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

Percentage Accurate: 67.9% → 89.4%

Time: 11.6s

Alternatives: 22

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+161} \lor \neg \left(t \leq 1.1 \cdot 10^{+176}\right):\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.5e+161) (not (<= t 1.1e+176)))
   (+ y (/ (- a z) (/ t (- y x))))
   (fma (- y x) (/ (- z t) (- a t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e+161) || !(t <= 1.1e+176)) {
		tmp = y + ((a - z) / (t / (y - x)));
	} else {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.5e+161) || !(t <= 1.1e+176))
		tmp = Float64(y + Float64(Float64(a - z) / Float64(t / Float64(y - x))));
	else
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.5e+161], N[Not[LessEqual[t, 1.1e+176]], $MachinePrecision]], N[(y + N[(N[(a - z), $MachinePrecision] / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.50000000000000061e161 or 1.10000000000000004e176 < t

   1. Initial program 24.1%

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

   3. Taylor expanded in t around inf 75.2%

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

      1. associate--l+ 75.2%

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

      2. distribute-lft-out-- 75.2%

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

      3. div-sub 75.2%

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

      4. mul-1-neg 75.2%

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

      5. unsub-neg 75.2%

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

      6. div-sub 75.2%

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

      7. associate-/l* 83.6%

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

      8. associate-/l* 93.7%

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

      9. distribute-rgt-out-- 93.7%

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

   5. Simplified 93.7%

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

      1. *-commutative 93.7%

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

      2. clear-num 93.7%

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

      3. un-div-inv 93.8%

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

   7. Applied egg-rr 93.8%

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

   if -9.50000000000000061e161 < t < 1.10000000000000004e176

   1. Initial program 77.4%

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

      1. +-commutative 77.4%

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

      2. associate-/l* 94.0%

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

      3. fma-define 94.1%

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

   3. Simplified 94.1%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+161} \lor \neg \left(t \leq 1.1 \cdot 10^{+176}\right):\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.032:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+178}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- a z) (/ t (- y x))))))
   (if (<= t -6.2e+95)
     t_1
     (if (<= t 0.032)
       (+ x (/ (* (- y x) (- z t)) (- a t)))
       (if (<= t 1.6e+178) (+ x (* y (/ (- z t) (- a t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((a - z) / (t / (y - x)));
	double tmp;
	if (t <= -6.2e+95) {
		tmp = t_1;
	} else if (t <= 0.032) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else if (t <= 1.6e+178) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((a - z) / (t / (y - x)))
    if (t <= (-6.2d+95)) then
        tmp = t_1
    else if (t <= 0.032d0) then
        tmp = x + (((y - x) * (z - t)) / (a - t))
    else if (t <= 1.6d+178) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((a - z) / (t / (y - x)));
	double tmp;
	if (t <= -6.2e+95) {
		tmp = t_1;
	} else if (t <= 0.032) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else if (t <= 1.6e+178) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((a - z) / (t / (y - x)))
	tmp = 0
	if t <= -6.2e+95:
		tmp = t_1
	elif t <= 0.032:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	elif t <= 1.6e+178:
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(a - z) / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -6.2e+95)
		tmp = t_1;
	elseif (t <= 0.032)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	elseif (t <= 1.6e+178)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((a - z) / (t / (y - x)));
	tmp = 0.0;
	if (t <= -6.2e+95)
		tmp = t_1;
	elseif (t <= 0.032)
		tmp = x + (((y - x) * (z - t)) / (a - t));
	elseif (t <= 1.6e+178)
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(a - z), $MachinePrecision] / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+95], t$95$1, If[LessEqual[t, 0.032], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+178], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.2000000000000006e95 or 1.6e178 < t

   1. Initial program 24.1%

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

   3. Taylor expanded in t around inf 74.6%

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

      1. associate--l+ 74.6%

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

      2. distribute-lft-out-- 74.6%

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

      3. div-sub 74.6%

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

      4. mul-1-neg 74.6%

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

      5. unsub-neg 74.6%

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

      6. div-sub 74.6%

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

      7. associate-/l* 81.7%

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

      8. associate-/l* 90.3%

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

      9. distribute-rgt-out-- 90.3%

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

   5. Simplified 90.3%

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

      1. *-commutative 90.3%

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

      2. clear-num 90.3%

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

      3. un-div-inv 90.4%

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

   7. Applied egg-rr 90.4%

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

   if -6.2000000000000006e95 < t < 0.032000000000000001

   1. Initial program 84.8%

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

   if 0.032000000000000001 < t < 1.6e178

   1. Initial program 56.6%

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

   3. Taylor expanded in y around inf 55.8%

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

      1. associate-/l* 86.2%

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

   5. Simplified 86.2%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+95}:\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq 0.032:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+178}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+51}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+179}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.2e+51)
   (+ y (* (- z a) (/ (- x y) t)))
   (if (<= t 1.25e-108)
     (+ x (/ (- y x) (/ (- a t) z)))
     (if (<= t 9.5e+179)
       (+ x (* y (/ (- z t) (- a t))))
       (+ y (/ (- a z) (/ t (- y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+51) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else if (t <= 1.25e-108) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else if (t <= 9.5e+179) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + ((a - z) / (t / (y - 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 (t <= (-7.2d+51)) then
        tmp = y + ((z - a) * ((x - y) / t))
    else if (t <= 1.25d-108) then
        tmp = x + ((y - x) / ((a - t) / z))
    else if (t <= 9.5d+179) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = y + ((a - z) / (t / (y - 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 (t <= -7.2e+51) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else if (t <= 1.25e-108) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else if (t <= 9.5e+179) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + ((a - z) / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.2e+51:
		tmp = y + ((z - a) * ((x - y) / t))
	elif t <= 1.25e-108:
		tmp = x + ((y - x) / ((a - t) / z))
	elif t <= 9.5e+179:
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = y + ((a - z) / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.2e+51)
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	elseif (t <= 1.25e-108)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / z)));
	elseif (t <= 9.5e+179)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(a - z) / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.2e+51)
		tmp = y + ((z - a) * ((x - y) / t));
	elseif (t <= 1.25e-108)
		tmp = x + ((y - x) / ((a - t) / z));
	elseif (t <= 9.5e+179)
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = y + ((a - z) / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.2e+51], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-108], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+179], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(a - z), $MachinePrecision] / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.20000000000000022e51

