Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 90.9%

Time: 16.4s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.4% 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: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-302} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-249}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-302) (not (<= t_1 2e-249)))
     t_1
     (+ t (* (/ (- y a) z) (- x t))))))

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 <= -1e-302) || !(t_1 <= 2e-249)) {
		tmp = t_1;
	} else {
		tmp = t + (((y - a) / z) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-302)) .or. (.not. (t_1 <= 2d-249))) then
        tmp = t_1
    else
        tmp = t + (((y - a) / z) * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-302) || !(t_1 <= 2e-249)) {
		tmp = t_1;
	} else {
		tmp = t + (((y - a) / z) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-302) or not (t_1 <= 2e-249):
		tmp = t_1
	else:
		tmp = t + (((y - a) / z) * (x - t))
	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 <= -1e-302) || !(t_1 <= 2e-249))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(y - a) / z) * Float64(x - t)));
	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 <= -1e-302) || ~((t_1 <= 2e-249)))
		tmp = t_1;
	else
		tmp = t + (((y - a) / z) * (x - t));
	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, -1e-302], N[Not[LessEqual[t$95$1, 2e-249]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $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)))) < -9.9999999999999996e-303 or 2.00000000000000011e-249 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.8%

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

   if -9.9999999999999996e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2.00000000000000011e-249

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 81.8%

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

      1. associate--l+ 81.8%

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

      2. distribute-lft-out-- 81.8%

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

      3. div-sub 81.8%

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

      4. mul-1-neg 81.8%

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

      5. unsub-neg 81.8%

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

      6. distribute-rgt-out-- 81.8%

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

      7. associate-/l* 93.9%

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

   5. Simplified 93.9%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-302} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-249}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 59.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ t_3 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-283}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+40}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z))))
        (t_2 (+ x (* y (/ (- t x) a))))
        (t_3 (* (- y z) (/ t (- a z)))))
   (if (<= a -1.7e+34)
     t_2
     (if (<= a -6e-166)
       t_1
       (if (<= a 6.4e-283)
         t_3
         (if (<= a 1.5e-133) t_1 (if (<= a 1.6e+40) t_3 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 = x + (y * ((t - x) / a));
	double t_3 = (y - z) * (t / (a - z));
	double tmp;
	if (a <= -1.7e+34) {
		tmp = t_2;
	} else if (a <= -6e-166) {
		tmp = t_1;
	} else if (a <= 6.4e-283) {
		tmp = t_3;
	} else if (a <= 1.5e-133) {
		tmp = t_1;
	} else if (a <= 1.6e+40) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = x + (y * ((t - x) / a))
    t_3 = (y - z) * (t / (a - z))
    if (a <= (-1.7d+34)) then
        tmp = t_2
    else if (a <= (-6d-166)) then
        tmp = t_1
    else if (a <= 6.4d-283) then
        tmp = t_3
    else if (a <= 1.5d-133) then
        tmp = t_1
    else if (a <= 1.6d+40) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double t_3 = (y - z) * (t / (a - z));
	double tmp;
	if (a <= -1.7e+34) {
		tmp = t_2;
	} else if (a <= -6e-166) {
		tmp = t_1;
	} else if (a <= 6.4e-283) {
		tmp = t_3;
	} else if (a <= 1.5e-133) {
		tmp = t_1;
	} else if (a <= 1.6e+40) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = x + (y * ((t - x) / a))
	t_3 = (y - z) * (t / (a - z))
	tmp = 0
	if a <= -1.7e+34:
		tmp = t_2
	elif a <= -6e-166:
		tmp = t_1
	elif a <= 6.4e-283:
		tmp = t_3
	elif a <= 1.5e-133:
		tmp = t_1
	elif a <= 1.6e+40:
		tmp = t_3
	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(x + Float64(y * Float64(Float64(t - x) / a)))
	t_3 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (a <= -1.7e+34)
		tmp = t_2;
	elseif (a <= -6e-166)
		tmp = t_1;
	elseif (a <= 6.4e-283)
		tmp = t_3;
	elseif (a <= 1.5e-133)
		tmp = t_1;
	elseif (a <= 1.6e+40)
		tmp = t_3;
	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 = x + (y * ((t - x) / a));
	t_3 = (y - z) * (t / (a - z));
	tmp = 0.0;
	if (a <= -1.7e+34)
		tmp = t_2;
	elseif (a <= -6e-166)
		tmp = t_1;
	elseif (a <= 6.4e-283)
		tmp = t_3;
	elseif (a <= 1.5e-133)
		tmp = t_1;
	elseif (a <= 1.6e+40)
		tmp = t_3;
	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[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+34], t$95$2, If[LessEqual[a, -6e-166], t$95$1, If[LessEqual[a, 6.4e-283], t$95$3, If[LessEqual[a, 1.5e-133], t$95$1, If[LessEqual[a, 1.6e+40], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.7e34 or 1.5999999999999999e40 < a

   1. Initial program 86.3%

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

   3. Taylor expanded in z around 0 61.7%

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

      1. associate-/l* 70.7%

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

   5. Simplified 70.7%

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

   if -1.7e34 < a < -6.0000000000000005e-166 or 6.40000000000000023e-283 < a < 1.5000000000000001e-133

   1. Initial program 74.4%

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

   3. Taylor expanded in y around inf 64.7%

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

      1. div-sub 66.0%

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

   5. Simplified 66.0%

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

   if -6.0000000000000005e-166 < a < 6.40000000000000023e-283 or 1.5000000000000001e-133 < a < 1.5999999999999999e40

   1. Initial program 79.8%

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

   3. Taylor expanded in x around 0 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-/l* 72.9%

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

   5. Simplified 72.9%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+34}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-283}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+40}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+33}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-281}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.96 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (* (- y z) (/ t (- a z)))))
   (if (<= a -3.5e+33)
     (+ x (* y (/ (- t x) a)))
     (if (<= a -4.6e-165)
       t_1
       (if (<= a 1.8e-281)
         t_2
         (if (<= a 6.8e-134)
           t_1
           (if (<= a 1.96e+40) t_2 (+ x (* (- t x) (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = (y - z) * (t / (a - z));
	double tmp;
	if (a <= -3.5e+33) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -4.6e-165) {
		tmp = t_1;
	} else if (a <= 1.8e-281) {
		tmp = t_2;
	} else if (a <= 6.8e-134) {
		tmp = t_1;
	} else if (a <= 1.96e+40) {
		tmp = t_2;
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = (y - z) * (t / (a - z))
    if (a <= (-3.5d+33)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= (-4.6d-165)) then
        tmp = t_1
    else if (a <= 1.8d-281) then
        tmp = t_2
    else if (a <= 6.8d-134) then
        tmp = t_1
    else if (a <= 1.96d+40) then
        tmp = t_2
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = (y - z) * (t / (a - z));
	double tmp;
	if (a <= -3.5e+33) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -4.6e-165) {
		tmp = t_1;
	} else if (a <= 1.8e-281) {
		tmp = t_2;
	} else if (a <= 6.8e-134) {
		tmp = t_1;
	} else if (a <= 1.96e+40) {
		tmp = t_2;
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = (y - z) * (t / (a - z))
	tmp = 0
	if a <= -3.5e+33:
		tmp = x + (y * ((t - x) / a))
	elif a <= -4.6e-165:
		tmp = t_1
	elif a <= 1.8e-281:
		tmp = t_2
	elif a <= 6.8e-134:
		tmp = t_1
	elif a <= 1.96e+40:
		tmp = t_2
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (a <= -3.5e+33)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= -4.6e-165)
		tmp = t_1;
	elseif (a <= 1.8e-281)
		tmp = t_2;
	elseif (a <= 6.8e-134)
		tmp = t_1;
	elseif (a <= 1.96e+40)
		tmp = t_2;
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = (y - z) * (t / (a - z));
	tmp = 0.0;
	if (a <= -3.5e+33)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= -4.6e-165)
		tmp = t_1;
	elseif (a <= 1.8e-281)
		tmp = t_2;
	elseif (a <= 6.8e-134)
		tmp = t_1;
	elseif (a <= 1.96e+40)
		tmp = t_2;
	else
		tmp = x + ((t - x) * (y / a));
	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[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+33], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.6e-165], t$95$1, If[LessEqual[a, 1.8e-281], t$95$2, If[LessEqual[a, 6.8e-134], t$95$1, If[LessEqual[a, 1.96e+40], t$95$2, N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.5000000000000001e33

