
	elif a <= -2.55e-216:
		tmp = (y - z) * (t / (a - z))
	elif a <= -4.9e-236:
		tmp = (x * y) / z
	elif a <= 5e-105:
		tmp = t_1
	elif a <= 2.55e-31:
		tmp = t_2
	elif a <= 150000.0:
		tmp = t_1
	elif a <= 4.3e+136:
		tmp = x - (y * ((x - t) / a))
	elif a <= 7.1e+152:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_2 = Float64(t - Float64(a * Float64(x / z)))
	t_3 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -6.6e+42)
		tmp = t_3;
	elseif (a <= -2.55e-216)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (a <= -4.9e-236)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 5e-105)
		tmp = t_1;
	elseif (a <= 2.55e-31)
		tmp = t_2;
	elseif (a <= 150000.0)
		tmp = t_1;
	elseif (a <= 4.3e+136)
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	elseif (a <= 7.1e+152)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	t_2 = t - (a * (x / z));
	t_3 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -6.6e+42)
		tmp = t_3;
	elseif (a <= -2.55e-216)
		tmp = (y - z) * (t / (a - z));
	elseif (a <= -4.9e-236)
		tmp = (x * y) / z;
	elseif (a <= 5e-105)
		tmp = t_1;
	elseif (a <= 2.55e-31)
		tmp = t_2;
	elseif (a <= 150000.0)
		tmp = t_1;
	elseif (a <= 4.3e+136)
		tmp = x - (y * ((x - t) / a));
	elseif (a <= 7.1e+152)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.6e+42], t$95$3, If[LessEqual[a, -2.55e-216], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.9e-236], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 5e-105], t$95$1, If[LessEqual[a, 2.55e-31], t$95$2, If[LessEqual[a, 150000.0], t$95$1, If[LessEqual[a, 4.3e+136], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.1e+152], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -6.5999999999999998e42 or 7.10000000000000017e152 < a

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-/l* 76.9%

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

   5. Simplified 76.9%

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

   if -6.5999999999999998e42 < a < -2.5500000000000001e-216

   1. Initial program 78.9%

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

   3. Taylor expanded in x around 0 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-/l* 66.1%

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

   5. Simplified 66.1%

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

   if -2.5500000000000001e-216 < a < -4.8999999999999997e-236

   1. Initial program 41.5%

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

   3. Taylor expanded in y around -inf 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

      3. distribute-lft-neg-out 100.0%

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

      4. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in a around 0 100.0%

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

   if -4.8999999999999997e-236 < a < 4.99999999999999963e-105 or 2.5499999999999999e-31 < a < 1.5e5

   1. Initial program 67.3%

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

      1. clear-num 66.6%

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

      2. un-div-inv 66.5%

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

   4. Applied egg-rr 66.5%

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

   5. Taylor expanded in y around inf 59.2%

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

      1. div-sub 62.6%

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

      2. associate-*r/ 66.9%

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

      3. associate-*l/ 72.7%

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

   7. Simplified 72.7%

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

   if 4.99999999999999963e-105 < a < 2.5499999999999999e-31 or 4.2999999999999999e136 < a < 7.10000000000000017e152

   1. Initial program 52.7%

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

   3. Taylor expanded in z around -inf 62.2%

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

   4. Taylor expanded in a around inf 65.3%

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

      1. associate-/l* 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in x around inf 65.3%

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

      1. associate-/l* 66.8%

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

   9. Simplified 66.8%

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

   if 1.5e5 < a < 4.2999999999999999e136

   1. Initial program 80.1%

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

   3. Taylor expanded in z around 0 66.8%

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

      1. associate-/l* 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+42}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-216}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-236}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-105}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-31}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 150000:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+136}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq 7.1 \cdot 10^{+152}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.7 \cdot 10^{-121}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-282}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-283}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-252}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 0.0034:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= a -1.35e+90)
     x
     (if (<= a -9.2e+38)
       t_1
       (if (<= a -6.7e-121)
         t
         (if (<= a -2.9e-216)
           t_1
           (if (<= a -3.35e-282)
             (/ (* x y) z)
             (if (<= a 1.25e-283)
               t
               (if (<= a 4e-252)
                 (* x (/ y z))
                 (if (<= a 2.6e-113) t_1 (if (<= a 0.0034) t x)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (a <= -1.35e+90) {
		tmp = x;
	} else if (a <= -9.2e+38) {
		tmp = t_1;
	} else if (a <= -6.7e-121) {
		tmp = t;
	} else if (a <= -2.9e-216) {
		tmp = t_1;
	} else if (a <= -3.35e-282) {
		tmp = (x * y) / z;
	} else if (a <= 1.25e-283) {
		tmp = t;
	} else if (a <= 4e-252) {
		tmp = x * (y / z);
	} else if (a <= 2.6e-113) {
		tmp = t_1;
	} else if (a <= 0.0034) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (a <= (-1.35d+90)) then
        tmp = x
    else if (a <= (-9.2d+38)) then
        tmp = t_1
    else if (a <= (-6.7d-121)) then
        tmp = t
    else if (a <= (-2.9d-216)) then
        tmp = t_1
    else if (a <= (-3.35d-282)) then
        tmp = (x * y) / z
    else if (a <= 1.25d-283) then
        tmp = t
    else if (a <= 4d-252) then
        tmp = x * (y / z)
    else if (a <= 2.6d-113) then
        tmp = t_1
    else if (a <= 0.0034d0) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (a <= -1.35e+90) {
		tmp = x;
	} else if (a <= -9.2e+38) {
		tmp = t_1;
	} else if (a <= -6.7e-121) {
		tmp = t;
	} else if (a <= -2.9e-216) {
		tmp = t_1;
	} else if (a <= -3.35e-282) {
		tmp = (x * y) / z;
	} else if (a <= 1.25e-283) {
		tmp = t;
	} else if (a <= 4e-252) {
		tmp = x * (y / z);
	} else if (a <= 2.6e-113) {
		tmp = t_1;
	} else if (a <= 0.0034) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if a <= -1.35e+90:
		tmp = x
	elif a <= -9.2e+38:
		tmp = t_1
	elif a <= -6.7e-121:
		tmp = t
	elif a <= -2.9e-216:
		tmp = t_1
	elif a <= -3.35e-282:
		tmp = (x * y) / z
	elif a <= 1.25e-283:
		tmp = t
	elif a <= 4e-252:
		tmp = x * (y / z)
	elif a <= 2.6e-113:
		tmp = t_1
	elif a <= 0.0034:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (a <= -1.35e+90)
		tmp = x;
	elseif (a <= -9.2e+38)
		tmp = t_1;
	elseif (a <= -6.7e-121)
		tmp = t;
	elseif (a <= -2.9e-216)
		tmp = t_1;
	elseif (a <= -3.35e-282)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 1.25e-283)
		tmp = t;
	elseif (a <= 4e-252)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 2.6e-113)
		tmp = t_1;
	elseif (a <= 0.0034)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (a <= -1.35e+90)
		tmp = x;
	elseif (a <= -9.2e+38)
		tmp = t_1;
	elseif (a <= -6.7e-121)
		tmp = t;
	elseif (a <= -2.9e-216)
		tmp = t_1;
	elseif (a <= -3.35e-282)
		tmp = (x * y) / z;
	elseif (a <= 1.25e-283)
		tmp = t;
	elseif (a <= 4e-252)
		tmp = x * (y / z);
	elseif (a <= 2.6e-113)
		tmp = t_1;
	elseif (a <= 0.0034)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.35e+90], x, If[LessEqual[a, -9.2e+38], t$95$1, If[LessEqual[a, -6.7e-121], t, If[LessEqual[a, -2.9e-216], t$95$1, If[LessEqual[a, -3.35e-282], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.25e-283], t, If[LessEqual[a, 4e-252], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-113], t$95$1, If[LessEqual[a, 0.0034], t, x]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.35e90 or 0.00339999999999999981 < a

