Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.8% → 92.5%

Time: 15.2s

Alternatives: 20

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: 79.8% 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: 92.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t - x}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-238} \lor \neg \left(t_2 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{t_1}, t + \left(\frac{a}{t_1} + \frac{\left(y \cdot a\right) \cdot \left(x - t\right)}{z \cdot z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (- t x))) (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_2 -2e-238) (not (<= t_2 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+
      (/ (* a a) (/ (* z z) (- t x)))
      (fma
       -1.0
       (/ y t_1)
       (+ t (+ (/ a t_1) (/ (* (* y a) (- x t)) (* z z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (t - x);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_2 <= -2e-238) || !(t_2 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = ((a * a) / ((z * z) / (t - x))) + fma(-1.0, (y / t_1), (t + ((a / t_1) + (((y * a) * (x - t)) / (z * z)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(t - x))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_2 <= -2e-238) || !(t_2 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(Float64(Float64(a * a) / Float64(Float64(z * z) / Float64(t - x))) + fma(-1.0, Float64(y / t_1), Float64(t + Float64(Float64(a / t_1) + Float64(Float64(Float64(y * a) * Float64(x - t)) / Float64(z * z))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e-238], N[Not[LessEqual[t$95$2, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * a), $MachinePrecision] / N[(N[(z * z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 * N[(y / t$95$1), $MachinePrecision] + N[(t + N[(N[(a / t$95$1), $MachinePrecision] + N[(N[(N[(y * a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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-238 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 75.9%

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

      3. associate-*r/ 92.8%

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

      4. clear-num 92.7%

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

      5. un-div-inv 93.0%

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

   3. Applied egg-rr 93.0%

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

   if -2e-238 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

      1. +-commutative 3.3%

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

      2. fma-def 4.4%

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

   3. Simplified 4.4%

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

   4. Taylor expanded in z around inf 78.0%

      \[\leadsto \color{blue}{\frac{{a}^{2} \cdot \left(t - x\right)}{{z}^{2}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 74.3%

         \[\leadsto \color{blue}{\frac{{a}^{2}}{\frac{{z}^{2}}{t - x}}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      2. unpow2 74.3%

         \[\leadsto \frac{\color{blue}{a \cdot a}}{\frac{{z}^{2}}{t - x}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      3. unpow2 74.3%

         \[\leadsto \frac{a \cdot a}{\frac{\color{blue}{z \cdot z}}{t - x}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      4. fma-def 74.3%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \color{blue}{\mathsf{fma}\left(-1, \frac{y \cdot \left(t - x\right)}{z}, t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)} \]

      5. associate-/l* 84.8%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \color{blue}{\frac{y}{\frac{z}{t - x}}}, t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right) \]

      6. associate-/l* 84.9%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\color{blue}{\frac{a}{\frac{z}{t - x}}} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right) \]

      7. mul-1-neg 84.9%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\frac{a}{\frac{z}{t - x}} + \color{blue}{\left(-\frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)}\right)\right) \]

      8. associate-*r* 88.6%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\frac{a}{\frac{z}{t - x}} + \left(-\frac{\color{blue}{\left(y \cdot a\right) \cdot \left(t - x\right)}}{{z}^{2}}\right)\right)\right) \]

      9. unpow2 88.6%

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

   6. Simplified 88.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-238} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\frac{a}{\frac{z}{t - x}} + \frac{\left(y \cdot a\right) \cdot \left(x - t\right)}{z \cdot z}\right)\right)\\ \end{array} \]

Alternative 2: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-140} \lor \neg \left(t_1 \leq 5 \cdot 10^{-304}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-140) (not (<= t_1 5e-304)))
     t_1
     (+ t (/ (* (- t x) (- a y)) 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-140) || !(t_1 <= 5e-304)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-140)) .or. (.not. (t_1 <= 5d-304))) then
        tmp = t_1
    else
        tmp = t + (((t - x) * (a - y)) / 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-140) || !(t_1 <= 5e-304)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - y)) / 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-140) or not (t_1 <= 5e-304):
		tmp = t_1
	else:
		tmp = t + (((t - x) * (a - y)) / 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-140) || !(t_1 <= 5e-304))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / 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-140) || ~((t_1 <= 5e-304)))
		tmp = t_1;
	else
		tmp = t + (((t - x) * (a - y)) / 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-140], N[Not[LessEqual[t$95$1, 5e-304]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $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-140 or 4.99999999999999965e-304 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.2%

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

   if -2e-140 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.99999999999999965e-304

   1. Initial program 12.1%

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

   2. Taylor expanded in z around inf 77.2%

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

      1. +-commutative 77.2%

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

      2. associate--l+ 77.2%

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

      3. associate-*r/ 77.2%

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

      4. associate-*r/ 77.2%

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

      5. div-sub 77.2%

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

      6. distribute-lft-out-- 77.2%

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

      7. mul-1-neg 77.2%

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

      8. distribute-neg-frac 77.2%

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

      9. unsub-neg 77.2%

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

      10. distribute-rgt-out-- 77.2%

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

   4. Simplified 77.2%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-140} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-304}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 3: 92.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-238} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-238) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (* (- t x) (- a y)) 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-238) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-238)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((t - x) * (a - y)) / 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-238) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / 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-238) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / 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-238) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / 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-238) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((t - x) * (a - y)) / 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-238], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $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-238 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 75.9%