   1. Initial program 88.5%

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

   3. Taylor expanded in z around 0 58.7%

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

      1. associate-/l* 74.7%

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

   5. Simplified 74.7%

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

   if -3.5000000000000001e33 < a < -4.6000000000000001e-165 or 1.80000000000000003e-281 < a < 6.79999999999999954e-134

   1. Initial program 74.4%

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

   3. Taylor expanded in y around inf 64.7%

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

      1. div-sub 66.0%

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

   5. Simplified 66.0%

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

   if -4.6000000000000001e-165 < a < 1.80000000000000003e-281 or 6.79999999999999954e-134 < a < 1.95999999999999995e40

   1. Initial program 79.8%

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

   3. Taylor expanded in x around 0 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-/l* 72.9%

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

   5. Simplified 72.9%

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

   if 1.95999999999999995e40 < a

   1. Initial program 84.6%

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

   3. Taylor expanded in z around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-/l* 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+33}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-281}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.96 \cdot 10^{+40}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-159}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{-282}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e+51)
   x
   (if (<= a -4.4e-159)
     (* t (/ y (- a z)))
     (if (<= a -1.06e-282)
       t
       (if (<= a 5e-109)
         (* x (/ y (- z a)))
         (if (<= a 3e+40) (* t (/ (- y z) a)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+51) {
		tmp = x;
	} else if (a <= -4.4e-159) {
		tmp = t * (y / (a - z));
	} else if (a <= -1.06e-282) {
		tmp = t;
	} else if (a <= 5e-109) {
		tmp = x * (y / (z - a));
	} else if (a <= 3e+40) {
		tmp = t * ((y - z) / a);
	} 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 <= (-7d+51)) then
        tmp = x
    else if (a <= (-4.4d-159)) then
        tmp = t * (y / (a - z))
    else if (a <= (-1.06d-282)) then
        tmp = t
    else if (a <= 5d-109) then
        tmp = x * (y / (z - a))
    else if (a <= 3d+40) then
        tmp = t * ((y - z) / a)
    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 <= -7e+51) {
		tmp = x;
	} else if (a <= -4.4e-159) {
		tmp = t * (y / (a - z));
	} else if (a <= -1.06e-282) {
		tmp = t;
	} else if (a <= 5e-109) {
		tmp = x * (y / (z - a));
	} else if (a <= 3e+40) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e+51:
		tmp = x
	elif a <= -4.4e-159:
		tmp = t * (y / (a - z))
	elif a <= -1.06e-282:
		tmp = t
	elif a <= 5e-109:
		tmp = x * (y / (z - a))
	elif a <= 3e+40:
		tmp = t * ((y - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e+51)
		tmp = x;
	elseif (a <= -4.4e-159)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (a <= -1.06e-282)
		tmp = t;
	elseif (a <= 5e-109)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (a <= 3e+40)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e+51)
		tmp = x;
	elseif (a <= -4.4e-159)
		tmp = t * (y / (a - z));
	elseif (a <= -1.06e-282)
		tmp = t;
	elseif (a <= 5e-109)
		tmp = x * (y / (z - a));
	elseif (a <= 3e+40)
		tmp = t * ((y - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e+51], x, If[LessEqual[a, -4.4e-159], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.06e-282], t, If[LessEqual[a, 5e-109], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e+40], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7e51 or 3.0000000000000002e40 < a

   1. Initial program 85.9%

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

   3. Taylor expanded in a around inf 45.7%

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

   if -7e51 < a < -4.4e-159

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-/l* 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in y around inf 36.6%

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

      1. associate-/l* 41.7%

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

   8. Simplified 41.7%

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

   if -4.4e-159 < a < -1.0600000000000001e-282

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf 55.7%

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

   if -1.0600000000000001e-282 < a < 5.0000000000000002e-109

   1. Initial program 66.2%

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

   3. Taylor expanded in t around 0 34.6%

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

      1. mul-1-neg 34.6%

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

      2. associate-/l* 39.0%

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

      3. distribute-rgt-neg-in 39.0%

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

      4. distribute-frac-neg2 39.0%

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

      5. neg-sub0 39.0%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{0 - \left(a - z\right)}} \]

      6. associate--r- 39.0%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{\left(0 - a\right) + z}} \]

      7. neg-sub0 39.0%

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

   5. Simplified 39.0%

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

   6. Taylor expanded in y around inf 46.2%

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

      1. associate-/l* 48.2%

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

   8. Simplified 48.2%

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

   if 5.0000000000000002e-109 < a < 3.0000000000000002e40

   1. Initial program 85.5%

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

   3. Taylor expanded in x around 0 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-/l* 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in a around inf 43.5%

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

      1. associate-/l* 43.3%

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

   8. Simplified 43.3%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-159}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{-282}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+95)
   t
   (if (<= z -1.15e-46)
     x
     (if (<= z 1.02e-82)
       (* t (/ y (- a z)))
       (if (<= z 7.8e+18) x (if (<= z 5.7e+116) (* x (/ (- y a) z)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+95) {
		tmp = t;
	} else if (z <= -1.15e-46) {
		tmp = x;
	} else if (z <= 1.02e-82) {
		tmp = t * (y / (a - z));
	} else if (z <= 7.8e+18) {
		tmp = x;
	} else if (z <= 5.7e+116) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.2d+95)) then
        tmp = t
    else if (z <= (-1.15d-46)) then
        tmp = x
    else if (z <= 1.02d-82) then
        tmp = t * (y / (a - z))
    else if (z <= 7.8d+18) then
        tmp = x
    else if (z <= 5.7d+116) then
        tmp = x * ((y - a) / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+95) {
		tmp = t;
	} else if (z <= -1.15e-46) {
		tmp = x;
	} else if (z <= 1.02e-82) {
		tmp = t * (y / (a - z));
	} else if (z <= 7.8e+18) {
		tmp = x;
	} else if (z <= 5.7e+116) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+95:
		tmp = t
	elif z <= -1.15e-46:
		tmp = x
	elif z <= 1.02e-82:
		tmp = t * (y / (a - z))
	elif z <= 7.8e+18:
		tmp = x
	elif z <= 5.7e+116:
		tmp = x * ((y - a) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+95)
		tmp = t;
	elseif (z <= -1.15e-46)
		tmp = x;
	elseif (z <= 1.02e-82)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 7.8e+18)
		tmp = x;
	elseif (z <= 5.7e+116)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e+95)
		tmp = t;
	elseif (z <= -1.15e-46)
		tmp = x;
	elseif (z <= 1.02e-82)
		tmp = t * (y / (a - z));
	elseif (z <= 7.8e+18)
		tmp = x;
	elseif (z <= 5.7e+116)
		tmp = x * ((y - a) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+95], t, If[LessEqual[z, -1.15e-46], x, If[LessEqual[z, 1.02e-82], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+18], x, If[LessEqual[z, 5.7e+116], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.19999999999999981e95 or 5.69999999999999983e116 < z

   1. Initial program 63.6%

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

   3. Taylor expanded in z around inf 48.3%

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

   if -5.19999999999999981e95 < z < -1.15e-46 or 1.02000000000000007e-82 < z < 7.8e18