   1. Initial program 84.8%

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

   3. Taylor expanded in a around inf 49.9%

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

   if -1.35e90 < a < -9.2000000000000005e38 or -6.7000000000000001e-121 < a < -2.9000000000000001e-216 or 3.99999999999999977e-252 < a < 2.5999999999999999e-113

   1. Initial program 74.3%

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

   3. Taylor expanded in x around 0 62.5%

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

      1. *-commutative 62.5%

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

      2. associate-/l* 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in y around inf 46.4%

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

      1. associate-/l* 48.2%

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

   8. Simplified 48.2%

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

   if -9.2000000000000005e38 < a < -6.7000000000000001e-121 or -3.3500000000000001e-282 < a < 1.25e-283 or 2.5999999999999999e-113 < a < 0.00339999999999999981

   1. Initial program 75.9%

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

   3. Taylor expanded in z around inf 44.6%

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

   if -2.9000000000000001e-216 < a < -3.3500000000000001e-282

   1. Initial program 61.0%

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

   3. Taylor expanded in y around -inf 80.8%

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

   4. Taylor expanded in t around 0 61.3%

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

      1. associate-*r/ 61.3%

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

      2. mul-1-neg 61.3%

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

      3. distribute-lft-neg-out 61.3%

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

      4. *-commutative 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in a around 0 61.3%

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

   if 1.25e-283 < a < 3.99999999999999977e-252

   1. Initial program 24.4%

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

   3. Taylor expanded in y around -inf 61.6%

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

   4. Taylor expanded in t around 0 61.6%

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

      1. associate-*r/ 61.6%

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

      2. mul-1-neg 61.6%

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

      3. distribute-lft-neg-out 61.6%

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

      4. *-commutative 61.6%

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

   6. Simplified 61.6%

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

   7. Taylor expanded in a around 0 41.9%

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

      1. associate-/l* 60.6%

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

   9. Simplified 60.6%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -6.7 \cdot 10^{-121}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-282}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-283}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-252}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 0.0034:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-185} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-185) (not (<= t_1 0.0)))
     t_1
     (- t (* (- t x) (/ (- y a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-185) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) * ((y - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-185)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t - ((t - x) * ((y - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-185) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) * ((y - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-185) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t - ((t - x) * ((y - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-185) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(t - x) * Float64(Float64(y - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-185) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t - ((t - x) * ((y - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-185], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t - N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-185 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.5%

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

   if -2e-185 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 7.1%

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

   3. Taylor expanded in z around inf 81.1%

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

      1. associate--l+ 81.1%

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

      2. distribute-lft-out-- 81.1%

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

      3. div-sub 81.1%

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

      4. mul-1-neg 81.1%

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

      5. unsub-neg 81.1%

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

      6. distribute-rgt-out-- 81.3%

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

      7. associate-/l* 95.0%

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

   5. Simplified 95.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-185} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-120}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-284}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-284}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 175:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))))
   (if (<= a -3.6e+89)
     x
     (if (<= a -2.8e-64)
       t_1
       (if (<= a -1.4e-120)
         t
         (if (<= a -8.6e-216)
           (* t (/ y (- a z)))
           (if (<= a -6.2e-284)
             (/ (* x y) z)
             (if (<= a 9.2e-284) t (if (<= a 175.0) t_1 x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (a <= -3.6e+89) {
		tmp = x;
	} else if (a <= -2.8e-64) {
		tmp = t_1;
	} else if (a <= -1.4e-120) {
		tmp = t;
	} else if (a <= -8.6e-216) {
		tmp = t * (y / (a - z));
	} else if (a <= -6.2e-284) {
		tmp = (x * y) / z;
	} else if (a <= 9.2e-284) {
		tmp = t;
	} else if (a <= 175.0) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    if (a <= (-3.6d+89)) then
        tmp = x
    else if (a <= (-2.8d-64)) then
        tmp = t_1
    else if (a <= (-1.4d-120)) then
        tmp = t
    else if (a <= (-8.6d-216)) then
        tmp = t * (y / (a - z))
    else if (a <= (-6.2d-284)) then
        tmp = (x * y) / z
    else if (a <= 9.2d-284) then
        tmp = t
    else if (a <= 175.0d0) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (a <= -3.6e+89) {
		tmp = x;
	} else if (a <= -2.8e-64) {
		tmp = t_1;
	} else if (a <= -1.4e-120) {
		tmp = t;
	} else if (a <= -8.6e-216) {
		tmp = t * (y / (a - z));
	} else if (a <= -6.2e-284) {
		tmp = (x * y) / z;
	} else if (a <= 9.2e-284) {
		tmp = t;
	} else if (a <= 175.0) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	tmp = 0
	if a <= -3.6e+89:
		tmp = x
	elif a <= -2.8e-64:
		tmp = t_1
	elif a <= -1.4e-120:
		tmp = t
	elif a <= -8.6e-216:
		tmp = t * (y / (a - z))
	elif a <= -6.2e-284:
		tmp = (x * y) / z
	elif a <= 9.2e-284:
		tmp = t
	elif a <= 175.0:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (a <= -3.6e+89)
		tmp = x;
	elseif (a <= -2.8e-64)
		tmp = t_1;
	elseif (a <= -1.4e-120)
		tmp = t;
	elseif (a <= -8.6e-216)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (a <= -6.2e-284)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 9.2e-284)
		tmp = t;
	elseif (a <= 175.0)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	tmp = 0.0;
	if (a <= -3.6e+89)
		tmp = x;
	elseif (a <= -2.8e-64)
		tmp = t_1;
	elseif (a <= -1.4e-120)
		tmp = t;
	elseif (a <= -8.6e-216)
		tmp = t * (y / (a - z));
	elseif (a <= -6.2e-284)
		tmp = (x * y) / z;
	elseif (a <= 9.2e-284)
		tmp = t;
	elseif (a <= 175.0)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e+89], x, If[LessEqual[a, -2.8e-64], t$95$1, If[LessEqual[a, -1.4e-120], t, If[LessEqual[a, -8.6e-216], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.2e-284], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 9.2e-284], t, If[LessEqual[a, 175.0], t$95$1, x]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.6e89 or 175 < a

