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

Percentage Accurate: 68.3% → 86.2%

Time: 27.1s

Alternatives: 24

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+100} \lor \neg \left(z \leq 5.9 \cdot 10^{+143}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.25e+100) (not (<= z 5.9e+143)))
   (+ t (* (/ (- t x) z) (- a y)))
   (+ x (/ (- y z) (/ (- a z) (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.25e+100) || !(z <= 5.9e+143)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - 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 ((z <= (-3.25d+100)) .or. (.not. (z <= 5.9d+143))) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x + ((y - z) / ((a - z) / (t - 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 ((z <= -3.25e+100) || !(z <= 5.9e+143)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.25e+100) or not (z <= 5.9e+143):
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.25e+100) || !(z <= 5.9e+143))
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.25e+100) || ~((z <= 5.9e+143)))
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.25e+100], N[Not[LessEqual[z, 5.9e+143]], $MachinePrecision]], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.25e100 or 5.8999999999999999e143 < z

   1. Initial program 27.3%

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

      1. associate-/l* 56.9%

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

   3. Simplified 56.9%

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

   5. Taylor expanded in z around inf 68.0%

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

      1. associate--l+ 68.0%

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

      2. distribute-lft-out-- 68.0%

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

      3. div-sub 68.0%

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

      4. mul-1-neg 68.0%

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

      5. unsub-neg 68.0%

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

      6. div-sub 68.0%

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

      7. associate-/l* 79.1%

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

      8. associate-/l* 91.9%

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

      9. distribute-rgt-out-- 91.9%

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

   7. Simplified 91.9%

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

   if -3.25e100 < z < 5.8999999999999999e143

   1. Initial program 82.4%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

      1. clear-num 89.6%

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

      2. un-div-inv 90.2%

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

   6. Applied egg-rr 90.2%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+100} \lor \neg \left(z \leq 5.9 \cdot 10^{+143}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(--1\right) - \frac{y}{a}\right)\\ t_2 := x - \frac{x \cdot y}{a}\\ t_3 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{-121}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-236}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;t \leq 13500000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- (- -1.0) (/ y a))))
        (t_2 (- x (/ (* x y) a)))
        (t_3 (* t (/ (- y z) (- a z)))))
   (if (<= t -3.2e-121)
     t_3
     (if (<= t -1.4e-236)
       t_2
       (if (<= t 8.5e-262)
         (/ (* x (- y a)) z)
         (if (<= t 6.5e-241)
           t_1
           (if (<= t 1.2e-192)
             (* x (/ (- y a) z))
             (if (<= t 2.15e-168)
               t_2
               (if (<= t 5.5e-135)
                 t_3
                 (if (<= t 5.5e-18)
                   (/ (* y (- x t)) z)
                   (if (<= t 13500000000000.0) t_1 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (-(-1.0) - (y / a));
	double t_2 = x - ((x * y) / a);
	double t_3 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3.2e-121) {
		tmp = t_3;
	} else if (t <= -1.4e-236) {
		tmp = t_2;
	} else if (t <= 8.5e-262) {
		tmp = (x * (y - a)) / z;
	} else if (t <= 6.5e-241) {
		tmp = t_1;
	} else if (t <= 1.2e-192) {
		tmp = x * ((y - a) / z);
	} else if (t <= 2.15e-168) {
		tmp = t_2;
	} else if (t <= 5.5e-135) {
		tmp = t_3;
	} else if (t <= 5.5e-18) {
		tmp = (y * (x - t)) / z;
	} else if (t <= 13500000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (-(-1.0d0) - (y / a))
    t_2 = x - ((x * y) / a)
    t_3 = t * ((y - z) / (a - z))
    if (t <= (-3.2d-121)) then
        tmp = t_3
    else if (t <= (-1.4d-236)) then
        tmp = t_2
    else if (t <= 8.5d-262) then
        tmp = (x * (y - a)) / z
    else if (t <= 6.5d-241) then
        tmp = t_1
    else if (t <= 1.2d-192) then
        tmp = x * ((y - a) / z)
    else if (t <= 2.15d-168) then
        tmp = t_2
    else if (t <= 5.5d-135) then
        tmp = t_3
    else if (t <= 5.5d-18) then
        tmp = (y * (x - t)) / z
    else if (t <= 13500000000000.0d0) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (-(-1.0) - (y / a));
	double t_2 = x - ((x * y) / a);
	double t_3 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3.2e-121) {
		tmp = t_3;
	} else if (t <= -1.4e-236) {
		tmp = t_2;
	} else if (t <= 8.5e-262) {
		tmp = (x * (y - a)) / z;
	} else if (t <= 6.5e-241) {
		tmp = t_1;
	} else if (t <= 1.2e-192) {
		tmp = x * ((y - a) / z);
	} else if (t <= 2.15e-168) {
		tmp = t_2;
	} else if (t <= 5.5e-135) {
		tmp = t_3;
	} else if (t <= 5.5e-18) {
		tmp = (y * (x - t)) / z;
	} else if (t <= 13500000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (-(-1.0) - (y / a))
	t_2 = x - ((x * y) / a)
	t_3 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -3.2e-121:
		tmp = t_3
	elif t <= -1.4e-236:
		tmp = t_2
	elif t <= 8.5e-262:
		tmp = (x * (y - a)) / z
	elif t <= 6.5e-241:
		tmp = t_1
	elif t <= 1.2e-192:
		tmp = x * ((y - a) / z)
	elif t <= 2.15e-168:
		tmp = t_2
	elif t <= 5.5e-135:
		tmp = t_3
	elif t <= 5.5e-18:
		tmp = (y * (x - t)) / z
	elif t <= 13500000000000.0:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(-(-1.0)) - Float64(y / a)))
	t_2 = Float64(x - Float64(Float64(x * y) / a))
	t_3 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -3.2e-121)
		tmp = t_3;
	elseif (t <= -1.4e-236)
		tmp = t_2;
	elseif (t <= 8.5e-262)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (t <= 6.5e-241)
		tmp = t_1;
	elseif (t <= 1.2e-192)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (t <= 2.15e-168)
		tmp = t_2;
	elseif (t <= 5.5e-135)
		tmp = t_3;
	elseif (t <= 5.5e-18)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (t <= 13500000000000.0)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (-(-1.0) - (y / a));
	t_2 = x - ((x * y) / a);
	t_3 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -3.2e-121)
		tmp = t_3;
	elseif (t <= -1.4e-236)
		tmp = t_2;
	elseif (t <= 8.5e-262)
		tmp = (x * (y - a)) / z;
	elseif (t <= 6.5e-241)
		tmp = t_1;
	elseif (t <= 1.2e-192)
		tmp = x * ((y - a) / z);
	elseif (t <= 2.15e-168)
		tmp = t_2;
	elseif (t <= 5.5e-135)
		tmp = t_3;
	elseif (t <= 5.5e-18)
		tmp = (y * (x - t)) / z;
	elseif (t <= 13500000000000.0)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[((--1.0) - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e-121], t$95$3, If[LessEqual[t, -1.4e-236], t$95$2, If[LessEqual[t, 8.5e-262], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 6.5e-241], t$95$1, If[LessEqual[t, 1.2e-192], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e-168], t$95$2, If[LessEqual[t, 5.5e-135], t$95$3, If[LessEqual[t, 5.5e-18], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 13500000000000.0], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.20000000000000019e-121 or 2.14999999999999998e-168 < t < 5.4999999999999999e-135 or 1.35e13 < t

   1. Initial program 65.8%

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

      1. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in x around 0 49.1%

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

      1. associate-/l* 71.0%

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

   7. Simplified 71.0%

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

   if -3.20000000000000019e-121 < t < -1.39999999999999993e-236 or 1.2e-192 < t < 2.14999999999999998e-168

   1. Initial program 69.9%

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

      1. associate-/l* 72.2%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in x around -inf 72.4%

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

      1. associate-*r* 72.4%

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

      2. neg-mul-1 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in z around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. *-commutative 58.7%

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

      3. distribute-rgt-neg-in 58.7%

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

      4. sub-neg 58.7%

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

      5. metadata-eval 58.7%

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

   10. Simplified 58.7%

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

   11. Taylor expanded in y around 0 58.7%

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

       1. mul-1-neg 58.7%

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

       2. associate-*r/ 58.7%

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

       3. unsub-neg 58.7%

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

       4. associate-*r/ 58.7%

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

   13. Simplified 58.7%

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

   if -1.39999999999999993e-236 < t < 8.5e-262

   1. Initial program 55.9%

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

      1. associate-/l* 60.3%

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

   3. Simplified 60.3%

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

   5. Taylor expanded in x around -inf 61.1%

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

      1. associate-*r* 61.1%

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

      2. neg-mul-1 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in z around -inf 64.2%

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

   if 8.5e-262 < t < 6.4999999999999998e-241 or 5.5e-18 < t < 1.35e13

   1. Initial program 52.2%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in x around -inf 99.8%

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

      1. associate-*r* 99.8%

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

      2. neg-mul-1 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. *-commutative 88.3%

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

      3. distribute-rgt-neg-in 88.3%

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

      4. sub-neg 88.3%

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

      5. metadata-eval 88.3%

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

   10. Simplified 88.3%

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

   if 6.4999999999999998e-241 < t < 1.2e-192

   1. Initial program 58.6%

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

      1. associate-/l* 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in x around -inf 72.5%

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

      1. associate-*r* 72.5%

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

      2. neg-mul-1 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in z around -inf 58.2%

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

      1. associate-/l* 65.0%

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

   10. Simplified 65.0%

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

   if 5.4999999999999999e-135 < t < 5.5e-18

   1. Initial program 74.6%

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

      1. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in y around inf 69.3%

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

      1. div-sub 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in a around 0 54.0%