   1. Initial program 30.9%

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

   3. Taylor expanded in t around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. distribute-lft-out-- 69.2%

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

      3. div-sub 69.2%

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

      4. mul-1-neg 69.2%

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

      5. unsub-neg 69.2%

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

      6. div-sub 69.2%

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

      7. associate-/l* 73.2%

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

      8. associate-/l* 77.5%

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

      9. distribute-rgt-out-- 77.5%

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

   5. Simplified 77.5%

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

   if -7.20000000000000022e51 < t < 1.25e-108

   1. Initial program 85.1%

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

      1. clear-num 85.0%

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

      2. associate-/r/ 85.0%

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

   4. Applied egg-rr 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*l* 96.7%

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

      3. div-inv 96.7%

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

      4. clear-num 96.7%

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

      5. un-div-inv 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in z around inf 86.8%

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

   if 1.25e-108 < t < 9.5e179

   1. Initial program 72.2%

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

   3. Taylor expanded in y around inf 64.1%

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

      1. associate-/l* 81.9%

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

   5. Simplified 81.9%

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

   if 9.5e179 < t

   1. Initial program 24.0%

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

   3. Taylor expanded in t around inf 76.5%

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

      1. associate--l+ 76.5%

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

      2. distribute-lft-out-- 76.5%

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

      3. div-sub 76.5%

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

      4. mul-1-neg 76.5%

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

      5. unsub-neg 76.5%

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

      6. div-sub 76.5%

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

      7. associate-/l* 86.5%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   5. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+51}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+179}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -2.45 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+178}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- z a) (/ (- x y) t)))))
   (if (<= t -2.45e+51)
     t_1
     (if (<= t 1.1e-107)
       (+ x (/ (- y x) (/ (- a t) z)))
       (if (<= t 2.2e+178) (+ x (* y (/ (- z t) (- a t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -2.45e+51) {
		tmp = t_1;
	} else if (t <= 1.1e-107) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else if (t <= 2.2e+178) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((z - a) * ((x - y) / t))
    if (t <= (-2.45d+51)) then
        tmp = t_1
    else if (t <= 1.1d-107) then
        tmp = x + ((y - x) / ((a - t) / z))
    else if (t <= 2.2d+178) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -2.45e+51) {
		tmp = t_1;
	} else if (t <= 1.1e-107) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else if (t <= 2.2e+178) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((z - a) * ((x - y) / t))
	tmp = 0
	if t <= -2.45e+51:
		tmp = t_1
	elif t <= 1.1e-107:
		tmp = x + ((y - x) / ((a - t) / z))
	elif t <= 2.2e+178:
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -2.45e+51)
		tmp = t_1;
	elseif (t <= 1.1e-107)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / z)));
	elseif (t <= 2.2e+178)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((z - a) * ((x - y) / t));
	tmp = 0.0;
	if (t <= -2.45e+51)
		tmp = t_1;
	elseif (t <= 1.1e-107)
		tmp = x + ((y - x) / ((a - t) / z));
	elseif (t <= 2.2e+178)
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.45e+51], t$95$1, If[LessEqual[t, 1.1e-107], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+178], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.44999999999999992e51 or 2.19999999999999997e178 < t

   1. Initial program 28.3%

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

   3. Taylor expanded in t around inf 72.0%

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

      1. associate--l+ 72.0%

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

      2. distribute-lft-out-- 72.0%

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

      3. div-sub 72.0%

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

      4. mul-1-neg 72.0%

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

      5. unsub-neg 72.0%

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

      6. div-sub 72.0%

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

      7. associate-/l* 78.3%

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

      8. associate-/l* 86.1%

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

      9. distribute-rgt-out-- 86.1%

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

   5. Simplified 86.1%

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

   if -2.44999999999999992e51 < t < 1.10000000000000006e-107

   1. Initial program 85.1%

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

      1. clear-num 85.0%

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

      2. associate-/r/ 85.0%

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

   4. Applied egg-rr 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*l* 96.7%

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

      3. div-inv 96.7%

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

      4. clear-num 96.7%

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

      5. un-div-inv 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in z around inf 86.8%

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

   if 1.10000000000000006e-107 < t < 2.19999999999999997e178

   1. Initial program 72.2%

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

   3. Taylor expanded in y around inf 64.1%

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

      1. associate-/l* 81.9%

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

   5. Simplified 81.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+51}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+178}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+186}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* (/ x t) (- a z)))))
   (if (<= t -6.8e+51)
     t_1
     (if (<= t 1.15e-107)
       (+ x (/ (- y x) (/ (- a t) z)))
       (if (<= t 2.05e+186) (+ x (* y (/ (- z t) (- a t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - ((x / t) * (a - z));
	double tmp;
	if (t <= -6.8e+51) {
		tmp = t_1;
	} else if (t <= 1.15e-107) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else if (t <= 2.05e+186) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - ((x / t) * (a - z))
    if (t <= (-6.8d+51)) then
        tmp = t_1
    else if (t <= 1.15d-107) then
        tmp = x + ((y - x) / ((a - t) / z))
    else if (t <= 2.05d+186) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - ((x / t) * (a - z));
	double tmp;
	if (t <= -6.8e+51) {
		tmp = t_1;
	} else if (t <= 1.15e-107) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else if (t <= 2.05e+186) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - ((x / t) * (a - z))
	tmp = 0
	if t <= -6.8e+51:
		tmp = t_1
	elif t <= 1.15e-107:
		tmp = x + ((y - x) / ((a - t) / z))
	elif t <= 2.05e+186:
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(Float64(x / t) * Float64(a - z)))
	tmp = 0.0
	if (t <= -6.8e+51)
		tmp = t_1;
	elseif (t <= 1.15e-107)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / z)));
	elseif (t <= 2.05e+186)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - ((x / t) * (a - z));
	tmp = 0.0;
	if (t <= -6.8e+51)
		tmp = t_1;
	elseif (t <= 1.15e-107)
		tmp = x + ((y - x) / ((a - t) / z));
	elseif (t <= 2.05e+186)
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(N[(x / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+51], t$95$1, If[LessEqual[t, 1.15e-107], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e+186], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.79999999999999969e51 or 2.05e186 < t