   1. Initial program 85.6%

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

   3. Taylor expanded in a around inf 50.3%

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

   if -3.6e89 < a < -2.80000000000000004e-64 or 9.2e-284 < a < 175

   1. Initial program 70.6%

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

   3. Taylor expanded in z around inf 61.2%

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

      1. associate--l+ 61.2%

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

      2. distribute-lft-out-- 61.2%

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

      3. div-sub 62.7%

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

      4. mul-1-neg 62.7%

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

      5. unsub-neg 62.7%

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

      6. distribute-rgt-out-- 62.7%

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

      7. associate-/l* 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in t around 0 29.6%

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

      1. associate-/l* 39.1%

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

   8. Simplified 39.1%

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

   if -2.80000000000000004e-64 < a < -1.39999999999999997e-120 or -6.1999999999999996e-284 < a < 9.2e-284

   1. Initial program 78.3%

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

   3. Taylor expanded in z around inf 56.9%

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

   if -1.39999999999999997e-120 < a < -8.5999999999999995e-216

   1. Initial program 73.0%

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

   3. Taylor expanded in x around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-/l* 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in y around inf 49.7%

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

      1. associate-/l* 54.1%

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

   8. Simplified 54.1%

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

   if -8.5999999999999995e-216 < a < -6.1999999999999996e-284

   1. Initial program 61.0%

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

   3. Taylor expanded in y around -inf 80.8%

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

   4. Taylor expanded in t around 0 61.3%

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

      1. associate-*r/ 61.3%

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

      2. mul-1-neg 61.3%

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

      3. distribute-lft-neg-out 61.3%

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

      4. *-commutative 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in a around 0 61.3%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-120}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-284}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-284}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 175:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-192}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-264}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-56}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= y -2.6e-66)
     t_1
     (if (<= y -3.35e-192)
       t
       (if (<= y -1.2e-264)
         x
         (if (<= y -2e-296)
           t
           (if (<= y 9.5e-220) x (if (<= y 1.05e-56) t t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.6e-66) {
		tmp = t_1;
	} else if (y <= -3.35e-192) {
		tmp = t;
	} else if (y <= -1.2e-264) {
		tmp = x;
	} else if (y <= -2e-296) {
		tmp = t;
	} else if (y <= 9.5e-220) {
		tmp = x;
	} else if (y <= 1.05e-56) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    if (y <= (-2.6d-66)) then
        tmp = t_1
    else if (y <= (-3.35d-192)) then
        tmp = t
    else if (y <= (-1.2d-264)) then
        tmp = x
    else if (y <= (-2d-296)) then
        tmp = t
    else if (y <= 9.5d-220) then
        tmp = x
    else if (y <= 1.05d-56) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.6e-66) {
		tmp = t_1;
	} else if (y <= -3.35e-192) {
		tmp = t;
	} else if (y <= -1.2e-264) {
		tmp = x;
	} else if (y <= -2e-296) {
		tmp = t;
	} else if (y <= 9.5e-220) {
		tmp = x;
	} else if (y <= 1.05e-56) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -2.6e-66:
		tmp = t_1
	elif y <= -3.35e-192:
		tmp = t
	elif y <= -1.2e-264:
		tmp = x
	elif y <= -2e-296:
		tmp = t
	elif y <= 9.5e-220:
		tmp = x
	elif y <= 1.05e-56:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -2.6e-66)
		tmp = t_1;
	elseif (y <= -3.35e-192)
		tmp = t;
	elseif (y <= -1.2e-264)
		tmp = x;
	elseif (y <= -2e-296)
		tmp = t;
	elseif (y <= 9.5e-220)
		tmp = x;
	elseif (y <= 1.05e-56)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -2.6e-66)
		tmp = t_1;
	elseif (y <= -3.35e-192)
		tmp = t;
	elseif (y <= -1.2e-264)
		tmp = x;
	elseif (y <= -2e-296)
		tmp = t;
	elseif (y <= 9.5e-220)
		tmp = x;
	elseif (y <= 1.05e-56)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e-66], t$95$1, If[LessEqual[y, -3.35e-192], t, If[LessEqual[y, -1.2e-264], x, If[LessEqual[y, -2e-296], t, If[LessEqual[y, 9.5e-220], x, If[LessEqual[y, 1.05e-56], t, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5999999999999999e-66 or 1.05000000000000003e-56 < y

   1. Initial program 81.0%

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

   3. Taylor expanded in y around inf 65.4%

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

      1. div-sub 66.7%

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

   5. Simplified 66.7%

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

   if -2.5999999999999999e-66 < y < -3.34999999999999995e-192 or -1.1999999999999999e-264 < y < -2e-296 or 9.50000000000000062e-220 < y < 1.05000000000000003e-56

   1. Initial program 69.0%

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

   3. Taylor expanded in z around inf 44.6%

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

   if -3.34999999999999995e-192 < y < -1.1999999999999999e-264 or -2e-296 < y < 9.50000000000000062e-220

