Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.3% → 90.8%

Time: 30.1s

Alternatives: 24

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-295} \lor \neg \left(t\_2 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, t\_1, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (or (<= t_2 -2e-295) (not (<= t_2 0.0)))
     (fma (- y z) t_1 x)
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if ((t_2 <= -2e-295) || !(t_2 <= 0.0)) {
		tmp = fma((y - z), t_1, x);
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if ((t_2 <= -2e-295) || !(t_2 <= 0.0))
		tmp = fma(Float64(y - z), t_1, x);
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e-295], N[Not[LessEqual[t$95$2, 0.0]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $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)))) < -2.00000000000000012e-295 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.7%

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

      1. +-commutative 90.7%

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

      2. fma-define 90.7%

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

   3. Simplified 90.7%

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

   if -2.00000000000000012e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.1%

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

   3. Taylor expanded in z around inf 80.9%

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

      1. associate--l+ 80.9%

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

      2. distribute-lft-out-- 80.9%

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

      3. div-sub 80.9%

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

      4. mul-1-neg 80.9%

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

      5. unsub-neg 80.9%

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

      6. distribute-rgt-out-- 80.9%

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

      7. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-295} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-295} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-295) (not (<= t_1 0.0)))
     t_1
     (+ t (/ (- x t) (/ z (- y a)))))))

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-295) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-295)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (z / (y - a)))
    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-295) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	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-295) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	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-295) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	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-295) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	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-295], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $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)))) < -2.00000000000000012e-295 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.7%

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

   if -2.00000000000000012e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.1%

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

   3. Taylor expanded in z around inf 80.9%

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

      1. associate--l+ 80.9%

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

      2. distribute-lft-out-- 80.9%

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

      3. div-sub 80.9%

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

      4. mul-1-neg 80.9%

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

      5. unsub-neg 80.9%

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

      6. distribute-rgt-out-- 80.9%

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

      7. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-295} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{+141}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2000 \lor \neg \left(a \leq 1.2 \cdot 10^{+48}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a (- y z))))))
   (if (<= a -2.4e+160)
     t_1
     (if (<= a -1.45e+141)
       (/ t (/ (- a z) (- y z)))
       (if (<= a -1.7e+27)
         t_1
         (if (<= a 3.2e-117)
           (+ t (/ (- x t) (/ z y)))
           (if (or (<= a 2000.0) (not (<= a 1.2e+48)))
             t_1
             (+ t (* x (/ (- y a) z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -2.4e+160) {
		tmp = t_1;
	} else if (a <= -1.45e+141) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -1.7e+27) {
		tmp = t_1;
	} else if (a <= 3.2e-117) {
		tmp = t + ((x - t) / (z / y));
	} else if ((a <= 2000.0) || !(a <= 1.2e+48)) {
		tmp = t_1;
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) / (a / (y - z)))
    if (a <= (-2.4d+160)) then
        tmp = t_1
    else if (a <= (-1.45d+141)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= (-1.7d+27)) then
        tmp = t_1
    else if (a <= 3.2d-117) then
        tmp = t + ((x - t) / (z / y))
    else if ((a <= 2000.0d0) .or. (.not. (a <= 1.2d+48))) then
        tmp = t_1
    else
        tmp = t + (x * ((y - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -2.4e+160) {
		tmp = t_1;
	} else if (a <= -1.45e+141) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -1.7e+27) {
		tmp = t_1;
	} else if (a <= 3.2e-117) {
		tmp = t + ((x - t) / (z / y));
	} else if ((a <= 2000.0) || !(a <= 1.2e+48)) {
		tmp = t_1;
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / (y - z)))
	tmp = 0
	if a <= -2.4e+160:
		tmp = t_1
	elif a <= -1.45e+141:
		tmp = t / ((a - z) / (y - z))
	elif a <= -1.7e+27:
		tmp = t_1
	elif a <= 3.2e-117:
		tmp = t + ((x - t) / (z / y))
	elif (a <= 2000.0) or not (a <= 1.2e+48):
		tmp = t_1
	else:
		tmp = t + (x * ((y - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -2.4e+160)
		tmp = t_1;
	elseif (a <= -1.45e+141)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= -1.7e+27)
		tmp = t_1;
	elseif (a <= 3.2e-117)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif ((a <= 2000.0) || !(a <= 1.2e+48))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / (y - z)));
	tmp = 0.0;
	if (a <= -2.4e+160)
		tmp = t_1;
	elseif (a <= -1.45e+141)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= -1.7e+27)
		tmp = t_1;
	elseif (a <= 3.2e-117)
		tmp = t + ((x - t) / (z / y));
	elseif ((a <= 2000.0) || ~((a <= 1.2e+48)))
		tmp = t_1;
	else
		tmp = t + (x * ((y - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+160], t$95$1, If[LessEqual[a, -1.45e+141], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.7e+27], t$95$1, If[LessEqual[a, 3.2e-117], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 2000.0], N[Not[LessEqual[a, 1.2e+48]], $MachinePrecision]], t$95$1, N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.4000000000000001e160 or -1.45000000000000003e141 < a < -1.7e27 or 3.19999999999999995e-117 < a < 2e3 or 1.2000000000000001e48 < a

   1. Initial program 87.4%

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

   3. Taylor expanded in a around inf 66.4%

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

      1. associate-/l* 79.0%

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

   5. Simplified 79.0%

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

   if -2.4000000000000001e160 < a < -1.45000000000000003e141

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0 17.3%

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

      1. associate-/l* 72.3%

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

   5. Simplified 72.3%

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

   if -1.7e27 < a < 3.19999999999999995e-117

   1. Initial program 74.0%

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

   3. Taylor expanded in z around inf 87.4%

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

      1. associate--l+ 87.4%

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

      2. distribute-lft-out-- 87.4%

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

      3. div-sub 87.4%

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

      4. mul-1-neg 87.4%

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

      5. unsub-neg 87.4%

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

      6. distribute-rgt-out-- 87.4%

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

      7. associate-/l* 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in y around inf 84.2%

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

   if 2e3 < a < 1.2000000000000001e48

   1. Initial program 35.1%

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

   3. Taylor expanded in z around inf 57.9%

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

      1. associate--l+ 57.9%

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

      2. distribute-lft-out-- 57.9%

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

      3. div-sub 57.9%

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

      4. mul-1-neg 57.9%

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

      5. unsub-neg 57.9%

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

      6. distribute-rgt-out-- 57.9%

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

      7. associate-/l* 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in t around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-*r/ 88.8%

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

      3. distribute-lft-neg-in 88.8%

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

   8. Simplified 88.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+160}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{+141}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2000 \lor \neg \left(a \leq 1.2 \cdot 10^{+48}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.62 \cdot 10^{+140}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 11500000 \lor \neg \left(a \leq 1.4 \cdot 10^{+48}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a (- y z))))))
   (if (<= a -2.4e+160)
     t_1
     (if (<= a -1.62e+140)
       (/ t (/ (- a z) (- y z)))
       (if (<= a -1.12e+27)
         t_1
         (if (<= a 3.2e-117)
           (+ t (/ (* (- t x) (- a y)) z))
           (if (or (<= a 11500000.0) (not (<= a 1.4e+48)))
             t_1
             (+ t (* x (/ (- y a) z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -2.4e+160) {
		tmp = t_1;
	} else if (a <= -1.62e+140) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -1.12e+27) {
		tmp = t_1;
	} else if (a <= 3.2e-117) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if ((a <= 11500000.0) || !(a <= 1.4e+48)) {
		tmp = t_1;
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) / (a / (y - z)))
    if (a <= (-2.4d+160)) then
        tmp = t_1
    else if (a <= (-1.62d+140)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= (-1.12d+27)) then
        tmp = t_1
    else if (a <= 3.2d-117) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if ((a <= 11500000.0d0) .or. (.not. (a <= 1.4d+48))) then
        tmp = t_1
    else
        tmp = t + (x * ((y - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -2.4e+160) {
		tmp = t_1;
	} else if (a <= -1.62e+140) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -1.12e+27) {
		tmp = t_1;
	} else if (a <= 3.2e-117) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if ((a <= 11500000.0) || !(a <= 1.4e+48)) {
		tmp = t_1;
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / (y - z)))
	tmp = 0
	if a <= -2.4e+160:
		tmp = t_1
	elif a <= -1.62e+140:
		tmp = t / ((a - z) / (y - z))
	elif a <= -1.12e+27:
		tmp = t_1
	elif a <= 3.2e-117:
		tmp = t + (((t - x) * (a - y)) / z)
	elif (a <= 11500000.0) or not (a <= 1.4e+48):
		tmp = t_1
	else:
		tmp = t + (x * ((y - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -2.4e+160)
		tmp = t_1;
	elseif (a <= -1.62e+140)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= -1.12e+27)
		tmp = t_1;
	elseif (a <= 3.2e-117)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif ((a <= 11500000.0) || !(a <= 1.4e+48))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / (y - z)));
	tmp = 0.0;
	if (a <= -2.4e+160)
		tmp = t_1;
	elseif (a <= -1.62e+140)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= -1.12e+27)
		tmp = t_1;
	elseif (a <= 3.2e-117)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif ((a <= 11500000.0) || ~((a <= 1.4e+48)))
		tmp = t_1;
	else
		tmp = t + (x * ((y - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+160], t$95$1, If[LessEqual[a, -1.62e+140], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.12e+27], t$95$1, If[LessEqual[a, 3.2e-117], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 11500000.0], N[Not[LessEqual[a, 1.4e+48]], $MachinePrecision]], t$95$1, N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.4000000000000001e160 or -1.62000000000000007e140 < a < -1.12e27 or 3.19999999999999995e-117 < a < 1.15e7 or 1.40000000000000006e48 < a