   1. Initial program 26.4%

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

   3. Taylor expanded in t around inf 71.2%

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

      1. associate--l+ 71.2%

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

      2. distribute-lft-out-- 71.2%

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

      3. div-sub 71.2%

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

      4. mul-1-neg 71.2%

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

      5. unsub-neg 71.2%

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

      6. div-sub 71.2%

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

      7. associate-/l* 77.7%

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

      8. associate-/l* 85.7%

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

      9. distribute-rgt-out-- 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in y around 0 82.9%

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

      1. neg-mul-1 82.9%

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

      2. distribute-neg-frac 82.9%

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

   8. Simplified 82.9%

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

   if -6.79999999999999969e51 < t < 1.15000000000000002e-107

   1. Initial program 85.1%

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

      1. clear-num 85.0%

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

      2. associate-/r/ 85.0%

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

   4. Applied egg-rr 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*l* 96.7%

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

      3. div-inv 96.7%

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

      4. clear-num 96.7%

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

      5. un-div-inv 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in z around inf 86.8%

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

   if 1.15000000000000002e-107 < t < 2.05e186

   1. Initial program 73.1%

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

   3. Taylor expanded in y around inf 65.3%

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

      1. associate-/l* 82.4%

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

   5. Simplified 82.4%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+51}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+186}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-104}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+181}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9e+66)
   y
   (if (<= t -1.7e-104)
     (+ y x)
     (if (<= t 9.2e-129) x (if (<= t 7.5e+181) (+ y x) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e+66) {
		tmp = y;
	} else if (t <= -1.7e-104) {
		tmp = y + x;
	} else if (t <= 9.2e-129) {
		tmp = x;
	} else if (t <= 7.5e+181) {
		tmp = y + x;
	} else {
		tmp = 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 (t <= (-9d+66)) then
        tmp = y
    else if (t <= (-1.7d-104)) then
        tmp = y + x
    else if (t <= 9.2d-129) then
        tmp = x
    else if (t <= 7.5d+181) then
        tmp = y + x
    else
        tmp = 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 (t <= -9e+66) {
		tmp = y;
	} else if (t <= -1.7e-104) {
		tmp = y + x;
	} else if (t <= 9.2e-129) {
		tmp = x;
	} else if (t <= 7.5e+181) {
		tmp = y + x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9e+66:
		tmp = y
	elif t <= -1.7e-104:
		tmp = y + x
	elif t <= 9.2e-129:
		tmp = x
	elif t <= 7.5e+181:
		tmp = y + x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9e+66)
		tmp = y;
	elseif (t <= -1.7e-104)
		tmp = Float64(y + x);
	elseif (t <= 9.2e-129)
		tmp = x;
	elseif (t <= 7.5e+181)
		tmp = Float64(y + x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9e+66)
		tmp = y;
	elseif (t <= -1.7e-104)
		tmp = y + x;
	elseif (t <= 9.2e-129)
		tmp = x;
	elseif (t <= 7.5e+181)
		tmp = y + x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9e+66], y, If[LessEqual[t, -1.7e-104], N[(y + x), $MachinePrecision], If[LessEqual[t, 9.2e-129], x, If[LessEqual[t, 7.5e+181], N[(y + x), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.9999999999999997e66 or 7.5000000000000005e181 < t

   1. Initial program 24.6%

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

   3. Taylor expanded in t around inf 66.0%

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

   if -8.9999999999999997e66 < t < -1.70000000000000008e-104 or 9.1999999999999998e-129 < t < 7.5000000000000005e181

   1. Initial program 76.9%

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

   3. Taylor expanded in y around inf 66.4%

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

      1. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in t around inf 40.6%

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

   if -1.70000000000000008e-104 < t < 9.1999999999999998e-129

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf 34.7%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-104}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+181}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.56 \cdot 10^{+159} \lor \neg \left(t \leq 1.8 \cdot 10^{+185}\right):\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t - a}{t - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.56e+159) (not (<= t 1.8e+185)))
   (+ y (/ (- a z) (/ t (- y x))))
   (+ x (/ (- y x) (/ (- t a) (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.56e+159) || !(t <= 1.8e+185)) {
		tmp = y + ((a - z) / (t / (y - x)));
	} else {
		tmp = x + ((y - x) / ((t - a) / (t - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.56d+159)) .or. (.not. (t <= 1.8d+185))) then
        tmp = y + ((a - z) / (t / (y - x)))
    else
        tmp = x + ((y - x) / ((t - a) / (t - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.56e+159) || !(t <= 1.8e+185)) {
		tmp = y + ((a - z) / (t / (y - x)));
	} else {
		tmp = x + ((y - x) / ((t - a) / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.56e+159) or not (t <= 1.8e+185):
		tmp = y + ((a - z) / (t / (y - x)))
	else:
		tmp = x + ((y - x) / ((t - a) / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.56e+159) || !(t <= 1.8e+185))
		tmp = Float64(y + Float64(Float64(a - z) / Float64(t / Float64(y - x))));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(t - a) / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.56e+159) || ~((t <= 1.8e+185)))
		tmp = y + ((a - z) / (t / (y - x)));
	else
		tmp = x + ((y - x) / ((t - a) / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.56e+159], N[Not[LessEqual[t, 1.8e+185]], $MachinePrecision]], N[(y + N[(N[(a - z), $MachinePrecision] / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.56e159 or 1.80000000000000014e185 < t