   1. Initial program 92.9%

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

   3. Taylor expanded in a around inf 48.3%

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

   if -1.15e-46 < z < 1.02000000000000007e-82

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/l* 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in y around inf 44.1%

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

      1. associate-/l* 45.9%

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

   8. Simplified 45.9%

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

   if 7.8e18 < z < 5.69999999999999983e116

   1. Initial program 69.4%

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

   3. Taylor expanded in z around inf 74.8%

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

      1. associate--l+ 74.8%

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

      2. distribute-lft-out-- 74.8%

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

      3. div-sub 74.8%

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

      4. mul-1-neg 74.8%

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

      5. unsub-neg 74.8%

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

      6. distribute-rgt-out-- 81.1%

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

      7. associate-/l* 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in t around 0 51.2%

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

      1. associate-/l* 51.0%

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

   8. Simplified 51.0%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.48 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{x \cdot z}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+94)
   t
   (if (<= z -1.48e-46)
     x
     (if (<= z 6.6e-83)
       (* t (/ y (- a z)))
       (if (<= z 3.7e+18)
         (+ x (/ (* x z) a))
         (if (<= z 1.35e+116) (* x (/ (- y a) z)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+94) {
		tmp = t;
	} else if (z <= -1.48e-46) {
		tmp = x;
	} else if (z <= 6.6e-83) {
		tmp = t * (y / (a - z));
	} else if (z <= 3.7e+18) {
		tmp = x + ((x * z) / a);
	} else if (z <= 1.35e+116) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.5d+94)) then
        tmp = t
    else if (z <= (-1.48d-46)) then
        tmp = x
    else if (z <= 6.6d-83) then
        tmp = t * (y / (a - z))
    else if (z <= 3.7d+18) then
        tmp = x + ((x * z) / a)
    else if (z <= 1.35d+116) then
        tmp = x * ((y - a) / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+94) {
		tmp = t;
	} else if (z <= -1.48e-46) {
		tmp = x;
	} else if (z <= 6.6e-83) {
		tmp = t * (y / (a - z));
	} else if (z <= 3.7e+18) {
		tmp = x + ((x * z) / a);
	} else if (z <= 1.35e+116) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+94:
		tmp = t
	elif z <= -1.48e-46:
		tmp = x
	elif z <= 6.6e-83:
		tmp = t * (y / (a - z))
	elif z <= 3.7e+18:
		tmp = x + ((x * z) / a)
	elif z <= 1.35e+116:
		tmp = x * ((y - a) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+94)
		tmp = t;
	elseif (z <= -1.48e-46)
		tmp = x;
	elseif (z <= 6.6e-83)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 3.7e+18)
		tmp = Float64(x + Float64(Float64(x * z) / a));
	elseif (z <= 1.35e+116)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+94)
		tmp = t;
	elseif (z <= -1.48e-46)
		tmp = x;
	elseif (z <= 6.6e-83)
		tmp = t * (y / (a - z));
	elseif (z <= 3.7e+18)
		tmp = x + ((x * z) / a);
	elseif (z <= 1.35e+116)
		tmp = x * ((y - a) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+94], t, If[LessEqual[z, -1.48e-46], x, If[LessEqual[z, 6.6e-83], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+18], N[(x + N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+116], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.49999999999999976e94 or 1.35e116 < z

   1. Initial program 63.6%

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

   3. Taylor expanded in z around inf 48.3%

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

   if -6.49999999999999976e94 < z < -1.48e-46

   1. Initial program 94.5%

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

   3. Taylor expanded in a around inf 45.3%

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

   if -1.48e-46 < z < 6.5999999999999999e-83

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/l* 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in y around inf 44.1%

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

      1. associate-/l* 45.9%

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

   8. Simplified 45.9%

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

   if 6.5999999999999999e-83 < z < 3.7e18

   1. Initial program 89.9%

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

   3. Taylor expanded in t around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. associate-/l* 69.4%

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

      3. distribute-rgt-neg-in 69.4%

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

      4. distribute-frac-neg2 69.4%

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

      5. neg-sub0 69.4%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{0 - \left(a - z\right)}} \]

      6. associate--r- 69.4%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{\left(0 - a\right) + z}} \]

      7. neg-sub0 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in y around 0 53.8%

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

      1. mul-1-neg 53.8%

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

      2. unsub-neg 53.8%

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

      3. *-commutative 53.8%

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

   8. Simplified 53.8%

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

   9. Taylor expanded in z around 0 59.3%

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

   if 3.7e18 < z < 1.35e116

   1. Initial program 69.4%

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

   3. Taylor expanded in z around inf 74.8%

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

      1. associate--l+ 74.8%

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

      2. distribute-lft-out-- 74.8%

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

      3. div-sub 74.8%

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

      4. mul-1-neg 74.8%

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

      5. unsub-neg 74.8%

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

      6. distribute-rgt-out-- 81.1%

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

      7. associate-/l* 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in t around 0 51.2%

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

      1. associate-/l* 51.0%

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

   8. Simplified 51.0%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.48 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{x \cdot z}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e+94)
   t
   (if (<= z -7.5e-200)
     x
     (if (<= z 2.3e-82)
       (* t (/ y a))
       (if (<= z 9.5e+17)
         x
         (if (<= z 3.9e+118) (* x (/ y z)) (if (<= z 5.2e+126) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+94) {
		tmp = t;
	} else if (z <= -7.5e-200) {
		tmp = x;
	} else if (z <= 2.3e-82) {
		tmp = t * (y / a);
	} else if (z <= 9.5e+17) {
		tmp = x;
	} else if (z <= 3.9e+118) {
		tmp = x * (y / z);
	} else if (z <= 5.2e+126) {
		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 <= (-6d+94)) then
        tmp = t
    else if (z <= (-7.5d-200)) then
        tmp = x
    else if (z <= 2.3d-82) then
        tmp = t * (y / a)
    else if (z <= 9.5d+17) then
        tmp = x
    else if (z <= 3.9d+118) then
        tmp = x * (y / z)
    else if (z <= 5.2d+126) 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 <= -6e+94) {
		tmp = t;
	} else if (z <= -7.5e-200) {
		tmp = x;
	} else if (z <= 2.3e-82) {
		tmp = t * (y / a);
	} else if (z <= 9.5e+17) {
		tmp = x;
	} else if (z <= 3.9e+118) {
		tmp = x * (y / z);
	} else if (z <= 5.2e+126) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e+94:
		tmp = t
	elif z <= -7.5e-200:
		tmp = x
	elif z <= 2.3e-82:
		tmp = t * (y / a)
	elif z <= 9.5e+17:
		tmp = x
	elif z <= 3.9e+118:
		tmp = x * (y / z)
	elif z <= 5.2e+126:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e+94)
		tmp = t;
	elseif (z <= -7.5e-200)
		tmp = x;
	elseif (z <= 2.3e-82)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 9.5e+17)
		tmp = x;
	elseif (z <= 3.9e+118)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 5.2e+126)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6e+94)
		tmp = t;
	elseif (z <= -7.5e-200)
		tmp = x;
	elseif (z <= 2.3e-82)
		tmp = t * (y / a);
	elseif (z <= 9.5e+17)
		tmp = x;
	elseif (z <= 3.9e+118)
		tmp = x * (y / z);
	elseif (z <= 5.2e+126)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e+94], t, If[LessEqual[z, -7.5e-200], x, If[LessEqual[z, 2.3e-82], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+17], x, If[LessEqual[z, 3.9e+118], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+126], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.0000000000000001e94 or 5.1999999999999999e126 < z

   1. Initial program 61.8%

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

   3. Taylor expanded in z around inf 49.4%

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

   if -6.0000000000000001e94 < z < -7.49999999999999958e-200 or 2.29999999999999997e-82 < z < 9.5e17 or 3.9e118 < z < 5.1999999999999999e126