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

      1. associate-*r/ 54.0%

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

      2. associate-*r* 54.0%

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

      3. neg-mul-1 54.0%

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

   10. Simplified 54.0%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-121}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-236}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(\left(--1\right) - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-168}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;t \leq 13500000000000:\\ \;\;\;\;x \cdot \left(\left(--1\right) - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ t_3 := x - \frac{x \cdot y}{a}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-237}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(\left(--1\right) - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-168}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z))))
        (t_2 (* t (/ (- y z) (- a z))))
        (t_3 (- x (/ (* x y) a))))
   (if (<= t -1.5e+18)
     t_2
     (if (<= t -8.5e-40)
       t_1
       (if (<= t -5e-122)
         t_2
         (if (<= t -1.05e-237)
           t_3
           (if (<= t 9e-262)
             (/ (* x (- y a)) z)
             (if (<= t 4.9e-241)
               (* x (- (- -1.0) (/ y a)))
               (if (<= t 3.6e-193)
                 (* x (/ (- y a) z))
                 (if (<= t 1.8e-168) t_3 (if (<= t 8.5e+45) t_1 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double t_3 = x - ((x * y) / a);
	double tmp;
	if (t <= -1.5e+18) {
		tmp = t_2;
	} else if (t <= -8.5e-40) {
		tmp = t_1;
	} else if (t <= -5e-122) {
		tmp = t_2;
	} else if (t <= -1.05e-237) {
		tmp = t_3;
	} else if (t <= 9e-262) {
		tmp = (x * (y - a)) / z;
	} else if (t <= 4.9e-241) {
		tmp = x * (-(-1.0) - (y / a));
	} else if (t <= 3.6e-193) {
		tmp = x * ((y - a) / z);
	} else if (t <= 1.8e-168) {
		tmp = t_3;
	} else if (t <= 8.5e+45) {
		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) :: t_3
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = t * ((y - z) / (a - z))
    t_3 = x - ((x * y) / a)
    if (t <= (-1.5d+18)) then
        tmp = t_2
    else if (t <= (-8.5d-40)) then
        tmp = t_1
    else if (t <= (-5d-122)) then
        tmp = t_2
    else if (t <= (-1.05d-237)) then
        tmp = t_3
    else if (t <= 9d-262) then
        tmp = (x * (y - a)) / z
    else if (t <= 4.9d-241) then
        tmp = x * (-(-1.0d0) - (y / a))
    else if (t <= 3.6d-193) then
        tmp = x * ((y - a) / z)
    else if (t <= 1.8d-168) then
        tmp = t_3
    else if (t <= 8.5d+45) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double t_3 = x - ((x * y) / a);
	double tmp;
	if (t <= -1.5e+18) {
		tmp = t_2;
	} else if (t <= -8.5e-40) {
		tmp = t_1;
	} else if (t <= -5e-122) {
		tmp = t_2;
	} else if (t <= -1.05e-237) {
		tmp = t_3;
	} else if (t <= 9e-262) {
		tmp = (x * (y - a)) / z;
	} else if (t <= 4.9e-241) {
		tmp = x * (-(-1.0) - (y / a));
	} else if (t <= 3.6e-193) {
		tmp = x * ((y - a) / z);
	} else if (t <= 1.8e-168) {
		tmp = t_3;
	} else if (t <= 8.5e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = t * ((y - z) / (a - z))
	t_3 = x - ((x * y) / a)
	tmp = 0
	if t <= -1.5e+18:
		tmp = t_2
	elif t <= -8.5e-40:
		tmp = t_1
	elif t <= -5e-122:
		tmp = t_2
	elif t <= -1.05e-237:
		tmp = t_3
	elif t <= 9e-262:
		tmp = (x * (y - a)) / z
	elif t <= 4.9e-241:
		tmp = x * (-(-1.0) - (y / a))
	elif t <= 3.6e-193:
		tmp = x * ((y - a) / z)
	elif t <= 1.8e-168:
		tmp = t_3
	elif t <= 8.5e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_3 = Float64(x - Float64(Float64(x * y) / a))
	tmp = 0.0
	if (t <= -1.5e+18)
		tmp = t_2;
	elseif (t <= -8.5e-40)
		tmp = t_1;
	elseif (t <= -5e-122)
		tmp = t_2;
	elseif (t <= -1.05e-237)
		tmp = t_3;
	elseif (t <= 9e-262)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (t <= 4.9e-241)
		tmp = Float64(x * Float64(Float64(-(-1.0)) - Float64(y / a)));
	elseif (t <= 3.6e-193)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (t <= 1.8e-168)
		tmp = t_3;
	elseif (t <= 8.5e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = t * ((y - z) / (a - z));
	t_3 = x - ((x * y) / a);
	tmp = 0.0;
	if (t <= -1.5e+18)
		tmp = t_2;
	elseif (t <= -8.5e-40)
		tmp = t_1;
	elseif (t <= -5e-122)
		tmp = t_2;
	elseif (t <= -1.05e-237)
		tmp = t_3;
	elseif (t <= 9e-262)
		tmp = (x * (y - a)) / z;
	elseif (t <= 4.9e-241)
		tmp = x * (-(-1.0) - (y / a));
	elseif (t <= 3.6e-193)
		tmp = x * ((y - a) / z);
	elseif (t <= 1.8e-168)
		tmp = t_3;
	elseif (t <= 8.5e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+18], t$95$2, If[LessEqual[t, -8.5e-40], t$95$1, If[LessEqual[t, -5e-122], t$95$2, If[LessEqual[t, -1.05e-237], t$95$3, If[LessEqual[t, 9e-262], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 4.9e-241], N[(x * N[((--1.0) - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-193], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-168], t$95$3, If[LessEqual[t, 8.5e+45], t$95$1, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.5e18 or -8.4999999999999998e-40 < t < -4.9999999999999999e-122 or 8.4999999999999996e45 < t

   1. Initial program 61.7%

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

      1. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in x around 0 48.2%

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

      1. associate-/l* 74.8%

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

   7. Simplified 74.8%

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

   if -1.5e18 < t < -8.4999999999999998e-40 or 1.7999999999999999e-168 < t < 8.4999999999999996e45

   1. Initial program 76.2%

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

      1. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in y around inf 70.1%

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

      1. div-sub 70.1%

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

   7. Simplified 70.1%

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

   if -4.9999999999999999e-122 < t < -1.0500000000000001e-237 or 3.5999999999999999e-193 < t < 1.7999999999999999e-168

   1. Initial program 69.9%

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

      1. associate-/l* 72.2%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in x around -inf 72.4%

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

      1. associate-*r* 72.4%

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

      2. neg-mul-1 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in z around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. *-commutative 58.7%

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

      3. distribute-rgt-neg-in 58.7%

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

      4. sub-neg 58.7%

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

      5. metadata-eval 58.7%

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

   10. Simplified 58.7%

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

   11. Taylor expanded in y around 0 58.7%

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

       1. mul-1-neg 58.7%

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

       2. associate-*r/ 58.7%

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

       3. unsub-neg 58.7%

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

       4. associate-*r/ 58.7%

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

   13. Simplified 58.7%

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

   if -1.0500000000000001e-237 < t < 8.99999999999999997e-262

   1. Initial program 55.9%

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

      1. associate-/l* 60.3%

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

   3. Simplified 60.3%

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

   5. Taylor expanded in x around -inf 61.1%

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

      1. associate-*r* 61.1%

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

      2. neg-mul-1 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in z around -inf 64.2%

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

   if 8.99999999999999997e-262 < t < 4.8999999999999998e-241

   1. Initial program 76.5%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in x around -inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

   if 4.8999999999999998e-241 < t < 3.5999999999999999e-193

   1. Initial program 58.6%

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

      1. associate-/l* 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in x around -inf 72.5%

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

      1. associate-*r* 72.5%

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

      2. neg-mul-1 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in z around -inf 58.2%

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

      1. associate-/l* 65.0%

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

   10. Simplified 65.0%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-122}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-237}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(\left(--1\right) - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-168}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := \left(y - z\right) \cdot \frac{t}{a - z}\\ t_3 := x - \frac{x \cdot y}{a}\\ \mathbf{if}\;t \leq -2.65 \cdot 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-237}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-261}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \left(\left(--1\right) - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-168}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z))))
        (t_2 (* (- y z) (/ t (- a z))))
        (t_3 (- x (/ (* x y) a))))
   (if (<= t -2.65e+97)
     t_2
     (if (<= t -1.25e-39)
       t_1
       (if (<= t -2.75e-123)
         (* t (/ (- y z) (- a z)))
         (if (<= t -2.3e-237)
           t_3
           (if (<= t 1.16e-261)
             (/ (* x (- y a)) z)
             (if (<= t 1.16e-240)
               (* x (- (- -1.0) (/ y a)))
               (if (<= t 3.5e-192)
                 (* x (/ (- y a) z))
                 (if (<= t 1.22e-168) t_3 (if (<= t 5.5e+47) t_1 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 = (y - z) * (t / (a - z));
	double t_3 = x - ((x * y) / a);
	double tmp;
	if (t <= -2.65e+97) {
		tmp = t_2;
	} else if (t <= -1.25e-39) {
		tmp = t_1;
	} else if (t <= -2.75e-123) {
		tmp = t * ((y - z) / (a - z));
	} else if (t <= -2.3e-237) {
		tmp = t_3;
	} else if (t <= 1.16e-261) {
		tmp = (x * (y - a)) / z;
	} else if (t <= 1.16e-240) {
		tmp = x * (-(-1.0) - (y / a));
	} else if (t <= 3.5e-192) {
		tmp = x * ((y - a) / z);
	} else if (t <= 1.22e-168) {
		tmp = t_3;
	} else if (t <= 5.5e+47) {
		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) :: t_3
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = (y - z) * (t / (a - z))
    t_3 = x - ((x * y) / a)
    if (t <= (-2.65d+97)) then
        tmp = t_2
    else if (t <= (-1.25d-39)) then
        tmp = t_1
    else if (t <= (-2.75d-123)) then
        tmp = t * ((y - z) / (a - z))
    else if (t <= (-2.3d-237)) then
        tmp = t_3
    else if (t <= 1.16d-261) then
        tmp = (x * (y - a)) / z
    else if (t <= 1.16d-240) then
        tmp = x * (-(-1.0d0) - (y / a))
    else if (t <= 3.5d-192) then
        tmp = x * ((y - a) / z)
    else if (t <= 1.22d-168) then
        tmp = t_3
    else if (t <= 5.5d+47) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = (y - z) * (t / (a - z));
	double t_3 = x - ((x * y) / a);
	double tmp;
	if (t <= -2.65e+97) {
		tmp = t_2;
	} else if (t <= -1.25e-39) {
		tmp = t_1;
	} else if (t <= -2.75e-123) {
		tmp = t * ((y - z) / (a - z));
	} else if (t <= -2.3e-237) {
		tmp = t_3;
	} else if (t <= 1.16e-261) {
		tmp = (x * (y - a)) / z;
	} else if (t <= 1.16e-240) {
		tmp = x * (-(-1.0) - (y / a));
	} else if (t <= 3.5e-192) {
		tmp = x * ((y - a) / z);
	} else if (t <= 1.22e-168) {
		tmp = t_3;
	} else if (t <= 5.5e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = (y - z) * (t / (a - z))
	t_3 = x - ((x * y) / a)
	tmp = 0
	if t <= -2.65e+97:
		tmp = t_2
	elif t <= -1.25e-39:
		tmp = t_1
	elif t <= -2.75e-123:
		tmp = t * ((y - z) / (a - z))
	elif t <= -2.3e-237:
		tmp = t_3
	elif t <= 1.16e-261:
		tmp = (x * (y - a)) / z
	elif t <= 1.16e-240:
		tmp = x * (-(-1.0) - (y / a))
	elif t <= 3.5e-192:
		tmp = x * ((y - a) / z)
	elif t <= 1.22e-168:
		tmp = t_3
	elif t <= 5.5e+47:
		tmp = t_1
	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(Float64(y - z) * Float64(t / Float64(a - z)))
	t_3 = Float64(x - Float64(Float64(x * y) / a))
	tmp = 0.0
	if (t <= -2.65e+97)
		tmp = t_2;
	elseif (t <= -1.25e-39)
		tmp = t_1;
	elseif (t <= -2.75e-123)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (t <= -2.3e-237)
		tmp = t_3;
	elseif (t <= 1.16e-261)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (t <= 1.16e-240)
		tmp = Float64(x * Float64(Float64(-(-1.0)) - Float64(y / a)));
	elseif (t <= 3.5e-192)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (t <= 1.22e-168)
		tmp = t_3;
	elseif (t <= 5.5e+47)
		tmp = t_1;
	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 = (y - z) * (t / (a - z));
	t_3 = x - ((x * y) / a);
	tmp = 0.0;
	if (t <= -2.65e+97)
		tmp = t_2;
	elseif (t <= -1.25e-39)
		tmp = t_1;
	elseif (t <= -2.75e-123)
		tmp = t * ((y - z) / (a - z));
	elseif (t <= -2.3e-237)
		tmp = t_3;
	elseif (t <= 1.16e-261)
		tmp = (x * (y - a)) / z;
	elseif (t <= 1.16e-240)
		tmp = x * (-(-1.0) - (y / a));
	elseif (t <= 3.5e-192)
		tmp = x * ((y - a) / z);
	elseif (t <= 1.22e-168)
		tmp = t_3;
	elseif (t <= 5.5e+47)
		tmp = t_1;
	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[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.65e+97], t$95$2, If[LessEqual[t, -1.25e-39], t$95$1, If[LessEqual[t, -2.75e-123], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.3e-237], t$95$3, If[LessEqual[t, 1.16e-261], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 1.16e-240], N[(x * N[((--1.0) - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-192], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e-168], t$95$3, If[LessEqual[t, 5.5e+47], t$95$1, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -2.6500000000000001e97 or 5.4999999999999998e47 < t