   1. Initial program 22.7%

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

   3. Taylor expanded in t around inf 74.8%

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

      1. associate--l+ 74.8%

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

      2. distribute-lft-out-- 74.8%

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

      3. div-sub 74.8%

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

      4. mul-1-neg 74.8%

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

      5. unsub-neg 74.8%

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

      6. div-sub 74.8%

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

      7. associate-/l* 83.3%

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

      8. associate-/l* 93.6%

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

      9. distribute-rgt-out-- 93.6%

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

   5. Simplified 93.6%

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

      1. *-commutative 93.6%

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

      2. clear-num 93.6%

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

      3. un-div-inv 93.7%

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

   7. Applied egg-rr 93.7%

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

   if -1.56e159 < t < 1.80000000000000014e185

   1. Initial program 77.6%

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

      1. clear-num 77.5%

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

      2. associate-/r/ 77.5%

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

   4. Applied egg-rr 77.5%

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

      1. *-commutative 77.5%

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

      2. associate-*l* 94.0%

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

      3. div-inv 94.1%

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

      4. clear-num 94.0%

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

      5. un-div-inv 94.1%

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

   6. Applied egg-rr 94.1%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.56 \cdot 10^{+159} \lor \neg \left(t \leq 1.8 \cdot 10^{+185}\right):\\ \;\;\;\;y + \frac{a - z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t - a}{t - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{-67} \lor \neg \left(a \leq 6.2 \cdot 10^{-126}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z \cdot \left(y - x\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.7e-67) (not (<= a 6.2e-126)))
   (+ x (* y (/ (- z t) (- a t))))
   (- y (/ (* z (- y x)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.7e-67) || !(a <= 6.2e-126)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y - ((z * (y - x)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.7d-67)) .or. (.not. (a <= 6.2d-126))) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = y - ((z * (y - x)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.7e-67) || !(a <= 6.2e-126)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y - ((z * (y - x)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.7e-67) or not (a <= 6.2e-126):
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = y - ((z * (y - x)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.7e-67) || !(a <= 6.2e-126))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y - Float64(Float64(z * Float64(y - x)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.7e-67) || ~((a <= 6.2e-126)))
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = y - ((z * (y - x)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.7e-67], N[Not[LessEqual[a, 6.2e-126]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.7000000000000002e-67 or 6.2000000000000003e-126 < a

   1. Initial program 72.0%

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

   3. Taylor expanded in y around inf 65.8%

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

      1. associate-/l* 82.3%

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

   5. Simplified 82.3%

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

   if -5.7000000000000002e-67 < a < 6.2000000000000003e-126

   1. Initial program 53.1%

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

   3. Taylor expanded in t around inf 85.0%

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

      1. associate--l+ 85.0%

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

      2. distribute-lft-out-- 85.0%

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

      3. div-sub 85.0%

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

      4. mul-1-neg 85.0%

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

      5. unsub-neg 85.0%

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

      6. div-sub 85.0%

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

      7. associate-/l* 83.7%

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

      8. associate-/l* 76.7%

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

      9. distribute-rgt-out-- 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in z around inf 79.9%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{-67} \lor \neg \left(a \leq 6.2 \cdot 10^{-126}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z \cdot \left(y - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+67} \lor \neg \left(t \leq 8 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{y}{\frac{t - a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.8e+67) (not (<= t 8e-125)))
   (/ y (/ (- t a) (- t z)))
   (+ x (/ (- y x) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+67) || !(t <= 8e-125)) {
		tmp = y / ((t - a) / (t - z));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.8d+67)) .or. (.not. (t <= 8d-125))) then
        tmp = y / ((t - a) / (t - z))
    else
        tmp = x + ((y - x) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+67) || !(t <= 8e-125)) {
		tmp = y / ((t - a) / (t - z));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.8e+67) or not (t <= 8e-125):
		tmp = y / ((t - a) / (t - z))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.8e+67) || !(t <= 8e-125))
		tmp = Float64(y / Float64(Float64(t - a) / Float64(t - z)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.8e+67) || ~((t <= 8e-125)))
		tmp = y / ((t - a) / (t - z));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.8e+67], N[Not[LessEqual[t, 8e-125]], $MachinePrecision]], N[(y / N[(N[(t - a), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.80000000000000004e67 or 8.0000000000000001e-125 < t