   1. Initial program 92.0%

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

   3. Taylor expanded in a around inf 42.5%

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

   if -7.49999999999999958e-200 < z < 2.29999999999999997e-82

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0 50.9%

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

      1. *-commutative 50.9%

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

      2. associate-/l* 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in z around 0 44.4%

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

      1. associate-/l* 48.0%

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

   8. Simplified 48.0%

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

   if 9.5e17 < z < 3.9e118

   1. Initial program 71.2%

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

   3. Taylor expanded in t around 0 25.7%

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

      1. mul-1-neg 25.7%

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

      2. associate-/l* 25.6%

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

      3. distribute-rgt-neg-in 25.6%

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

      4. distribute-frac-neg2 25.6%

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

      5. neg-sub0 25.6%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{0 - \left(a - z\right)}} \]

      6. associate--r- 25.6%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{\left(0 - a\right) + z}} \]

      7. neg-sub0 25.6%

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

   5. Simplified 25.6%

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

   6. Taylor expanded in y around inf 37.1%

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

      1. associate-/l* 36.9%

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

   8. Simplified 36.9%

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

   9. Taylor expanded in z around inf 37.0%

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

       1. associate-/l* 36.8%

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

   11. Simplified 36.8%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-199}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+117}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+94)
   t
   (if (<= z -1.6e-199)
     x
     (if (<= z 6.8e-83)
       (* t (/ y a))
       (if (<= z 5.2e+18)
         x
         (if (<= z 2.45e+117) (/ (* x y) z) (if (<= z 5.2e+126) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+94) {
		tmp = t;
	} else if (z <= -1.6e-199) {
		tmp = x;
	} else if (z <= 6.8e-83) {
		tmp = t * (y / a);
	} else if (z <= 5.2e+18) {
		tmp = x;
	} else if (z <= 2.45e+117) {
		tmp = (x * y) / z;
	} else if (z <= 5.2e+126) {
		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 <= (-3.8d+94)) then
        tmp = t
    else if (z <= (-1.6d-199)) then
        tmp = x
    else if (z <= 6.8d-83) then
        tmp = t * (y / a)
    else if (z <= 5.2d+18) then
        tmp = x
    else if (z <= 2.45d+117) then
        tmp = (x * y) / z
    else if (z <= 5.2d+126) 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 <= -3.8e+94) {
		tmp = t;
	} else if (z <= -1.6e-199) {
		tmp = x;
	} else if (z <= 6.8e-83) {
		tmp = t * (y / a);
	} else if (z <= 5.2e+18) {
		tmp = x;
	} else if (z <= 2.45e+117) {
		tmp = (x * y) / z;
	} else if (z <= 5.2e+126) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+94:
		tmp = t
	elif z <= -1.6e-199:
		tmp = x
	elif z <= 6.8e-83:
		tmp = t * (y / a)
	elif z <= 5.2e+18:
		tmp = x
	elif z <= 2.45e+117:
		tmp = (x * y) / z
	elif z <= 5.2e+126:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+94)
		tmp = t;
	elseif (z <= -1.6e-199)
		tmp = x;
	elseif (z <= 6.8e-83)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 5.2e+18)
		tmp = x;
	elseif (z <= 2.45e+117)
		tmp = Float64(Float64(x * y) / z);
	elseif (z <= 5.2e+126)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.8e+94)
		tmp = t;
	elseif (z <= -1.6e-199)
		tmp = x;
	elseif (z <= 6.8e-83)
		tmp = t * (y / a);
	elseif (z <= 5.2e+18)
		tmp = x;
	elseif (z <= 2.45e+117)
		tmp = (x * y) / z;
	elseif (z <= 5.2e+126)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+94], t, If[LessEqual[z, -1.6e-199], x, If[LessEqual[z, 6.8e-83], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+18], x, If[LessEqual[z, 2.45e+117], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5.2e+126], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7999999999999996e94 or 5.1999999999999999e126 < z

   1. Initial program 61.8%

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

   3. Taylor expanded in z around inf 49.4%

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

   if -3.7999999999999996e94 < z < -1.6e-199 or 6.7999999999999995e-83 < z < 5.2e18 or 2.45e117 < z < 5.1999999999999999e126

   1. Initial program 92.0%

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

   3. Taylor expanded in a around inf 42.5%

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

   if -1.6e-199 < z < 6.7999999999999995e-83

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0 50.9%

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

      1. *-commutative 50.9%

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

      2. associate-/l* 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in z around 0 44.4%

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

      1. associate-/l* 48.0%

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

   8. Simplified 48.0%

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

   if 5.2e18 < z < 2.45e117

   1. Initial program 71.2%

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

   3. Taylor expanded in t around 0 25.7%

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

      1. mul-1-neg 25.7%

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

      2. associate-/l* 25.6%

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

      3. distribute-rgt-neg-in 25.6%

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

      4. distribute-frac-neg2 25.6%

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

      5. neg-sub0 25.6%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{0 - \left(a - z\right)}} \]

      6. associate--r- 25.6%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{\left(0 - a\right) + z}} \]

      7. neg-sub0 25.6%

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

   5. Simplified 25.6%

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

   6. Taylor expanded in y around inf 37.1%

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

      1. associate-/l* 36.9%

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

   8. Simplified 36.9%

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

   9. Taylor expanded in z around inf 37.0%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-199}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+117}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+119}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.25e+95)
   t
   (if (<= z -9.2e-48)
     x
     (if (<= z 6.8e-83)
       (* t (/ y (- a z)))
       (if (<= z 1.5e+18)
         x
         (if (<= z 2.95e+119) (/ (* x y) z) (if (<= z 5.2e+126) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.25e+95) {
		tmp = t;
	} else if (z <= -9.2e-48) {
		tmp = x;
	} else if (z <= 6.8e-83) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.5e+18) {
		tmp = x;
	} else if (z <= 2.95e+119) {
		tmp = (x * y) / z;
	} else if (z <= 5.2e+126) {
		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 <= (-2.25d+95)) then
        tmp = t
    else if (z <= (-9.2d-48)) then
        tmp = x
    else if (z <= 6.8d-83) then
        tmp = t * (y / (a - z))
    else if (z <= 1.5d+18) then
        tmp = x
    else if (z <= 2.95d+119) then
        tmp = (x * y) / z
    else if (z <= 5.2d+126) 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 <= -2.25e+95) {
		tmp = t;
	} else if (z <= -9.2e-48) {
		tmp = x;
	} else if (z <= 6.8e-83) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.5e+18) {
		tmp = x;
	} else if (z <= 2.95e+119) {
		tmp = (x * y) / z;
	} else if (z <= 5.2e+126) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.25e+95:
		tmp = t
	elif z <= -9.2e-48:
		tmp = x
	elif z <= 6.8e-83:
		tmp = t * (y / (a - z))
	elif z <= 1.5e+18:
		tmp = x
	elif z <= 2.95e+119:
		tmp = (x * y) / z
	elif z <= 5.2e+126:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.25e+95)
		tmp = t;
	elseif (z <= -9.2e-48)
		tmp = x;
	elseif (z <= 6.8e-83)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1.5e+18)
		tmp = x;
	elseif (z <= 2.95e+119)
		tmp = Float64(Float64(x * y) / z);
	elseif (z <= 5.2e+126)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.25e+95)
		tmp = t;
	elseif (z <= -9.2e-48)
		tmp = x;
	elseif (z <= 6.8e-83)
		tmp = t * (y / (a - z));
	elseif (z <= 1.5e+18)
		tmp = x;
	elseif (z <= 2.95e+119)
		tmp = (x * y) / z;
	elseif (z <= 5.2e+126)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.25e+95], t, If[LessEqual[z, -9.2e-48], x, If[LessEqual[z, 6.8e-83], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+18], x, If[LessEqual[z, 2.95e+119], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5.2e+126], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.25000000000000008e95 or 5.1999999999999999e126 < z