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

      3. associate-*r/ 92.8%

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

      4. clear-num 92.7%

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

      5. un-div-inv 93.0%

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

   3. Applied egg-rr 93.0%

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

   if -2e-238 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

   2. Taylor expanded in z around inf 78.4%

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

      1. +-commutative 78.4%

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

      2. associate--l+ 78.4%

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

      3. associate-*r/ 78.4%

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

      4. associate-*r/ 78.4%

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

      5. div-sub 78.4%

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

      6. distribute-lft-out-- 78.4%

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

      7. mul-1-neg 78.4%

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

      8. distribute-neg-frac 78.4%

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

      9. unsub-neg 78.4%

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

      10. distribute-rgt-out-- 78.4%

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

   4. Simplified 78.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-238} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 4: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{a - z}\\ t_2 := t \cdot t_1\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - t_1\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (- a z))) (t_2 (* t t_1)))
   (if (<= z -2.35e+61)
     t_2
     (if (<= z -1e+49)
       (* x (- 1.0 t_1))
       (if (<= z -1.15e+33)
         t_2
         (if (<= z -8.2e+24)
           (* x (/ (- y a) z))
           (if (<= z 1.45e+47) (+ x (/ (- t x) (/ (- a z) y))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (a - z);
	double t_2 = t * t_1;
	double tmp;
	if (z <= -2.35e+61) {
		tmp = t_2;
	} else if (z <= -1e+49) {
		tmp = x * (1.0 - t_1);
	} else if (z <= -1.15e+33) {
		tmp = t_2;
	} else if (z <= -8.2e+24) {
		tmp = x * ((y - a) / z);
	} else if (z <= 1.45e+47) {
		tmp = x + ((t - x) / ((a - z) / y));
	} 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) / (a - z)
    t_2 = t * t_1
    if (z <= (-2.35d+61)) then
        tmp = t_2
    else if (z <= (-1d+49)) then
        tmp = x * (1.0d0 - t_1)
    else if (z <= (-1.15d+33)) then
        tmp = t_2
    else if (z <= (-8.2d+24)) then
        tmp = x * ((y - a) / z)
    else if (z <= 1.45d+47) then
        tmp = x + ((t - x) / ((a - z) / y))
    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) / (a - z);
	double t_2 = t * t_1;
	double tmp;
	if (z <= -2.35e+61) {
		tmp = t_2;
	} else if (z <= -1e+49) {
		tmp = x * (1.0 - t_1);
	} else if (z <= -1.15e+33) {
		tmp = t_2;
	} else if (z <= -8.2e+24) {
		tmp = x * ((y - a) / z);
	} else if (z <= 1.45e+47) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) / (a - z)
	t_2 = t * t_1
	tmp = 0
	if z <= -2.35e+61:
		tmp = t_2
	elif z <= -1e+49:
		tmp = x * (1.0 - t_1)
	elif z <= -1.15e+33:
		tmp = t_2
	elif z <= -8.2e+24:
		tmp = x * ((y - a) / z)
	elif z <= 1.45e+47:
		tmp = x + ((t - x) / ((a - z) / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(a - z))
	t_2 = Float64(t * t_1)
	tmp = 0.0
	if (z <= -2.35e+61)
		tmp = t_2;
	elseif (z <= -1e+49)
		tmp = Float64(x * Float64(1.0 - t_1));
	elseif (z <= -1.15e+33)
		tmp = t_2;
	elseif (z <= -8.2e+24)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= 1.45e+47)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) / (a - z);
	t_2 = t * t_1;
	tmp = 0.0;
	if (z <= -2.35e+61)
		tmp = t_2;
	elseif (z <= -1e+49)
		tmp = x * (1.0 - t_1);
	elseif (z <= -1.15e+33)
		tmp = t_2;
	elseif (z <= -8.2e+24)
		tmp = x * ((y - a) / z);
	elseif (z <= 1.45e+47)
		tmp = x + ((t - x) / ((a - z) / y));
	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[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * t$95$1), $MachinePrecision]}, If[LessEqual[z, -2.35e+61], t$95$2, If[LessEqual[z, -1e+49], N[(x * N[(1.0 - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e+33], t$95$2, If[LessEqual[z, -8.2e+24], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+47], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3499999999999999e61 or -9.99999999999999946e48 < z < -1.15000000000000005e33 or 1.4499999999999999e47 < z

   1. Initial program 65.6%

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

   2. Taylor expanded in t around inf 68.7%

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

      1. div-sub 68.7%

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

   4. Simplified 68.7%

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

   if -2.3499999999999999e61 < z < -9.99999999999999946e48

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

   4. Simplified 99.7%

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

   if -1.15000000000000005e33 < z < -8.2000000000000002e24

   1. Initial program 72.3%

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

   2. Taylor expanded in x around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   4. Simplified 58.8%

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

   5. Taylor expanded in z around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. sub-neg 82.1%

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

      3. mul-1-neg 82.1%

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

   7. Simplified 82.1%

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

   if -8.2000000000000002e24 < z < 1.4499999999999999e47

   1. Initial program 92.2%

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

      1. *-commutative 92.2%

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

      2. associate-*l/ 88.0%

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

      3. associate-*r/ 93.7%

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

      4. clear-num 93.5%

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

      5. un-div-inv 94.0%

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

   3. Applied egg-rr 94.0%

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

   4. Taylor expanded in y around inf 87.8%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 5: 45.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-257}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-71}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.8e+122)
     t
     (if (<= z -4.5e-230)
       t_1
       (if (<= z 1.6e-257)
         (/ y (/ a t))
         (if (<= z 1.26e-113)
           t_1
           (if (<= z 1.45e-71)
             (* y (/ t (- a z)))
             (if (<= z 3.4e+45) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.8e+122) {
		tmp = t;
	} else if (z <= -4.5e-230) {
		tmp = t_1;
	} else if (z <= 1.6e-257) {
		tmp = y / (a / t);
	} else if (z <= 1.26e-113) {
		tmp = t_1;
	} else if (z <= 1.45e-71) {
		tmp = y * (t / (a - z));
	} else if (z <= 3.4e+45) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-1.8d+122)) then
        tmp = t
    else if (z <= (-4.5d-230)) then
        tmp = t_1
    else if (z <= 1.6d-257) then
        tmp = y / (a / t)
    else if (z <= 1.26d-113) then
        tmp = t_1
    else if (z <= 1.45d-71) then
        tmp = y * (t / (a - z))
    else if (z <= 3.4d+45) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.8e+122) {
		tmp = t;
	} else if (z <= -4.5e-230) {
		tmp = t_1;
	} else if (z <= 1.6e-257) {
		tmp = y / (a / t);
	} else if (z <= 1.26e-113) {
		tmp = t_1;
	} else if (z <= 1.45e-71) {
		tmp = y * (t / (a - z));
	} else if (z <= 3.4e+45) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -1.8e+122:
		tmp = t
	elif z <= -4.5e-230:
		tmp = t_1
	elif z <= 1.6e-257:
		tmp = y / (a / t)
	elif z <= 1.26e-113:
		tmp = t_1
	elif z <= 1.45e-71:
		tmp = y * (t / (a - z))
	elif z <= 3.4e+45:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -1.8e+122)
		tmp = t;
	elseif (z <= -4.5e-230)
		tmp = t_1;
	elseif (z <= 1.6e-257)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 1.26e-113)
		tmp = t_1;
	elseif (z <= 1.45e-71)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= 3.4e+45)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -1.8e+122)
		tmp = t;
	elseif (z <= -4.5e-230)
		tmp = t_1;
	elseif (z <= 1.6e-257)
		tmp = y / (a / t);
	elseif (z <= 1.26e-113)
		tmp = t_1;
	elseif (z <= 1.45e-71)
		tmp = y * (t / (a - z));
	elseif (z <= 3.4e+45)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+122], t, If[LessEqual[z, -4.5e-230], t$95$1, If[LessEqual[z, 1.6e-257], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.26e-113], t$95$1, If[LessEqual[z, 1.45e-71], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+45], t$95$1, t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8000000000000001e122 or 3.4e45 < z