   1. Initial program 46.0%

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

      1. clear-num 45.9%

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

      2. associate-/r/ 45.9%

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

   4. Applied egg-rr 45.9%

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

      1. *-commutative 45.9%

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

      2. associate-*l* 76.7%

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

      3. div-inv 76.9%

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

      4. clear-num 76.8%

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

      5. un-div-inv 76.9%

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

   6. Applied egg-rr 76.9%

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

   7. Taylor expanded in x around 0 45.5%

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

      1. associate-/l* 71.8%

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

   9. Simplified 71.8%

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

       1. clear-num 71.8%

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

       2. un-div-inv 71.8%

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

   11. Applied egg-rr 71.8%

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

   if -4.80000000000000004e67 < t < 8.0000000000000001e-125

   1. Initial program 86.0%

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

      1. clear-num 85.9%

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

      2. associate-/r/ 85.9%

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

   4. Applied egg-rr 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*l* 97.5%

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

      3. div-inv 97.5%

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

      4. clear-num 97.5%

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

      5. un-div-inv 97.5%

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

   6. Applied egg-rr 97.5%

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

   7. Taylor expanded in t around 0 75.9%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+67} \lor \neg \left(t \leq 8 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{y}{\frac{t - a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+77} \lor \neg \left(t \leq 1.05 \cdot 10^{-124}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.5e+77) (not (<= t 1.05e-124)))
   (* y (/ (- z t) (- a t)))
   (+ x (/ (- y x) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e+77) || !(t <= 1.05e-124)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.5d+77)) .or. (.not. (t <= 1.05d-124))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + ((y - x) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e+77) || !(t <= 1.05e-124)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.5e+77) or not (t <= 1.05e-124):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.5e+77) || !(t <= 1.05e-124))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.5e+77) || ~((t <= 1.05e-124)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.5e+77], N[Not[LessEqual[t, 1.05e-124]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.50000000000000024e77 or 1.05e-124 < t

   1. Initial program 46.0%

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

      1. clear-num 45.9%

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

      2. associate-/r/ 45.9%

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

   4. Applied egg-rr 45.9%

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

      1. *-commutative 45.9%

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

      2. associate-*l* 76.7%

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

      3. div-inv 76.9%

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

      4. clear-num 76.8%

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

      5. un-div-inv 76.9%

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

   6. Applied egg-rr 76.9%

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

   7. Taylor expanded in x around 0 45.5%

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

      1. associate-/l* 71.8%

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

   9. Simplified 71.8%

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

   if -4.50000000000000024e77 < t < 1.05e-124

   1. Initial program 86.0%

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

      1. clear-num 85.9%

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

      2. associate-/r/ 85.9%

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

   4. Applied egg-rr 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*l* 97.5%

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

      3. div-inv 97.5%

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

      4. clear-num 97.5%

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

      5. un-div-inv 97.5%

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

   6. Applied egg-rr 97.5%

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

   7. Taylor expanded in t around 0 75.9%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+77} \lor \neg \left(t \leq 1.05 \cdot 10^{-124}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-99} \lor \neg \left(t \leq 10^{-124}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.4e-99) (not (<= t 1e-124)))
   (* y (/ (- z t) (- a t)))
   (+ x (* z (/ (- y x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.4e-99) || !(t <= 1e-124)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - 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 ((t <= (-5.4d-99)) .or. (.not. (t <= 1d-124))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z * ((y - 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 ((t <= -5.4e-99) || !(t <= 1e-124)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.4e-99) or not (t <= 1e-124):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z * ((y - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.4e-99) || !(t <= 1e-124))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.4e-99) || ~((t <= 1e-124)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z * ((y - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.4e-99], N[Not[LessEqual[t, 1e-124]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.4e-99 or 9.99999999999999933e-125 < t

   1. Initial program 54.6%

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

      1. clear-num 54.5%

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

      2. associate-/r/ 54.5%

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

   4. Applied egg-rr 54.5%

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

      1. *-commutative 54.5%

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

      2. associate-*l* 81.0%

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

      3. div-inv 81.1%

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

      4. clear-num 81.1%

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

      5. un-div-inv 81.1%

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

   6. Applied egg-rr 81.1%

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

   7. Taylor expanded in x around 0 45.9%

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

      1. associate-/l* 66.7%

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

   9. Simplified 66.7%

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

   if -5.4e-99 < t < 9.99999999999999933e-125

   1. Initial program 87.3%

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

   3. Taylor expanded in t around 0 78.0%

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

      1. associate-/l* 84.7%

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

   5. Simplified 84.7%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-99} \lor \neg \left(t \leq 10^{-124}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+54} \lor \neg \left(a \leq 3.25 \cdot 10^{+42}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.8e+54) (not (<= a 3.25e+42)))
   (+ x (* y (/ (- z t) a)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e+54) || !(a <= 3.25e+42)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = y * ((z - t) / (a - 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 ((a <= (-1.8d+54)) .or. (.not. (a <= 3.25d+42))) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = y * ((z - t) / (a - 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 ((a <= -1.8e+54) || !(a <= 3.25e+42)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.8e+54) or not (a <= 3.25e+42):
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.8e+54) || !(a <= 3.25e+42))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.8e+54) || ~((a <= 3.25e+42)))
		tmp = x + (y * ((z - t) / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.8e+54], N[Not[LessEqual[a, 3.25e+42]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8000000000000001e54 or 3.25000000000000026e42 < a

   1. Initial program 70.1%

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

   3. Taylor expanded in y around inf 70.2%

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

      1. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in a around inf 66.5%

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

      1. associate-/l* 78.6%

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

   8. Simplified 78.6%

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

   if -1.8000000000000001e54 < a < 3.25000000000000026e42

   1. Initial program 62.2%

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

      1. clear-num 62.2%

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

      2. associate-/r/ 62.2%

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

   4. Applied egg-rr 62.2%

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

      1. *-commutative 62.2%

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

      2. associate-*l* 79.4%

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

      3. div-inv 79.6%

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

      4. clear-num 79.5%

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

      5. un-div-inv 79.5%

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

   6. Applied egg-rr 79.5%

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

   7. Taylor expanded in x around 0 48.7%

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

      1. associate-/l* 64.6%

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

   9. Simplified 64.6%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+54} \lor \neg \left(a \leq 3.25 \cdot 10^{+42}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+141} \lor \neg \left(a \leq 1.65 \cdot 10^{+38}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.02e+141) (not (<= a 1.65e+38)))
   (+ x (* y (/ z a)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.02e+141) || !(a <= 1.65e+38)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * ((z - t) / (a - 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 ((a <= (-1.02d+141)) .or. (.not. (a <= 1.65d+38))) then
        tmp = x + (y * (z / a))
    else
        tmp = y * ((z - t) / (a - 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 ((a <= -1.02e+141) || !(a <= 1.65e+38)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.02e+141) or not (a <= 1.65e+38):
		tmp = x + (y * (z / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.02e+141) || !(a <= 1.65e+38))
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.02e+141) || ~((a <= 1.65e+38)))
		tmp = x + (y * (z / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.02e+141], N[Not[LessEqual[a, 1.65e+38]], $MachinePrecision]], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.02e141 or 1.65e38 < a