   1. Initial program 74.1%

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

   3. Taylor expanded in a around inf 56.7%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-192}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-264}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-56}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{z} \cdot \left(z - y\right)\\ t_2 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-282}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.06 \cdot 10^{-283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ t z) (- z y))) (t_2 (* y (/ (- x t) z))))
   (if (<= a -3.5e+89)
     x
     (if (<= a -2.4e+41)
       (* x (/ (- y a) z))
       (if (<= a -9.6e-216)
         t_1
         (if (<= a -5.7e-282)
           t_2
           (if (<= a 2.06e-283) t_1 (if (<= a 5.5e+47) t_2 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / z) * (z - y);
	double t_2 = y * ((x - t) / z);
	double tmp;
	if (a <= -3.5e+89) {
		tmp = x;
	} else if (a <= -2.4e+41) {
		tmp = x * ((y - a) / z);
	} else if (a <= -9.6e-216) {
		tmp = t_1;
	} else if (a <= -5.7e-282) {
		tmp = t_2;
	} else if (a <= 2.06e-283) {
		tmp = t_1;
	} else if (a <= 5.5e+47) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t / z) * (z - y)
    t_2 = y * ((x - t) / z)
    if (a <= (-3.5d+89)) then
        tmp = x
    else if (a <= (-2.4d+41)) then
        tmp = x * ((y - a) / z)
    else if (a <= (-9.6d-216)) then
        tmp = t_1
    else if (a <= (-5.7d-282)) then
        tmp = t_2
    else if (a <= 2.06d-283) then
        tmp = t_1
    else if (a <= 5.5d+47) then
        tmp = t_2
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / z) * (z - y);
	double t_2 = y * ((x - t) / z);
	double tmp;
	if (a <= -3.5e+89) {
		tmp = x;
	} else if (a <= -2.4e+41) {
		tmp = x * ((y - a) / z);
	} else if (a <= -9.6e-216) {
		tmp = t_1;
	} else if (a <= -5.7e-282) {
		tmp = t_2;
	} else if (a <= 2.06e-283) {
		tmp = t_1;
	} else if (a <= 5.5e+47) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t / z) * (z - y)
	t_2 = y * ((x - t) / z)
	tmp = 0
	if a <= -3.5e+89:
		tmp = x
	elif a <= -2.4e+41:
		tmp = x * ((y - a) / z)
	elif a <= -9.6e-216:
		tmp = t_1
	elif a <= -5.7e-282:
		tmp = t_2
	elif a <= 2.06e-283:
		tmp = t_1
	elif a <= 5.5e+47:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / z) * Float64(z - y))
	t_2 = Float64(y * Float64(Float64(x - t) / z))
	tmp = 0.0
	if (a <= -3.5e+89)
		tmp = x;
	elseif (a <= -2.4e+41)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= -9.6e-216)
		tmp = t_1;
	elseif (a <= -5.7e-282)
		tmp = t_2;
	elseif (a <= 2.06e-283)
		tmp = t_1;
	elseif (a <= 5.5e+47)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t / z) * (z - y);
	t_2 = y * ((x - t) / z);
	tmp = 0.0;
	if (a <= -3.5e+89)
		tmp = x;
	elseif (a <= -2.4e+41)
		tmp = x * ((y - a) / z);
	elseif (a <= -9.6e-216)
		tmp = t_1;
	elseif (a <= -5.7e-282)
		tmp = t_2;
	elseif (a <= 2.06e-283)
		tmp = t_1;
	elseif (a <= 5.5e+47)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+89], x, If[LessEqual[a, -2.4e+41], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.6e-216], t$95$1, If[LessEqual[a, -5.7e-282], t$95$2, If[LessEqual[a, 2.06e-283], t$95$1, If[LessEqual[a, 5.5e+47], t$95$2, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.5000000000000001e89 or 5.4999999999999998e47 < a

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf 51.8%

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

   if -3.5000000000000001e89 < a < -2.4000000000000002e41

   1. Initial program 73.1%

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

   3. Taylor expanded in z around inf 36.4%

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

      1. associate--l+ 36.4%

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

      2. distribute-lft-out-- 36.4%

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

      3. div-sub 36.5%

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

      4. mul-1-neg 36.5%

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

      5. unsub-neg 36.5%

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

      6. distribute-rgt-out-- 36.7%

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

      7. associate-/l* 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in t around 0 23.4%

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

      1. associate-/l* 45.5%

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

   8. Simplified 45.5%

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

   if -2.4000000000000002e41 < a < -9.60000000000000014e-216 or -5.7000000000000003e-282 < a < 2.06000000000000004e-283

   1. Initial program 77.7%

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

   3. Taylor expanded in x around 0 60.1%

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

      1. *-commutative 60.1%

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

      2. associate-/l* 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in a around 0 57.2%

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

      1. associate-*r/ 57.2%

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

      2. neg-mul-1 57.2%

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

   8. Simplified 57.2%

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

   if -9.60000000000000014e-216 < a < -5.7000000000000003e-282 or 2.06000000000000004e-283 < a < 5.4999999999999998e47

   1. Initial program 64.5%

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

   3. Taylor expanded in z around inf 74.4%

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

      1. associate--l+ 74.4%

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

      2. distribute-lft-out-- 74.4%

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

      3. div-sub 74.6%

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

      4. mul-1-neg 74.6%

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

      5. unsub-neg 74.6%

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

      6. distribute-rgt-out-- 74.6%

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

      7. associate-/l* 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in y around inf 52.4%