   1. Initial program 62.1%

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

   2. Taylor expanded in z around inf 60.0%

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

   if -1.8000000000000001e122 < z < -4.50000000000000004e-230 or 1.59999999999999993e-257 < z < 1.26000000000000003e-113 or 1.4499999999999999e-71 < z < 3.4e45

   1. Initial program 89.1%

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

   2. Taylor expanded in x around inf 60.4%

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

      1. mul-1-neg 60.4%

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

      2. unsub-neg 60.4%

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

   4. Simplified 60.4%

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

   5. Taylor expanded in z around 0 52.8%

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

   if -4.50000000000000004e-230 < z < 1.59999999999999993e-257

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 53.9%

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

      1. associate-/l* 63.9%

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

   4. Simplified 63.9%

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

   5. Taylor expanded in z around 0 53.9%

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

      1. associate-/l* 65.1%

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

   7. Simplified 65.1%

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

   if 1.26000000000000003e-113 < z < 1.4499999999999999e-71

   1. Initial program 93.0%

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

   2. Taylor expanded in y around inf 73.0%

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

   3. Taylor expanded in t around inf 65.7%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-230}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-257}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-71}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+60}:\\ \;\;\;\;t \cdot t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - t_1\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+27} \lor \neg \left(z \leq 3 \cdot 10^{+72}\right):\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (- a z))))
   (if (<= z -4.9e+60)
     (* t t_1)
     (if (<= z -6.2e+49)
       (* x (- 1.0 t_1))
       (if (or (<= z -2.5e+27) (not (<= z 3e+72)))
         (+ t (/ (* (- t x) (- a y)) z))
         (+ x (/ (- t x) (/ (- a z) y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (a - z);
	double tmp;
	if (z <= -4.9e+60) {
		tmp = t * t_1;
	} else if (z <= -6.2e+49) {
		tmp = x * (1.0 - t_1);
	} else if ((z <= -2.5e+27) || !(z <= 3e+72)) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) / (a - z)
    if (z <= (-4.9d+60)) then
        tmp = t * t_1
    else if (z <= (-6.2d+49)) then
        tmp = x * (1.0d0 - t_1)
    else if ((z <= (-2.5d+27)) .or. (.not. (z <= 3d+72))) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = x + ((t - x) / ((a - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (a - z);
	double tmp;
	if (z <= -4.9e+60) {
		tmp = t * t_1;
	} else if (z <= -6.2e+49) {
		tmp = x * (1.0 - t_1);
	} else if ((z <= -2.5e+27) || !(z <= 3e+72)) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) / (a - z)
	tmp = 0
	if z <= -4.9e+60:
		tmp = t * t_1
	elif z <= -6.2e+49:
		tmp = x * (1.0 - t_1)
	elif (z <= -2.5e+27) or not (z <= 3e+72):
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = x + ((t - x) / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(a - z))
	tmp = 0.0
	if (z <= -4.9e+60)
		tmp = Float64(t * t_1);
	elseif (z <= -6.2e+49)
		tmp = Float64(x * Float64(1.0 - t_1));
	elseif ((z <= -2.5e+27) || !(z <= 3e+72))
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) / (a - z);
	tmp = 0.0;
	if (z <= -4.9e+60)
		tmp = t * t_1;
	elseif (z <= -6.2e+49)
		tmp = x * (1.0 - t_1);
	elseif ((z <= -2.5e+27) || ~((z <= 3e+72)))
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = x + ((t - x) / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.9e+60], N[(t * t$95$1), $MachinePrecision], If[LessEqual[z, -6.2e+49], N[(x * N[(1.0 - t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.5e+27], N[Not[LessEqual[z, 3e+72]], $MachinePrecision]], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.9000000000000003e60

   1. Initial program 65.7%

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

   2. Taylor expanded in t around inf 71.9%

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

      1. div-sub 71.9%

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

   4. Simplified 71.9%

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

   if -4.9000000000000003e60 < z < -6.19999999999999985e49

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

   4. Simplified 99.7%

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

   if -6.19999999999999985e49 < z < -2.4999999999999999e27 or 3.00000000000000003e72 < z

   1. Initial program 60.7%

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

   2. Taylor expanded in z around inf 71.7%

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

      1. +-commutative 71.7%

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

      2. associate--l+ 71.7%

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

      3. associate-*r/ 71.7%

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

      4. associate-*r/ 71.7%

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

      5. div-sub 71.7%

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

      6. distribute-lft-out-- 71.7%

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

      7. mul-1-neg 71.7%

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

      8. distribute-neg-frac 71.7%

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

      9. unsub-neg 71.7%

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

      10. distribute-rgt-out-- 71.9%

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

   4. Simplified 71.9%

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

   if -2.4999999999999999e27 < z < 3.00000000000000003e72

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 88.7%

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

      3. associate-*r/ 94.1%

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

      4. clear-num 93.9%

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

      5. un-div-inv 94.4%

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

   3. Applied egg-rr 94.4%

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

   4. Taylor expanded in y around inf 85.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+27} \lor \neg \left(z \leq 3 \cdot 10^{+72}\right):\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \end{array} \]