   1. Initial program 61.8%

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

   3. Taylor expanded in z around inf 49.4%

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

   if -2.25000000000000008e95 < z < -9.2000000000000003e-48 or 6.7999999999999995e-83 < z < 1.5e18 or 2.95e119 < z < 5.1999999999999999e126

   1. Initial program 93.3%

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

   3. Taylor expanded in a around inf 49.4%

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

   if -9.2000000000000003e-48 < z < 6.7999999999999995e-83

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/l* 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in y around inf 44.1%

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

      1. associate-/l* 45.9%

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

   8. Simplified 45.9%

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

   if 1.5e18 < z < 2.95e119

   1. Initial program 71.2%

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

   3. Taylor expanded in t around 0 25.7%

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

      1. mul-1-neg 25.7%

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

      2. associate-/l* 25.6%

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

      3. distribute-rgt-neg-in 25.6%

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

      4. distribute-frac-neg2 25.6%

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

      5. neg-sub0 25.6%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{0 - \left(a - z\right)}} \]

      6. associate--r- 25.6%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{\left(0 - a\right) + z}} \]

      7. neg-sub0 25.6%

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

   5. Simplified 25.6%

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

   6. Taylor expanded in y around inf 37.1%

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

      1. associate-/l* 36.9%

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

   8. Simplified 36.9%

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

   9. Taylor expanded in z around inf 37.0%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+119}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+41}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- y a) z) (- x t)))))
   (if (<= z -1.25e+68)
     t_1
     (if (<= z -1.45e-37)
       (* x (- 1.0 (/ (- y z) (- a z))))
       (if (<= z -4.2e-187)
         (* y (/ (- t x) (- a z)))
         (if (<= z 1.15e+41) (+ x (* (- t x) (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((y - a) / z) * (x - t));
	double tmp;
	if (z <= -1.25e+68) {
		tmp = t_1;
	} else if (z <= -1.45e-37) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else if (z <= -4.2e-187) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.15e+41) {
		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 + (((y - a) / z) * (x - t))
    if (z <= (-1.25d+68)) then
        tmp = t_1
    else if (z <= (-1.45d-37)) then
        tmp = x * (1.0d0 - ((y - z) / (a - z)))
    else if (z <= (-4.2d-187)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.15d+41) 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 + (((y - a) / z) * (x - t));
	double tmp;
	if (z <= -1.25e+68) {
		tmp = t_1;
	} else if (z <= -1.45e-37) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else if (z <= -4.2e-187) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.15e+41) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((y - a) / z) * (x - t))
	tmp = 0
	if z <= -1.25e+68:
		tmp = t_1
	elif z <= -1.45e-37:
		tmp = x * (1.0 - ((y - z) / (a - z)))
	elif z <= -4.2e-187:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.15e+41:
		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(Float64(y - a) / z) * Float64(x - t)))
	tmp = 0.0
	if (z <= -1.25e+68)
		tmp = t_1;
	elseif (z <= -1.45e-37)
		tmp = Float64(x * Float64(1.0 - Float64(Float64(y - z) / Float64(a - z))));
	elseif (z <= -4.2e-187)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.15e+41)
		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 + (((y - a) / z) * (x - t));
	tmp = 0.0;
	if (z <= -1.25e+68)
		tmp = t_1;
	elseif (z <= -1.45e-37)
		tmp = x * (1.0 - ((y - z) / (a - z)));
	elseif (z <= -4.2e-187)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.15e+41)
		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[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+68], t$95$1, If[LessEqual[z, -1.45e-37], N[(x * N[(1.0 - N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-187], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+41], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2500000000000001e68 or 1.1499999999999999e41 < z

   1. Initial program 65.9%

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

   3. Taylor expanded in z around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. distribute-lft-out-- 64.2%

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

      3. div-sub 64.2%

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

      4. mul-1-neg 64.2%

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

      5. unsub-neg 64.2%

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

      6. distribute-rgt-out-- 64.3%

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

      7. associate-/l* 79.7%

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

   5. Simplified 79.7%

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

   if -1.2500000000000001e68 < z < -1.45000000000000002e-37

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. unsub-neg 72.0%

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

   5. Simplified 72.0%

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

   if -1.45000000000000002e-37 < z < -4.19999999999999985e-187

   1. Initial program 89.4%

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

   3. Taylor expanded in y around inf 68.7%

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

      1. div-sub 68.8%

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

   5. Simplified 68.8%

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

   if -4.19999999999999985e-187 < z < 1.1499999999999999e41

   1. Initial program 91.1%

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

   3. Taylor expanded in z around 0 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+68}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+41}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+65}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+41}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+65)
   (+ t (/ (- t x) (/ z (- a y))))
   (if (<= z -3.7e-39)
     (* x (- 1.0 (/ (- y z) (- a z))))
     (if (<= z -4.2e-187)
       (* y (/ (- t x) (- a z)))
       (if (<= z 5.8e+41)
         (+ x (* (- t x) (/ y a)))
         (+ t (* (/ (- y a) z) (- x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+65) {
		tmp = t + ((t - x) / (z / (a - y)));
	} else if (z <= -3.7e-39) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else if (z <= -4.2e-187) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 5.8e+41) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + (((y - a) / z) * (x - 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 <= (-5.2d+65)) then
        tmp = t + ((t - x) / (z / (a - y)))
    else if (z <= (-3.7d-39)) then
        tmp = x * (1.0d0 - ((y - z) / (a - z)))
    else if (z <= (-4.2d-187)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 5.8d+41) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t + (((y - a) / z) * (x - 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 <= -5.2e+65) {
		tmp = t + ((t - x) / (z / (a - y)));
	} else if (z <= -3.7e-39) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else if (z <= -4.2e-187) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 5.8e+41) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + (((y - a) / z) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+65:
		tmp = t + ((t - x) / (z / (a - y)))
	elif z <= -3.7e-39:
		tmp = x * (1.0 - ((y - z) / (a - z)))
	elif z <= -4.2e-187:
		tmp = y * ((t - x) / (a - z))
	elif z <= 5.8e+41:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t + (((y - a) / z) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+65)
		tmp = Float64(t + Float64(Float64(t - x) / Float64(z / Float64(a - y))));
	elseif (z <= -3.7e-39)
		tmp = Float64(x * Float64(1.0 - Float64(Float64(y - z) / Float64(a - z))));
	elseif (z <= -4.2e-187)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 5.8e+41)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t + Float64(Float64(Float64(y - a) / z) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e+65)
		tmp = t + ((t - x) / (z / (a - y)));
	elseif (z <= -3.7e-39)
		tmp = x * (1.0 - ((y - z) / (a - z)));
	elseif (z <= -4.2e-187)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 5.8e+41)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t + (((y - a) / z) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+65], N[(t + N[(N[(t - x), $MachinePrecision] / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.7e-39], N[(x * N[(1.0 - N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-187], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+41], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.20000000000000005e65