   1. Initial program 69.5%

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

   3. Taylor expanded in t around 0 60.1%

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

   4. Taylor expanded in y around inf 62.7%

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

      1. associate-/l* 74.2%

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

   6. Simplified 74.2%

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

   if -1.02e141 < a < 1.65e38

   1. Initial program 63.0%

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

      1. clear-num 63.0%

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

      2. associate-/r/ 63.0%

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

   4. Applied egg-rr 63.0%

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

      1. *-commutative 63.0%

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

      2. associate-*l* 80.8%

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

      3. div-inv 80.9%

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

      4. clear-num 80.9%

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

      5. un-div-inv 80.9%

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

   6. Applied egg-rr 80.9%

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

   7. Taylor expanded in x around 0 48.0%

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

      1. associate-/l* 64.0%

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

   9. Simplified 64.0%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+141} \lor \neg \left(a \leq 1.65 \cdot 10^{+38}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+51}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-124}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t - a}{t - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.9e+51)
   (- y (* (/ x t) (- a z)))
   (if (<= t 1.05e-124) (+ x (/ (- y x) (/ a z))) (/ y (/ (- t a) (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+51) {
		tmp = y - ((x / t) * (a - z));
	} else if (t <= 1.05e-124) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = y / ((t - a) / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.9d+51)) then
        tmp = y - ((x / t) * (a - z))
    else if (t <= 1.05d-124) then
        tmp = x + ((y - x) / (a / z))
    else
        tmp = y / ((t - a) / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+51) {
		tmp = y - ((x / t) * (a - z));
	} else if (t <= 1.05e-124) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = y / ((t - a) / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.9e+51:
		tmp = y - ((x / t) * (a - z))
	elif t <= 1.05e-124:
		tmp = x + ((y - x) / (a / z))
	else:
		tmp = y / ((t - a) / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.9e+51)
		tmp = Float64(y - Float64(Float64(x / t) * Float64(a - z)));
	elseif (t <= 1.05e-124)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	else
		tmp = Float64(y / Float64(Float64(t - a) / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.9e+51)
		tmp = y - ((x / t) * (a - z));
	elseif (t <= 1.05e-124)
		tmp = x + ((y - x) / (a / z));
	else
		tmp = y / ((t - a) / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.9e+51], N[(y - N[(N[(x / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-124], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(t - a), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8999999999999999e51

   1. Initial program 30.9%

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

   3. Taylor expanded in t around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. distribute-lft-out-- 69.2%

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

      3. div-sub 69.2%

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

      4. mul-1-neg 69.2%

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

      5. unsub-neg 69.2%

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

      6. div-sub 69.2%

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

      7. associate-/l* 73.2%

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

      8. associate-/l* 77.5%

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

      9. distribute-rgt-out-- 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in y around 0 75.7%

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

      1. neg-mul-1 75.7%

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

      2. distribute-neg-frac 75.7%

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

   8. Simplified 75.7%

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

   if -1.8999999999999999e51 < t < 1.05e-124

   1. Initial program 86.2%

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

      1. clear-num 86.1%

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

      2. associate-/r/ 86.1%

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

   4. Applied egg-rr 86.1%

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

      1. *-commutative 86.1%

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

      2. associate-*l* 98.2%

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

      3. div-inv 98.2%

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

      4. clear-num 98.2%

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

      5. un-div-inv 98.2%

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

   6. Applied egg-rr 98.2%

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

   7. Taylor expanded in t around 0 78.0%

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

   if 1.05e-124 < t

   1. Initial program 55.8%

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

      1. clear-num 55.7%

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

      2. associate-/r/ 55.7%

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

   4. Applied egg-rr 55.7%

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

      1. *-commutative 55.7%

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

      2. associate-*l* 81.7%

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

      3. div-inv 81.8%

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

      4. clear-num 81.8%

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

      5. un-div-inv 81.8%

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

   6. Applied egg-rr 81.8%

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

   7. Taylor expanded in x around 0 46.8%

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

      1. associate-/l* 68.6%

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

   9. Simplified 68.6%

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

       1. clear-num 68.6%

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

       2. un-div-inv 68.6%

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

   11. Applied egg-rr 68.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+51}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-124}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t - a}{t - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+51}:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t - a}{t - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.9e+51)
   (- y (* x (/ (- a z) t)))
   (if (<= t 8e-125) (+ x (/ (- y x) (/ a z))) (/ y (/ (- t a) (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+51) {
		tmp = y - (x * ((a - z) / t));
	} else if (t <= 8e-125) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = y / ((t - a) / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.9d+51)) then
        tmp = y - (x * ((a - z) / t))
    else if (t <= 8d-125) then
        tmp = x + ((y - x) / (a / z))
    else
        tmp = y / ((t - a) / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+51) {
		tmp = y - (x * ((a - z) / t));
	} else if (t <= 8e-125) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = y / ((t - a) / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.9e+51:
		tmp = y - (x * ((a - z) / t))
	elif t <= 8e-125:
		tmp = x + ((y - x) / (a / z))
	else:
		tmp = y / ((t - a) / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.9e+51)
		tmp = Float64(y - Float64(x * Float64(Float64(a - z) / t)));
	elseif (t <= 8e-125)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	else
		tmp = Float64(y / Float64(Float64(t - a) / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.9e+51)
		tmp = y - (x * ((a - z) / t));
	elseif (t <= 8e-125)
		tmp = x + ((y - x) / (a / z));
	else
		tmp = y / ((t - a) / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.9e+51], N[(y - N[(x * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-125], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(t - a), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8999999999999999e51