   1. Initial program 59.5%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in x around 0 49.2%

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

      1. *-commutative 49.2%

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

      2. associate-/l* 83.4%

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

   7. Applied egg-rr 83.4%

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

   if -2.6500000000000001e97 < t < -1.25e-39 or 1.22000000000000003e-168 < t < 5.4999999999999998e47

   1. Initial program 75.4%

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

      1. associate-/l* 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in y around inf 65.1%

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

      1. div-sub 65.1%

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

   7. Simplified 65.1%

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

   if -1.25e-39 < t < -2.75e-123

   1. Initial program 60.7%

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

      1. associate-/l* 55.2%

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

   3. Simplified 55.2%

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

   5. Taylor expanded in x around 0 51.2%

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

      1. associate-/l* 57.1%

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

   7. Simplified 57.1%

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

   if -2.75e-123 < t < -2.30000000000000011e-237 or 3.50000000000000014e-192 < t < 1.22000000000000003e-168

   1. Initial program 69.9%

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

      1. associate-/l* 72.2%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in x around -inf 72.4%

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

      1. associate-*r* 72.4%

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

      2. neg-mul-1 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in z around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. *-commutative 58.7%

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

      3. distribute-rgt-neg-in 58.7%

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

      4. sub-neg 58.7%

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

      5. metadata-eval 58.7%

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

   10. Simplified 58.7%

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

   11. Taylor expanded in y around 0 58.7%

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

       1. mul-1-neg 58.7%

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

       2. associate-*r/ 58.7%

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

       3. unsub-neg 58.7%

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

       4. associate-*r/ 58.7%

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

   13. Simplified 58.7%

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

   if -2.30000000000000011e-237 < t < 1.15999999999999999e-261

   1. Initial program 55.9%

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

      1. associate-/l* 60.3%

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

   3. Simplified 60.3%

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

   5. Taylor expanded in x around -inf 61.1%

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

      1. associate-*r* 61.1%

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

      2. neg-mul-1 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in z around -inf 64.2%

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

   if 1.15999999999999999e-261 < t < 1.16e-240

   1. Initial program 76.5%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in x around -inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

   if 1.16e-240 < t < 3.50000000000000014e-192

   1. Initial program 58.6%

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

      1. associate-/l* 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in x around -inf 72.5%

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

      1. associate-*r* 72.5%

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

      2. neg-mul-1 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in z around -inf 58.2%

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

      1. associate-/l* 65.0%

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

   10. Simplified 65.0%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+97}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-237}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-261}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \left(\left(--1\right) - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-168}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -320:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -0.0019:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-131}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-251}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))))
   (if (<= a -3.7e+31)
     x
     (if (<= a -320.0)
       t
       (if (<= a -0.0019)
         t_1
         (if (<= a -4.2e-131)
           (* t (/ y (- a z)))
           (if (<= a 3.3e-298)
             t_1
             (if (<= a 6e-251) t (if (<= a 6.6e+65) t_1 x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (a <= -3.7e+31) {
		tmp = x;
	} else if (a <= -320.0) {
		tmp = t;
	} else if (a <= -0.0019) {
		tmp = t_1;
	} else if (a <= -4.2e-131) {
		tmp = t * (y / (a - z));
	} else if (a <= 3.3e-298) {
		tmp = t_1;
	} else if (a <= 6e-251) {
		tmp = t;
	} else if (a <= 6.6e+65) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    if (a <= (-3.7d+31)) then
        tmp = x
    else if (a <= (-320.0d0)) then
        tmp = t
    else if (a <= (-0.0019d0)) then
        tmp = t_1
    else if (a <= (-4.2d-131)) then
        tmp = t * (y / (a - z))
    else if (a <= 3.3d-298) then
        tmp = t_1
    else if (a <= 6d-251) then
        tmp = t
    else if (a <= 6.6d+65) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (a <= -3.7e+31) {
		tmp = x;
	} else if (a <= -320.0) {
		tmp = t;
	} else if (a <= -0.0019) {
		tmp = t_1;
	} else if (a <= -4.2e-131) {
		tmp = t * (y / (a - z));
	} else if (a <= 3.3e-298) {
		tmp = t_1;
	} else if (a <= 6e-251) {
		tmp = t;
	} else if (a <= 6.6e+65) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	tmp = 0
	if a <= -3.7e+31:
		tmp = x
	elif a <= -320.0:
		tmp = t
	elif a <= -0.0019:
		tmp = t_1
	elif a <= -4.2e-131:
		tmp = t * (y / (a - z))
	elif a <= 3.3e-298:
		tmp = t_1
	elif a <= 6e-251:
		tmp = t
	elif a <= 6.6e+65:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (a <= -3.7e+31)
		tmp = x;
	elseif (a <= -320.0)
		tmp = t;
	elseif (a <= -0.0019)
		tmp = t_1;
	elseif (a <= -4.2e-131)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (a <= 3.3e-298)
		tmp = t_1;
	elseif (a <= 6e-251)
		tmp = t;
	elseif (a <= 6.6e+65)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	tmp = 0.0;
	if (a <= -3.7e+31)
		tmp = x;
	elseif (a <= -320.0)
		tmp = t;
	elseif (a <= -0.0019)
		tmp = t_1;
	elseif (a <= -4.2e-131)
		tmp = t * (y / (a - z));
	elseif (a <= 3.3e-298)
		tmp = t_1;
	elseif (a <= 6e-251)
		tmp = t;
	elseif (a <= 6.6e+65)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e+31], x, If[LessEqual[a, -320.0], t, If[LessEqual[a, -0.0019], t$95$1, If[LessEqual[a, -4.2e-131], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e-298], t$95$1, If[LessEqual[a, 6e-251], t, If[LessEqual[a, 6.6e+65], t$95$1, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.6999999999999998e31 or 6.60000000000000046e65 < a

   1. Initial program 68.2%

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

      1. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in a around inf 44.8%

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

   if -3.6999999999999998e31 < a < -320 or 3.3000000000000002e-298 < a < 5.9999999999999997e-251

   1. Initial program 45.4%

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

      1. associate-/l* 69.2%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in z around inf 64.4%

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

   if -320 < a < -0.0019 or -4.19999999999999994e-131 < a < 3.3000000000000002e-298 or 5.9999999999999997e-251 < a < 6.60000000000000046e65

   1. Initial program 63.3%

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

      1. associate-/l* 67.0%

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

   3. Simplified 67.0%

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

   5. Taylor expanded in x around -inf 47.2%

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

      1. associate-*r* 47.2%

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

      2. neg-mul-1 47.2%

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

   7. Simplified 47.2%

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

   8. Taylor expanded in z around -inf 46.0%

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

      1. associate-/l* 44.4%

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

   10. Simplified 44.4%

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

   if -0.0019 < a < -4.19999999999999994e-131

   1. Initial program 76.0%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in y around inf 68.9%

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

      1. div-sub 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in t around inf 45.2%

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

      1. associate-/l* 45.2%

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

   10. Simplified 45.2%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -320:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -0.0019:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-131}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-251}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+180}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-243}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))))
   (if (<= z -1.75e+180)
     t
     (if (<= z -6.4e-37)
       t_1
       (if (<= z -4.6e-80)
         (* y (/ t (- a z)))
         (if (<= z -1.7e-87)
           t_1
           (if (<= z -4.1e-243)
             (- x (/ (* x y) a))
             (if (<= z 9e-49)
               (* y (/ (- t x) a))
               (if (<= z 5.8e+117) x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (z <= -1.75e+180) {
		tmp = t;
	} else if (z <= -6.4e-37) {
		tmp = t_1;
	} else if (z <= -4.6e-80) {
		tmp = y * (t / (a - z));
	} else if (z <= -1.7e-87) {
		tmp = t_1;
	} else if (z <= -4.1e-243) {
		tmp = x - ((x * y) / a);
	} else if (z <= 9e-49) {
		tmp = y * ((t - x) / a);
	} else if (z <= 5.8e+117) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    if (z <= (-1.75d+180)) then
        tmp = t
    else if (z <= (-6.4d-37)) then
        tmp = t_1
    else if (z <= (-4.6d-80)) then
        tmp = y * (t / (a - z))
    else if (z <= (-1.7d-87)) then
        tmp = t_1
    else if (z <= (-4.1d-243)) then
        tmp = x - ((x * y) / a)
    else if (z <= 9d-49) then
        tmp = y * ((t - x) / a)
    else if (z <= 5.8d+117) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (z <= -1.75e+180) {
		tmp = t;
	} else if (z <= -6.4e-37) {
		tmp = t_1;
	} else if (z <= -4.6e-80) {
		tmp = y * (t / (a - z));
	} else if (z <= -1.7e-87) {
		tmp = t_1;
	} else if (z <= -4.1e-243) {
		tmp = x - ((x * y) / a);
	} else if (z <= 9e-49) {
		tmp = y * ((t - x) / a);
	} else if (z <= 5.8e+117) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	tmp = 0
	if z <= -1.75e+180:
		tmp = t
	elif z <= -6.4e-37:
		tmp = t_1
	elif z <= -4.6e-80:
		tmp = y * (t / (a - z))
	elif z <= -1.7e-87:
		tmp = t_1
	elif z <= -4.1e-243:
		tmp = x - ((x * y) / a)
	elif z <= 9e-49:
		tmp = y * ((t - x) / a)
	elif z <= 5.8e+117:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (z <= -1.75e+180)
		tmp = t;
	elseif (z <= -6.4e-37)
		tmp = t_1;
	elseif (z <= -4.6e-80)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= -1.7e-87)
		tmp = t_1;
	elseif (z <= -4.1e-243)
		tmp = Float64(x - Float64(Float64(x * y) / a));
	elseif (z <= 9e-49)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 5.8e+117)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	tmp = 0.0;
	if (z <= -1.75e+180)
		tmp = t;
	elseif (z <= -6.4e-37)
		tmp = t_1;
	elseif (z <= -4.6e-80)
		tmp = y * (t / (a - z));
	elseif (z <= -1.7e-87)
		tmp = t_1;
	elseif (z <= -4.1e-243)
		tmp = x - ((x * y) / a);
	elseif (z <= 9e-49)
		tmp = y * ((t - x) / a);
	elseif (z <= 5.8e+117)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+180], t, If[LessEqual[z, -6.4e-37], t$95$1, If[LessEqual[z, -4.6e-80], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e-87], t$95$1, If[LessEqual[z, -4.1e-243], N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-49], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+117], x, t]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.7499999999999999e180 or 5.80000000000000055e117 < z