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

      1. div-sub 55.2%

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

   8. Simplified 55.2%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-216}:\\ \;\;\;\;\frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.06 \cdot 10^{-283}:\\ \;\;\;\;\frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-120}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-215}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e+89)
   x
   (if (<= a -2.55e-73)
     (* x (/ (- y a) z))
     (if (<= a -2.5e-120)
       t
       (if (<= a -1.4e-215)
         (* t (/ y (- a z)))
         (if (<= a 7.2e+44) (* y (/ (- x t) z)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+89) {
		tmp = x;
	} else if (a <= -2.55e-73) {
		tmp = x * ((y - a) / z);
	} else if (a <= -2.5e-120) {
		tmp = t;
	} else if (a <= -1.4e-215) {
		tmp = t * (y / (a - z));
	} else if (a <= 7.2e+44) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.5d+89)) then
        tmp = x
    else if (a <= (-2.55d-73)) then
        tmp = x * ((y - a) / z)
    else if (a <= (-2.5d-120)) then
        tmp = t
    else if (a <= (-1.4d-215)) then
        tmp = t * (y / (a - z))
    else if (a <= 7.2d+44) then
        tmp = y * ((x - t) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+89) {
		tmp = x;
	} else if (a <= -2.55e-73) {
		tmp = x * ((y - a) / z);
	} else if (a <= -2.5e-120) {
		tmp = t;
	} else if (a <= -1.4e-215) {
		tmp = t * (y / (a - z));
	} else if (a <= 7.2e+44) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.5e+89:
		tmp = x
	elif a <= -2.55e-73:
		tmp = x * ((y - a) / z)
	elif a <= -2.5e-120:
		tmp = t
	elif a <= -1.4e-215:
		tmp = t * (y / (a - z))
	elif a <= 7.2e+44:
		tmp = y * ((x - t) / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e+89)
		tmp = x;
	elseif (a <= -2.55e-73)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= -2.5e-120)
		tmp = t;
	elseif (a <= -1.4e-215)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (a <= 7.2e+44)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.5e+89)
		tmp = x;
	elseif (a <= -2.55e-73)
		tmp = x * ((y - a) / z);
	elseif (a <= -2.5e-120)
		tmp = t;
	elseif (a <= -1.4e-215)
		tmp = t * (y / (a - z));
	elseif (a <= 7.2e+44)
		tmp = y * ((x - t) / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e+89], x, If[LessEqual[a, -2.55e-73], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.5e-120], t, If[LessEqual[a, -1.4e-215], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+44], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.5000000000000001e89 or 7.2e44 < a

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf 51.8%

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

   if -3.5000000000000001e89 < a < -2.55e-73

   1. Initial program 78.4%

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

   3. Taylor expanded in z around inf 49.2%

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

      1. associate--l+ 49.2%

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

      2. distribute-lft-out-- 49.2%

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

      3. div-sub 52.2%

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

      4. mul-1-neg 52.2%

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

      5. unsub-neg 52.2%

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

      6. distribute-rgt-out-- 52.3%

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

      7. associate-/l* 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in t around 0 28.0%

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

      1. associate-/l* 42.0%

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

   8. Simplified 42.0%

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

   if -2.55e-73 < a < -2.50000000000000003e-120

   1. Initial program 81.9%

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

   3. Taylor expanded in z around inf 63.9%

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

   if -2.50000000000000003e-120 < a < -1.39999999999999993e-215

   1. Initial program 73.0%

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

   3. Taylor expanded in x around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-/l* 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in y around inf 49.7%

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

      1. associate-/l* 54.1%

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

   8. Simplified 54.1%

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

   if -1.39999999999999993e-215 < a < 7.2e44

   1. Initial program 65.9%

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

   3. Taylor expanded in z around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. distribute-lft-out-- 77.1%

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

      3. div-sub 77.3%

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

      4. mul-1-neg 77.3%

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

      5. unsub-neg 77.3%

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

      6. distribute-rgt-out-- 77.3%

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

      7. associate-/l* 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in y around inf 50.5%

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

      1. div-sub 52.9%

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

   8. Simplified 52.9%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-120}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-215}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-216}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-281}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1700000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -5.1e+51)
     x
     (if (<= a -4.5e-216)
       t
       (if (<= a -4.7e-284)
         t_1
         (if (<= a 1.6e-281) t (if (<= a 1700000.0) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -5.1e+51) {
		tmp = x;
	} else if (a <= -4.5e-216) {
		tmp = t;
	} else if (a <= -4.7e-284) {
		tmp = t_1;
	} else if (a <= 1.6e-281) {
		tmp = t;
	} else if (a <= 1700000.0) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-5.1d+51)) then
        tmp = x
    else if (a <= (-4.5d-216)) then
        tmp = t
    else if (a <= (-4.7d-284)) then
        tmp = t_1
    else if (a <= 1.6d-281) then
        tmp = t
    else if (a <= 1700000.0d0) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -5.1e+51) {
		tmp = x;
	} else if (a <= -4.5e-216) {
		tmp = t;
	} else if (a <= -4.7e-284) {
		tmp = t_1;
	} else if (a <= 1.6e-281) {
		tmp = t;
	} else if (a <= 1700000.0) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -5.1e+51:
		tmp = x
	elif a <= -4.5e-216:
		tmp = t
	elif a <= -4.7e-284:
		tmp = t_1
	elif a <= 1.6e-281:
		tmp = t
	elif a <= 1700000.0:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -5.1e+51)
		tmp = x;
	elseif (a <= -4.5e-216)
		tmp = t;
	elseif (a <= -4.7e-284)
		tmp = t_1;
	elseif (a <= 1.6e-281)
		tmp = t;
	elseif (a <= 1700000.0)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -5.1e+51)
		tmp = x;
	elseif (a <= -4.5e-216)
		tmp = t;
	elseif (a <= -4.7e-284)
		tmp = t_1;
	elseif (a <= 1.6e-281)
		tmp = t;
	elseif (a <= 1700000.0)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.1e+51], x, If[LessEqual[a, -4.5e-216], t, If[LessEqual[a, -4.7e-284], t$95$1, If[LessEqual[a, 1.6e-281], t, If[LessEqual[a, 1700000.0], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.1000000000000001e51 or 1.7e6 < a

   1. Initial program 85.4%

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

   3. Taylor expanded in a around inf 46.8%

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

   if -5.1000000000000001e51 < a < -4.4999999999999999e-216 or -4.70000000000000022e-284 < a < 1.6e-281

   1. Initial program 76.3%

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

   3. Taylor expanded in z around inf 39.8%

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

   if -4.4999999999999999e-216 < a < -4.70000000000000022e-284 or 1.6e-281 < a < 1.7e6