Alternative 7: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y - z}{\frac{a - z}{x}}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+27} \lor \neg \left(z \leq 7.2 \cdot 10^{+71}\right):\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.9e+60)
   (* t (/ (- y z) (- a z)))
   (if (<= z -2.8e+49)
     (- x (/ (- y z) (/ (- a z) x)))
     (if (or (<= z -2.25e+27) (not (<= z 7.2e+71)))
       (+ t (/ (* (- t x) (- a y)) z))
       (+ x (/ (- t x) (/ (- a z) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.9e+60) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -2.8e+49) {
		tmp = x - ((y - z) / ((a - z) / x));
	} else if ((z <= -2.25e+27) || !(z <= 7.2e+71)) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.9d+60)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= (-2.8d+49)) then
        tmp = x - ((y - z) / ((a - z) / x))
    else if ((z <= (-2.25d+27)) .or. (.not. (z <= 7.2d+71))) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = x + ((t - x) / ((a - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.9e+60) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -2.8e+49) {
		tmp = x - ((y - z) / ((a - z) / x));
	} else if ((z <= -2.25e+27) || !(z <= 7.2e+71)) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.9e+60:
		tmp = t * ((y - z) / (a - z))
	elif z <= -2.8e+49:
		tmp = x - ((y - z) / ((a - z) / x))
	elif (z <= -2.25e+27) or not (z <= 7.2e+71):
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = x + ((t - x) / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.9e+60)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= -2.8e+49)
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(a - z) / x)));
	elseif ((z <= -2.25e+27) || !(z <= 7.2e+71))
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.9e+60)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= -2.8e+49)
		tmp = x - ((y - z) / ((a - z) / x));
	elseif ((z <= -2.25e+27) || ~((z <= 7.2e+71)))
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = x + ((t - x) / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.9e+60], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e+49], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.25e+27], N[Not[LessEqual[z, 7.2e+71]], $MachinePrecision]], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.9000000000000003e60

   1. Initial program 65.7%

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

   2. Taylor expanded in t around inf 71.9%

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

      1. div-sub 71.9%

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

   4. Simplified 71.9%

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

   if -4.9000000000000003e60 < z < -2.7999999999999998e49

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 81.7%

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

      1. +-commutative 81.7%

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

      2. mul-1-neg 81.7%

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

      3. unsub-neg 81.7%

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

      4. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   if -2.7999999999999998e49 < z < -2.25e27 or 7.1999999999999999e71 < z

   1. Initial program 60.7%

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

   2. Taylor expanded in z around inf 71.7%

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

      1. +-commutative 71.7%

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

      2. associate--l+ 71.7%

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

      3. associate-*r/ 71.7%

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

      4. associate-*r/ 71.7%

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

      5. div-sub 71.7%

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

      6. distribute-lft-out-- 71.7%

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

      7. mul-1-neg 71.7%

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

      8. distribute-neg-frac 71.7%

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

      9. unsub-neg 71.7%

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

      10. distribute-rgt-out-- 71.9%

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

   4. Simplified 71.9%

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

   if -2.25e27 < z < 7.1999999999999999e71

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 88.7%

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

      3. associate-*r/ 94.1%

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

      4. clear-num 93.9%

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

      5. un-div-inv 94.4%

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

   3. Applied egg-rr 94.4%

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

   4. Taylor expanded in y around inf 85.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y - z}{\frac{a - z}{x}}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+27} \lor \neg \left(z \leq 7.2 \cdot 10^{+71}\right):\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \end{array} \]

Alternative 8: 47.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -2.1e+122)
     t
     (if (<= z -8.5e-14)
       (/ y (/ z (- x t)))
       (if (<= z -1.16e-192)
         t_1
         (if (<= z 2.4e-257)
           (* y (/ (- t x) a))
           (if (<= z 2.5e+46) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.1e+122) {
		tmp = t;
	} else if (z <= -8.5e-14) {
		tmp = y / (z / (x - t));
	} else if (z <= -1.16e-192) {
		tmp = t_1;
	} else if (z <= 2.4e-257) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.5e+46) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-2.1d+122)) then
        tmp = t
    else if (z <= (-8.5d-14)) then
        tmp = y / (z / (x - t))
    else if (z <= (-1.16d-192)) then
        tmp = t_1
    else if (z <= 2.4d-257) then
        tmp = y * ((t - x) / a)
    else if (z <= 2.5d+46) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.1e+122) {
		tmp = t;
	} else if (z <= -8.5e-14) {
		tmp = y / (z / (x - t));
	} else if (z <= -1.16e-192) {
		tmp = t_1;
	} else if (z <= 2.4e-257) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.5e+46) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -2.1e+122:
		tmp = t
	elif z <= -8.5e-14:
		tmp = y / (z / (x - t))
	elif z <= -1.16e-192:
		tmp = t_1
	elif z <= 2.4e-257:
		tmp = y * ((t - x) / a)
	elif z <= 2.5e+46:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -2.1e+122)
		tmp = t;
	elseif (z <= -8.5e-14)
		tmp = Float64(y / Float64(z / Float64(x - t)));
	elseif (z <= -1.16e-192)
		tmp = t_1;
	elseif (z <= 2.4e-257)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 2.5e+46)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -2.1e+122)
		tmp = t;
	elseif (z <= -8.5e-14)
		tmp = y / (z / (x - t));
	elseif (z <= -1.16e-192)
		tmp = t_1;
	elseif (z <= 2.4e-257)
		tmp = y * ((t - x) / a);
	elseif (z <= 2.5e+46)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+122], t, If[LessEqual[z, -8.5e-14], N[(y / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.16e-192], t$95$1, If[LessEqual[z, 2.4e-257], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+46], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.10000000000000016e122 or 2.5000000000000001e46 < z

   1. Initial program 62.1%

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

   2. Taylor expanded in z around inf 60.0%

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

   if -2.10000000000000016e122 < z < -8.50000000000000038e-14

   1. Initial program 82.8%

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

   2. Taylor expanded in y around inf 49.3%

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

   3. Taylor expanded in z around inf 35.3%

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

      1. distribute-lft-out-- 35.3%

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

      2. neg-mul-1 35.3%

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

      3. associate-/l* 43.4%

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

   5. Simplified 43.4%

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

   if -8.50000000000000038e-14 < z < -1.16000000000000003e-192 or 2.40000000000000017e-257 < z < 2.5000000000000001e46