   1. Initial program 87.4%

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

   3. Taylor expanded in a around inf 66.4%

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

      1. associate-/l* 79.0%

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

   5. Simplified 79.0%

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

   if -2.4000000000000001e160 < a < -1.62000000000000007e140

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0 17.3%

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

      1. associate-/l* 72.3%

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

   5. Simplified 72.3%

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

   if -1.12e27 < a < 3.19999999999999995e-117

   1. Initial program 74.0%

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

      1. clear-num 73.6%

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

      2. associate-/r/ 73.9%

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

   4. Applied egg-rr 73.9%

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

   5. Taylor expanded in z around inf 87.4%

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

      1. associate--l+ 87.4%

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

      2. associate-*r/ 87.4%

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

      3. associate-*r/ 87.4%

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

      4. div-sub 87.4%

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

      5. distribute-lft-out-- 87.4%

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

      6. associate-*r/ 87.4%

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

      7. mul-1-neg 87.4%

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

      8. unsub-neg 87.4%

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

      9. distribute-rgt-out-- 87.4%

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

   7. Simplified 87.4%

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

   if 1.15e7 < a < 1.40000000000000006e48

   1. Initial program 35.1%

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

   3. Taylor expanded in z around inf 57.9%

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

      1. associate--l+ 57.9%

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

      2. distribute-lft-out-- 57.9%

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

      3. div-sub 57.9%

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

      4. mul-1-neg 57.9%

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

      5. unsub-neg 57.9%

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

      6. distribute-rgt-out-- 57.9%

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

      7. associate-/l* 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in t around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-*r/ 88.8%

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

      3. distribute-lft-neg-in 88.8%

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

   8. Simplified 88.8%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+160}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -1.62 \cdot 10^{+140}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 11500000 \lor \neg \left(a \leq 1.4 \cdot 10^{+48}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+139}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{+23}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-14}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z y)))) (t_2 (+ x (* (- y z) (/ t a)))))
   (if (<= a -2.4e+160)
     t_2
     (if (<= a -4.2e+139)
       (* (- y z) (/ t (- a z)))
       (if (<= a -1.26e+23)
         (+ x (* (- t x) (/ y a)))
         (if (<= a 9.8e-130)
           t_1
           (if (<= a 1.4e-14)
             (* (- t x) (/ y (- a z)))
             (if (<= a 5.5e+48) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / y));
	double t_2 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -2.4e+160) {
		tmp = t_2;
	} else if (a <= -4.2e+139) {
		tmp = (y - z) * (t / (a - z));
	} else if (a <= -1.26e+23) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 9.8e-130) {
		tmp = t_1;
	} else if (a <= 1.4e-14) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 5.5e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + ((x - t) / (z / y))
    t_2 = x + ((y - z) * (t / a))
    if (a <= (-2.4d+160)) then
        tmp = t_2
    else if (a <= (-4.2d+139)) then
        tmp = (y - z) * (t / (a - z))
    else if (a <= (-1.26d+23)) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= 9.8d-130) then
        tmp = t_1
    else if (a <= 1.4d-14) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 5.5d+48) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / y));
	double t_2 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -2.4e+160) {
		tmp = t_2;
	} else if (a <= -4.2e+139) {
		tmp = (y - z) * (t / (a - z));
	} else if (a <= -1.26e+23) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 9.8e-130) {
		tmp = t_1;
	} else if (a <= 1.4e-14) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 5.5e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / y))
	t_2 = x + ((y - z) * (t / a))
	tmp = 0
	if a <= -2.4e+160:
		tmp = t_2
	elif a <= -4.2e+139:
		tmp = (y - z) * (t / (a - z))
	elif a <= -1.26e+23:
		tmp = x + ((t - x) * (y / a))
	elif a <= 9.8e-130:
		tmp = t_1
	elif a <= 1.4e-14:
		tmp = (t - x) * (y / (a - z))
	elif a <= 5.5e+48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / y)))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(t / a)))
	tmp = 0.0
	if (a <= -2.4e+160)
		tmp = t_2;
	elseif (a <= -4.2e+139)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (a <= -1.26e+23)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= 9.8e-130)
		tmp = t_1;
	elseif (a <= 1.4e-14)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 5.5e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / y));
	t_2 = x + ((y - z) * (t / a));
	tmp = 0.0;
	if (a <= -2.4e+160)
		tmp = t_2;
	elseif (a <= -4.2e+139)
		tmp = (y - z) * (t / (a - z));
	elseif (a <= -1.26e+23)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= 9.8e-130)
		tmp = t_1;
	elseif (a <= 1.4e-14)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 5.5e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+160], t$95$2, If[LessEqual[a, -4.2e+139], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.26e+23], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.8e-130], t$95$1, If[LessEqual[a, 1.4e-14], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e+48], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.4000000000000001e160 or 5.5000000000000002e48 < a

   1. Initial program 89.3%

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

   3. Taylor expanded in a around inf 68.7%

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

      1. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in t around inf 75.1%

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

      1. associate-*l/ 78.3%

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

      2. *-commutative 78.3%

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

   8. Simplified 78.3%

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

   if -2.4000000000000001e160 < a < -4.1999999999999997e139

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0 26.3%

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

      1. associate-/l* 75.4%

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

      2. associate-/r/ 75.2%

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

   5. Simplified 75.2%

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

   if -4.1999999999999997e139 < a < -1.26000000000000004e23

   1. Initial program 75.6%

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

   3. Taylor expanded in z around 0 58.4%

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

      1. associate-/l* 58.4%

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

      2. associate-/r/ 58.5%

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

   5. Simplified 58.5%

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

   if -1.26000000000000004e23 < a < 9.80000000000000036e-130 or 1.4e-14 < a < 5.5000000000000002e48

   1. Initial program 71.2%

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

   3. Taylor expanded in z around inf 82.3%

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

      1. associate--l+ 82.3%

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

      2. distribute-lft-out-- 82.3%

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

      3. div-sub 82.3%

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

      4. mul-1-neg 82.3%

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

      5. unsub-neg 82.3%

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

      6. distribute-rgt-out-- 82.3%

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

      7. associate-/l* 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in y around inf 79.9%

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

   if 9.80000000000000036e-130 < a < 1.4e-14

   1. Initial program 93.7%

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

      1. clear-num 93.7%

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

      2. associate-/r/ 93.4%

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

   4. Applied egg-rr 93.4%

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

   5. Taylor expanded in y around inf 77.9%

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

      1. div-sub 77.8%

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

      2. associate-*r/ 77.6%

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

      3. associate-*l/ 78.0%

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

   7. Simplified 78.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+160}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+139}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{+23}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-130}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-14}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+48}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+139}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{+20}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-15}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z y)))) (t_2 (+ x (* (- y z) (/ t a)))))
   (if (<= a -2.4e+160)
     t_2
     (if (<= a -4.2e+139)
       (/ t (/ (- a z) (- y z)))
       (if (<= a -3.7e+20)
         (+ x (* (- t x) (/ y a)))
         (if (<= a 3.4e-132)
           t_1
           (if (<= a 4.2e-15)
             (* (- t x) (/ y (- a z)))
             (if (<= a 1.3e+48) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / y));
	double t_2 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -2.4e+160) {
		tmp = t_2;
	} else if (a <= -4.2e+139) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -3.7e+20) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 3.4e-132) {
		tmp = t_1;
	} else if (a <= 4.2e-15) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 1.3e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + ((x - t) / (z / y))
    t_2 = x + ((y - z) * (t / a))
    if (a <= (-2.4d+160)) then
        tmp = t_2
    else if (a <= (-4.2d+139)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= (-3.7d+20)) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= 3.4d-132) then
        tmp = t_1
    else if (a <= 4.2d-15) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 1.3d+48) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / y));
	double t_2 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -2.4e+160) {
		tmp = t_2;
	} else if (a <= -4.2e+139) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -3.7e+20) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 3.4e-132) {
		tmp = t_1;
	} else if (a <= 4.2e-15) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 1.3e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / y))
	t_2 = x + ((y - z) * (t / a))
	tmp = 0
	if a <= -2.4e+160:
		tmp = t_2
	elif a <= -4.2e+139:
		tmp = t / ((a - z) / (y - z))
	elif a <= -3.7e+20:
		tmp = x + ((t - x) * (y / a))
	elif a <= 3.4e-132:
		tmp = t_1
	elif a <= 4.2e-15:
		tmp = (t - x) * (y / (a - z))
	elif a <= 1.3e+48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / y)))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(t / a)))
	tmp = 0.0
	if (a <= -2.4e+160)
		tmp = t_2;
	elseif (a <= -4.2e+139)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= -3.7e+20)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= 3.4e-132)
		tmp = t_1;
	elseif (a <= 4.2e-15)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 1.3e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / y));
	t_2 = x + ((y - z) * (t / a));
	tmp = 0.0;
	if (a <= -2.4e+160)
		tmp = t_2;
	elseif (a <= -4.2e+139)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= -3.7e+20)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= 3.4e-132)
		tmp = t_1;
	elseif (a <= 4.2e-15)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 1.3e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+160], t$95$2, If[LessEqual[a, -4.2e+139], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.7e+20], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-132], t$95$1, If[LessEqual[a, 4.2e-15], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+48], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.4000000000000001e160 or 1.29999999999999998e48 < a