   1. Initial program 63.6%

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

   3. Taylor expanded in y around -inf 62.9%

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

   4. Taylor expanded in t around 0 39.7%

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

      1. associate-*r/ 39.7%

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

      2. mul-1-neg 39.7%

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

      3. distribute-lft-neg-out 39.7%

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

      4. *-commutative 39.7%

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

   6. Simplified 39.7%

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

   7. Taylor expanded in a around 0 37.0%

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

      1. associate-/l* 41.3%

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

   9. Simplified 41.3%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-216}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-281}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1700000:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-216}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-282}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-283}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.7:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e+53)
   x
   (if (<= a -1.45e-216)
     t
     (if (<= a -2.9e-282)
       (/ (* x y) z)
       (if (<= a 5.2e-283) t (if (<= a 2.7) (* x (/ y z)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+53) {
		tmp = x;
	} else if (a <= -1.45e-216) {
		tmp = t;
	} else if (a <= -2.9e-282) {
		tmp = (x * y) / z;
	} else if (a <= 5.2e-283) {
		tmp = t;
	} else if (a <= 2.7) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.6d+53)) then
        tmp = x
    else if (a <= (-1.45d-216)) then
        tmp = t
    else if (a <= (-2.9d-282)) then
        tmp = (x * y) / z
    else if (a <= 5.2d-283) then
        tmp = t
    else if (a <= 2.7d0) then
        tmp = x * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+53) {
		tmp = x;
	} else if (a <= -1.45e-216) {
		tmp = t;
	} else if (a <= -2.9e-282) {
		tmp = (x * y) / z;
	} else if (a <= 5.2e-283) {
		tmp = t;
	} else if (a <= 2.7) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.6e+53:
		tmp = x
	elif a <= -1.45e-216:
		tmp = t
	elif a <= -2.9e-282:
		tmp = (x * y) / z
	elif a <= 5.2e-283:
		tmp = t
	elif a <= 2.7:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.6e+53)
		tmp = x;
	elseif (a <= -1.45e-216)
		tmp = t;
	elseif (a <= -2.9e-282)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 5.2e-283)
		tmp = t;
	elseif (a <= 2.7)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.6e+53)
		tmp = x;
	elseif (a <= -1.45e-216)
		tmp = t;
	elseif (a <= -2.9e-282)
		tmp = (x * y) / z;
	elseif (a <= 5.2e-283)
		tmp = t;
	elseif (a <= 2.7)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.6e+53], x, If[LessEqual[a, -1.45e-216], t, If[LessEqual[a, -2.9e-282], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 5.2e-283], t, If[LessEqual[a, 2.7], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.6e53 or 2.7000000000000002 < a

   1. Initial program 85.4%

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

   3. Taylor expanded in a around inf 46.8%

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

   if -3.6e53 < a < -1.45e-216 or -2.89999999999999998e-282 < a < 5.2000000000000002e-283

   1. Initial program 76.3%

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

   3. Taylor expanded in z around inf 39.8%

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

   if -1.45e-216 < a < -2.89999999999999998e-282

   1. Initial program 61.0%

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

   3. Taylor expanded in y around -inf 80.8%

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

   4. Taylor expanded in t around 0 61.3%

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

      1. associate-*r/ 61.3%

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

      2. mul-1-neg 61.3%

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

      3. distribute-lft-neg-out 61.3%

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

      4. *-commutative 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in a around 0 61.3%

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

   if 5.2000000000000002e-283 < a < 2.7000000000000002

   1. Initial program 64.8%

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

   3. Taylor expanded in y around -inf 55.1%

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

   4. Taylor expanded in t around 0 30.2%

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

      1. associate-*r/ 30.2%

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

      2. mul-1-neg 30.2%

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

      3. distribute-lft-neg-out 30.2%

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

      4. *-commutative 30.2%

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

   6. Simplified 30.2%

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

   7. Taylor expanded in a around 0 26.5%

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

      1. associate-/l* 32.7%

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

   9. Simplified 32.7%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-216}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-282}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-283}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.7:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))) (t_2 (* y (/ (- t x) (- a z)))))
   (if (<= y -2.7e+45)
     t_2
     (if (<= y -1.1e-191)
       t_1
       (if (<= y -7.2e-275) x (if (<= y 6.5e-55) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.7e+45) {
		tmp = t_2;
	} else if (y <= -1.1e-191) {
		tmp = t_1;
	} else if (y <= -7.2e-275) {
		tmp = x;
	} else if (y <= 6.5e-55) {
		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 = (y - z) * (t / (a - z))
    t_2 = y * ((t - x) / (a - z))
    if (y <= (-2.7d+45)) then
        tmp = t_2
    else if (y <= (-1.1d-191)) then
        tmp = t_1
    else if (y <= (-7.2d-275)) then
        tmp = x
    else if (y <= 6.5d-55) 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 = (y - z) * (t / (a - z));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.7e+45) {
		tmp = t_2;
	} else if (y <= -1.1e-191) {
		tmp = t_1;
	} else if (y <= -7.2e-275) {
		tmp = x;
	} else if (y <= 6.5e-55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	t_2 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -2.7e+45:
		tmp = t_2
	elif y <= -1.1e-191:
		tmp = t_1
	elif y <= -7.2e-275:
		tmp = x
	elif y <= 6.5e-55:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	t_2 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -2.7e+45)
		tmp = t_2;
	elseif (y <= -1.1e-191)
		tmp = t_1;
	elseif (y <= -7.2e-275)
		tmp = x;
	elseif (y <= 6.5e-55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / (a - z));
	t_2 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -2.7e+45)
		tmp = t_2;
	elseif (y <= -1.1e-191)
		tmp = t_1;
	elseif (y <= -7.2e-275)
		tmp = x;
	elseif (y <= 6.5e-55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+45], t$95$2, If[LessEqual[y, -1.1e-191], t$95$1, If[LessEqual[y, -7.2e-275], x, If[LessEqual[y, 6.5e-55], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.69999999999999984e45 or 6.50000000000000006e-55 < y

   1. Initial program 81.1%

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

   3. Taylor expanded in y around inf 70.8%

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

      1. div-sub 72.4%

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

   5. Simplified 72.4%

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

   if -2.69999999999999984e45 < y < -1.09999999999999999e-191 or -7.1999999999999994e-275 < y < 6.50000000000000006e-55