   1. Initial program 91.5%

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

   2. Taylor expanded in x around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. unsub-neg 62.6%

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

   4. Simplified 62.6%

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

   5. Taylor expanded in z around 0 57.9%

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

   if -1.16000000000000003e-192 < z < 2.40000000000000017e-257

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 75.4%

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

   3. Taylor expanded in a around inf 79.0%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 59.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+22} \lor \neg \left(x \leq 4.2 \cdot 10^{+133}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= x -2.6e+113)
     t_1
     (if (<= x -4e+59)
       (* x (/ (- y a) z))
       (if (or (<= x -9e+22) (not (<= x 4.2e+133)))
         t_1
         (* t (/ (- y z) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -2.6e+113) {
		tmp = t_1;
	} else if (x <= -4e+59) {
		tmp = x * ((y - a) / z);
	} else if ((x <= -9e+22) || !(x <= 4.2e+133)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (x <= (-2.6d+113)) then
        tmp = t_1
    else if (x <= (-4d+59)) then
        tmp = x * ((y - a) / z)
    else if ((x <= (-9d+22)) .or. (.not. (x <= 4.2d+133))) then
        tmp = t_1
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -2.6e+113) {
		tmp = t_1;
	} else if (x <= -4e+59) {
		tmp = x * ((y - a) / z);
	} else if ((x <= -9e+22) || !(x <= 4.2e+133)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -2.6e+113:
		tmp = t_1
	elif x <= -4e+59:
		tmp = x * ((y - a) / z)
	elif (x <= -9e+22) or not (x <= 4.2e+133):
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -2.6e+113)
		tmp = t_1;
	elseif (x <= -4e+59)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif ((x <= -9e+22) || !(x <= 4.2e+133))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -2.6e+113)
		tmp = t_1;
	elseif (x <= -4e+59)
		tmp = x * ((y - a) / z);
	elseif ((x <= -9e+22) || ~((x <= 4.2e+133)))
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+113], t$95$1, If[LessEqual[x, -4e+59], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -9e+22], N[Not[LessEqual[x, 4.2e+133]], $MachinePrecision]], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5999999999999999e113 or -3.99999999999999989e59 < x < -8.9999999999999996e22 or 4.2e133 < x

   1. Initial program 78.6%

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

   2. Taylor expanded in x around inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. unsub-neg 70.2%

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

   4. Simplified 70.2%

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

   5. Taylor expanded in z around 0 64.2%

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

   if -2.5999999999999999e113 < x < -3.99999999999999989e59

   1. Initial program 38.3%

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

   2. Taylor expanded in x around inf 38.4%

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

      1. mul-1-neg 38.4%

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

      2. unsub-neg 38.4%

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

   4. Simplified 38.4%

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

   5. Taylor expanded in z around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. sub-neg 83.3%

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

      3. mul-1-neg 83.3%

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

   7. Simplified 83.3%

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

   if -8.9999999999999996e22 < x < 4.2e133

   1. Initial program 83.9%

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

   2. Taylor expanded in t around inf 72.9%

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

      1. div-sub 72.9%

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

   4. Simplified 72.9%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+22} \lor \neg \left(x \leq 4.2 \cdot 10^{+133}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 10: 60.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -2.85 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= x -2.85e+113)
     t_1
     (if (<= x -4.9e+63)
       (* x (/ (- y a) z))
       (if (<= x -1.9e+23)
         t_1
         (if (<= x 3.1e+29)
           (* t (/ (- y z) (- a z)))
           (+ x (/ (- t x) (/ a y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -2.85e+113) {
		tmp = t_1;
	} else if (x <= -4.9e+63) {
		tmp = x * ((y - a) / z);
	} else if (x <= -1.9e+23) {
		tmp = t_1;
	} else if (x <= 3.1e+29) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (x <= (-2.85d+113)) then
        tmp = t_1
    else if (x <= (-4.9d+63)) then
        tmp = x * ((y - a) / z)
    else if (x <= (-1.9d+23)) then
        tmp = t_1
    else if (x <= 3.1d+29) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -2.85e+113) {
		tmp = t_1;
	} else if (x <= -4.9e+63) {
		tmp = x * ((y - a) / z);
	} else if (x <= -1.9e+23) {
		tmp = t_1;
	} else if (x <= 3.1e+29) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -2.85e+113:
		tmp = t_1
	elif x <= -4.9e+63:
		tmp = x * ((y - a) / z)
	elif x <= -1.9e+23:
		tmp = t_1
	elif x <= 3.1e+29:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -2.85e+113)
		tmp = t_1;
	elseif (x <= -4.9e+63)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (x <= -1.9e+23)
		tmp = t_1;
	elseif (x <= 3.1e+29)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -2.85e+113)
		tmp = t_1;
	elseif (x <= -4.9e+63)
		tmp = x * ((y - a) / z);
	elseif (x <= -1.9e+23)
		tmp = t_1;
	elseif (x <= 3.1e+29)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.85e+113], t$95$1, If[LessEqual[x, -4.9e+63], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e+23], t$95$1, If[LessEqual[x, 3.1e+29], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.8499999999999999e113 or -4.8999999999999997e63 < x < -1.89999999999999987e23