   1. Initial program 89.3%

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

   3. Taylor expanded in a around inf 68.7%

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

      1. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in t around inf 75.1%

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

      1. associate-*l/ 78.3%

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

      2. *-commutative 78.3%

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

   8. Simplified 78.3%

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

   if -2.4000000000000001e160 < a < -4.1999999999999997e139

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0 26.3%

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

      1. associate-/l* 75.4%

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

   5. Simplified 75.4%

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

   if -4.1999999999999997e139 < a < -3.7e20

   1. Initial program 75.6%

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

   3. Taylor expanded in z around 0 58.4%

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

      1. associate-/l* 58.4%

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

      2. associate-/r/ 58.5%

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

   5. Simplified 58.5%

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

   if -3.7e20 < a < 3.39999999999999983e-132 or 4.19999999999999962e-15 < a < 1.29999999999999998e48

   1. Initial program 71.2%

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

   3. Taylor expanded in z around inf 82.3%

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

      1. associate--l+ 82.3%

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

      2. distribute-lft-out-- 82.3%

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

      3. div-sub 82.3%

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

      4. mul-1-neg 82.3%

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

      5. unsub-neg 82.3%

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

      6. distribute-rgt-out-- 82.3%

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

      7. associate-/l* 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in y around inf 79.9%

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

   if 3.39999999999999983e-132 < a < 4.19999999999999962e-15

   1. Initial program 93.7%

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

      1. clear-num 93.7%

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

      2. associate-/r/ 93.4%

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

   4. Applied egg-rr 93.4%

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

   5. Taylor expanded in y around inf 77.9%

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

      1. div-sub 77.8%

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

      2. associate-*r/ 77.6%

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

      3. associate-*l/ 78.0%

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

   7. Simplified 78.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+160}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+139}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{+20}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-132}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-15}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+48}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{+139}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+20}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-130}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-15}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+48}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t a)))))
   (if (<= a -2.5e+160)
     t_1
     (if (<= a -1.1e+139)
       (/ t (/ (- a z) (- y z)))
       (if (<= a -1e+20)
         (+ x (* (- t x) (/ y a)))
         (if (<= a 9.8e-130)
           (+ t (/ (- x t) (/ z y)))
           (if (<= a 6.2e-15)
             (* (- t x) (/ y (- a z)))
             (if (<= a 1.9e+48) (+ t (* x (/ (- y a) z))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -2.5e+160) {
		tmp = t_1;
	} else if (a <= -1.1e+139) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -1e+20) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 9.8e-130) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 6.2e-15) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 1.9e+48) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * (t / a))
    if (a <= (-2.5d+160)) then
        tmp = t_1
    else if (a <= (-1.1d+139)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= (-1d+20)) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= 9.8d-130) then
        tmp = t + ((x - t) / (z / y))
    else if (a <= 6.2d-15) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 1.9d+48) then
        tmp = t + (x * ((y - a) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -2.5e+160) {
		tmp = t_1;
	} else if (a <= -1.1e+139) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -1e+20) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 9.8e-130) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 6.2e-15) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 1.9e+48) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / a))
	tmp = 0
	if a <= -2.5e+160:
		tmp = t_1
	elif a <= -1.1e+139:
		tmp = t / ((a - z) / (y - z))
	elif a <= -1e+20:
		tmp = x + ((t - x) * (y / a))
	elif a <= 9.8e-130:
		tmp = t + ((x - t) / (z / y))
	elif a <= 6.2e-15:
		tmp = (t - x) * (y / (a - z))
	elif a <= 1.9e+48:
		tmp = t + (x * ((y - a) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / a)))
	tmp = 0.0
	if (a <= -2.5e+160)
		tmp = t_1;
	elseif (a <= -1.1e+139)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= -1e+20)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= 9.8e-130)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif (a <= 6.2e-15)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 1.9e+48)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / a));
	tmp = 0.0;
	if (a <= -2.5e+160)
		tmp = t_1;
	elseif (a <= -1.1e+139)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= -1e+20)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= 9.8e-130)
		tmp = t + ((x - t) / (z / y));
	elseif (a <= 6.2e-15)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 1.9e+48)
		tmp = t + (x * ((y - a) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e+160], t$95$1, If[LessEqual[a, -1.1e+139], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e+20], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.8e-130], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-15], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+48], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.5000000000000001e160 or 1.9e48 < a

   1. Initial program 89.3%

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

   3. Taylor expanded in a around inf 68.7%

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

      1. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in t around inf 75.1%

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

      1. associate-*l/ 78.3%

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

      2. *-commutative 78.3%

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

   8. Simplified 78.3%

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

   if -2.5000000000000001e160 < a < -1.1e139

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0 26.3%

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

      1. associate-/l* 75.4%

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

   5. Simplified 75.4%

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

   if -1.1e139 < a < -1e20

   1. Initial program 75.6%

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

   3. Taylor expanded in z around 0 58.4%

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

      1. associate-/l* 58.4%

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

      2. associate-/r/ 58.5%

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

   5. Simplified 58.5%

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

   if -1e20 < a < 9.80000000000000036e-130

   1. Initial program 74.2%

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

   3. Taylor expanded in z around inf 87.0%

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

      1. associate--l+ 87.0%

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

      2. distribute-lft-out-- 87.0%

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

      3. div-sub 87.0%

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

      4. mul-1-neg 87.0%

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

      5. unsub-neg 87.0%

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

      6. distribute-rgt-out-- 87.0%

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

      7. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in y around inf 84.7%

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

   if 9.80000000000000036e-130 < a < 6.1999999999999998e-15

   1. Initial program 93.7%

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

      1. clear-num 93.7%

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

      2. associate-/r/ 93.4%

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

   4. Applied egg-rr 93.4%

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

   5. Taylor expanded in y around inf 77.9%

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

      1. div-sub 77.8%

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

      2. associate-*r/ 77.6%

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

      3. associate-*l/ 78.0%

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

   7. Simplified 78.0%

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

   if 6.1999999999999998e-15 < a < 1.9e48

   1. Initial program 51.6%

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

   3. Taylor expanded in z around inf 51.9%

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

      1. associate--l+ 51.9%

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

      2. distribute-lft-out-- 51.9%

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

      3. div-sub 51.9%

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

      4. mul-1-neg 51.9%

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

      5. unsub-neg 51.9%

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

      6. distribute-rgt-out-- 51.9%

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

      7. associate-/l* 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in t around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. associate-*r/ 71.8%

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

      3. distribute-lft-neg-in 71.8%

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

   8. Simplified 71.8%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+160}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{+139}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+20}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-130}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-15}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+48}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := t \cdot \frac{-z}{a - z}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+136}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (* t (/ (- z) (- a z)))))
   (if (<= z -4.8e+136)
     t_2
     (if (<= z 1.45e-215)
       t_1
       (if (<= z 3.1e-120)
         (* x (+ (/ (- z y) a) 1.0))
         (if (<= z 8.8e-91)
           t_1
           (if (<= z 8.8e+136) (- x (/ (* z t) a)) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t * (-z / (a - z));
	double tmp;
	if (z <= -4.8e+136) {
		tmp = t_2;
	} else if (z <= 1.45e-215) {
		tmp = t_1;
	} else if (z <= 3.1e-120) {
		tmp = x * (((z - y) / a) + 1.0);
	} else if (z <= 8.8e-91) {
		tmp = t_1;
	} else if (z <= 8.8e+136) {
		tmp = x - ((z * t) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = t * (-z / (a - z))
    if (z <= (-4.8d+136)) then
        tmp = t_2
    else if (z <= 1.45d-215) then
        tmp = t_1
    else if (z <= 3.1d-120) then
        tmp = x * (((z - y) / a) + 1.0d0)
    else if (z <= 8.8d-91) then
        tmp = t_1
    else if (z <= 8.8d+136) then
        tmp = x - ((z * t) / a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t * (-z / (a - z));
	double tmp;
	if (z <= -4.8e+136) {
		tmp = t_2;
	} else if (z <= 1.45e-215) {
		tmp = t_1;
	} else if (z <= 3.1e-120) {
		tmp = x * (((z - y) / a) + 1.0);
	} else if (z <= 8.8e-91) {
		tmp = t_1;
	} else if (z <= 8.8e+136) {
		tmp = x - ((z * t) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = t * (-z / (a - z))
	tmp = 0
	if z <= -4.8e+136:
		tmp = t_2
	elif z <= 1.45e-215:
		tmp = t_1
	elif z <= 3.1e-120:
		tmp = x * (((z - y) / a) + 1.0)
	elif z <= 8.8e-91:
		tmp = t_1
	elif z <= 8.8e+136:
		tmp = x - ((z * t) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(t * Float64(Float64(-z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -4.8e+136)
		tmp = t_2;
	elseif (z <= 1.45e-215)
		tmp = t_1;
	elseif (z <= 3.1e-120)
		tmp = Float64(x * Float64(Float64(Float64(z - y) / a) + 1.0));
	elseif (z <= 8.8e-91)
		tmp = t_1;
	elseif (z <= 8.8e+136)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = t * (-z / (a - z));
	tmp = 0.0;
	if (z <= -4.8e+136)
		tmp = t_2;
	elseif (z <= 1.45e-215)
		tmp = t_1;
	elseif (z <= 3.1e-120)
		tmp = x * (((z - y) / a) + 1.0);
	elseif (z <= 8.8e-91)
		tmp = t_1;
	elseif (z <= 8.8e+136)
		tmp = x - ((z * t) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[((-z) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+136], t$95$2, If[LessEqual[z, 1.45e-215], t$95$1, If[LessEqual[z, 3.1e-120], N[(x * N[(N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e-91], t$95$1, If[LessEqual[z, 8.8e+136], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8000000000000001e136 or 8.7999999999999998e136 < z