   1. Initial program 73.7%

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

   3. Taylor expanded in x around 0 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-/l* 50.6%

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

   5. Simplified 50.6%

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

   if -1.09999999999999999e-191 < y < -7.1999999999999994e-275

   1. Initial program 69.3%

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

   3. Taylor expanded in a around inf 55.6%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-191}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-55}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-270}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))) (t_2 (* (- t x) (/ y (- a z)))))
   (if (<= y -1.9e+48)
     t_2
     (if (<= y -8.8e-193)
       t_1
       (if (<= y -1.45e-270) x (if (<= y 1.02e-54) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -1.9e+48) {
		tmp = t_2;
	} else if (y <= -8.8e-193) {
		tmp = t_1;
	} else if (y <= -1.45e-270) {
		tmp = x;
	} else if (y <= 1.02e-54) {
		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 = (y - z) * (t / (a - z))
    t_2 = (t - x) * (y / (a - z))
    if (y <= (-1.9d+48)) then
        tmp = t_2
    else if (y <= (-8.8d-193)) then
        tmp = t_1
    else if (y <= (-1.45d-270)) then
        tmp = x
    else if (y <= 1.02d-54) 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 = (y - z) * (t / (a - z));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -1.9e+48) {
		tmp = t_2;
	} else if (y <= -8.8e-193) {
		tmp = t_1;
	} else if (y <= -1.45e-270) {
		tmp = x;
	} else if (y <= 1.02e-54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	t_2 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -1.9e+48:
		tmp = t_2
	elif y <= -8.8e-193:
		tmp = t_1
	elif y <= -1.45e-270:
		tmp = x
	elif y <= 1.02e-54:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	t_2 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -1.9e+48)
		tmp = t_2;
	elseif (y <= -8.8e-193)
		tmp = t_1;
	elseif (y <= -1.45e-270)
		tmp = x;
	elseif (y <= 1.02e-54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / (a - z));
	t_2 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (y <= -1.9e+48)
		tmp = t_2;
	elseif (y <= -8.8e-193)
		tmp = t_1;
	elseif (y <= -1.45e-270)
		tmp = x;
	elseif (y <= 1.02e-54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+48], t$95$2, If[LessEqual[y, -8.8e-193], t$95$1, If[LessEqual[y, -1.45e-270], x, If[LessEqual[y, 1.02e-54], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9e48 or 1.01999999999999999e-54 < y

   1. Initial program 81.1%

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

      1. clear-num 80.6%

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

      2. un-div-inv 80.8%

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

   4. Applied egg-rr 80.8%

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

   5. Taylor expanded in y around inf 70.8%

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

      1. div-sub 72.4%

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

      2. associate-*r/ 63.3%

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

      3. associate-*l/ 75.8%

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

   7. Simplified 75.8%

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

   if -1.9e48 < y < -8.79999999999999906e-193 or -1.44999999999999991e-270 < y < 1.01999999999999999e-54

   1. Initial program 73.7%

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

   3. Taylor expanded in x around 0 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-/l* 50.6%

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

   5. Simplified 50.6%

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

   if -8.79999999999999906e-193 < y < -1.44999999999999991e-270

   1. Initial program 69.3%

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

   3. Taylor expanded in a around inf 55.6%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+48}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-193}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-270}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-54}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-294}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-60}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))))
   (if (<= y -1.55e-65)
     t_1
     (if (<= y 7e-294)
       (- t (* a (/ x z)))
       (if (<= y 6.9e-220)
         x
         (if (<= y 9.8e-60) (* (- y z) (/ t (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -1.55e-65) {
		tmp = t_1;
	} else if (y <= 7e-294) {
		tmp = t - (a * (x / z));
	} else if (y <= 6.9e-220) {
		tmp = x;
	} else if (y <= 9.8e-60) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    if (y <= (-1.55d-65)) then
        tmp = t_1
    else if (y <= 7d-294) then
        tmp = t - (a * (x / z))
    else if (y <= 6.9d-220) then
        tmp = x
    else if (y <= 9.8d-60) then
        tmp = (y - z) * (t / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -1.55e-65) {
		tmp = t_1;
	} else if (y <= 7e-294) {
		tmp = t - (a * (x / z));
	} else if (y <= 6.9e-220) {
		tmp = x;
	} else if (y <= 9.8e-60) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -1.55e-65:
		tmp = t_1
	elif y <= 7e-294:
		tmp = t - (a * (x / z))
	elif y <= 6.9e-220:
		tmp = x
	elif y <= 9.8e-60:
		tmp = (y - z) * (t / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -1.55e-65)
		tmp = t_1;
	elseif (y <= 7e-294)
		tmp = Float64(t - Float64(a * Float64(x / z)));
	elseif (y <= 6.9e-220)
		tmp = x;
	elseif (y <= 9.8e-60)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (y <= -1.55e-65)
		tmp = t_1;
	elseif (y <= 7e-294)
		tmp = t - (a * (x / z));
	elseif (y <= 6.9e-220)
		tmp = x;
	elseif (y <= 9.8e-60)
		tmp = (y - z) * (t / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e-65], t$95$1, If[LessEqual[y, 7e-294], N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.9e-220], x, If[LessEqual[y, 9.8e-60], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.55000000000000008e-65 or 9.79999999999999977e-60 < y