   1. Initial program 30.9%

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

   3. Taylor expanded in t around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. distribute-lft-out-- 69.2%

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

      3. div-sub 69.2%

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

      4. mul-1-neg 69.2%

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

      5. unsub-neg 69.2%

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

      6. div-sub 69.2%

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

      7. associate-/l* 73.2%

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

      8. associate-/l* 77.5%

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

      9. distribute-rgt-out-- 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in y around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. associate-/l* 73.4%

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

      3. distribute-lft-neg-in 73.4%

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

   8. Simplified 73.4%

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

   if -1.8999999999999999e51 < t < 8.0000000000000001e-125

   1. Initial program 86.2%

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

      1. clear-num 86.1%

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

      2. associate-/r/ 86.1%

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

   4. Applied egg-rr 86.1%

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

      1. *-commutative 86.1%

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

      2. associate-*l* 98.2%

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

      3. div-inv 98.2%

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

      4. clear-num 98.2%

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

      5. un-div-inv 98.2%

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

   6. Applied egg-rr 98.2%

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

   7. Taylor expanded in t around 0 78.0%

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

   if 8.0000000000000001e-125 < t

   1. Initial program 55.8%

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

      1. clear-num 55.7%

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

      2. associate-/r/ 55.7%

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

   4. Applied egg-rr 55.7%

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

      1. *-commutative 55.7%

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

      2. associate-*l* 81.7%

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

      3. div-inv 81.8%

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

      4. clear-num 81.8%

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

      5. un-div-inv 81.8%

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

   6. Applied egg-rr 81.8%

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

   7. Taylor expanded in x around 0 46.8%

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

      1. associate-/l* 68.6%

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

   9. Simplified 68.6%

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

       1. clear-num 68.6%

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

       2. un-div-inv 68.6%

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

   11. Applied egg-rr 68.6%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+51}:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t - a}{t - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+51} \lor \neg \left(a \leq 9.8 \cdot 10^{+35}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.5e+51) (not (<= a 9.8e+35)))
   (+ x (* y (/ z a)))
   (* y (/ (- t z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.5e+51) || !(a <= 9.8e+35)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * ((t - z) / 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 ((a <= (-5.5d+51)) .or. (.not. (a <= 9.8d+35))) then
        tmp = x + (y * (z / a))
    else
        tmp = y * ((t - z) / 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 ((a <= -5.5e+51) || !(a <= 9.8e+35)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * ((t - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.5e+51) or not (a <= 9.8e+35):
		tmp = x + (y * (z / a))
	else:
		tmp = y * ((t - z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.5e+51) || !(a <= 9.8e+35))
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y * Float64(Float64(t - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.5e+51) || ~((a <= 9.8e+35)))
		tmp = x + (y * (z / a));
	else
		tmp = y * ((t - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.5e+51], N[Not[LessEqual[a, 9.8e+35]], $MachinePrecision]], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5e51 or 9.8000000000000005e35 < a

   1. Initial program 70.1%

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

   3. Taylor expanded in t around 0 59.7%

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

   4. Taylor expanded in y around inf 60.2%

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

      1. associate-/l* 70.5%

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

   6. Simplified 70.5%

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

   if -5.5e51 < a < 9.8000000000000005e35

   1. Initial program 62.2%

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

      1. clear-num 62.2%

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

      2. associate-/r/ 62.2%

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

   4. Applied egg-rr 62.2%

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

      1. *-commutative 62.2%

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

      2. associate-*l* 79.4%

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

      3. div-inv 79.6%

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

      4. clear-num 79.5%

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

      5. un-div-inv 79.5%

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

   6. Applied egg-rr 79.5%

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

   7. Taylor expanded in x around 0 48.7%

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

      1. associate-/l* 64.6%

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

   9. Simplified 64.6%

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

   10. Taylor expanded in a around 0 56.7%

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

       1. mul-1-neg 56.7%

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

   12. Simplified 56.7%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+51} \lor \neg \left(a \leq 9.8 \cdot 10^{+35}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 56.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+54} \lor \neg \left(a \leq 3.45 \cdot 10^{+34}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1e+54) (not (<= a 3.45e+34)))
   (+ x (* y (/ z a)))
   (* y (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1e+54) || !(a <= 3.45e+34)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * (1.0 - (z / 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 ((a <= (-1d+54)) .or. (.not. (a <= 3.45d+34))) then
        tmp = x + (y * (z / a))
    else
        tmp = y * (1.0d0 - (z / 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 ((a <= -1e+54) || !(a <= 3.45e+34)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1e+54) or not (a <= 3.45e+34):
		tmp = x + (y * (z / a))
	else:
		tmp = y * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1e+54) || !(a <= 3.45e+34))
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1e+54) || ~((a <= 3.45e+34)))
		tmp = x + (y * (z / a));
	else
		tmp = y * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1e+54], N[Not[LessEqual[a, 3.45e+34]], $MachinePrecision]], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0000000000000001e54 or 3.45000000000000019e34 < a