   1. Initial program 68.0%

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

   3. Taylor expanded in z around inf 67.0%

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

      1. associate--l+ 67.0%

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

      2. distribute-lft-out-- 67.0%

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

      3. div-sub 67.0%

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

      4. mul-1-neg 67.0%

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

      5. unsub-neg 67.0%

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

      6. distribute-rgt-out-- 67.2%

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

      7. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

      1. clear-num 80.6%

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

      2. un-div-inv 80.7%

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

   7. Applied egg-rr 80.7%

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

   if -5.20000000000000005e65 < z < -3.70000000000000015e-39

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. unsub-neg 72.0%

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

   5. Simplified 72.0%

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

   if -3.70000000000000015e-39 < z < -4.19999999999999985e-187

   1. Initial program 89.4%

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

   3. Taylor expanded in y around inf 68.7%

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

      1. div-sub 68.8%

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

   5. Simplified 68.8%

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

   if -4.19999999999999985e-187 < z < 5.79999999999999977e41

   1. Initial program 91.1%

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

   3. Taylor expanded in z around 0 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 78.3%

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

   5. Simplified 78.3%

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

   if 5.79999999999999977e41 < z

   1. Initial program 62.8%

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

   3. Taylor expanded in z around inf 59.9%

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

      1. associate--l+ 59.9%

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

      2. distribute-lft-out-- 59.9%

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

      3. div-sub 59.9%

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

      4. mul-1-neg 59.9%

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

      5. unsub-neg 59.9%

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

      6. distribute-rgt-out-- 60.0%

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

      7. associate-/l* 78.4%

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

   5. Simplified 78.4%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+65}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+41}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z}{z - a}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-132}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 28500000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ z (- z a)))) (t_2 (* y (/ (- t x) (- a z)))))
   (if (<= y -1.6e-132)
     t_2
     (if (<= y -7e-231)
       t_1
       (if (<= y -1.9e-278) x (if (<= y 28500000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -1.6e-132) {
		tmp = t_2;
	} else if (y <= -7e-231) {
		tmp = t_1;
	} else if (y <= -1.9e-278) {
		tmp = x;
	} else if (y <= 28500000000.0) {
		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 = t * (z / (z - a))
    t_2 = y * ((t - x) / (a - z))
    if (y <= (-1.6d-132)) then
        tmp = t_2
    else if (y <= (-7d-231)) then
        tmp = t_1
    else if (y <= (-1.9d-278)) then
        tmp = x
    else if (y <= 28500000000.0d0) 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 = t * (z / (z - a));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -1.6e-132) {
		tmp = t_2;
	} else if (y <= -7e-231) {
		tmp = t_1;
	} else if (y <= -1.9e-278) {
		tmp = x;
	} else if (y <= 28500000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (z / (z - a))
	t_2 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -1.6e-132:
		tmp = t_2
	elif y <= -7e-231:
		tmp = t_1
	elif y <= -1.9e-278:
		tmp = x
	elif y <= 28500000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z / Float64(z - a)))
	t_2 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -1.6e-132)
		tmp = t_2;
	elseif (y <= -7e-231)
		tmp = t_1;
	elseif (y <= -1.9e-278)
		tmp = x;
	elseif (y <= 28500000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z / (z - a));
	t_2 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -1.6e-132)
		tmp = t_2;
	elseif (y <= -7e-231)
		tmp = t_1;
	elseif (y <= -1.9e-278)
		tmp = x;
	elseif (y <= 28500000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e-132], t$95$2, If[LessEqual[y, -7e-231], t$95$1, If[LessEqual[y, -1.9e-278], x, If[LessEqual[y, 28500000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6000000000000001e-132 or 2.85e10 < y

   1. Initial program 87.9%

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

   3. Taylor expanded in y around inf 65.6%

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

      1. div-sub 66.2%

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

   5. Simplified 66.2%

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

   if -1.6000000000000001e-132 < y < -7.0000000000000002e-231 or -1.8999999999999999e-278 < y < 2.85e10

   1. Initial program 68.4%

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

   3. Taylor expanded in x around 0 48.0%

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

      1. *-commutative 48.0%

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

      2. associate-/l* 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in y around 0 40.7%

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

      1. mul-1-neg 40.7%

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

      2. associate-/l* 52.6%

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

   8. Simplified 52.6%

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

   if -7.0000000000000002e-231 < y < -1.8999999999999999e-278

   1. Initial program 75.7%

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

   3. Taylor expanded in a around inf 71.4%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 28500000000:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+30}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-131}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+40}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.4e+30)
   (+ x (* y (/ (- t x) a)))
   (if (<= a -3.8e-157)
     (* y (/ (- t x) (- a z)))
     (if (<= a 2.5e-131)
       (- t (/ (* y (- t x)) z))
       (if (<= a 2.3e+40)
         (* (- y z) (/ t (- a z)))
         (+ x (* (- t x) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e+30) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -3.8e-157) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 2.5e-131) {
		tmp = t - ((y * (t - x)) / z);
	} else if (a <= 2.3e+40) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.4d+30)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= (-3.8d-157)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 2.5d-131) then
        tmp = t - ((y * (t - x)) / z)
    else if (a <= 2.3d+40) then
        tmp = (y - z) * (t / (a - z))
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e+30) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -3.8e-157) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 2.5e-131) {
		tmp = t - ((y * (t - x)) / z);
	} else if (a <= 2.3e+40) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.4e+30:
		tmp = x + (y * ((t - x) / a))
	elif a <= -3.8e-157:
		tmp = y * ((t - x) / (a - z))
	elif a <= 2.5e-131:
		tmp = t - ((y * (t - x)) / z)
	elif a <= 2.3e+40:
		tmp = (y - z) * (t / (a - z))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.4e+30)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= -3.8e-157)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 2.5e-131)
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	elseif (a <= 2.3e+40)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.4e+30)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= -3.8e-157)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 2.5e-131)
		tmp = t - ((y * (t - x)) / z);
	elseif (a <= 2.3e+40)
		tmp = (y - z) * (t / (a - z));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.4e+30], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e-157], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e-131], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+40], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.39999999999999992e30

   1. Initial program 88.5%

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

   3. Taylor expanded in z around 0 58.7%

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

      1. associate-/l* 74.7%

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

   5. Simplified 74.7%

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

   if -1.39999999999999992e30 < a < -3.8000000000000002e-157

   1. Initial program 85.2%

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

   3. Taylor expanded in y around inf 65.0%

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

      1. div-sub 65.1%

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

   5. Simplified 65.1%

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

   if -3.8000000000000002e-157 < a < 2.5000000000000002e-131

   1. Initial program 67.8%

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

   3. Taylor expanded in z around inf 90.3%

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

      1. associate--l+ 90.3%

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

      2. distribute-lft-out-- 90.3%

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

      3. div-sub 90.3%

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

      4. mul-1-neg 90.3%

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

      5. unsub-neg 90.3%

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

      6. distribute-rgt-out-- 90.3%

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

      7. associate-/l* 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in y around inf 90.4%

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

   if 2.5000000000000002e-131 < a < 2.29999999999999994e40

   1. Initial program 84.3%

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

   3. Taylor expanded in x around 0 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-/l* 73.3%

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

   5. Simplified 73.3%

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

   if 2.29999999999999994e40 < a

   1. Initial program 84.6%

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

   3. Taylor expanded in z around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-/l* 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+30}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-131}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+40}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-142}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-132}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+40}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.7e+29)
   (+ x (* y (/ (- t x) a)))
   (if (<= a -3.4e-142)
     (/ y (/ (- a z) (- t x)))
     (if (<= a 3.6e-132)
       (- t (/ (* y (- t x)) z))
       (if (<= a 2.2e+40)
         (* (- y z) (/ t (- a z)))
         (+ x (* (- t x) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.7e+29) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -3.4e-142) {
		tmp = y / ((a - z) / (t - x));
	} else if (a <= 3.6e-132) {
		tmp = t - ((y * (t - x)) / z);
	} else if (a <= 2.2e+40) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.7d+29)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= (-3.4d-142)) then
        tmp = y / ((a - z) / (t - x))
    else if (a <= 3.6d-132) then
        tmp = t - ((y * (t - x)) / z)
    else if (a <= 2.2d+40) then
        tmp = (y - z) * (t / (a - z))
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.7e+29) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= -3.4e-142) {
		tmp = y / ((a - z) / (t - x));
	} else if (a <= 3.6e-132) {
		tmp = t - ((y * (t - x)) / z);
	} else if (a <= 2.2e+40) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.7e+29:
		tmp = x + (y * ((t - x) / a))
	elif a <= -3.4e-142:
		tmp = y / ((a - z) / (t - x))
	elif a <= 3.6e-132:
		tmp = t - ((y * (t - x)) / z)
	elif a <= 2.2e+40:
		tmp = (y - z) * (t / (a - z))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.7e+29)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= -3.4e-142)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (a <= 3.6e-132)
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	elseif (a <= 2.2e+40)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.7e+29)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= -3.4e-142)
		tmp = y / ((a - z) / (t - x));
	elseif (a <= 3.6e-132)
		tmp = t - ((y * (t - x)) / z);
	elseif (a <= 2.2e+40)
		tmp = (y - z) * (t / (a - z));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.7e+29], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.4e-142], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e-132], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+40], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.7e29