   1. Initial program 81.0%

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

      1. clear-num 80.6%

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

      2. un-div-inv 80.8%

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

   4. Applied egg-rr 80.8%

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

   5. Taylor expanded in y around inf 65.4%

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

      1. div-sub 66.7%

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

      2. associate-*r/ 60.0%

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

      3. associate-*l/ 69.9%

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

   7. Simplified 69.9%

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

   if -1.55000000000000008e-65 < y < 7.00000000000000064e-294

   1. Initial program 69.6%

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

   3. Taylor expanded in z around -inf 55.3%

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

   4. Taylor expanded in a around inf 53.0%

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

      1. associate-/l* 49.3%

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

   6. Simplified 49.3%

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

   7. Taylor expanded in x around inf 53.5%

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

      1. associate-/l* 51.9%

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

   9. Simplified 51.9%

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

   if 7.00000000000000064e-294 < y < 6.89999999999999981e-220

   1. Initial program 80.3%

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

   3. Taylor expanded in a around inf 61.4%

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

   if 6.89999999999999981e-220 < y < 9.79999999999999977e-60

   1. Initial program 68.0%

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

   3. Taylor expanded in x around 0 42.1%

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

      1. *-commutative 42.1%

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

      2. associate-/l* 48.5%

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

   5. Simplified 48.5%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-65}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-294}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-60}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+45}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+136}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq 7.1 \cdot 10^{+152}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))))
   (if (<= a -1.8e+62)
     t_1
     (if (<= a 2.7e+45)
       (+ t (* (/ y z) (- x t)))
       (if (<= a 4.3e+136)
         (- x (* y (/ (- x t) a)))
         (if (<= a 7.1e+152) (- t (* a (/ x z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -1.8e+62) {
		tmp = t_1;
	} else if (a <= 2.7e+45) {
		tmp = t + ((y / z) * (x - t));
	} else if (a <= 4.3e+136) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= 7.1e+152) {
		tmp = t - (a * (x / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    if (a <= (-1.8d+62)) then
        tmp = t_1
    else if (a <= 2.7d+45) then
        tmp = t + ((y / z) * (x - t))
    else if (a <= 4.3d+136) then
        tmp = x - (y * ((x - t) / a))
    else if (a <= 7.1d+152) then
        tmp = t - (a * (x / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -1.8e+62) {
		tmp = t_1;
	} else if (a <= 2.7e+45) {
		tmp = t + ((y / z) * (x - t));
	} else if (a <= 4.3e+136) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= 7.1e+152) {
		tmp = t - (a * (x / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -1.8e+62:
		tmp = t_1
	elif a <= 2.7e+45:
		tmp = t + ((y / z) * (x - t))
	elif a <= 4.3e+136:
		tmp = x - (y * ((x - t) / a))
	elif a <= 7.1e+152:
		tmp = t - (a * (x / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.8e+62)
		tmp = t_1;
	elseif (a <= 2.7e+45)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	elseif (a <= 4.3e+136)
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	elseif (a <= 7.1e+152)
		tmp = Float64(t - Float64(a * Float64(x / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -1.8e+62)
		tmp = t_1;
	elseif (a <= 2.7e+45)
		tmp = t + ((y / z) * (x - t));
	elseif (a <= 4.3e+136)
		tmp = x - (y * ((x - t) / a));
	elseif (a <= 7.1e+152)
		tmp = t - (a * (x / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+62], t$95$1, If[LessEqual[a, 2.7e+45], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3e+136], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.1e+152], N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.8e62 or 7.10000000000000017e152 < a

   1. Initial program 92.1%

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

   3. Taylor expanded in z around 0 65.9%

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

      1. *-commutative 65.9%

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

      2. associate-/l* 81.3%

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

   5. Simplified 81.3%

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

   if -1.8e62 < a < 2.69999999999999984e45

   1. Initial program 71.2%

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

   3. Taylor expanded in z around inf 70.9%

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

      1. associate--l+ 70.9%

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

      2. distribute-lft-out-- 70.9%

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

      3. div-sub 71.7%

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

      4. mul-1-neg 71.7%

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

      5. unsub-neg 71.7%

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

      6. distribute-rgt-out-- 71.7%

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

      7. associate-/l* 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in y around inf 76.6%

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

   if 2.69999999999999984e45 < a < 4.2999999999999999e136

   1. Initial program 82.3%

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

   3. Taylor expanded in z around 0 73.5%

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

      1. associate-/l* 76.3%

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

   5. Simplified 76.3%

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

   if 4.2999999999999999e136 < a < 7.10000000000000017e152

   1. Initial program 33.4%

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

   3. Taylor expanded in z around -inf 71.8%

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

   4. Taylor expanded in a around inf 71.8%

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

      1. associate-/l* 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in x around inf 71.8%

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

      1. associate-/l* 75.5%

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

   9. Simplified 75.5%

      \[\leadsto t + -1 \cdot \color{blue}{\left(a \cdot \frac{x}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+62}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+45}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+136}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq 7.1 \cdot 10^{+152}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-15} \lor \neg \left(z \leq 340000000000\right):\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e-15) (not (<= z 340000000000.0)))
   (- t (* (- t x) (/ (- y a) z)))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e-15) || !(z <= 340000000000.0)) {
		tmp = t - ((t - x) * ((y - a) / z));
	} else {
		tmp = x + ((t - x) * (y / 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 <= (-2.3d-15)) .or. (.not. (z <= 340000000000.0d0))) then
        tmp = t - ((t - x) * ((y - a) / z))
    else
        tmp = x + ((t - x) * (y / 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 <= -2.3e-15) || !(z <= 340000000000.0)) {
		tmp = t - ((t - x) * ((y - a) / z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e-15) or not (z <= 340000000000.0):
		tmp = t - ((t - x) * ((y - a) / z))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e-15) || !(z <= 340000000000.0))
		tmp = Float64(t - Float64(Float64(t - x) * Float64(Float64(y - a) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.3e-15) || ~((z <= 340000000000.0)))
		tmp = t - ((t - x) * ((y - a) / z));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.3e-15], N[Not[LessEqual[z, 340000000000.0]], $MachinePrecision]], N[(t - N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999999e-15 or 3.4e11 < z

   1. Initial program 66.9%

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

   3. Taylor expanded in z around inf 61.4%

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

      1. associate--l+ 61.4%

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

      2. distribute-lft-out-- 61.4%

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

      3. div-sub 61.4%

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

      4. mul-1-neg 61.4%

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

      5. unsub-neg 61.4%

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

      6. distribute-rgt-out-- 62.2%

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

      7. associate-/l* 75.3%

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

   5. Simplified 75.3%

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

   if -2.2999999999999999e-15 < z < 3.4e11

   1. Initial program 89.1%

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

   3. Taylor expanded in z around 0 71.0%

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

      1. *-commutative 71.0%

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

      2. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-15} \lor \neg \left(z \leq 340000000000\right):\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.0024:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.8e+55) x (if (<= a 0.0024) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e+55) {
		tmp = x;
	} else if (a <= 0.0024) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.8d+55)) then
        tmp = x
    else if (a <= 0.0024d0) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e+55) {
		tmp = x;
	} else if (a <= 0.0024) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.8e+55:
		tmp = x
	elif a <= 0.0024:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.8e+55)
		tmp = x;
	elseif (a <= 0.0024)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.8e+55)
		tmp = x;
	elseif (a <= 0.0024)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.8e+55], x, If[LessEqual[a, 0.0024], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.7999999999999997e55 or 0.00239999999999999979 < a

   1. Initial program 84.7%

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

   3. Taylor expanded in a around inf 46.4%

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

   if -5.7999999999999997e55 < a < 0.00239999999999999979

   1. Initial program 70.9%

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

   3. Taylor expanded in z around inf 32.2%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.0024:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.0% 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 77.1%

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

3. Taylor expanded in z around inf 21.5%

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

4. Final simplification 21.5%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024130 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))