   1. Initial program 80.2%

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

   2. Taylor expanded in x around inf 69.0%

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

      1. mul-1-neg 69.0%

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

      2. unsub-neg 69.0%

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

   4. Simplified 69.0%

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

   5. Taylor expanded in z around 0 64.9%

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

   if -2.8499999999999999e113 < x < -4.8999999999999997e63

   1. Initial program 38.3%

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

   2. Taylor expanded in x around inf 38.4%

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

      1. mul-1-neg 38.4%

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

      2. unsub-neg 38.4%

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

   4. Simplified 38.4%

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

   5. Taylor expanded in z around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. sub-neg 83.3%

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

      3. mul-1-neg 83.3%

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

   7. Simplified 83.3%

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

   if -1.89999999999999987e23 < x < 3.0999999999999999e29

   1. Initial program 83.7%

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

   2. Taylor expanded in t around inf 75.5%

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

      1. div-sub 75.5%

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

   4. Simplified 75.5%

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

   if 3.0999999999999999e29 < x

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*l/ 69.7%

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

      3. associate-*r/ 83.2%

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

      4. clear-num 83.2%

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

      5. un-div-inv 83.2%

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

   3. Applied egg-rr 83.2%

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

   4. Taylor expanded in z around 0 61.7%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]

Alternative 11: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y - z}{\frac{a}{x}}\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- y z) (/ a x)))))
   (if (<= x -5.6e+112)
     t_1
     (if (<= x -4.6e+38)
       (* x (/ (- y a) z))
       (if (<= x -2.15e+23)
         t_1
         (if (<= x 9e+30)
           (* t (/ (- y z) (- a z)))
           (+ x (/ (- t x) (/ a y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) / (a / x));
	double tmp;
	if (x <= -5.6e+112) {
		tmp = t_1;
	} else if (x <= -4.6e+38) {
		tmp = x * ((y - a) / z);
	} else if (x <= -2.15e+23) {
		tmp = t_1;
	} else if (x <= 9e+30) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y - z) / (a / x))
    if (x <= (-5.6d+112)) then
        tmp = t_1
    else if (x <= (-4.6d+38)) then
        tmp = x * ((y - a) / z)
    else if (x <= (-2.15d+23)) then
        tmp = t_1
    else if (x <= 9d+30) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) / (a / x));
	double tmp;
	if (x <= -5.6e+112) {
		tmp = t_1;
	} else if (x <= -4.6e+38) {
		tmp = x * ((y - a) / z);
	} else if (x <= -2.15e+23) {
		tmp = t_1;
	} else if (x <= 9e+30) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) / (a / x))
	tmp = 0
	if x <= -5.6e+112:
		tmp = t_1
	elif x <= -4.6e+38:
		tmp = x * ((y - a) / z)
	elif x <= -2.15e+23:
		tmp = t_1
	elif x <= 9e+30:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) / Float64(a / x)))
	tmp = 0.0
	if (x <= -5.6e+112)
		tmp = t_1;
	elseif (x <= -4.6e+38)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (x <= -2.15e+23)
		tmp = t_1;
	elseif (x <= 9e+30)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) / (a / x));
	tmp = 0.0;
	if (x <= -5.6e+112)
		tmp = t_1;
	elseif (x <= -4.6e+38)
		tmp = x * ((y - a) / z);
	elseif (x <= -2.15e+23)
		tmp = t_1;
	elseif (x <= 9e+30)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y - z), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.6e+112], t$95$1, If[LessEqual[x, -4.6e+38], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.15e+23], t$95$1, If[LessEqual[x, 9e+30], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.6000000000000003e112 or -4.6000000000000002e38 < x < -2.1499999999999999e23

   1. Initial program 82.1%

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

   2. Taylor expanded in x around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. unsub-neg 71.6%

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

   4. Simplified 71.6%

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

   5. Taylor expanded in a around -inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. associate-/l* 67.8%

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

   7. Simplified 67.8%

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

   if -5.6000000000000003e112 < x < -4.6000000000000002e38

   1. Initial program 47.0%

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

   2. Taylor expanded in x around inf 39.7%

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

      1. mul-1-neg 39.7%

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

      2. unsub-neg 39.7%

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

   4. Simplified 39.7%

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

   5. Taylor expanded in z around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. sub-neg 66.9%

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

      3. mul-1-neg 66.9%

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

   7. Simplified 66.9%

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

   if -2.1499999999999999e23 < x < 8.9999999999999999e30

   1. Initial program 83.7%

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

   2. Taylor expanded in t around inf 75.5%

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

      1. div-sub 75.5%

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

   4. Simplified 75.5%

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

   if 8.9999999999999999e30 < x

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*l/ 69.7%

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

      3. associate-*r/ 83.2%

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

      4. clear-num 83.2%

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

      5. un-div-inv 83.2%

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

   3. Applied egg-rr 83.2%

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

   4. Taylor expanded in z around 0 61.7%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+112}:\\ \;\;\;\;x - \frac{y - z}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{+23}:\\ \;\;\;\;x - \frac{y - z}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]

Alternative 12: 59.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y - z}{\frac{a}{x}}\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- y z) (/ a x)))))
   (if (<= x -5.4e+113)
     t_1
     (if (<= x -2.25e+38)
       (* x (/ (- y a) z))
       (if (<= x -4.3e+23)
         t_1
         (if (<= x 6.8e+30)
           (/ t (/ (- a z) (- y z)))
           (+ x (/ (- t x) (/ a y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) / (a / x));
	double tmp;
	if (x <= -5.4e+113) {
		tmp = t_1;
	} else if (x <= -2.25e+38) {
		tmp = x * ((y - a) / z);
	} else if (x <= -4.3e+23) {
		tmp = t_1;
	} else if (x <= 6.8e+30) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y - z) / (a / x))
    if (x <= (-5.4d+113)) then
        tmp = t_1
    else if (x <= (-2.25d+38)) then
        tmp = x * ((y - a) / z)
    else if (x <= (-4.3d+23)) then
        tmp = t_1
    else if (x <= 6.8d+30) then
        tmp = t / ((a - z) / (y - z))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) / (a / x));
	double tmp;
	if (x <= -5.4e+113) {
		tmp = t_1;
	} else if (x <= -2.25e+38) {
		tmp = x * ((y - a) / z);
	} else if (x <= -4.3e+23) {
		tmp = t_1;
	} else if (x <= 6.8e+30) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) / (a / x))
	tmp = 0
	if x <= -5.4e+113:
		tmp = t_1
	elif x <= -2.25e+38:
		tmp = x * ((y - a) / z)
	elif x <= -4.3e+23:
		tmp = t_1
	elif x <= 6.8e+30:
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) / Float64(a / x)))
	tmp = 0.0
	if (x <= -5.4e+113)
		tmp = t_1;
	elseif (x <= -2.25e+38)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (x <= -4.3e+23)
		tmp = t_1;
	elseif (x <= 6.8e+30)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) / (a / x));
	tmp = 0.0;
	if (x <= -5.4e+113)
		tmp = t_1;
	elseif (x <= -2.25e+38)
		tmp = x * ((y - a) / z);
	elseif (x <= -4.3e+23)
		tmp = t_1;
	elseif (x <= 6.8e+30)
		tmp = t / ((a - z) / (y - z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y - z), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.4e+113], t$95$1, If[LessEqual[x, -2.25e+38], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.3e+23], t$95$1, If[LessEqual[x, 6.8e+30], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.40000000000000022e113 or -2.2499999999999999e38 < x < -4.2999999999999999e23

   1. Initial program 82.1%

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

   2. Taylor expanded in x around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. unsub-neg 71.6%

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

   4. Simplified 71.6%

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

   5. Taylor expanded in a around -inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. associate-/l* 67.8%

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

   7. Simplified 67.8%

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

   if -5.40000000000000022e113 < x < -2.2499999999999999e38

   1. Initial program 47.0%

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

   2. Taylor expanded in x around inf 39.7%

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

      1. mul-1-neg 39.7%

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

      2. unsub-neg 39.7%

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

   4. Simplified 39.7%

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

   5. Taylor expanded in z around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. sub-neg 66.9%

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

      3. mul-1-neg 66.9%

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

   7. Simplified 66.9%

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

   if -4.2999999999999999e23 < x < 6.8000000000000005e30

   1. Initial program 83.7%

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

   2. Taylor expanded in x around 0 62.5%

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

      1. associate-/l* 75.7%

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

   4. Simplified 75.7%

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

   if 6.8000000000000005e30 < x

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*l/ 69.7%

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

      3. associate-*r/ 83.2%

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

      4. clear-num 83.2%

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

      5. un-div-inv 83.2%

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

   3. Applied egg-rr 83.2%

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

   4. Taylor expanded in z around 0 61.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+113}:\\ \;\;\;\;x - \frac{y - z}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+23}:\\ \;\;\;\;x - \frac{y - z}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]