   1. Initial program 88.5%

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

   3. Taylor expanded in z around 0 58.7%

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

      1. associate-/l* 74.7%

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

   5. Simplified 74.7%

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

   if -2.7e29 < a < -3.40000000000000029e-142

   1. Initial program 84.9%

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

   3. Taylor expanded in y around -inf 56.5%

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

      1. associate-/l* 64.3%

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

      2. clear-num 64.2%

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

      3. div-inv 64.4%

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

      4. add-cube-cbrt 63.7%

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

      5. *-un-lft-identity 63.7%

         \[\leadsto \frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}{\color{blue}{1 \cdot \frac{a - z}{t - x}}} \]

      6. times-frac 63.7%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t - x}}} \]

      7. pow2 63.7%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t - x}} \]

   5. Applied egg-rr 63.7%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t - x}}} \]
   6. Step-by-step derivation

      1. times-frac 63.7%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{1 \cdot \frac{a - z}{t - x}}} \]

      2. unpow2 63.7%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}{1 \cdot \frac{a - z}{t - x}} \]

      3. rem-3cbrt-lft 64.4%

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

      4. *-lft-identity 64.4%

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

   7. Simplified 64.4%

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

   if -3.40000000000000029e-142 < a < 3.60000000000000007e-132

   1. Initial program 68.3%

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

   3. Taylor expanded in z around inf 90.4%

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

      1. associate--l+ 90.4%

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

      2. distribute-lft-out-- 90.4%

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

      3. div-sub 90.4%

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

      4. mul-1-neg 90.4%

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

      5. unsub-neg 90.4%

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

      6. distribute-rgt-out-- 90.4%

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

      7. associate-/l* 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in y around inf 90.5%

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

   if 3.60000000000000007e-132 < a < 2.1999999999999999e40

   1. Initial program 84.3%

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

   3. Taylor expanded in x around 0 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-/l* 73.3%

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

   5. Simplified 73.3%

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

   if 2.1999999999999999e40 < a

   1. Initial program 84.6%

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

   3. Taylor expanded in z around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-/l* 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-142}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-132}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+40}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))))
   (if (<= z -1.4e+96)
     t
     (if (<= z 5.3e-148)
       t_1
       (if (<= z 6.4e-83) (* t (/ (- y z) a)) (if (<= z 4.7e+86) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double tmp;
	if (z <= -1.4e+96) {
		tmp = t;
	} else if (z <= 5.3e-148) {
		tmp = t_1;
	} else if (z <= 6.4e-83) {
		tmp = t * ((y - z) / a);
	} else if (z <= 4.7e+86) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    if (z <= (-1.4d+96)) then
        tmp = t
    else if (z <= 5.3d-148) then
        tmp = t_1
    else if (z <= 6.4d-83) then
        tmp = t * ((y - z) / a)
    else if (z <= 4.7d+86) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double tmp;
	if (z <= -1.4e+96) {
		tmp = t;
	} else if (z <= 5.3e-148) {
		tmp = t_1;
	} else if (z <= 6.4e-83) {
		tmp = t * ((y - z) / a);
	} else if (z <= 4.7e+86) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	tmp = 0
	if z <= -1.4e+96:
		tmp = t
	elif z <= 5.3e-148:
		tmp = t_1
	elif z <= 6.4e-83:
		tmp = t * ((y - z) / a)
	elif z <= 4.7e+86:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (z <= -1.4e+96)
		tmp = t;
	elseif (z <= 5.3e-148)
		tmp = t_1;
	elseif (z <= 6.4e-83)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 4.7e+86)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	tmp = 0.0;
	if (z <= -1.4e+96)
		tmp = t;
	elseif (z <= 5.3e-148)
		tmp = t_1;
	elseif (z <= 6.4e-83)
		tmp = t * ((y - z) / a);
	elseif (z <= 4.7e+86)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+96], t, If[LessEqual[z, 5.3e-148], t$95$1, If[LessEqual[z, 6.4e-83], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e+86], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e96 or 4.7000000000000002e86 < z

   1. Initial program 63.5%

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

   3. Taylor expanded in z around inf 47.3%

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

   if -1.4e96 < z < 5.29999999999999995e-148 or 6.4000000000000002e-83 < z < 4.7000000000000002e86

   1. Initial program 91.1%

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

   3. Taylor expanded in t around 0 54.3%

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

      1. mul-1-neg 54.3%

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

      2. associate-/l* 59.1%

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

      3. distribute-rgt-neg-in 59.1%

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

      4. distribute-frac-neg2 59.1%

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

      5. neg-sub0 59.1%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{0 - \left(a - z\right)}} \]

      6. associate--r- 59.1%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{\left(0 - a\right) + z}} \]

      7. neg-sub0 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in z around 0 50.1%

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

      1. mul-1-neg 50.1%

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

      2. unsub-neg 50.1%

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

      3. associate-/l* 54.4%

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

   8. Simplified 54.4%

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

   if 5.29999999999999995e-148 < z < 6.4000000000000002e-83

   1. Initial program 81.4%

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

   3. Taylor expanded in x around 0 56.9%

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

      1. *-commutative 56.9%

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

      2. associate-/l* 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in a around inf 52.3%

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

      1. associate-/l* 62.6%

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

   8. Simplified 62.6%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-148}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+86}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (* t (/ z (- z a)))))
   (if (<= z -9.5e+94)
     t_2
     (if (<= z 6.2e-149)
       t_1
       (if (<= z 2.2e-82) (* t (/ (- y z) a)) (if (<= z 4.4e+67) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -9.5e+94) {
		tmp = t_2;
	} else if (z <= 6.2e-149) {
		tmp = t_1;
	} else if (z <= 2.2e-82) {
		tmp = t * ((y - z) / a);
	} else if (z <= 4.4e+67) {
		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 - (x * (y / a))
    t_2 = t * (z / (z - a))
    if (z <= (-9.5d+94)) then
        tmp = t_2
    else if (z <= 6.2d-149) then
        tmp = t_1
    else if (z <= 2.2d-82) then
        tmp = t * ((y - z) / a)
    else if (z <= 4.4d+67) 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 - (x * (y / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -9.5e+94) {
		tmp = t_2;
	} else if (z <= 6.2e-149) {
		tmp = t_1;
	} else if (z <= 2.2e-82) {
		tmp = t * ((y - z) / a);
	} else if (z <= 4.4e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = t * (z / (z - a))
	tmp = 0
	if z <= -9.5e+94:
		tmp = t_2
	elif z <= 6.2e-149:
		tmp = t_1
	elif z <= 2.2e-82:
		tmp = t * ((y - z) / a)
	elif z <= 4.4e+67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -9.5e+94)
		tmp = t_2;
	elseif (z <= 6.2e-149)
		tmp = t_1;
	elseif (z <= 2.2e-82)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 4.4e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -9.5e+94)
		tmp = t_2;
	elseif (z <= 6.2e-149)
		tmp = t_1;
	elseif (z <= 2.2e-82)
		tmp = t * ((y - z) / a);
	elseif (z <= 4.4e+67)
		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[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+94], t$95$2, If[LessEqual[z, 6.2e-149], t$95$1, If[LessEqual[z, 2.2e-82], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+67], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999998e94 or 4.4e67 < z