   1. Initial program 70.1%

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

   3. Taylor expanded in t around 0 59.7%

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

   4. Taylor expanded in y around inf 60.2%

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

      1. associate-/l* 70.5%

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

   6. Simplified 70.5%

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

   if -1.0000000000000001e54 < a < 3.45000000000000019e34

   1. Initial program 62.2%

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

      1. clear-num 62.2%

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

      2. associate-/r/ 62.2%

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

   4. Applied egg-rr 62.2%

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

      1. *-commutative 62.2%

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

      2. associate-*l* 79.4%

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

      3. div-inv 79.6%

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

      4. clear-num 79.5%

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

      5. un-div-inv 79.5%

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

   6. Applied egg-rr 79.5%

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

   7. Taylor expanded in x around 0 48.7%

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

      1. associate-/l* 64.6%

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

   9. Simplified 64.6%

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

   10. Taylor expanded in a around 0 56.7%

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

       1. mul-1-neg 56.7%

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

       2. div-sub 56.7%

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

       3. sub-neg 56.7%

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

       4. *-inverses 56.7%

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

       5. metadata-eval 56.7%

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

   12. Simplified 56.7%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+54} \lor \neg \left(a \leq 3.45 \cdot 10^{+34}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 54.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+65}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+104}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.8e+65) y (if (<= t 3.6e+104) (+ x (* y (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e+65) {
		tmp = y;
	} else if (t <= 3.6e+104) {
		tmp = x + (y * (z / a));
	} else {
		tmp = 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 (t <= (-6.8d+65)) then
        tmp = y
    else if (t <= 3.6d+104) then
        tmp = x + (y * (z / a))
    else
        tmp = 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 (t <= -6.8e+65) {
		tmp = y;
	} else if (t <= 3.6e+104) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.8e+65:
		tmp = y
	elif t <= 3.6e+104:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.8e+65)
		tmp = y;
	elseif (t <= 3.6e+104)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.8e+65)
		tmp = y;
	elseif (t <= 3.6e+104)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.8e+65], y, If[LessEqual[t, 3.6e+104], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -6.7999999999999999e65 or 3.60000000000000001e104 < t

   1. Initial program 27.5%

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

   3. Taylor expanded in t around inf 64.2%

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

   if -6.7999999999999999e65 < t < 3.60000000000000001e104

   1. Initial program 83.8%

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

   3. Taylor expanded in t around 0 59.2%

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

   4. Taylor expanded in y around inf 49.9%

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

      1. associate-/l* 56.0%

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

   6. Simplified 56.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 48.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{+68}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.4e+68) y (if (<= t 4.5e+104) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.4e+68) {
		tmp = y;
	} else if (t <= 4.5e+104) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = 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 (t <= (-8.4d+68)) then
        tmp = y
    else if (t <= 4.5d+104) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = 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 (t <= -8.4e+68) {
		tmp = y;
	} else if (t <= 4.5e+104) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.4e+68:
		tmp = y
	elif t <= 4.5e+104:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.4e+68)
		tmp = y;
	elseif (t <= 4.5e+104)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.4e+68)
		tmp = y;
	elseif (t <= 4.5e+104)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.4e+68], y, If[LessEqual[t, 4.5e+104], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -8.40000000000000003e68 or 4.4999999999999998e104 < t

   1. Initial program 26.6%

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

   3. Taylor expanded in t around inf 65.0%

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

   if -8.40000000000000003e68 < t < 4.4999999999999998e104

   1. Initial program 83.9%

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

   3. Taylor expanded in t around 0 58.9%

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

   4. Taylor expanded in x around inf 47.0%

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

      1. mul-1-neg 47.0%

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

      2. unsub-neg 47.0%

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

   6. Simplified 47.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 38.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+148} \lor \neg \left(z \leq 2 \cdot 10^{-36}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.06e+148) (not (<= z 2e-36))) (* y (/ z a)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.06e+148) || !(z <= 2e-36)) {
		tmp = y * (z / a);
	} else {
		tmp = y + 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 <= (-1.06d+148)) .or. (.not. (z <= 2d-36))) then
        tmp = y * (z / a)
    else
        tmp = y + 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 <= -1.06e+148) || !(z <= 2e-36)) {
		tmp = y * (z / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.06e+148) or not (z <= 2e-36):
		tmp = y * (z / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.06e+148) || !(z <= 2e-36))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.06e+148) || ~((z <= 2e-36)))
		tmp = y * (z / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.06e+148], N[Not[LessEqual[z, 2e-36]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.06e148 or 1.9999999999999999e-36 < z

   1. Initial program 66.4%

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

      1. clear-num 66.3%

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

      2. associate-/r/ 66.3%

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

   4. Applied egg-rr 66.3%

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

      1. *-commutative 66.3%

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

      2. associate-*l* 93.6%

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

      3. div-inv 93.7%

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

      4. clear-num 93.6%

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

      5. un-div-inv 93.7%

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

   6. Applied egg-rr 93.7%

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

   7. Taylor expanded in x around 0 41.6%

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

      1. associate-/l* 59.6%

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

   9. Simplified 59.6%

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

   10. Taylor expanded in t around 0 30.9%

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

       1. associate-/l* 41.0%

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

   12. Simplified 41.0%

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

   if -1.06e148 < z < 1.9999999999999999e-36

   1. Initial program 64.7%

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

   3. Taylor expanded in y around inf 57.7%

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

      1. *-commutative 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in t around inf 47.6%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+148} \lor \neg \left(z \leq 2 \cdot 10^{-36}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 39.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 310000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.7e+53) x (if (<= a 310000.0) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e+53) {
		tmp = x;
	} else if (a <= 310000.0) {
		tmp = y;
	} 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 <= (-1.7d+53)) then
        tmp = x
    else if (a <= 310000.0d0) then
        tmp = y
    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 <= -1.7e+53) {
		tmp = x;
	} else if (a <= 310000.0) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.7e+53:
		tmp = x
	elif a <= 310000.0:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.7e+53)
		tmp = x;
	elseif (a <= 310000.0)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.7e+53)
		tmp = x;
	elseif (a <= 310000.0)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.7e+53], x, If[LessEqual[a, 310000.0], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.69999999999999999e53 or 3.1e5 < a

   1. Initial program 72.7%

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

   3. Taylor expanded in a around inf 41.7%

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

   if -1.69999999999999999e53 < a < 3.1e5

   1. Initial program 59.6%

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

   3. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 25.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

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
end function

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 65.4%

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

3. Taylor expanded in a around inf 23.1%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024106 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))