   1. Initial program 23.8%

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

      1. associate-/l* 54.9%

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

   3. Simplified 54.9%

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

   5. Taylor expanded in z around inf 55.1%

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

   if -1.7499999999999999e180 < z < -6.3999999999999998e-37 or -4.5999999999999996e-80 < z < -1.6999999999999999e-87

   1. Initial program 68.2%

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

      1. associate-/l* 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in x around -inf 50.8%

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

      1. associate-*r* 50.8%

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

      2. neg-mul-1 50.8%

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

   7. Simplified 50.8%

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

   8. Taylor expanded in z around -inf 37.1%

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

      1. associate-/l* 39.3%

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

   10. Simplified 39.3%

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

   if -6.3999999999999998e-37 < z < -4.5999999999999996e-80

   1. Initial program 90.3%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in y around inf 65.7%

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

      1. div-sub 65.7%

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

   7. Simplified 65.7%

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

   8. Taylor expanded in t around inf 65.9%

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

   if -1.6999999999999999e-87 < z < -4.09999999999999981e-243

   1. Initial program 93.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around -inf 73.4%

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

      1. associate-*r* 73.4%

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

      2. neg-mul-1 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in z around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. *-commutative 64.1%

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

      3. distribute-rgt-neg-in 64.1%

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

      4. sub-neg 64.1%

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

      5. metadata-eval 64.1%

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

   10. Simplified 64.1%

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

   11. Taylor expanded in y around 0 57.8%

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

       1. mul-1-neg 57.8%

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

       2. associate-*r/ 64.1%

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

       3. unsub-neg 64.1%

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

       4. associate-*r/ 57.8%

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

   13. Simplified 57.8%

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

   if -4.09999999999999981e-243 < z < 9.0000000000000004e-49

   1. Initial program 89.3%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in y around inf 72.4%

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

      1. div-sub 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in a around inf 61.5%

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

   if 9.0000000000000004e-49 < z < 5.80000000000000055e117

   1. Initial program 70.2%

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

      1. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in a around inf 41.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+180}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-243}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6800000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -5.3e+106)
     t
     (if (<= z -1.8e+41)
       x
       (if (<= z -6800000000000.0)
         t
         (if (<= z -3.2e-135)
           t_1
           (if (<= z -1.15e-238)
             x
             (if (<= z 3.2e-62) t_1 (if (<= z 3.1e+110) x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -5.3e+106) {
		tmp = t;
	} else if (z <= -1.8e+41) {
		tmp = x;
	} else if (z <= -6800000000000.0) {
		tmp = t;
	} else if (z <= -3.2e-135) {
		tmp = t_1;
	} else if (z <= -1.15e-238) {
		tmp = x;
	} else if (z <= 3.2e-62) {
		tmp = t_1;
	} else if (z <= 3.1e+110) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-5.3d+106)) then
        tmp = t
    else if (z <= (-1.8d+41)) then
        tmp = x
    else if (z <= (-6800000000000.0d0)) then
        tmp = t
    else if (z <= (-3.2d-135)) then
        tmp = t_1
    else if (z <= (-1.15d-238)) then
        tmp = x
    else if (z <= 3.2d-62) then
        tmp = t_1
    else if (z <= 3.1d+110) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -5.3e+106) {
		tmp = t;
	} else if (z <= -1.8e+41) {
		tmp = x;
	} else if (z <= -6800000000000.0) {
		tmp = t;
	} else if (z <= -3.2e-135) {
		tmp = t_1;
	} else if (z <= -1.15e-238) {
		tmp = x;
	} else if (z <= 3.2e-62) {
		tmp = t_1;
	} else if (z <= 3.1e+110) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -5.3e+106:
		tmp = t
	elif z <= -1.8e+41:
		tmp = x
	elif z <= -6800000000000.0:
		tmp = t
	elif z <= -3.2e-135:
		tmp = t_1
	elif z <= -1.15e-238:
		tmp = x
	elif z <= 3.2e-62:
		tmp = t_1
	elif z <= 3.1e+110:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -5.3e+106)
		tmp = t;
	elseif (z <= -1.8e+41)
		tmp = x;
	elseif (z <= -6800000000000.0)
		tmp = t;
	elseif (z <= -3.2e-135)
		tmp = t_1;
	elseif (z <= -1.15e-238)
		tmp = x;
	elseif (z <= 3.2e-62)
		tmp = t_1;
	elseif (z <= 3.1e+110)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -5.3e+106)
		tmp = t;
	elseif (z <= -1.8e+41)
		tmp = x;
	elseif (z <= -6800000000000.0)
		tmp = t;
	elseif (z <= -3.2e-135)
		tmp = t_1;
	elseif (z <= -1.15e-238)
		tmp = x;
	elseif (z <= 3.2e-62)
		tmp = t_1;
	elseif (z <= 3.1e+110)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.3e+106], t, If[LessEqual[z, -1.8e+41], x, If[LessEqual[z, -6800000000000.0], t, If[LessEqual[z, -3.2e-135], t$95$1, If[LessEqual[z, -1.15e-238], x, If[LessEqual[z, 3.2e-62], t$95$1, If[LessEqual[z, 3.1e+110], x, t]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.3e106 or -1.80000000000000013e41 < z < -6.8e12 or 3.10000000000000017e110 < z

   1. Initial program 32.8%

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

      1. associate-/l* 60.6%

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

   3. Simplified 60.6%

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

   5. Taylor expanded in z around inf 51.6%

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

   if -5.3e106 < z < -1.80000000000000013e41 or -3.2e-135 < z < -1.15000000000000002e-238 or 3.20000000000000021e-62 < z < 3.10000000000000017e110

   1. Initial program 74.7%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in a around inf 43.6%

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

   if -6.8e12 < z < -3.2e-135 or -1.15000000000000002e-238 < z < 3.20000000000000021e-62

   1. Initial program 86.8%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in x around 0 47.3%

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

      1. *-commutative 47.3%

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

      2. associate-/l* 53.2%

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

   7. Applied egg-rr 53.2%

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

   8. Taylor expanded in z around 0 33.4%

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

      1. associate-/l* 38.4%

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

   10. Simplified 38.4%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6800000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -8.5e+106)
     t
     (if (<= z -1.56e+41)
       x
       (if (<= z -2.8e+33)
         (* x (/ y z))
         (if (<= z -1.35e-129)
           t_1
           (if (<= z -1.7e-239)
             x
             (if (<= z 4.8e-63) t_1 (if (<= z 3.1e+110) x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -8.5e+106) {
		tmp = t;
	} else if (z <= -1.56e+41) {
		tmp = x;
	} else if (z <= -2.8e+33) {
		tmp = x * (y / z);
	} else if (z <= -1.35e-129) {
		tmp = t_1;
	} else if (z <= -1.7e-239) {
		tmp = x;
	} else if (z <= 4.8e-63) {
		tmp = t_1;
	} else if (z <= 3.1e+110) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-8.5d+106)) then
        tmp = t
    else if (z <= (-1.56d+41)) then
        tmp = x
    else if (z <= (-2.8d+33)) then
        tmp = x * (y / z)
    else if (z <= (-1.35d-129)) then
        tmp = t_1
    else if (z <= (-1.7d-239)) then
        tmp = x
    else if (z <= 4.8d-63) then
        tmp = t_1
    else if (z <= 3.1d+110) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -8.5e+106) {
		tmp = t;
	} else if (z <= -1.56e+41) {
		tmp = x;
	} else if (z <= -2.8e+33) {
		tmp = x * (y / z);
	} else if (z <= -1.35e-129) {
		tmp = t_1;
	} else if (z <= -1.7e-239) {
		tmp = x;
	} else if (z <= 4.8e-63) {
		tmp = t_1;
	} else if (z <= 3.1e+110) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -8.5e+106:
		tmp = t
	elif z <= -1.56e+41:
		tmp = x
	elif z <= -2.8e+33:
		tmp = x * (y / z)
	elif z <= -1.35e-129:
		tmp = t_1
	elif z <= -1.7e-239:
		tmp = x
	elif z <= 4.8e-63:
		tmp = t_1
	elif z <= 3.1e+110:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -8.5e+106)
		tmp = t;
	elseif (z <= -1.56e+41)
		tmp = x;
	elseif (z <= -2.8e+33)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -1.35e-129)
		tmp = t_1;
	elseif (z <= -1.7e-239)
		tmp = x;
	elseif (z <= 4.8e-63)
		tmp = t_1;
	elseif (z <= 3.1e+110)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -8.5e+106)
		tmp = t;
	elseif (z <= -1.56e+41)
		tmp = x;
	elseif (z <= -2.8e+33)
		tmp = x * (y / z);
	elseif (z <= -1.35e-129)
		tmp = t_1;
	elseif (z <= -1.7e-239)
		tmp = x;
	elseif (z <= 4.8e-63)
		tmp = t_1;
	elseif (z <= 3.1e+110)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+106], t, If[LessEqual[z, -1.56e+41], x, If[LessEqual[z, -2.8e+33], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.35e-129], t$95$1, If[LessEqual[z, -1.7e-239], x, If[LessEqual[z, 4.8e-63], t$95$1, If[LessEqual[z, 3.1e+110], x, t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.4999999999999992e106 or 3.10000000000000017e110 < z

   1. Initial program 28.9%

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

      1. associate-/l* 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in z around inf 52.8%

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

   if -8.4999999999999992e106 < z < -1.56e41 or -1.35e-129 < z < -1.7e-239 or 4.8000000000000001e-63 < z < 3.10000000000000017e110

   1. Initial program 74.7%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in a around inf 43.6%

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

   if -1.56e41 < z < -2.8000000000000001e33

   1. Initial program 74.7%

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

      1. associate-/l* 74.7%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in x around -inf 52.3%