   1. Initial program 63.4%

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

   3. Taylor expanded in x around 0 39.7%

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

      1. *-commutative 39.7%

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

      2. associate-/l* 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in y around 0 35.0%

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

      1. mul-1-neg 35.0%

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

      2. associate-/l* 52.0%

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

   8. Simplified 52.0%

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

   if -9.4999999999999998e94 < z < 6.19999999999999974e-149 or 2.19999999999999986e-82 < z < 4.4e67

   1. Initial program 92.1%

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

   3. Taylor expanded in t around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. associate-/l* 60.4%

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

      3. distribute-rgt-neg-in 60.4%

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

      4. distribute-frac-neg2 60.4%

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

      5. neg-sub0 60.4%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{0 - \left(a - z\right)}} \]

      6. associate--r- 60.4%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{\left(0 - a\right) + z}} \]

      7. neg-sub0 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in z around 0 51.1%

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

      1. mul-1-neg 51.1%

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

      2. unsub-neg 51.1%

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

      3. associate-/l* 55.5%

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

   8. Simplified 55.5%

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

   if 6.19999999999999974e-149 < z < 2.19999999999999986e-82

   1. Initial program 81.4%

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

   3. Taylor expanded in x around 0 56.9%

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

      1. *-commutative 56.9%

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

      2. associate-/l* 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in a around inf 52.3%

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

      1. associate-/l* 62.6%

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

   8. Simplified 62.6%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-149}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+67}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 55.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+69}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+244}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))))
   (if (<= x -3.6e+27)
     t_1
     (if (<= x 2.4e+69)
       (* (- y z) (/ t (- a z)))
       (if (<= x 7.5e+244) t_1 (* y (/ (- t x) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double tmp;
	if (x <= -3.6e+27) {
		tmp = t_1;
	} else if (x <= 2.4e+69) {
		tmp = (y - z) * (t / (a - z));
	} else if (x <= 7.5e+244) {
		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 - (x * (y / a))
    if (x <= (-3.6d+27)) then
        tmp = t_1
    else if (x <= 2.4d+69) then
        tmp = (y - z) * (t / (a - z))
    else if (x <= 7.5d+244) 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 - (x * (y / a));
	double tmp;
	if (x <= -3.6e+27) {
		tmp = t_1;
	} else if (x <= 2.4e+69) {
		tmp = (y - z) * (t / (a - z));
	} else if (x <= 7.5e+244) {
		tmp = t_1;
	} else {
		tmp = y * ((t - x) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	tmp = 0
	if x <= -3.6e+27:
		tmp = t_1
	elif x <= 2.4e+69:
		tmp = (y - z) * (t / (a - z))
	elif x <= 7.5e+244:
		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(x * Float64(y / a)))
	tmp = 0.0
	if (x <= -3.6e+27)
		tmp = t_1;
	elseif (x <= 2.4e+69)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (x <= 7.5e+244)
		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 - (x * (y / a));
	tmp = 0.0;
	if (x <= -3.6e+27)
		tmp = t_1;
	elseif (x <= 2.4e+69)
		tmp = (y - z) * (t / (a - z));
	elseif (x <= 7.5e+244)
		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[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e+27], t$95$1, If[LessEqual[x, 2.4e+69], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+244], 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 x < -3.59999999999999983e27 or 2.4000000000000002e69 < x < 7.5e244

   1. Initial program 72.6%

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

   3. Taylor expanded in t around 0 54.2%

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

      1. mul-1-neg 54.2%

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

      2. associate-/l* 63.3%

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

      3. distribute-rgt-neg-in 63.3%

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

      4. distribute-frac-neg2 63.3%

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

      5. neg-sub0 63.3%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{0 - \left(a - z\right)}} \]

      6. associate--r- 63.3%

         \[\leadsto x + x \cdot \frac{y - z}{\color{blue}{\left(0 - a\right) + z}} \]

      7. neg-sub0 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in z around 0 52.6%

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

      1. mul-1-neg 52.6%

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

      2. unsub-neg 52.6%

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

      3. associate-/l* 58.5%

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

   8. Simplified 58.5%

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

   if -3.59999999999999983e27 < x < 2.4000000000000002e69

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-/l* 66.0%

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

   5. Simplified 66.0%

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

   if 7.5e244 < x

   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 inf 88.5%

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

      1. div-sub 88.5%

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

   5. Simplified 88.5%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+27}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+69}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+244}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-199}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+94)
   t
   (if (<= z -1.05e-199)
     x
     (if (<= z 1.15e-82) (* t (/ y a)) (if (<= z 1.55e+21) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+94) {
		tmp = t;
	} else if (z <= -1.05e-199) {
		tmp = x;
	} else if (z <= 1.15e-82) {
		tmp = t * (y / a);
	} else if (z <= 1.55e+21) {
		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 <= (-9.5d+94)) then
        tmp = t
    else if (z <= (-1.05d-199)) then
        tmp = x
    else if (z <= 1.15d-82) then
        tmp = t * (y / a)
    else if (z <= 1.55d+21) 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 <= -9.5e+94) {
		tmp = t;
	} else if (z <= -1.05e-199) {
		tmp = x;
	} else if (z <= 1.15e-82) {
		tmp = t * (y / a);
	} else if (z <= 1.55e+21) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e+94:
		tmp = t
	elif z <= -1.05e-199:
		tmp = x
	elif z <= 1.15e-82:
		tmp = t * (y / a)
	elif z <= 1.55e+21:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+94)
		tmp = t;
	elseif (z <= -1.05e-199)
		tmp = x;
	elseif (z <= 1.15e-82)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 1.55e+21)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e+94)
		tmp = t;
	elseif (z <= -1.05e-199)
		tmp = x;
	elseif (z <= 1.15e-82)
		tmp = t * (y / a);
	elseif (z <= 1.55e+21)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+94], t, If[LessEqual[z, -1.05e-199], x, If[LessEqual[z, 1.15e-82], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+21], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999998e94 or 1.55e21 < z

   1. Initial program 64.2%

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

   3. Taylor expanded in z around inf 43.9%

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

   if -9.4999999999999998e94 < z < -1.05000000000000001e-199 or 1.14999999999999998e-82 < z < 1.55e21

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf 41.2%

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

   if -1.05000000000000001e-199 < z < 1.14999999999999998e-82

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0 50.9%

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

      1. *-commutative 50.9%

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

      2. associate-/l* 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in z around 0 44.4%

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

      1. associate-/l* 48.0%

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

   8. Simplified 48.0%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-199}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+94) t (if (<= z 5.6e+20) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+94) {
		tmp = t;
	} else if (z <= 5.6e+20) {
		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 <= (-9.5d+94)) then
        tmp = t
    else if (z <= 5.6d+20) 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 <= -9.5e+94) {
		tmp = t;
	} else if (z <= 5.6e+20) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e+94:
		tmp = t
	elif z <= 5.6e+20:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+94)
		tmp = t;
	elseif (z <= 5.6e+20)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e+94)
		tmp = t;
	elseif (z <= 5.6e+20)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+94], t, If[LessEqual[z, 5.6e+20], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999998e94 or 5.6e20 < z

   1. Initial program 64.2%

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

   3. Taylor expanded in z around inf 43.9%

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

   if -9.4999999999999998e94 < z < 5.6e20

   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 32.5%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 24.8% 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 80.8%

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

3. Taylor expanded in z around inf 23.2%

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

4. Final simplification 23.2%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024089 
(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)))))