   1. Initial program 58.2%

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

   3. Taylor expanded in x around 0 30.9%

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

      1. associate-/l* 69.7%

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

      2. associate-/r/ 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in y around 0 30.7%

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

      1. mul-1-neg 30.7%

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

      2. associate-/l* 63.0%

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

   8. Simplified 63.0%

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

      1. div-inv 63.0%

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

      2. clear-num 63.0%

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

   10. Applied egg-rr 63.0%

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

   if -4.8000000000000001e136 < z < 1.45e-215 or 3.10000000000000019e-120 < z < 8.8000000000000003e-91

   1. Initial program 91.4%

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

   3. Taylor expanded in y around inf 62.8%

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

      1. div-sub 62.8%

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

   5. Simplified 62.8%

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

   if 1.45e-215 < z < 3.10000000000000019e-120

   1. Initial program 91.3%

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

   3. Taylor expanded in a around inf 74.6%

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

      1. associate-/l* 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in x around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. unsub-neg 70.8%

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

   8. Simplified 70.8%

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

   if 8.8000000000000003e-91 < z < 8.7999999999999998e136

   1. Initial program 82.2%

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

   3. Taylor expanded in y around 0 48.4%

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

      1. mul-1-neg 48.4%

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

      2. unsub-neg 48.4%

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

      3. associate-*r/ 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in a around inf 46.9%

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

      1. mul-1-neg 46.9%

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

      2. unsub-neg 46.9%

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

      3. associate-/l* 55.3%

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

   8. Simplified 55.3%

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

   9. Taylor expanded in t around inf 55.3%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-215}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+24}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+139}:\\ \;\;\;\;x + \frac{x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y a))))
   (if (<= z -2.4e+24)
     t
     (if (<= z 1.02e-215)
       t_1
       (if (<= z 1.55e-120)
         x
         (if (<= z 3.2e-92)
           t_1
           (if (<= z 9.6e+139) (+ x (/ x (/ a z))) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / a);
	double tmp;
	if (z <= -2.4e+24) {
		tmp = t;
	} else if (z <= 1.02e-215) {
		tmp = t_1;
	} else if (z <= 1.55e-120) {
		tmp = x;
	} else if (z <= 3.2e-92) {
		tmp = t_1;
	} else if (z <= 9.6e+139) {
		tmp = x + (x / (a / z));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * (y / a)
    if (z <= (-2.4d+24)) then
        tmp = t
    else if (z <= 1.02d-215) then
        tmp = t_1
    else if (z <= 1.55d-120) then
        tmp = x
    else if (z <= 3.2d-92) then
        tmp = t_1
    else if (z <= 9.6d+139) then
        tmp = x + (x / (a / z))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / a);
	double tmp;
	if (z <= -2.4e+24) {
		tmp = t;
	} else if (z <= 1.02e-215) {
		tmp = t_1;
	} else if (z <= 1.55e-120) {
		tmp = x;
	} else if (z <= 3.2e-92) {
		tmp = t_1;
	} else if (z <= 9.6e+139) {
		tmp = x + (x / (a / z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / a)
	tmp = 0
	if z <= -2.4e+24:
		tmp = t
	elif z <= 1.02e-215:
		tmp = t_1
	elif z <= 1.55e-120:
		tmp = x
	elif z <= 3.2e-92:
		tmp = t_1
	elif z <= 9.6e+139:
		tmp = x + (x / (a / z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / a))
	tmp = 0.0
	if (z <= -2.4e+24)
		tmp = t;
	elseif (z <= 1.02e-215)
		tmp = t_1;
	elseif (z <= 1.55e-120)
		tmp = x;
	elseif (z <= 3.2e-92)
		tmp = t_1;
	elseif (z <= 9.6e+139)
		tmp = Float64(x + Float64(x / Float64(a / z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / a);
	tmp = 0.0;
	if (z <= -2.4e+24)
		tmp = t;
	elseif (z <= 1.02e-215)
		tmp = t_1;
	elseif (z <= 1.55e-120)
		tmp = x;
	elseif (z <= 3.2e-92)
		tmp = t_1;
	elseif (z <= 9.6e+139)
		tmp = x + (x / (a / z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+24], t, If[LessEqual[z, 1.02e-215], t$95$1, If[LessEqual[z, 1.55e-120], x, If[LessEqual[z, 3.2e-92], t$95$1, If[LessEqual[z, 9.6e+139], N[(x + N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4000000000000001e24 or 9.60000000000000032e139 < z

   1. Initial program 62.5%

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

   3. Taylor expanded in z around inf 49.6%

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

   if -2.4000000000000001e24 < z < 1.0200000000000001e-215 or 1.5500000000000001e-120 < z < 3.1999999999999997e-92

   1. Initial program 95.0%

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

      1. clear-num 94.3%

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

      2. associate-/r/ 94.9%

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in y around inf 68.3%

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

      1. div-sub 68.3%

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

      2. associate-*r/ 64.2%

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

      3. associate-*l/ 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in a around inf 52.5%

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

   if 1.0200000000000001e-215 < z < 1.5500000000000001e-120

   1. Initial program 91.3%

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

   3. Taylor expanded in a around inf 54.1%

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

   if 3.1999999999999997e-92 < z < 9.60000000000000032e139

   1. Initial program 82.2%

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

   3. Taylor expanded in y around 0 48.4%

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

      1. mul-1-neg 48.4%

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

      2. unsub-neg 48.4%

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

      3. associate-*r/ 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in a around inf 46.9%

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

      1. mul-1-neg 46.9%

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

      2. unsub-neg 46.9%

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

      3. associate-/l* 55.3%

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

   8. Simplified 55.3%

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

   9. Taylor expanded in t around 0 38.6%

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

       1. sub-neg 38.6%

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

       2. mul-1-neg 38.6%

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

       3. remove-double-neg 38.6%

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

       4. associate-/l* 46.9%

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

   11. Simplified 46.9%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+24}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-215}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-92}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+139}:\\ \;\;\;\;x + \frac{x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+140}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{+61} \lor \neg \left(a \leq 2.4 \cdot 10^{-14}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t a)))))
   (if (<= a -2.5e+160)
     t_1
     (if (<= a -2.6e+140)
       (* (- y z) (/ t (- a z)))
       (if (or (<= a -7.4e+61) (not (<= a 2.4e-14)))
         t_1
         (* y (/ (- t x) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -2.5e+160) {
		tmp = t_1;
	} else if (a <= -2.6e+140) {
		tmp = (y - z) * (t / (a - z));
	} else if ((a <= -7.4e+61) || !(a <= 2.4e-14)) {
		tmp = t_1;
	} else {
		tmp = y * ((t - x) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * (t / a))
    if (a <= (-2.5d+160)) then
        tmp = t_1
    else if (a <= (-2.6d+140)) then
        tmp = (y - z) * (t / (a - z))
    else if ((a <= (-7.4d+61)) .or. (.not. (a <= 2.4d-14))) then
        tmp = t_1
    else
        tmp = y * ((t - x) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -2.5e+160) {
		tmp = t_1;
	} else if (a <= -2.6e+140) {
		tmp = (y - z) * (t / (a - z));
	} else if ((a <= -7.4e+61) || !(a <= 2.4e-14)) {
		tmp = t_1;
	} else {
		tmp = y * ((t - x) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / a))
	tmp = 0
	if a <= -2.5e+160:
		tmp = t_1
	elif a <= -2.6e+140:
		tmp = (y - z) * (t / (a - z))
	elif (a <= -7.4e+61) or not (a <= 2.4e-14):
		tmp = t_1
	else:
		tmp = y * ((t - x) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / a)))
	tmp = 0.0
	if (a <= -2.5e+160)
		tmp = t_1;
	elseif (a <= -2.6e+140)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif ((a <= -7.4e+61) || !(a <= 2.4e-14))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / a));
	tmp = 0.0;
	if (a <= -2.5e+160)
		tmp = t_1;
	elseif (a <= -2.6e+140)
		tmp = (y - z) * (t / (a - z));
	elseif ((a <= -7.4e+61) || ~((a <= 2.4e-14)))
		tmp = t_1;
	else
		tmp = y * ((t - x) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e+160], t$95$1, If[LessEqual[a, -2.6e+140], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -7.4e+61], N[Not[LessEqual[a, 2.4e-14]], $MachinePrecision]], t$95$1, N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5000000000000001e160 or -2.6000000000000001e140 < a < -7.40000000000000005e61 or 2.4e-14 < a