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

      1. associate-*r* 52.3%

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

      2. neg-mul-1 52.3%

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

   7. Simplified 52.3%

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

   8. Taylor expanded in a around 0 53.5%

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

      1. associate-/l* 53.5%

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

   10. Simplified 53.5%

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

   if -2.8000000000000001e33 < z < -1.35e-129 or -1.7e-239 < z < 4.8000000000000001e-63

   1. Initial program 87.0%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in x around 0 47.4%

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

      1. *-commutative 47.4%

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

      2. associate-/l* 53.2%

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

   7. Applied egg-rr 53.2%

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

   8. Taylor expanded in z around 0 32.8%

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

      1. associate-/l* 37.7%

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

   10. Simplified 37.7%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-129}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-239}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t a))))
   (if (<= z -3.4e+107)
     t
     (if (<= z -1.56e+41)
       x
       (if (<= z -3e+33)
         (* x (/ y z))
         (if (<= z -3.3e-130)
           t_1
           (if (<= z -2.8e-236)
             x
             (if (<= z 3e-64) t_1 (if (<= z 1.65e+112) x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (z <= -3.4e+107) {
		tmp = t;
	} else if (z <= -1.56e+41) {
		tmp = x;
	} else if (z <= -3e+33) {
		tmp = x * (y / z);
	} else if (z <= -3.3e-130) {
		tmp = t_1;
	} else if (z <= -2.8e-236) {
		tmp = x;
	} else if (z <= 3e-64) {
		tmp = t_1;
	} else if (z <= 1.65e+112) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / a)
    if (z <= (-3.4d+107)) then
        tmp = t
    else if (z <= (-1.56d+41)) then
        tmp = x
    else if (z <= (-3d+33)) then
        tmp = x * (y / z)
    else if (z <= (-3.3d-130)) then
        tmp = t_1
    else if (z <= (-2.8d-236)) then
        tmp = x
    else if (z <= 3d-64) then
        tmp = t_1
    else if (z <= 1.65d+112) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (z <= -3.4e+107) {
		tmp = t;
	} else if (z <= -1.56e+41) {
		tmp = x;
	} else if (z <= -3e+33) {
		tmp = x * (y / z);
	} else if (z <= -3.3e-130) {
		tmp = t_1;
	} else if (z <= -2.8e-236) {
		tmp = x;
	} else if (z <= 3e-64) {
		tmp = t_1;
	} else if (z <= 1.65e+112) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	tmp = 0
	if z <= -3.4e+107:
		tmp = t
	elif z <= -1.56e+41:
		tmp = x
	elif z <= -3e+33:
		tmp = x * (y / z)
	elif z <= -3.3e-130:
		tmp = t_1
	elif z <= -2.8e-236:
		tmp = x
	elif z <= 3e-64:
		tmp = t_1
	elif z <= 1.65e+112:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	tmp = 0.0
	if (z <= -3.4e+107)
		tmp = t;
	elseif (z <= -1.56e+41)
		tmp = x;
	elseif (z <= -3e+33)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -3.3e-130)
		tmp = t_1;
	elseif (z <= -2.8e-236)
		tmp = x;
	elseif (z <= 3e-64)
		tmp = t_1;
	elseif (z <= 1.65e+112)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	tmp = 0.0;
	if (z <= -3.4e+107)
		tmp = t;
	elseif (z <= -1.56e+41)
		tmp = x;
	elseif (z <= -3e+33)
		tmp = x * (y / z);
	elseif (z <= -3.3e-130)
		tmp = t_1;
	elseif (z <= -2.8e-236)
		tmp = x;
	elseif (z <= 3e-64)
		tmp = t_1;
	elseif (z <= 1.65e+112)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+107], t, If[LessEqual[z, -1.56e+41], x, If[LessEqual[z, -3e+33], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-130], t$95$1, If[LessEqual[z, -2.8e-236], x, If[LessEqual[z, 3e-64], t$95$1, If[LessEqual[z, 1.65e+112], x, t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3999999999999997e107 or 1.64999999999999995e112 < z

   1. Initial program 28.9%

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

      1. associate-/l* 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in z around inf 52.8%

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

   if -3.3999999999999997e107 < z < -1.56e41 or -3.2999999999999998e-130 < z < -2.79999999999999986e-236 or 3.0000000000000001e-64 < z < 1.64999999999999995e112

   1. Initial program 74.7%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in a around inf 43.6%

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

   if -1.56e41 < z < -2.99999999999999984e33

   1. Initial program 74.7%

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

      1. associate-/l* 74.7%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in x around -inf 52.3%

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

      1. associate-*r* 52.3%

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

      2. neg-mul-1 52.3%

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

   7. Simplified 52.3%

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

   8. Taylor expanded in a around 0 53.5%

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

      1. associate-/l* 53.5%

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

   10. Simplified 53.5%

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

   if -2.99999999999999984e33 < z < -3.2999999999999998e-130 or -2.79999999999999986e-236 < z < 3.0000000000000001e-64

   1. Initial program 87.0%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in y around inf 67.5%

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

      1. div-sub 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in t around inf 44.7%

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

   9. Taylor expanded in a around inf 38.7%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t a))))
   (if (<= z -5.3e+110)
     t
     (if (<= z -1.9e+41)
       x
       (if (<= z -2.8e+33)
         (/ x (/ z y))
         (if (<= z -8.5e-135)
           t_1
           (if (<= z -7.6e-240)
             x
             (if (<= z 1e-60) t_1 (if (<= z 1.35e+114) x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (z <= -5.3e+110) {
		tmp = t;
	} else if (z <= -1.9e+41) {
		tmp = x;
	} else if (z <= -2.8e+33) {
		tmp = x / (z / y);
	} else if (z <= -8.5e-135) {
		tmp = t_1;
	} else if (z <= -7.6e-240) {
		tmp = x;
	} else if (z <= 1e-60) {
		tmp = t_1;
	} else if (z <= 1.35e+114) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / a)
    if (z <= (-5.3d+110)) then
        tmp = t
    else if (z <= (-1.9d+41)) then
        tmp = x
    else if (z <= (-2.8d+33)) then
        tmp = x / (z / y)
    else if (z <= (-8.5d-135)) then
        tmp = t_1
    else if (z <= (-7.6d-240)) then
        tmp = x
    else if (z <= 1d-60) then
        tmp = t_1
    else if (z <= 1.35d+114) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (z <= -5.3e+110) {
		tmp = t;
	} else if (z <= -1.9e+41) {
		tmp = x;
	} else if (z <= -2.8e+33) {
		tmp = x / (z / y);
	} else if (z <= -8.5e-135) {
		tmp = t_1;
	} else if (z <= -7.6e-240) {
		tmp = x;
	} else if (z <= 1e-60) {
		tmp = t_1;
	} else if (z <= 1.35e+114) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	tmp = 0
	if z <= -5.3e+110:
		tmp = t
	elif z <= -1.9e+41:
		tmp = x
	elif z <= -2.8e+33:
		tmp = x / (z / y)
	elif z <= -8.5e-135:
		tmp = t_1
	elif z <= -7.6e-240:
		tmp = x
	elif z <= 1e-60:
		tmp = t_1
	elif z <= 1.35e+114:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	tmp = 0.0
	if (z <= -5.3e+110)
		tmp = t;
	elseif (z <= -1.9e+41)
		tmp = x;
	elseif (z <= -2.8e+33)
		tmp = Float64(x / Float64(z / y));
	elseif (z <= -8.5e-135)
		tmp = t_1;
	elseif (z <= -7.6e-240)
		tmp = x;
	elseif (z <= 1e-60)
		tmp = t_1;
	elseif (z <= 1.35e+114)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	tmp = 0.0;
	if (z <= -5.3e+110)
		tmp = t;
	elseif (z <= -1.9e+41)
		tmp = x;
	elseif (z <= -2.8e+33)
		tmp = x / (z / y);
	elseif (z <= -8.5e-135)
		tmp = t_1;
	elseif (z <= -7.6e-240)
		tmp = x;
	elseif (z <= 1e-60)
		tmp = t_1;
	elseif (z <= 1.35e+114)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.3e+110], t, If[LessEqual[z, -1.9e+41], x, If[LessEqual[z, -2.8e+33], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.5e-135], t$95$1, If[LessEqual[z, -7.6e-240], x, If[LessEqual[z, 1e-60], t$95$1, If[LessEqual[z, 1.35e+114], x, t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.2999999999999998e110 or 1.35e114 < z

   1. Initial program 28.9%

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

      1. associate-/l* 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in z around inf 52.8%

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

   if -5.2999999999999998e110 < z < -1.9000000000000001e41 or -8.49999999999999942e-135 < z < -7.59999999999999977e-240 or 9.9999999999999997e-61 < z < 1.35e114

   1. Initial program 74.7%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in a around inf 43.6%

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

   if -1.9000000000000001e41 < z < -2.8000000000000001e33

   1. Initial program 74.7%

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

      1. associate-/l* 74.7%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in x around -inf 52.3%

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

      1. associate-*r* 52.3%

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

      2. neg-mul-1 52.3%

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

   7. Simplified 52.3%

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

   8. Taylor expanded in a around 0 53.5%

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

      1. associate-/l* 53.5%

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

   10. Simplified 53.5%

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

       1. clear-num 53.5%

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

       2. un-div-inv 53.9%

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

   12. Applied egg-rr 53.9%

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

   if -2.8000000000000001e33 < z < -8.49999999999999942e-135 or -7.59999999999999977e-240 < z < 9.9999999999999997e-61

   1. Initial program 87.0%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in y around inf 67.5%

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

      1. div-sub 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in t around inf 44.7%