Alternative 13: 46.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-257}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.8e+122)
     t
     (if (<= z -6.6e-232)
       t_1
       (if (<= z 1.8e-257) (/ y (/ a t)) (if (<= z 1.06e+46) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.8e+122) {
		tmp = t;
	} else if (z <= -6.6e-232) {
		tmp = t_1;
	} else if (z <= 1.8e-257) {
		tmp = y / (a / t);
	} else if (z <= 1.06e+46) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-1.8d+122)) then
        tmp = t
    else if (z <= (-6.6d-232)) then
        tmp = t_1
    else if (z <= 1.8d-257) then
        tmp = y / (a / t)
    else if (z <= 1.06d+46) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.8e+122) {
		tmp = t;
	} else if (z <= -6.6e-232) {
		tmp = t_1;
	} else if (z <= 1.8e-257) {
		tmp = y / (a / t);
	} else if (z <= 1.06e+46) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -1.8e+122:
		tmp = t
	elif z <= -6.6e-232:
		tmp = t_1
	elif z <= 1.8e-257:
		tmp = y / (a / t)
	elif z <= 1.06e+46:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -1.8e+122)
		tmp = t;
	elseif (z <= -6.6e-232)
		tmp = t_1;
	elseif (z <= 1.8e-257)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 1.06e+46)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -1.8e+122)
		tmp = t;
	elseif (z <= -6.6e-232)
		tmp = t_1;
	elseif (z <= 1.8e-257)
		tmp = y / (a / t);
	elseif (z <= 1.06e+46)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+122], t, If[LessEqual[z, -6.6e-232], t$95$1, If[LessEqual[z, 1.8e-257], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e+46], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8000000000000001e122 or 1.05999999999999998e46 < z

   1. Initial program 62.1%

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

   2. Taylor expanded in z around inf 60.0%

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

   if -1.8000000000000001e122 < z < -6.5999999999999997e-232 or 1.80000000000000003e-257 < z < 1.05999999999999998e46

   1. Initial program 89.5%

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

   2. Taylor expanded in x around inf 58.0%

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

      1. mul-1-neg 58.0%

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

      2. unsub-neg 58.0%

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

   4. Simplified 58.0%

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

   5. Taylor expanded in z around 0 51.2%

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

   if -6.5999999999999997e-232 < z < 1.80000000000000003e-257

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 53.9%

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

      1. associate-/l* 63.9%

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

   4. Simplified 63.9%

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

   5. Taylor expanded in z around 0 53.9%

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

      1. associate-/l* 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-257}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 47.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-256}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -2.3e+122)
     t
     (if (<= z -4.1e-193)
       t_1
       (if (<= z 1e-256) (* y (/ (- t x) a)) (if (<= z 1.18e+47) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.3e+122) {
		tmp = t;
	} else if (z <= -4.1e-193) {
		tmp = t_1;
	} else if (z <= 1e-256) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.18e+47) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-2.3d+122)) then
        tmp = t
    else if (z <= (-4.1d-193)) then
        tmp = t_1
    else if (z <= 1d-256) then
        tmp = y * ((t - x) / a)
    else if (z <= 1.18d+47) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.3e+122) {
		tmp = t;
	} else if (z <= -4.1e-193) {
		tmp = t_1;
	} else if (z <= 1e-256) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.18e+47) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -2.3e+122:
		tmp = t
	elif z <= -4.1e-193:
		tmp = t_1
	elif z <= 1e-256:
		tmp = y * ((t - x) / a)
	elif z <= 1.18e+47:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -2.3e+122)
		tmp = t;
	elseif (z <= -4.1e-193)
		tmp = t_1;
	elseif (z <= 1e-256)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 1.18e+47)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -2.3e+122)
		tmp = t;
	elseif (z <= -4.1e-193)
		tmp = t_1;
	elseif (z <= 1e-256)
		tmp = y * ((t - x) / a);
	elseif (z <= 1.18e+47)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+122], t, If[LessEqual[z, -4.1e-193], t$95$1, If[LessEqual[z, 1e-256], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.18e+47], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3000000000000001e122 or 1.18e47 < z

   1. Initial program 62.1%

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

   2. Taylor expanded in z around inf 60.0%

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

   if -2.3000000000000001e122 < z < -4.10000000000000003e-193 or 9.99999999999999977e-257 < z < 1.18e47

   1. Initial program 89.3%

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

   2. Taylor expanded in x around inf 57.8%

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

      1. mul-1-neg 57.8%

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

      2. unsub-neg 57.8%

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

   4. Simplified 57.8%

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

   5. Taylor expanded in z around 0 50.8%

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

   if -4.10000000000000003e-193 < z < 9.99999999999999977e-257

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 75.4%

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

   3. Taylor expanded in a around inf 79.0%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 10^{-256}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 64.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+20} \lor \neg \left(x \leq 4.4 \cdot 10^{+134}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.4e+20) (not (<= x 4.4e+134)))
   (* x (- 1.0 (/ (- y z) (- a z))))
   (/ t (/ (- a z) (- y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.4e+20) || !(x <= 4.4e+134)) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.4d+20)) .or. (.not. (x <= 4.4d+134))) then
        tmp = x * (1.0d0 - ((y - z) / (a - z)))
    else
        tmp = t / ((a - z) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.4e+20) || !(x <= 4.4e+134)) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.4e+20) or not (x <= 4.4e+134):
		tmp = x * (1.0 - ((y - z) / (a - z)))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.4e+20) || !(x <= 4.4e+134))
		tmp = Float64(x * Float64(1.0 - Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.4e+20) || ~((x <= 4.4e+134)))
		tmp = x * (1.0 - ((y - z) / (a - z)));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.4e+20], N[Not[LessEqual[x, 4.4e+134]], $MachinePrecision]], N[(x * N[(1.0 - N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4e20 or 4.4e134 < x