   1. Initial program 84.1%

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

   3. Taylor expanded in a around inf 63.4%

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

      1. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in t around inf 69.8%

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

      1. associate-*l/ 72.2%

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

      2. *-commutative 72.2%

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

   8. Simplified 72.2%

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

   if -2.5000000000000001e160 < a < -2.6000000000000001e140

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0 17.3%

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

      1. associate-/l* 72.3%

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

      2. associate-/r/ 72.1%

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

   5. Simplified 72.1%

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

   if -7.40000000000000005e61 < a < 2.4e-14

   1. Initial program 76.6%

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

   3. Taylor expanded in y around inf 61.9%

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

      1. div-sub 61.9%

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

   5. Simplified 61.9%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+160}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+140}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{+61} \lor \neg \left(a \leq 2.4 \cdot 10^{-14}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{z - y}{a} + 1\right)\\ t_2 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{-126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 330000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ (/ (- z y) a) 1.0))) (t_2 (* (- y z) (/ t (- a z)))))
   (if (<= t -1.25e-126)
     t_2
     (if (<= t 2.75e-135)
       t_1
       (if (<= t 3e-57)
         (* y (/ (- t x) (- a z)))
         (if (<= t 330000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (((z - y) / a) + 1.0);
	double t_2 = (y - z) * (t / (a - z));
	double tmp;
	if (t <= -1.25e-126) {
		tmp = t_2;
	} else if (t <= 2.75e-135) {
		tmp = t_1;
	} else if (t <= 3e-57) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 330000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (((z - y) / a) + 1.0d0)
    t_2 = (y - z) * (t / (a - z))
    if (t <= (-1.25d-126)) then
        tmp = t_2
    else if (t <= 2.75d-135) then
        tmp = t_1
    else if (t <= 3d-57) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= 330000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (((z - y) / a) + 1.0);
	double t_2 = (y - z) * (t / (a - z));
	double tmp;
	if (t <= -1.25e-126) {
		tmp = t_2;
	} else if (t <= 2.75e-135) {
		tmp = t_1;
	} else if (t <= 3e-57) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 330000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (((z - y) / a) + 1.0)
	t_2 = (y - z) * (t / (a - z))
	tmp = 0
	if t <= -1.25e-126:
		tmp = t_2
	elif t <= 2.75e-135:
		tmp = t_1
	elif t <= 3e-57:
		tmp = y * ((t - x) / (a - z))
	elif t <= 330000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(Float64(z - y) / a) + 1.0))
	t_2 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (t <= -1.25e-126)
		tmp = t_2;
	elseif (t <= 2.75e-135)
		tmp = t_1;
	elseif (t <= 3e-57)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= 330000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (((z - y) / a) + 1.0);
	t_2 = (y - z) * (t / (a - z));
	tmp = 0.0;
	if (t <= -1.25e-126)
		tmp = t_2;
	elseif (t <= 2.75e-135)
		tmp = t_1;
	elseif (t <= 3e-57)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= 330000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e-126], t$95$2, If[LessEqual[t, 2.75e-135], t$95$1, If[LessEqual[t, 3e-57], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 330000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25000000000000001e-126 or 3.3e5 < t

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0 48.9%

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

      1. associate-/l* 68.5%

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

      2. associate-/r/ 65.9%

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

   5. Simplified 65.9%

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

   if -1.25000000000000001e-126 < t < 2.75e-135 or 3.00000000000000001e-57 < t < 3.3e5

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 59.7%

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

      1. associate-/l* 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in x around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. unsub-neg 66.6%

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

   8. Simplified 66.6%

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

   if 2.75e-135 < t < 3.00000000000000001e-57

   1. Initial program 57.4%

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

   3. Taylor expanded in y around inf 52.5%

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

      1. div-sub 52.5%

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

   5. Simplified 52.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-126}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-135}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 330000:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{z - y}{a} + 1\right)\\ t_2 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{-126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-54}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 1750:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ (/ (- z y) a) 1.0))) (t_2 (* (- y z) (/ t (- a z)))))
   (if (<= t -1.25e-126)
     t_2
     (if (<= t 4.2e-135)
       t_1
       (if (<= t 4.5e-54)
         (* (- t x) (/ y (- a z)))
         (if (<= t 1750.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (((z - y) / a) + 1.0);
	double t_2 = (y - z) * (t / (a - z));
	double tmp;
	if (t <= -1.25e-126) {
		tmp = t_2;
	} else if (t <= 4.2e-135) {
		tmp = t_1;
	} else if (t <= 4.5e-54) {
		tmp = (t - x) * (y / (a - z));
	} else if (t <= 1750.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (((z - y) / a) + 1.0d0)
    t_2 = (y - z) * (t / (a - z))
    if (t <= (-1.25d-126)) then
        tmp = t_2
    else if (t <= 4.2d-135) then
        tmp = t_1
    else if (t <= 4.5d-54) then
        tmp = (t - x) * (y / (a - z))
    else if (t <= 1750.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (((z - y) / a) + 1.0);
	double t_2 = (y - z) * (t / (a - z));
	double tmp;
	if (t <= -1.25e-126) {
		tmp = t_2;
	} else if (t <= 4.2e-135) {
		tmp = t_1;
	} else if (t <= 4.5e-54) {
		tmp = (t - x) * (y / (a - z));
	} else if (t <= 1750.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (((z - y) / a) + 1.0)
	t_2 = (y - z) * (t / (a - z))
	tmp = 0
	if t <= -1.25e-126:
		tmp = t_2
	elif t <= 4.2e-135:
		tmp = t_1
	elif t <= 4.5e-54:
		tmp = (t - x) * (y / (a - z))
	elif t <= 1750.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(Float64(z - y) / a) + 1.0))
	t_2 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (t <= -1.25e-126)
		tmp = t_2;
	elseif (t <= 4.2e-135)
		tmp = t_1;
	elseif (t <= 4.5e-54)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (t <= 1750.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (((z - y) / a) + 1.0);
	t_2 = (y - z) * (t / (a - z));
	tmp = 0.0;
	if (t <= -1.25e-126)
		tmp = t_2;
	elseif (t <= 4.2e-135)
		tmp = t_1;
	elseif (t <= 4.5e-54)
		tmp = (t - x) * (y / (a - z));
	elseif (t <= 1750.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e-126], t$95$2, If[LessEqual[t, 4.2e-135], t$95$1, If[LessEqual[t, 4.5e-54], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1750.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25000000000000001e-126 or 1750 < t

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0 48.9%

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

      1. associate-/l* 68.5%

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

      2. associate-/r/ 65.9%

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

   5. Simplified 65.9%

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

   if -1.25000000000000001e-126 < t < 4.2e-135 or 4.4999999999999998e-54 < t < 1750

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 59.7%

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

      1. associate-/l* 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in x around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. unsub-neg 66.6%

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

   8. Simplified 66.6%

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

   if 4.2e-135 < t < 4.4999999999999998e-54

   1. Initial program 57.4%

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

      1. clear-num 54.5%

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

      2. associate-/r/ 57.4%

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

   4. Applied egg-rr 57.4%

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

   5. Taylor expanded in y around inf 52.5%

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

      1. div-sub 52.5%

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

      2. associate-*r/ 58.7%

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

      3. associate-*l/ 54.1%

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

   7. Simplified 54.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-126}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-135}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-54}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t \leq 1750:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+130}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t (- a z)))))
   (if (<= z -1.3e+130)
     t
     (if (<= z -3.4e-105)
       t_1
       (if (<= z -8.4e-168)
         (* y (/ x z))
         (if (<= z 1.08e-215) t_1 (if (<= z 5.4e+137) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (a - z));
	double tmp;
	if (z <= -1.3e+130) {
		tmp = t;
	} else if (z <= -3.4e-105) {
		tmp = t_1;
	} else if (z <= -8.4e-168) {
		tmp = y * (x / z);
	} else if (z <= 1.08e-215) {
		tmp = t_1;
	} else if (z <= 5.4e+137) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (a - z))
    if (z <= (-1.3d+130)) then
        tmp = t
    else if (z <= (-3.4d-105)) then
        tmp = t_1
    else if (z <= (-8.4d-168)) then
        tmp = y * (x / z)
    else if (z <= 1.08d-215) then
        tmp = t_1
    else if (z <= 5.4d+137) 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 t_1 = y * (t / (a - z));
	double tmp;
	if (z <= -1.3e+130) {
		tmp = t;
	} else if (z <= -3.4e-105) {
		tmp = t_1;
	} else if (z <= -8.4e-168) {
		tmp = y * (x / z);
	} else if (z <= 1.08e-215) {
		tmp = t_1;
	} else if (z <= 5.4e+137) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / (a - z))
	tmp = 0
	if z <= -1.3e+130:
		tmp = t
	elif z <= -3.4e-105:
		tmp = t_1
	elif z <= -8.4e-168:
		tmp = y * (x / z)
	elif z <= 1.08e-215:
		tmp = t_1
	elif z <= 5.4e+137:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.3e+130)
		tmp = t;
	elseif (z <= -3.4e-105)
		tmp = t_1;
	elseif (z <= -8.4e-168)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 1.08e-215)
		tmp = t_1;
	elseif (z <= 5.4e+137)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / (a - z));
	tmp = 0.0;
	if (z <= -1.3e+130)
		tmp = t;
	elseif (z <= -3.4e-105)
		tmp = t_1;
	elseif (z <= -8.4e-168)
		tmp = y * (x / z);
	elseif (z <= 1.08e-215)
		tmp = t_1;
	elseif (z <= 5.4e+137)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+130], t, If[LessEqual[z, -3.4e-105], t$95$1, If[LessEqual[z, -8.4e-168], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e-215], t$95$1, If[LessEqual[z, 5.4e+137], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2999999999999999e130 or 5.40000000000000034e137 < z