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

   9. Taylor expanded in a around inf 38.7%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{-60}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a t))))
   (if (<= z -8e+109)
     t
     (if (<= z -1.7e+41)
       x
       (if (<= z -2.8e+33)
         (/ x (/ z y))
         (if (<= z -1.3e-129)
           t_1
           (if (<= z -2.7e-238)
             x
             (if (<= z 7.8e-59) t_1 (if (<= z 2.25e+111) x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / t);
	double tmp;
	if (z <= -8e+109) {
		tmp = t;
	} else if (z <= -1.7e+41) {
		tmp = x;
	} else if (z <= -2.8e+33) {
		tmp = x / (z / y);
	} else if (z <= -1.3e-129) {
		tmp = t_1;
	} else if (z <= -2.7e-238) {
		tmp = x;
	} else if (z <= 7.8e-59) {
		tmp = t_1;
	} else if (z <= 2.25e+111) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (a / t)
    if (z <= (-8d+109)) then
        tmp = t
    else if (z <= (-1.7d+41)) then
        tmp = x
    else if (z <= (-2.8d+33)) then
        tmp = x / (z / y)
    else if (z <= (-1.3d-129)) then
        tmp = t_1
    else if (z <= (-2.7d-238)) then
        tmp = x
    else if (z <= 7.8d-59) then
        tmp = t_1
    else if (z <= 2.25d+111) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / t);
	double tmp;
	if (z <= -8e+109) {
		tmp = t;
	} else if (z <= -1.7e+41) {
		tmp = x;
	} else if (z <= -2.8e+33) {
		tmp = x / (z / y);
	} else if (z <= -1.3e-129) {
		tmp = t_1;
	} else if (z <= -2.7e-238) {
		tmp = x;
	} else if (z <= 7.8e-59) {
		tmp = t_1;
	} else if (z <= 2.25e+111) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / t)
	tmp = 0
	if z <= -8e+109:
		tmp = t
	elif z <= -1.7e+41:
		tmp = x
	elif z <= -2.8e+33:
		tmp = x / (z / y)
	elif z <= -1.3e-129:
		tmp = t_1
	elif z <= -2.7e-238:
		tmp = x
	elif z <= 7.8e-59:
		tmp = t_1
	elif z <= 2.25e+111:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / t))
	tmp = 0.0
	if (z <= -8e+109)
		tmp = t;
	elseif (z <= -1.7e+41)
		tmp = x;
	elseif (z <= -2.8e+33)
		tmp = Float64(x / Float64(z / y));
	elseif (z <= -1.3e-129)
		tmp = t_1;
	elseif (z <= -2.7e-238)
		tmp = x;
	elseif (z <= 7.8e-59)
		tmp = t_1;
	elseif (z <= 2.25e+111)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / t);
	tmp = 0.0;
	if (z <= -8e+109)
		tmp = t;
	elseif (z <= -1.7e+41)
		tmp = x;
	elseif (z <= -2.8e+33)
		tmp = x / (z / y);
	elseif (z <= -1.3e-129)
		tmp = t_1;
	elseif (z <= -2.7e-238)
		tmp = x;
	elseif (z <= 7.8e-59)
		tmp = t_1;
	elseif (z <= 2.25e+111)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+109], t, If[LessEqual[z, -1.7e+41], x, If[LessEqual[z, -2.8e+33], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-129], t$95$1, If[LessEqual[z, -2.7e-238], x, If[LessEqual[z, 7.8e-59], t$95$1, If[LessEqual[z, 2.25e+111], x, t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.99999999999999985e109 or 2.25e111 < z

   1. Initial program 28.9%

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

      1. associate-/l* 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in z around inf 52.8%

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

   if -7.99999999999999985e109 < z < -1.69999999999999999e41 or -1.3e-129 < z < -2.69999999999999991e-238 or 7.80000000000000038e-59 < z < 2.25e111

   1. Initial program 74.7%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in a around inf 43.6%

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

   if -1.69999999999999999e41 < z < -2.8000000000000001e33

   1. Initial program 74.7%

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

      1. associate-/l* 74.7%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in x around -inf 52.3%

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

      1. associate-*r* 52.3%

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

      2. neg-mul-1 52.3%

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

   7. Simplified 52.3%

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

   8. Taylor expanded in a around 0 53.5%

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

      1. associate-/l* 53.5%

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

   10. Simplified 53.5%

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

       1. clear-num 53.5%

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

       2. un-div-inv 53.9%

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

   12. Applied egg-rr 53.9%

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

   if -2.8000000000000001e33 < z < -1.3e-129 or -2.69999999999999991e-238 < z < 7.80000000000000038e-59

   1. Initial program 87.0%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in y around inf 67.5%

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

      1. div-sub 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in t around inf 44.7%

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

      1. clear-num 44.7%

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

      2. un-div-inv 44.7%

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

   10. Applied egg-rr 44.7%

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

   11. Taylor expanded in a around inf 38.7%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-129}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.7 \cdot 10^{+180}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.7e+180)
   t
   (if (<= z -7.4e-38)
     (* x (/ (- y a) z))
     (if (<= z -9.5e-133)
       (* y (/ t (- a z)))
       (if (<= z -4e-236)
         x
         (if (<= z 2.4e-52) (* y (/ (- t x) a)) (if (<= z 1.6e+112) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.7e+180) {
		tmp = t;
	} else if (z <= -7.4e-38) {
		tmp = x * ((y - a) / z);
	} else if (z <= -9.5e-133) {
		tmp = y * (t / (a - z));
	} else if (z <= -4e-236) {
		tmp = x;
	} else if (z <= 2.4e-52) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.6e+112) {
		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 <= (-7.7d+180)) then
        tmp = t
    else if (z <= (-7.4d-38)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-9.5d-133)) then
        tmp = y * (t / (a - z))
    else if (z <= (-4d-236)) then
        tmp = x
    else if (z <= 2.4d-52) then
        tmp = y * ((t - x) / a)
    else if (z <= 1.6d+112) 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 <= -7.7e+180) {
		tmp = t;
	} else if (z <= -7.4e-38) {
		tmp = x * ((y - a) / z);
	} else if (z <= -9.5e-133) {
		tmp = y * (t / (a - z));
	} else if (z <= -4e-236) {
		tmp = x;
	} else if (z <= 2.4e-52) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.6e+112) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.7e+180:
		tmp = t
	elif z <= -7.4e-38:
		tmp = x * ((y - a) / z)
	elif z <= -9.5e-133:
		tmp = y * (t / (a - z))
	elif z <= -4e-236:
		tmp = x
	elif z <= 2.4e-52:
		tmp = y * ((t - x) / a)
	elif z <= 1.6e+112:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.7e+180)
		tmp = t;
	elseif (z <= -7.4e-38)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -9.5e-133)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= -4e-236)
		tmp = x;
	elseif (z <= 2.4e-52)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 1.6e+112)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.7e+180)
		tmp = t;
	elseif (z <= -7.4e-38)
		tmp = x * ((y - a) / z);
	elseif (z <= -9.5e-133)
		tmp = y * (t / (a - z));
	elseif (z <= -4e-236)
		tmp = x;
	elseif (z <= 2.4e-52)
		tmp = y * ((t - x) / a);
	elseif (z <= 1.6e+112)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.7e+180], t, If[LessEqual[z, -7.4e-38], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-133], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-236], x, If[LessEqual[z, 2.4e-52], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+112], x, t]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.70000000000000021e180 or 1.59999999999999993e112 < z

   1. Initial program 23.8%

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

      1. associate-/l* 54.9%

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

   3. Simplified 54.9%

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

   5. Taylor expanded in z around inf 55.1%

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

   if -7.70000000000000021e180 < z < -7.4e-38

   1. Initial program 68.2%

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

      1. associate-/l* 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in x around -inf 49.8%

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

      1. associate-*r* 49.8%

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

      2. neg-mul-1 49.8%

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

   7. Simplified 49.8%

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

   8. Taylor expanded in z around -inf 35.2%

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

      1. associate-/l* 37.5%

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

   10. Simplified 37.5%

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

   if -7.4e-38 < z < -9.4999999999999992e-133

   1. Initial program 90.6%

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

      1. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in y around inf 64.8%

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

      1. div-sub 64.9%

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

   7. Simplified 64.9%

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

   8. Taylor expanded in t around inf 47.2%

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

   if -9.4999999999999992e-133 < z < -4.0000000000000002e-236 or 2.4000000000000002e-52 < z < 1.59999999999999993e112

   1. Initial program 77.9%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in a around inf 47.4%

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

   if -4.0000000000000002e-236 < z < 2.4000000000000002e-52

   1. Initial program 89.3%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in y around inf 72.4%

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

      1. div-sub 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in a around inf 61.5%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.7 \cdot 10^{+180}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-237}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))))
   (if (<= z -4e+18)
     t_1
     (if (<= z -6e-80)
       (/ y (/ (- a z) t))
       (if (<= z -7.6e-237)
         (- x (/ (* x y) a))
         (if (<= z 5e-51) (* y (/ (- t x) a)) (if (<= z 1.05e+111) x t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (z <= -4e+18) {
		tmp = t_1;
	} else if (z <= -6e-80) {
		tmp = y / ((a - z) / t);
	} else if (z <= -7.6e-237) {
		tmp = x - ((x * y) / a);
	} else if (z <= 5e-51) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.05e+111) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    if (z <= (-4d+18)) then
        tmp = t_1
    else if (z <= (-6d-80)) then
        tmp = y / ((a - z) / t)
    else if (z <= (-7.6d-237)) then
        tmp = x - ((x * y) / a)
    else if (z <= 5d-51) then
        tmp = y * ((t - x) / a)
    else if (z <= 1.05d+111) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (z <= -4e+18) {
		tmp = t_1;
	} else if (z <= -6e-80) {
		tmp = y / ((a - z) / t);
	} else if (z <= -7.6e-237) {
		tmp = x - ((x * y) / a);
	} else if (z <= 5e-51) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.05e+111) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	tmp = 0
	if z <= -4e+18:
		tmp = t_1
	elif z <= -6e-80:
		tmp = y / ((a - z) / t)
	elif z <= -7.6e-237:
		tmp = x - ((x * y) / a)
	elif z <= 5e-51:
		tmp = y * ((t - x) / a)
	elif z <= 1.05e+111:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -4e+18)
		tmp = t_1;
	elseif (z <= -6e-80)
		tmp = Float64(y / Float64(Float64(a - z) / t));
	elseif (z <= -7.6e-237)
		tmp = Float64(x - Float64(Float64(x * y) / a));
	elseif (z <= 5e-51)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 1.05e+111)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	tmp = 0.0;
	if (z <= -4e+18)
		tmp = t_1;
	elseif (z <= -6e-80)
		tmp = y / ((a - z) / t);
	elseif (z <= -7.6e-237)
		tmp = x - ((x * y) / a);
	elseif (z <= 5e-51)
		tmp = y * ((t - x) / a);
	elseif (z <= 1.05e+111)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+18], t$95$1, If[LessEqual[z, -6e-80], N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-237], N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-51], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+111], x, t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4e18 or 1.04999999999999997e111 < z

   1. Initial program 38.5%

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

      1. associate-/l* 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in x around 0 32.6%

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

   6. Taylor expanded in a around 0 27.9%

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

      1. mul-1-neg 27.9%

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

      2. associate-/l* 51.5%

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

      3. distribute-rgt-neg-in 51.5%

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

   8. Simplified 51.5%

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

   if -4e18 < z < -6.00000000000000014e-80

   1. Initial program 78.0%

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

      1. associate-/l* 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in y around inf 62.4%

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

      1. div-sub 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in t around inf 48.9%

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

      1. clear-num 49.0%

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

      2. un-div-inv 49.0%

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

   10. Applied egg-rr 49.0%

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

   if -6.00000000000000014e-80 < z < -7.60000000000000047e-237

   1. Initial program 91.1%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around -inf 72.8%

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

      1. associate-*r* 72.8%

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

      2. neg-mul-1 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in z around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. *-commutative 61.7%