   1. Initial program 75.0%

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

   2. Taylor expanded in x around inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. unsub-neg 68.3%

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

   4. Simplified 68.3%

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

   if -1.4e20 < x < 4.4e134

   1. Initial program 84.0%

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

   2. Taylor expanded in x around 0 59.9%

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

      1. associate-/l* 73.3%

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

   4. Simplified 73.3%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+20} \lor \neg \left(x \leq 4.4 \cdot 10^{+134}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 16: 38.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+17)
   t
   (if (<= z -1.15e-192) x (if (<= z 9.5e+23) (* t (/ (- y z) a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+17) {
		tmp = t;
	} else if (z <= -1.15e-192) {
		tmp = x;
	} else if (z <= 9.5e+23) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.3d+17)) then
        tmp = t
    else if (z <= (-1.15d-192)) then
        tmp = x
    else if (z <= 9.5d+23) then
        tmp = t * ((y - z) / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+17) {
		tmp = t;
	} else if (z <= -1.15e-192) {
		tmp = x;
	} else if (z <= 9.5e+23) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+17:
		tmp = t
	elif z <= -1.15e-192:
		tmp = x
	elif z <= 9.5e+23:
		tmp = t * ((y - z) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+17)
		tmp = t;
	elseif (z <= -1.15e-192)
		tmp = x;
	elseif (z <= 9.5e+23)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+17)
		tmp = t;
	elseif (z <= -1.15e-192)
		tmp = x;
	elseif (z <= 9.5e+23)
		tmp = t * ((y - z) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+17], t, If[LessEqual[z, -1.15e-192], x, If[LessEqual[z, 9.5e+23], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e17 or 9.50000000000000038e23 < z

   1. Initial program 68.5%

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

   2. Taylor expanded in z around inf 49.3%

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

   if -1.3e17 < z < -1.15000000000000009e-192

   1. Initial program 91.7%

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

   2. Taylor expanded in a around inf 33.6%

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

   if -1.15000000000000009e-192 < z < 9.50000000000000038e23

   1. Initial program 92.9%

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

   2. Taylor expanded in t around inf 51.5%

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

      1. div-sub 51.5%

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

   4. Simplified 51.5%

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

   5. Taylor expanded in a around inf 46.8%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 36.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e+16)
   t
   (if (<= z -6.5e-193) x (if (<= z 1.55e+23) (* y (/ t a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e+16) {
		tmp = t;
	} else if (z <= -6.5e-193) {
		tmp = x;
	} else if (z <= 1.55e+23) {
		tmp = y * (t / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.6d+16)) then
        tmp = t
    else if (z <= (-6.5d-193)) then
        tmp = x
    else if (z <= 1.55d+23) then
        tmp = y * (t / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e+16) {
		tmp = t;
	} else if (z <= -6.5e-193) {
		tmp = x;
	} else if (z <= 1.55e+23) {
		tmp = y * (t / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e+16:
		tmp = t
	elif z <= -6.5e-193:
		tmp = x
	elif z <= 1.55e+23:
		tmp = y * (t / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.6e+16)
		tmp = t;
	elseif (z <= -6.5e-193)
		tmp = x;
	elseif (z <= 1.55e+23)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.6e+16)
		tmp = t;
	elseif (z <= -6.5e-193)
		tmp = x;
	elseif (z <= 1.55e+23)
		tmp = y * (t / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.6e+16], t, If[LessEqual[z, -6.5e-193], x, If[LessEqual[z, 1.55e+23], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e16 or 1.54999999999999985e23 < z

   1. Initial program 68.5%

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

   2. Taylor expanded in z around inf 49.3%

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

   if -3.6e16 < z < -6.5000000000000004e-193

   1. Initial program 91.7%

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

   2. Taylor expanded in a around inf 33.6%

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

   if -6.5000000000000004e-193 < z < 1.54999999999999985e23

   1. Initial program 92.9%

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

   2. Taylor expanded in x around 0 49.3%

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

      1. associate-/l* 52.3%

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

   4. Simplified 52.3%

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

   5. Taylor expanded in z around 0 43.9%

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

      1. associate-/r/ 43.2%

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

   7. Applied egg-rr 43.2%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 36.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+15)
   t
   (if (<= z -6.6e-193) x (if (<= z 1.45e+23) (/ t (/ a y)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+15) {
		tmp = t;
	} else if (z <= -6.6e-193) {
		tmp = x;
	} else if (z <= 1.45e+23) {
		tmp = t / (a / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.5d+15)) then
        tmp = t
    else if (z <= (-6.6d-193)) then
        tmp = x
    else if (z <= 1.45d+23) then
        tmp = t / (a / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+15) {
		tmp = t;
	} else if (z <= -6.6e-193) {
		tmp = x;
	} else if (z <= 1.45e+23) {
		tmp = t / (a / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+15:
		tmp = t
	elif z <= -6.6e-193:
		tmp = x
	elif z <= 1.45e+23:
		tmp = t / (a / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+15)
		tmp = t;
	elseif (z <= -6.6e-193)
		tmp = x;
	elseif (z <= 1.45e+23)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+15)
		tmp = t;
	elseif (z <= -6.6e-193)
		tmp = x;
	elseif (z <= 1.45e+23)
		tmp = t / (a / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+15], t, If[LessEqual[z, -6.6e-193], x, If[LessEqual[z, 1.45e+23], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5e15 or 1.45000000000000006e23 < z

   1. Initial program 68.5%

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

   2. Taylor expanded in z around inf 49.3%

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

   if -8.5e15 < z < -6.5999999999999998e-193

   1. Initial program 91.7%

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

   2. Taylor expanded in a around inf 33.6%

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

   if -6.5999999999999998e-193 < z < 1.45000000000000006e23

   1. Initial program 92.9%

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

   2. Taylor expanded in x around 0 49.3%

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

      1. associate-/l* 52.3%

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

   4. Simplified 52.3%

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

   5. Taylor expanded in z around 0 43.9%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 38.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+15) t (if (<= z 8.5e+43) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+15) {
		tmp = t;
	} else if (z <= 8.5e+43) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.5d+15)) then
        tmp = t
    else if (z <= 8.5d+43) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+15) {
		tmp = t;
	} else if (z <= 8.5e+43) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+15:
		tmp = t
	elif z <= 8.5e+43:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+15)
		tmp = t;
	elseif (z <= 8.5e+43)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+15)
		tmp = t;
	elseif (z <= 8.5e+43)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+15], t, If[LessEqual[z, 8.5e+43], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5e15 or 8.5e43 < z

   1. Initial program 68.2%

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

   2. Taylor expanded in z around inf 50.0%

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

   if -8.5e15 < z < 8.5e43

   1. Initial program 92.0%

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

   2. Taylor expanded in a around inf 30.2%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 25.1% 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 80.7%

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

2. Taylor expanded in z around inf 27.1%

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

3. Final simplification 27.1%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023185 
(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)))))