   1. Initial program 57.4%

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

   3. Taylor expanded in z around inf 57.4%

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

   if -1.2999999999999999e130 < z < -3.39999999999999992e-105 or -8.39999999999999976e-168 < z < 1.08e-215

   1. Initial program 90.7%

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

   3. Taylor expanded in x around 0 47.7%

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

      1. associate-/l* 51.5%

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

      2. associate-/r/ 50.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in y around inf 39.8%

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

      1. associate-*l/ 40.5%

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

      2. *-commutative 40.5%

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

   8. Simplified 40.5%

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

   if -3.39999999999999992e-105 < z < -8.39999999999999976e-168

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 73.6%

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

   4. Taylor expanded in a around 0 56.4%

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

      1. associate-*r/ 56.4%

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

      2. associate-*r* 56.4%

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

      3. neg-mul-1 56.4%

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

      4. *-commutative 56.4%

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

   6. Simplified 56.4%

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

   7. Taylor expanded in t around 0 47.3%

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

      1. associate-/l* 47.3%

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

      2. associate-/r/ 47.3%

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

   9. Simplified 47.3%

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

   if 1.08e-215 < z < 5.40000000000000034e137

   1. Initial program 86.1%

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

   3. Taylor expanded in a around inf 44.4%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+130}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-215}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y a))))
   (if (<= z -3.8e+24)
     t
     (if (<= z 1.08e-215)
       t_1
       (if (<= z 1.46e-120)
         x
         (if (<= z 7.4e-93) t_1 (if (<= z 1.25e+137) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / a);
	double tmp;
	if (z <= -3.8e+24) {
		tmp = t;
	} else if (z <= 1.08e-215) {
		tmp = t_1;
	} else if (z <= 1.46e-120) {
		tmp = x;
	} else if (z <= 7.4e-93) {
		tmp = t_1;
	} else if (z <= 1.25e+137) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * (y / a)
    if (z <= (-3.8d+24)) then
        tmp = t
    else if (z <= 1.08d-215) then
        tmp = t_1
    else if (z <= 1.46d-120) then
        tmp = x
    else if (z <= 7.4d-93) then
        tmp = t_1
    else if (z <= 1.25d+137) 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 t_1 = (t - x) * (y / a);
	double tmp;
	if (z <= -3.8e+24) {
		tmp = t;
	} else if (z <= 1.08e-215) {
		tmp = t_1;
	} else if (z <= 1.46e-120) {
		tmp = x;
	} else if (z <= 7.4e-93) {
		tmp = t_1;
	} else if (z <= 1.25e+137) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / a)
	tmp = 0
	if z <= -3.8e+24:
		tmp = t
	elif z <= 1.08e-215:
		tmp = t_1
	elif z <= 1.46e-120:
		tmp = x
	elif z <= 7.4e-93:
		tmp = t_1
	elif z <= 1.25e+137:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / a))
	tmp = 0.0
	if (z <= -3.8e+24)
		tmp = t;
	elseif (z <= 1.08e-215)
		tmp = t_1;
	elseif (z <= 1.46e-120)
		tmp = x;
	elseif (z <= 7.4e-93)
		tmp = t_1;
	elseif (z <= 1.25e+137)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / a);
	tmp = 0.0;
	if (z <= -3.8e+24)
		tmp = t;
	elseif (z <= 1.08e-215)
		tmp = t_1;
	elseif (z <= 1.46e-120)
		tmp = x;
	elseif (z <= 7.4e-93)
		tmp = t_1;
	elseif (z <= 1.25e+137)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+24], t, If[LessEqual[z, 1.08e-215], t$95$1, If[LessEqual[z, 1.46e-120], x, If[LessEqual[z, 7.4e-93], t$95$1, If[LessEqual[z, 1.25e+137], x, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000015e24 or 1.25e137 < z

   1. Initial program 62.5%

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

   3. Taylor expanded in z around inf 49.6%

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

   if -3.80000000000000015e24 < z < 1.08e-215 or 1.4599999999999999e-120 < z < 7.40000000000000005e-93

   1. Initial program 95.0%

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

      1. clear-num 94.3%

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

      2. associate-/r/ 94.9%

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in y around inf 68.3%

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

      1. div-sub 68.3%

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

      2. associate-*r/ 64.2%

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

      3. associate-*l/ 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in a around inf 52.5%

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

   if 1.08e-215 < z < 1.4599999999999999e-120 or 7.40000000000000005e-93 < z < 1.25e137

   1. Initial program 84.8%

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

   3. Taylor expanded in a around inf 48.1%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-215}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-93}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-z}{a - z}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+136}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z) (- a z)))))
   (if (<= z -7.2e+225)
     t_1
     (if (<= z -3.8e+15)
       (* (- y z) (/ t (- a z)))
       (if (<= z 8.2e+136) (+ x (* (- t x) (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-z / (a - z));
	double tmp;
	if (z <= -7.2e+225) {
		tmp = t_1;
	} else if (z <= -3.8e+15) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 8.2e+136) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (-z / (a - z))
    if (z <= (-7.2d+225)) then
        tmp = t_1
    else if (z <= (-3.8d+15)) then
        tmp = (y - z) * (t / (a - z))
    else if (z <= 8.2d+136) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-z / (a - z));
	double tmp;
	if (z <= -7.2e+225) {
		tmp = t_1;
	} else if (z <= -3.8e+15) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 8.2e+136) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (-z / (a - z))
	tmp = 0
	if z <= -7.2e+225:
		tmp = t_1
	elif z <= -3.8e+15:
		tmp = (y - z) * (t / (a - z))
	elif z <= 8.2e+136:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -7.2e+225)
		tmp = t_1;
	elseif (z <= -3.8e+15)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (z <= 8.2e+136)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-z / (a - z));
	tmp = 0.0;
	if (z <= -7.2e+225)
		tmp = t_1;
	elseif (z <= -3.8e+15)
		tmp = (y - z) * (t / (a - z));
	elseif (z <= 8.2e+136)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[((-z) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+225], t$95$1, If[LessEqual[z, -3.8e+15], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+136], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.1999999999999996e225 or 8.1999999999999995e136 < z

   1. Initial program 54.7%

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

   3. Taylor expanded in x around 0 29.4%

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

      1. associate-/l* 68.6%

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

      2. associate-/r/ 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in y around 0 29.3%

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

      1. mul-1-neg 29.3%

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

      2. associate-/l* 65.2%

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

   8. Simplified 65.2%

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

      1. div-inv 65.2%

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

      2. clear-num 65.3%

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

   10. Applied egg-rr 65.3%

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

   if -7.1999999999999996e225 < z < -3.8e15

   1. Initial program 76.1%

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

   3. Taylor expanded in x around 0 38.5%

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

      1. associate-/l* 59.8%

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

      2. associate-/r/ 59.7%

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

   5. Simplified 59.7%

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

   if -3.8e15 < z < 8.1999999999999995e136

   1. Initial program 89.9%

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

   3. Taylor expanded in z around 0 64.0%

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

      1. associate-/l* 66.5%

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

      2. associate-/r/ 69.3%

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

   5. Simplified 69.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+225}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+136}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-z}{a - z}\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-305}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+137}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z) (- a z)))))
   (if (<= z -2.55e+35)
     t_1
     (if (<= z 2.2e-305)
       (* (- t x) (/ y a))
       (if (<= z 8e+137) (- x (/ z (/ a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-z / (a - z));
	double tmp;
	if (z <= -2.55e+35) {
		tmp = t_1;
	} else if (z <= 2.2e-305) {
		tmp = (t - x) * (y / a);
	} else if (z <= 8e+137) {
		tmp = x - (z / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (-z / (a - z))
    if (z <= (-2.55d+35)) then
        tmp = t_1
    else if (z <= 2.2d-305) then
        tmp = (t - x) * (y / a)
    else if (z <= 8d+137) then
        tmp = x - (z / (a / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-z / (a - z));
	double tmp;
	if (z <= -2.55e+35) {
		tmp = t_1;
	} else if (z <= 2.2e-305) {
		tmp = (t - x) * (y / a);
	} else if (z <= 8e+137) {
		tmp = x - (z / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (-z / (a - z))
	tmp = 0
	if z <= -2.55e+35:
		tmp = t_1
	elif z <= 2.2e-305:
		tmp = (t - x) * (y / a)
	elif z <= 8e+137:
		tmp = x - (z / (a / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.55e+35)
		tmp = t_1;
	elseif (z <= 2.2e-305)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 8e+137)
		tmp = Float64(x - Float64(z / Float64(a / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-z / (a - z));
	tmp = 0.0;
	if (z <= -2.55e+35)
		tmp = t_1;
	elseif (z <= 2.2e-305)
		tmp = (t - x) * (y / a);
	elseif (z <= 8e+137)
		tmp = x - (z / (a / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[((-z) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e+35], t$95$1, If[LessEqual[z, 2.2e-305], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+137], N[(x - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.55000000000000009e35 or 8.0000000000000003e137 < z