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

      3. distribute-rgt-neg-in 61.7%

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

      4. sub-neg 61.7%

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

      5. metadata-eval 61.7%

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

   10. Simplified 61.7%

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

   11. Taylor expanded in y around 0 56.0%

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

       1. mul-1-neg 56.0%

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

       2. associate-*r/ 61.7%

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

       3. unsub-neg 61.7%

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

       4. associate-*r/ 56.0%

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

   13. Simplified 56.0%

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

   if -7.60000000000000047e-237 < z < 5.00000000000000004e-51

   1. Initial program 89.3%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in y around inf 72.4%

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

      1. div-sub 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in a around inf 61.5%

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

   if 5.00000000000000004e-51 < z < 1.04999999999999997e111

   1. Initial program 70.2%

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

      1. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in a around inf 41.3%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-237}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= a -5.2e+35)
     x
     (if (<= a -3.1e-135)
       t_1
       (if (<= a 3.6e-107) (* x (/ y z)) (if (<= a 2.6e+163) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (a <= -5.2e+35) {
		tmp = x;
	} else if (a <= -3.1e-135) {
		tmp = t_1;
	} else if (a <= 3.6e-107) {
		tmp = x * (y / z);
	} else if (a <= 2.6e+163) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (a <= (-5.2d+35)) then
        tmp = x
    else if (a <= (-3.1d-135)) then
        tmp = t_1
    else if (a <= 3.6d-107) then
        tmp = x * (y / z)
    else if (a <= 2.6d+163) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (a <= -5.2e+35) {
		tmp = x;
	} else if (a <= -3.1e-135) {
		tmp = t_1;
	} else if (a <= 3.6e-107) {
		tmp = x * (y / z);
	} else if (a <= 2.6e+163) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if a <= -5.2e+35:
		tmp = x
	elif a <= -3.1e-135:
		tmp = t_1
	elif a <= 3.6e-107:
		tmp = x * (y / z)
	elif a <= 2.6e+163:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (a <= -5.2e+35)
		tmp = x;
	elseif (a <= -3.1e-135)
		tmp = t_1;
	elseif (a <= 3.6e-107)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 2.6e+163)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (a <= -5.2e+35)
		tmp = x;
	elseif (a <= -3.1e-135)
		tmp = t_1;
	elseif (a <= 3.6e-107)
		tmp = x * (y / z);
	elseif (a <= 2.6e+163)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e+35], x, If[LessEqual[a, -3.1e-135], t$95$1, If[LessEqual[a, 3.6e-107], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+163], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.20000000000000013e35 or 2.6000000000000002e163 < a

   1. Initial program 67.8%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in a around inf 47.7%

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

   if -5.20000000000000013e35 < a < -3.1000000000000001e-135 or 3.59999999999999976e-107 < a < 2.6000000000000002e163

   1. Initial program 69.1%

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

      1. associate-/l* 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around inf 55.4%

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

      1. div-sub 55.5%

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

   7. Simplified 55.5%

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

   8. Taylor expanded in t around inf 34.5%

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

      1. associate-/l* 35.6%

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

   10. Simplified 35.6%

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

   if -3.1000000000000001e-135 < a < 3.59999999999999976e-107

   1. Initial program 58.4%

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

      1. associate-/l* 68.0%

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

   3. Simplified 68.0%

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

   5. Taylor expanded in x around -inf 47.1%

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

      1. associate-*r* 47.1%

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

      2. neg-mul-1 47.1%

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

   7. Simplified 47.1%

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

   8. Taylor expanded in a around 0 41.8%

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

      1. associate-/l* 42.1%

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

   10. Simplified 42.1%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.3e+32)
   x
   (if (<= a -1.25e-132)
     (* t (/ y (- a z)))
     (if (<= a 2.2e-89)
       (* x (/ y z))
       (if (<= a 1.1e+152) (* t (/ (- y z) a)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.3e+32) {
		tmp = x;
	} else if (a <= -1.25e-132) {
		tmp = t * (y / (a - z));
	} else if (a <= 2.2e-89) {
		tmp = x * (y / z);
	} else if (a <= 1.1e+152) {
		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 <= (-5.3d+32)) then
        tmp = x
    else if (a <= (-1.25d-132)) then
        tmp = t * (y / (a - z))
    else if (a <= 2.2d-89) then
        tmp = x * (y / z)
    else if (a <= 1.1d+152) 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 <= -5.3e+32) {
		tmp = x;
	} else if (a <= -1.25e-132) {
		tmp = t * (y / (a - z));
	} else if (a <= 2.2e-89) {
		tmp = x * (y / z);
	} else if (a <= 1.1e+152) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.3e+32:
		tmp = x
	elif a <= -1.25e-132:
		tmp = t * (y / (a - z))
	elif a <= 2.2e-89:
		tmp = x * (y / z)
	elif a <= 1.1e+152:
		tmp = t * ((y - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.3e+32)
		tmp = x;
	elseif (a <= -1.25e-132)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (a <= 2.2e-89)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.1e+152)
		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 <= -5.3e+32)
		tmp = x;
	elseif (a <= -1.25e-132)
		tmp = t * (y / (a - z));
	elseif (a <= 2.2e-89)
		tmp = x * (y / z);
	elseif (a <= 1.1e+152)
		tmp = t * ((y - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.3e+32], x, If[LessEqual[a, -1.25e-132], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-89], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e+152], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.2999999999999999e32 or 1.0999999999999999e152 < a

   1. Initial program 67.2%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in a around inf 47.2%

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

   if -5.2999999999999999e32 < a < -1.25e-132

   1. Initial program 65.0%

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

      1. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in y around inf 57.4%

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

      1. div-sub 57.4%

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

   7. Simplified 57.4%

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

   8. Taylor expanded in t around inf 36.6%

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

      1. associate-/l* 36.6%

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

   10. Simplified 36.6%

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

   if -1.25e-132 < a < 2.20000000000000012e-89

   1. Initial program 57.7%

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

      1. associate-/l* 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in x around -inf 46.5%

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

      1. associate-*r* 46.5%

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

      2. neg-mul-1 46.5%

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

   7. Simplified 46.5%

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

   8. Taylor expanded in a around 0 41.3%

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

      1. associate-/l* 41.6%

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

   10. Simplified 41.6%

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

   if 2.20000000000000012e-89 < a < 1.0999999999999999e152

   1. Initial program 75.8%

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

      1. associate-/l* 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in x around 0 47.1%

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

   6. Taylor expanded in a around inf 35.9%

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

      1. associate-/l* 38.1%

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

   8. Simplified 38.1%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \left(\left(--1\right) - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))))
   (if (<= z -3.2e+106)
     t_1
     (if (<= z -4.2e-242)
       (* x (- (- -1.0) (/ y a)))
       (if (<= z 1.95e-53) (* y (/ (- t x) a)) (if (<= z 6e+117) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (z <= -3.2e+106) {
		tmp = t_1;
	} else if (z <= -4.2e-242) {
		tmp = x * (-(-1.0) - (y / a));
	} else if (z <= 1.95e-53) {
		tmp = y * ((t - x) / a);
	} else if (z <= 6e+117) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    if (z <= (-3.2d+106)) then
        tmp = t_1
    else if (z <= (-4.2d-242)) then
        tmp = x * (-(-1.0d0) - (y / a))
    else if (z <= 1.95d-53) then
        tmp = y * ((t - x) / a)
    else if (z <= 6d+117) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (z <= -3.2e+106) {
		tmp = t_1;
	} else if (z <= -4.2e-242) {
		tmp = x * (-(-1.0) - (y / a));
	} else if (z <= 1.95e-53) {
		tmp = y * ((t - x) / a);
	} else if (z <= 6e+117) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	tmp = 0
	if z <= -3.2e+106:
		tmp = t_1
	elif z <= -4.2e-242:
		tmp = x * (-(-1.0) - (y / a))
	elif z <= 1.95e-53:
		tmp = y * ((t - x) / a)
	elif z <= 6e+117:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -3.2e+106)
		tmp = t_1;
	elseif (z <= -4.2e-242)
		tmp = Float64(x * Float64(Float64(-(-1.0)) - Float64(y / a)));
	elseif (z <= 1.95e-53)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 6e+117)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	tmp = 0.0;
	if (z <= -3.2e+106)
		tmp = t_1;
	elseif (z <= -4.2e-242)
		tmp = x * (-(-1.0) - (y / a));
	elseif (z <= 1.95e-53)
		tmp = y * ((t - x) / a);
	elseif (z <= 6e+117)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+106], t$95$1, If[LessEqual[z, -4.2e-242], N[(x * N[((--1.0) - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e-53], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+117], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1999999999999998e106 or 6e117 < z

   1. Initial program 28.9%

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

      1. associate-/l* 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in x around 0 30.9%

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

   6. Taylor expanded in a around 0 27.2%

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

      1. mul-1-neg 27.2%

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

      2. associate-/l* 58.4%

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

      3. distribute-rgt-neg-in 58.4%

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

   8. Simplified 58.4%

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

   if -3.1999999999999998e106 < z < -4.20000000000000037e-242

   1. Initial program 80.3%

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

      1. associate-/l* 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in x around -inf 56.1%

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

      1. associate-*r* 56.1%

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

      2. neg-mul-1 56.1%

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

   7. Simplified 56.1%

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

   8. Taylor expanded in z around 0 45.1%

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

      1. mul-1-neg 45.1%

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

      2. *-commutative 45.1%

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

      3. distribute-rgt-neg-in 45.1%

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

      4. sub-neg 45.1%

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

      5. metadata-eval 45.1%

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

   10. Simplified 45.1%

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

   if -4.20000000000000037e-242 < z < 1.9500000000000001e-53

   1. Initial program 89.3%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in y around inf 72.4%

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

      1. div-sub 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in a around inf 61.5%

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

   if 1.9500000000000001e-53 < z < 6e117

   1. Initial program 70.2%

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

      1. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in a around inf 41.3%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \left(\left(--1\right) - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+99} \lor \neg \left(z \leq 1.3 \cdot 10^{+144}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e+99) (not (<= z 1.3e+144)))
   (+ t (* (/ (- t x) z) (- a y)))
   (- x (* (/ (- t x) (- a z)) (- z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e+99) || !(z <= 1.3e+144)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x - (((t - x) / (a - z)) * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.3d+99)) .or. (.not. (z <= 1.3d+144))) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x - (((t - x) / (a - z)) * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e+99) || !(z <= 1.3e+144)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x - (((t - x) / (a - z)) * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e+99) or not (z <= 1.3e+144):
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x - (((t - x) / (a - z)) * (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e+99) || !(z <= 1.3e+144))
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x - Float64(Float64(Float64(t - x) / Float64(a - z)) * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.3e+99) || ~((z <= 1.3e+144)))
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x - (((t - x) / (a - z)) * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.3e+99], N[Not[LessEqual[z, 1.3e+144]], $MachinePrecision]], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.30000000000000019e99 or 1.2999999999999999e144 < z

   1. Initial program 27.3%

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

      1. associate-/l* 56.9%

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

   3. Simplified 56.9%

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

   5. Taylor expanded in z around inf 68.0%

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

      1. associate--l+ 68.0%

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

      2. distribute-lft-out-- 68.0%

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

      3. div-sub 68.0%

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

      4. mul-1-neg 68.0%

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

      5. unsub-neg 68.0%

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

      6. div-sub 68.0%

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

      7. associate-/l* 79.1%

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

      8. associate-/l* 91.9%

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

      9. distribute-rgt-out-- 91.9%

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

   7. Simplified 91.9%

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

   if -2.30000000000000019e99 < z < 1.2999999999999999e144

   1. Initial program 82.4%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+99} \lor \neg \left(z \leq 1.3 \cdot 10^{+144}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 33.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;x \leq -9.8 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))))
   (if (<= x -9.8e+44)
     t_1
     (if (<= x -1.6e-30) t (if (<= x 4e-65) (* y (/ t (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (x <= -9.8e+44) {
		tmp = t_1;
	} else if (x <= -1.6e-30) {
		tmp = t;
	} else if (x <= 4e-65) {
		tmp = y * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    if (x <= (-9.8d+44)) then
        tmp = t_1
    else if (x <= (-1.6d-30)) then
        tmp = t
    else if (x <= 4d-65) then
        tmp = y * (t / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (x <= -9.8e+44) {
		tmp = t_1;
	} else if (x <= -1.6e-30) {
		tmp = t;
	} else if (x <= 4e-65) {
		tmp = y * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	tmp = 0
	if x <= -9.8e+44:
		tmp = t_1
	elif x <= -1.6e-30:
		tmp = t
	elif x <= 4e-65:
		tmp = y * (t / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (x <= -9.8e+44)
		tmp = t_1;
	elseif (x <= -1.6e-30)
		tmp = t;
	elseif (x <= 4e-65)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	tmp = 0.0;
	if (x <= -9.8e+44)
		tmp = t_1;
	elseif (x <= -1.6e-30)
		tmp = t;
	elseif (x <= 4e-65)
		tmp = y * (t / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.8e+44], t$95$1, If[LessEqual[x, -1.6e-30], t, If[LessEqual[x, 4e-65], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.80000000000000071e44 or 3.99999999999999969e-65 < x

   1. Initial program 52.8%

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

      1. associate-/l* 70.1%

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

   3. Simplified 70.1%

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

   5. Taylor expanded in x around -inf 63.3%

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

      1. associate-*r* 63.3%

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

      2. neg-mul-1 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in z around -inf 38.4%

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

      1. associate-/l* 42.6%

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

   10. Simplified 42.6%

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

   if -9.80000000000000071e44 < x < -1.6e-30

   1. Initial program 61.8%

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

      1. associate-/l* 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in z around inf 45.2%

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

   if -1.6e-30 < x < 3.99999999999999969e-65

   1. Initial program 81.3%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in y around inf 55.3%

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

      1. div-sub 55.3%

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

   7. Simplified 55.3%

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

   8. Taylor expanded in t around inf 44.8%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 71.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+30} \lor \neg \left(z \leq 8.8 \cdot 10^{+79}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.2e+30) (not (<= z 8.8e+79)))
   (+ t (* (- y a) (/ x z)))
   (+ x (* (- y z) (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.2e+30) || !(z <= 8.8e+79)) {
		tmp = t + ((y - a) * (x / z));
	} else {
		tmp = x + ((y - z) * ((t - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.2d+30)) .or. (.not. (z <= 8.8d+79))) then
        tmp = t + ((y - a) * (x / z))
    else
        tmp = x + ((y - z) * ((t - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.2e+30) || !(z <= 8.8e+79)) {
		tmp = t + ((y - a) * (x / z));
	} else {
		tmp = x + ((y - z) * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.2e+30) or not (z <= 8.8e+79):
		tmp = t + ((y - a) * (x / z))
	else:
		tmp = x + ((y - z) * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.2e+30) || !(z <= 8.8e+79))
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.2e+30) || ~((z <= 8.8e+79)))
		tmp = t + ((y - a) * (x / z));
	else
		tmp = x + ((y - z) * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.2e+30], N[Not[LessEqual[z, 8.8e+79]], $MachinePrecision]], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e30 or 8.7999999999999996e79 < z

   1. Initial program 38.4%

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

      1. associate-/l* 61.9%

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

   3. Simplified 61.9%

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

   5. Taylor expanded in z around inf 65.7%

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

      1. associate--l+ 65.7%

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

      2. distribute-lft-out-- 65.7%

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

      3. div-sub 65.7%

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

      4. mul-1-neg 65.7%

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

      5. unsub-neg 65.7%

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

      6. div-sub 65.7%

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

      7. associate-/l* 73.8%

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

      8. associate-/l* 83.3%

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

      9. distribute-rgt-out-- 83.3%

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

   7. Simplified 83.3%

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

   8. Taylor expanded in t around 0 76.1%

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

      1. neg-mul-1 76.1%

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

      2. distribute-neg-frac2 76.1%

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

   10. Simplified 76.1%

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

   if -2.2e30 < z < 8.7999999999999996e79

   1. Initial program 85.1%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in a around inf 75.7%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+30} \lor \neg \left(z \leq 8.8 \cdot 10^{+79}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+23} \lor \neg \left(z \leq 9.4 \cdot 10^{+79}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.8e+23) (not (<= z 9.4e+79)))
   (+ t (* (/ (- t x) z) (- a y)))
   (+ x (* (- y z) (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.8e+23) || !(z <= 9.4e+79)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((y - z) * ((t - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7.8d+23)) .or. (.not. (z <= 9.4d+79))) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x + ((y - z) * ((t - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.8e+23) || !(z <= 9.4e+79)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((y - z) * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.8e+23) or not (z <= 9.4e+79):
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x + ((y - z) * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.8e+23) || !(z <= 9.4e+79))
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.8e+23) || ~((z <= 9.4e+79)))
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x + ((y - z) * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.8e+23], N[Not[LessEqual[z, 9.4e+79]], $MachinePrecision]], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000001e23 or 9.40000000000000045e79 < z

   1. Initial program 38.4%

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

      1. associate-/l* 61.9%

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

   3. Simplified 61.9%

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

   5. Taylor expanded in z around inf 65.7%

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

      1. associate--l+ 65.7%

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

      2. distribute-lft-out-- 65.7%

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

      3. div-sub 65.7%

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

      4. mul-1-neg 65.7%

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

      5. unsub-neg 65.7%

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

      6. div-sub 65.7%

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

      7. associate-/l* 73.8%

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

      8. associate-/l* 83.3%

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

      9. distribute-rgt-out-- 83.3%

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

   7. Simplified 83.3%

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

   if -7.8000000000000001e23 < z < 9.40000000000000045e79

   1. Initial program 85.1%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in a around inf 75.7%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+23} \lor \neg \left(z \leq 9.4 \cdot 10^{+79}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 66.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.92 \cdot 10^{+28} \lor \neg \left(z \leq 4.3 \cdot 10^{+17}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.92e+28) (not (<= z 4.3e+17)))
   (* t (/ (- y z) (- a z)))
   (+ x (* y (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.92e+28) || !(z <= 4.3e+17)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.92d+28)) .or. (.not. (z <= 4.3d+17))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y * ((t - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.92e+28) || !(z <= 4.3e+17)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.92e+28) or not (z <= 4.3e+17):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.92e+28) || !(z <= 4.3e+17))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.92e+28) || ~((z <= 4.3e+17)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.92e+28], N[Not[LessEqual[z, 4.3e+17]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.91999999999999998e28 or 4.3e17 < z

   1. Initial program 41.4%

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

      1. associate-/l* 64.6%

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

   3. Simplified 64.6%

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

   5. Taylor expanded in x around 0 32.8%

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

      1. associate-/l* 56.2%

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

   7. Simplified 56.2%

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

   if -1.91999999999999998e28 < z < 4.3e17

   1. Initial program 86.6%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in z around 0 65.5%

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

      1. associate-/l* 72.0%

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

   7. Simplified 72.0%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.92 \cdot 10^{+28} \lor \neg \left(z \leq 4.3 \cdot 10^{+17}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+30} \lor \neg \left(z \leq 4.8 \cdot 10^{+14}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.8e+30) (not (<= z 4.8e+14)))
   (+ t (* (- y a) (/ x z)))
   (+ x (* y (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e+30) || !(z <= 4.8e+14)) {
		tmp = t + ((y - a) * (x / z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.8d+30)) .or. (.not. (z <= 4.8d+14))) then
        tmp = t + ((y - a) * (x / z))
    else
        tmp = x + (y * ((t - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e+30) || !(z <= 4.8e+14)) {
		tmp = t + ((y - a) * (x / z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.8e+30) or not (z <= 4.8e+14):
		tmp = t + ((y - a) * (x / z))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.8e+30) || !(z <= 4.8e+14))
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.8e+30) || ~((z <= 4.8e+14)))
		tmp = t + ((y - a) * (x / z));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.8e+30], N[Not[LessEqual[z, 4.8e+14]], $MachinePrecision]], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8000000000000005e30 or 4.8e14 < z

   1. Initial program 41.0%

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

      1. associate-/l* 64.2%

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

   3. Simplified 64.2%

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

   5. Taylor expanded in z around inf 61.5%

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

      1. associate--l+ 61.5%

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

      2. distribute-lft-out-- 61.5%

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

      3. div-sub 61.5%

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

      4. mul-1-neg 61.5%

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

      5. unsub-neg 61.5%

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

      6. div-sub 61.5%

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

      7. associate-/l* 69.3%

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

      8. associate-/l* 77.6%

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

      9. distribute-rgt-out-- 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in t around 0 70.7%

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

      1. neg-mul-1 70.7%

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

      2. distribute-neg-frac2 70.7%

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

   10. Simplified 70.7%

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

   if -6.8000000000000005e30 < z < 4.8e14

   1. Initial program 88.4%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around 0 67.4%

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

      1. associate-/l* 73.4%

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

   7. Simplified 73.4%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+30} \lor \neg \left(z \leq 4.8 \cdot 10^{+14}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 37.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+106) t (if (<= z 3.1e+110) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+106) {
		tmp = t;
	} else if (z <= 3.1e+110) {
		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 <= (-2.7d+106)) then
        tmp = t
    else if (z <= 3.1d+110) 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 <= -2.7e+106) {
		tmp = t;
	} else if (z <= 3.1e+110) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+106:
		tmp = t
	elif z <= 3.1e+110:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+106)
		tmp = t;
	elseif (z <= 3.1e+110)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.7e+106)
		tmp = t;
	elseif (z <= 3.1e+110)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+106], t, If[LessEqual[z, 3.1e+110], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.70000000000000006e106 or 3.10000000000000017e110 < z

   1. Initial program 28.9%

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

      1. associate-/l* 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in z around inf 52.8%

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

   if -2.70000000000000006e106 < z < 3.10000000000000017e110

   1. Initial program 81.4%

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

      1. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in a around inf 31.2%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 24.2% 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 65.4%

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

   1. associate-/l* 79.8%

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

3. Simplified 79.8%

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

5. Taylor expanded in z around inf 22.1%

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

6. Final simplification 22.1%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))