   1. Initial program 61.2%

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

   3. Taylor expanded in x around 0 31.9%

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

      1. associate-/l* 65.8%

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

      2. associate-/r/ 53.7%

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

   5. Simplified 53.7%

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

   6. Taylor expanded in y around 0 29.6%

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

      1. mul-1-neg 29.6%

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

      2. associate-/l* 56.3%

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

   8. Simplified 56.3%

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

      1. div-inv 56.3%

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

      2. clear-num 56.3%

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

   10. Applied egg-rr 56.3%

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

   if -2.55000000000000009e35 < z < 2.19999999999999997e-305

   1. Initial program 93.7%

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

      1. clear-num 92.7%

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

      2. associate-/r/ 93.6%

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

   4. Applied egg-rr 93.6%

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

   5. Taylor expanded in y around inf 67.4%

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

      1. div-sub 67.4%

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

      2. associate-*r/ 64.9%

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

      3. associate-*l/ 67.8%

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

   7. Simplified 67.8%

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

   8. Taylor expanded in a around inf 51.4%

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

   if 2.19999999999999997e-305 < z < 8.0000000000000003e137

   1. Initial program 88.1%

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

   3. Taylor expanded in y around 0 47.0%

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

      1. mul-1-neg 47.0%

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

      2. unsub-neg 47.0%

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

      3. associate-*r/ 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in a around inf 46.9%

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

      1. mul-1-neg 46.9%

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

      2. unsub-neg 46.9%

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

      3. associate-/l* 53.4%

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

   8. Simplified 53.4%

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

   9. Taylor expanded in t around inf 52.5%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-305}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+137}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 44.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+35}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-307}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.9e+35)
   (/ (- t) (/ (- a z) z))
   (if (<= z 5.8e-307)
     (* (- t x) (/ y a))
     (if (<= z 8.2e+136) (- x (/ z (/ a t))) (* t (/ (- z) (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.9e+35) {
		tmp = -t / ((a - z) / z);
	} else if (z <= 5.8e-307) {
		tmp = (t - x) * (y / a);
	} else if (z <= 8.2e+136) {
		tmp = x - (z / (a / t));
	} else {
		tmp = t * (-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) :: tmp
    if (z <= (-5.9d+35)) then
        tmp = -t / ((a - z) / z)
    else if (z <= 5.8d-307) then
        tmp = (t - x) * (y / a)
    else if (z <= 8.2d+136) then
        tmp = x - (z / (a / t))
    else
        tmp = t * (-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 tmp;
	if (z <= -5.9e+35) {
		tmp = -t / ((a - z) / z);
	} else if (z <= 5.8e-307) {
		tmp = (t - x) * (y / a);
	} else if (z <= 8.2e+136) {
		tmp = x - (z / (a / t));
	} else {
		tmp = t * (-z / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.9e+35:
		tmp = -t / ((a - z) / z)
	elif z <= 5.8e-307:
		tmp = (t - x) * (y / a)
	elif z <= 8.2e+136:
		tmp = x - (z / (a / t))
	else:
		tmp = t * (-z / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.9e+35)
		tmp = Float64(Float64(-t) / Float64(Float64(a - z) / z));
	elseif (z <= 5.8e-307)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 8.2e+136)
		tmp = Float64(x - Float64(z / Float64(a / t)));
	else
		tmp = Float64(t * Float64(Float64(-z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.9e+35)
		tmp = -t / ((a - z) / z);
	elseif (z <= 5.8e-307)
		tmp = (t - x) * (y / a);
	elseif (z <= 8.2e+136)
		tmp = x - (z / (a / t));
	else
		tmp = t * (-z / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.9e+35], N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-307], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+136], N[(x - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[((-z) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.89999999999999985e35

   1. Initial program 66.6%

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

   3. Taylor expanded in x around 0 35.2%

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

      1. associate-/l* 70.2%

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

      2. associate-/r/ 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in y around 0 31.1%

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

      1. mul-1-neg 31.1%

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

      2. associate-/l* 56.7%

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

   8. Simplified 56.7%

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

   if -5.89999999999999985e35 < z < 5.8000000000000001e-307

   1. Initial program 93.7%

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

      1. clear-num 92.7%

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

      2. associate-/r/ 93.6%

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

   4. Applied egg-rr 93.6%

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

   5. Taylor expanded in y around inf 67.4%

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

      1. div-sub 67.4%

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

      2. associate-*r/ 64.9%

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

      3. associate-*l/ 67.8%

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

   7. Simplified 67.8%

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

   8. Taylor expanded in a around inf 51.4%

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

   if 5.8000000000000001e-307 < z < 8.1999999999999995e136

   1. Initial program 88.1%

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

   3. Taylor expanded in y around 0 47.0%

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

      1. mul-1-neg 47.0%

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

      2. unsub-neg 47.0%

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

      3. associate-*r/ 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in a around inf 46.9%

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

      1. mul-1-neg 46.9%

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

      2. unsub-neg 46.9%

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

      3. associate-/l* 53.4%

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

   8. Simplified 53.4%

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

   9. Taylor expanded in t around inf 52.5%

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

   if 8.1999999999999995e136 < z

   1. Initial program 54.5%

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

   3. Taylor expanded in x around 0 27.9%

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

      1. associate-/l* 60.4%

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

      2. associate-/r/ 44.4%

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

   5. Simplified 44.4%

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

   6. Taylor expanded in y around 0 27.7%

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

      1. mul-1-neg 27.7%

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

      2. associate-/l* 55.8%

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

   8. Simplified 55.8%

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

      1. div-inv 55.8%

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

      2. clear-num 55.9%

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

   10. Applied egg-rr 55.9%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+35}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-307}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+37}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e+37)
   (/ (- t) (/ (- a z) z))
   (if (<= z 1.9e-74)
     (* x (+ (/ (- z y) a) 1.0))
     (if (<= z 8e+136) (- x (/ (* z t) a)) (* t (/ (- z) (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+37) {
		tmp = -t / ((a - z) / z);
	} else if (z <= 1.9e-74) {
		tmp = x * (((z - y) / a) + 1.0);
	} else if (z <= 8e+136) {
		tmp = x - ((z * t) / a);
	} else {
		tmp = t * (-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) :: tmp
    if (z <= (-4d+37)) then
        tmp = -t / ((a - z) / z)
    else if (z <= 1.9d-74) then
        tmp = x * (((z - y) / a) + 1.0d0)
    else if (z <= 8d+136) then
        tmp = x - ((z * t) / a)
    else
        tmp = t * (-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 tmp;
	if (z <= -4e+37) {
		tmp = -t / ((a - z) / z);
	} else if (z <= 1.9e-74) {
		tmp = x * (((z - y) / a) + 1.0);
	} else if (z <= 8e+136) {
		tmp = x - ((z * t) / a);
	} else {
		tmp = t * (-z / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e+37:
		tmp = -t / ((a - z) / z)
	elif z <= 1.9e-74:
		tmp = x * (((z - y) / a) + 1.0)
	elif z <= 8e+136:
		tmp = x - ((z * t) / a)
	else:
		tmp = t * (-z / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e+37)
		tmp = Float64(Float64(-t) / Float64(Float64(a - z) / z));
	elseif (z <= 1.9e-74)
		tmp = Float64(x * Float64(Float64(Float64(z - y) / a) + 1.0));
	elseif (z <= 8e+136)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	else
		tmp = Float64(t * Float64(Float64(-z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4e+37)
		tmp = -t / ((a - z) / z);
	elseif (z <= 1.9e-74)
		tmp = x * (((z - y) / a) + 1.0);
	elseif (z <= 8e+136)
		tmp = x - ((z * t) / a);
	else
		tmp = t * (-z / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e+37], N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-74], N[(x * N[(N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+136], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t * N[((-z) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.99999999999999982e37

   1. Initial program 66.6%

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

   3. Taylor expanded in x around 0 35.2%

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

      1. associate-/l* 70.2%

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

      2. associate-/r/ 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in y around 0 31.1%

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

      1. mul-1-neg 31.1%

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

      2. associate-/l* 56.7%

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

   8. Simplified 56.7%

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

   if -3.99999999999999982e37 < z < 1.8999999999999998e-74

   1. Initial program 93.9%

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

   3. Taylor expanded in a around inf 70.1%

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

      1. associate-/l* 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in x around inf 51.2%

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

      1. mul-1-neg 51.2%

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

      2. unsub-neg 51.2%

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

   8. Simplified 51.2%

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

   if 1.8999999999999998e-74 < z < 8.00000000000000047e136

   1. Initial program 82.0%

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

   3. Taylor expanded in y around 0 48.0%

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

      1. mul-1-neg 48.0%

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

      2. unsub-neg 48.0%

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

      3. associate-*r/ 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in a around inf 48.3%

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

      1. mul-1-neg 48.3%

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

      2. unsub-neg 48.3%

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

      3. associate-/l* 57.6%

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

   8. Simplified 57.6%

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

   9. Taylor expanded in t around inf 57.6%

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

   if 8.00000000000000047e136 < z

   1. Initial program 54.5%

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

   3. Taylor expanded in x around 0 27.9%

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

      1. associate-/l* 60.4%

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

      2. associate-/r/ 44.4%

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

   5. Simplified 44.4%

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

   6. Taylor expanded in y around 0 27.7%

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

      1. mul-1-neg 27.7%

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

      2. associate-/l* 55.8%

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

   8. Simplified 55.8%

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

      1. div-inv 55.8%

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

      2. clear-num 55.9%

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

   10. Applied egg-rr 55.9%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+37}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 42.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+23}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-304}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+138}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+23)
   t
   (if (<= z 1.55e-304)
     (* (- t x) (/ y a))
     (if (<= z 1.4e+138) (- x (/ z (/ a t))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+23) {
		tmp = t;
	} else if (z <= 1.55e-304) {
		tmp = (t - x) * (y / a);
	} else if (z <= 1.4e+138) {
		tmp = x - (z / (a / t));
	} 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 <= (-5.5d+23)) then
        tmp = t
    else if (z <= 1.55d-304) then
        tmp = (t - x) * (y / a)
    else if (z <= 1.4d+138) then
        tmp = x - (z / (a / t))
    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 <= -5.5e+23) {
		tmp = t;
	} else if (z <= 1.55e-304) {
		tmp = (t - x) * (y / a);
	} else if (z <= 1.4e+138) {
		tmp = x - (z / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+23:
		tmp = t
	elif z <= 1.55e-304:
		tmp = (t - x) * (y / a)
	elif z <= 1.4e+138:
		tmp = x - (z / (a / t))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+23)
		tmp = t;
	elseif (z <= 1.55e-304)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 1.4e+138)
		tmp = Float64(x - Float64(z / Float64(a / t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+23)
		tmp = t;
	elseif (z <= 1.55e-304)
		tmp = (t - x) * (y / a);
	elseif (z <= 1.4e+138)
		tmp = x - (z / (a / t));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+23], t, If[LessEqual[z, 1.55e-304], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+138], N[(x - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.50000000000000004e23 or 1.4e138 < z

   1. Initial program 62.5%

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

   3. Taylor expanded in z around inf 49.6%

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

   if -5.50000000000000004e23 < z < 1.54999999999999992e-304

   1. Initial program 93.4%

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

      1. clear-num 92.4%

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

      2. associate-/r/ 93.3%

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

   4. Applied egg-rr 93.3%

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

   5. Taylor expanded in y around inf 68.9%

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

      1. div-sub 68.8%

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

      2. associate-*r/ 66.2%

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

      3. associate-*l/ 69.2%

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

   7. Simplified 69.2%

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

   8. Taylor expanded in a around inf 52.0%

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

   if 1.54999999999999992e-304 < z < 1.4e138

   1. Initial program 88.1%

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

   3. Taylor expanded in y around 0 47.0%

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

      1. mul-1-neg 47.0%

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

      2. unsub-neg 47.0%

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

      3. associate-*r/ 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in a around inf 46.9%

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

      1. mul-1-neg 46.9%

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

      2. unsub-neg 46.9%

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

      3. associate-/l* 53.4%

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

   8. Simplified 53.4%

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

   9. Taylor expanded in t around inf 52.5%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+23}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-304}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+138}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+15} \lor \neg \left(z \leq 6.5 \cdot 10^{+75}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.25e+15) (not (<= z 6.5e+75)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (/ (- t x) (/ a (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+15) || !(z <= 6.5e+75)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((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) :: tmp
    if ((z <= (-1.25d+15)) .or. (.not. (z <= 6.5d+75))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + ((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 tmp;
	if ((z <= -1.25e+15) || !(z <= 6.5e+75)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.25e+15) or not (z <= 6.5e+75):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + ((t - x) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.25e+15) || !(z <= 6.5e+75))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.25e+15) || ~((z <= 6.5e+75)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + ((t - x) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.25e+15], N[Not[LessEqual[z, 6.5e+75]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e15 or 6.4999999999999998e75 < z

   1. Initial program 65.2%

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

   3. Taylor expanded in z around inf 61.8%

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

      1. associate--l+ 61.8%

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

      2. distribute-lft-out-- 61.8%

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

      3. div-sub 61.8%

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

      4. mul-1-neg 61.8%

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

      5. unsub-neg 61.8%

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

      6. distribute-rgt-out-- 61.9%

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

      7. associate-/l* 77.6%

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

   5. Simplified 77.6%

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

   if -1.25e15 < z < 6.4999999999999998e75

   1. Initial program 91.3%

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

   3. Taylor expanded in a around inf 69.8%

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

      1. associate-/l* 76.9%

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

   5. Simplified 76.9%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+15} \lor \neg \left(z \leq 6.5 \cdot 10^{+75}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 36.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-215}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.46e-8)
   t
   (if (<= z 1.1e-215) (* y (/ t a)) (if (<= z 8.8e+138) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.46e-8) {
		tmp = t;
	} else if (z <= 1.1e-215) {
		tmp = y * (t / a);
	} else if (z <= 8.8e+138) {
		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 <= (-1.46d-8)) then
        tmp = t
    else if (z <= 1.1d-215) then
        tmp = y * (t / a)
    else if (z <= 8.8d+138) 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 <= -1.46e-8) {
		tmp = t;
	} else if (z <= 1.1e-215) {
		tmp = y * (t / a);
	} else if (z <= 8.8e+138) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.46e-8:
		tmp = t
	elif z <= 1.1e-215:
		tmp = y * (t / a)
	elif z <= 8.8e+138:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.46e-8)
		tmp = t;
	elseif (z <= 1.1e-215)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 8.8e+138)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.46e-8)
		tmp = t;
	elseif (z <= 1.1e-215)
		tmp = y * (t / a);
	elseif (z <= 8.8e+138)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.46e-8], t, If[LessEqual[z, 1.1e-215], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+138], x, t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.46e-8 or 8.8000000000000003e138 < z

   1. Initial program 64.1%

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

   3. Taylor expanded in z around inf 47.6%

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

   if -1.46e-8 < z < 1.09999999999999998e-215

   1. Initial program 94.3%

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

   3. Taylor expanded in x around 0 44.8%

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

      1. associate-/l* 45.7%

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

      2. associate-/r/ 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in a around inf 38.5%

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

      1. associate-/l* 39.8%

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

   8. Simplified 39.8%

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

   9. Taylor expanded in y around inf 36.0%

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

       1. associate-*l/ 35.6%

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

       2. *-commutative 35.6%

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

   11. Simplified 35.6%

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

   if 1.09999999999999998e-215 < z < 8.8000000000000003e138

   1. Initial program 86.1%

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

   3. Taylor expanded in a around inf 44.4%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-215}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 36.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.335:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-304}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.335)
   t
   (if (<= z -1.4e-304) (* t (/ y a)) (if (<= z 4.6e+137) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.335) {
		tmp = t;
	} else if (z <= -1.4e-304) {
		tmp = t * (y / a);
	} else if (z <= 4.6e+137) {
		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 <= (-0.335d0)) then
        tmp = t
    else if (z <= (-1.4d-304)) then
        tmp = t * (y / a)
    else if (z <= 4.6d+137) 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 <= -0.335) {
		tmp = t;
	} else if (z <= -1.4e-304) {
		tmp = t * (y / a);
	} else if (z <= 4.6e+137) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.335:
		tmp = t
	elif z <= -1.4e-304:
		tmp = t * (y / a)
	elif z <= 4.6e+137:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.335)
		tmp = t;
	elseif (z <= -1.4e-304)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 4.6e+137)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.335)
		tmp = t;
	elseif (z <= -1.4e-304)
		tmp = t * (y / a);
	elseif (z <= 4.6e+137)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.335], t, If[LessEqual[z, -1.4e-304], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+137], x, t]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.33500000000000002 or 4.59999999999999999e137 < z

   1. Initial program 64.1%

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

   3. Taylor expanded in z around inf 47.6%

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

   if -0.33500000000000002 < z < -1.3999999999999999e-304

   1. Initial program 92.9%

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

   3. Taylor expanded in x around 0 44.0%

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

      1. associate-/l* 46.4%

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

      2. associate-/r/ 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in a around inf 37.6%

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

      1. associate-/l* 40.8%

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

   8. Simplified 40.8%

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

   9. Taylor expanded in y around inf 34.6%

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

       1. associate-*l/ 34.1%

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

       2. *-commutative 34.1%

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

   11. Simplified 34.1%

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

   12. Taylor expanded in y around 0 34.6%

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

       1. *-commutative 34.6%

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

       2. associate-/l* 33.1%

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

       3. associate-/r/ 36.1%

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

   14. Simplified 36.1%

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

   if -1.3999999999999999e-304 < z < 4.59999999999999999e137

   1. Initial program 88.1%

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

   3. Taylor expanded in a around inf 43.4%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.335:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-304}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+49}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e+99) x (if (<= a 1.15e+49) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+99) {
		tmp = x;
	} else if (a <= 1.15e+49) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.5d+99)) then
        tmp = x
    else if (a <= 1.15d+49) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+99) {
		tmp = x;
	} else if (a <= 1.15e+49) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e+99:
		tmp = x
	elif a <= 1.15e+49:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e+99)
		tmp = x;
	elseif (a <= 1.15e+49)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e+99)
		tmp = x;
	elseif (a <= 1.15e+49)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e+99], x, If[LessEqual[a, 1.15e+49], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.5e99 or 1.15000000000000001e49 < a

   1. Initial program 88.5%

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

   3. Taylor expanded in a around inf 52.5%

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

   if -4.5e99 < a < 1.15000000000000001e49

   1. Initial program 73.9%

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

   3. Taylor expanded in z around inf 31.2%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+49}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 25.0% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 80.4%

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

3. Taylor expanded in z around inf 22.8%

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

4. Final simplification 22.8%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024034 
(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)))))