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

Percentage Accurate: 68.9% → 89.5%

Time: 14.6s

Alternatives: 19

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: 68.9% 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: 89.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+93} \lor \neg \left(t \leq 2.2 \cdot 10^{+145}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.4e+93) (not (<= t 2.2e+145)))
   (+ y (* (/ (- y x) t) (- a z)))
   (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 <= -3.4e+93) || !(t <= 2.2e+145)) {
		tmp = y + (((y - x) / t) * (a - z));
	} 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 <= -3.4e+93) || !(t <= 2.2e+145))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	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, -3.4e+93], N[Not[LessEqual[t, 2.2e+145]], $MachinePrecision]], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $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 < -3.4e93 or 2.20000000000000009e145 < t

   1. Initial program 37.5%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. associate--l+ 69.0%

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

      2. distribute-lft-out-- 69.0%

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

      3. div-sub 69.0%

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

      4. mul-1-neg 69.0%

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

      5. unsub-neg 69.0%

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

      6. div-sub 69.0%

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

      7. associate-/l* 82.0%

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

      8. associate-/l* 91.4%

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

      9. distribute-rgt-out-- 91.4%

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

   5. Simplified 91.4%

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

   if -3.4e93 < t < 2.20000000000000009e145

   1. Initial program 85.6%

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

      1. +-commutative 85.6%

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

      2. associate-/l* 94.2%

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

      3. fma-define 94.2%

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

   3. Simplified 94.2%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+93} \lor \neg \left(t \leq 2.2 \cdot 10^{+145}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-164}:\\ \;\;\;\;x + x \cdot \left(\frac{z - t}{a - t} \cdot \left(-1 + \frac{y}{x}\right)\right)\\ \mathbf{elif}\;t \leq 0.26:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \left(\left(\left(\frac{z}{a - t} + \frac{x}{y}\right) + x \cdot \frac{t - z}{y \cdot \left(a - t\right)}\right) + \frac{t}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (/ (- y x) t) (- a z)))))
   (if (<= t -2.2e+92)
     t_1
     (if (<= t -2.7e-164)
       (+ x (* x (* (/ (- z t) (- a t)) (+ -1.0 (/ y x)))))
       (if (<= t 0.26)
         (+ x (/ (* (- y x) (- z t)) (- a t)))
         (if (<= t 1.02e+145)
           (*
            y
            (+
             (+ (+ (/ z (- a t)) (/ x y)) (* x (/ (- t z) (* y (- a t)))))
             (/ t (- t a))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) / t) * (a - z));
	double tmp;
	if (t <= -2.2e+92) {
		tmp = t_1;
	} else if (t <= -2.7e-164) {
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))));
	} else if (t <= 0.26) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else if (t <= 1.02e+145) {
		tmp = y * ((((z / (a - t)) + (x / y)) + (x * ((t - z) / (y * (a - t))))) + (t / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (((y - x) / t) * (a - z))
    if (t <= (-2.2d+92)) then
        tmp = t_1
    else if (t <= (-2.7d-164)) then
        tmp = x + (x * (((z - t) / (a - t)) * ((-1.0d0) + (y / x))))
    else if (t <= 0.26d0) then
        tmp = x + (((y - x) * (z - t)) / (a - t))
    else if (t <= 1.02d+145) then
        tmp = y * ((((z / (a - t)) + (x / y)) + (x * ((t - z) / (y * (a - t))))) + (t / (t - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) / t) * (a - z));
	double tmp;
	if (t <= -2.2e+92) {
		tmp = t_1;
	} else if (t <= -2.7e-164) {
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))));
	} else if (t <= 0.26) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else if (t <= 1.02e+145) {
		tmp = y * ((((z / (a - t)) + (x / y)) + (x * ((t - z) / (y * (a - t))))) + (t / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (((y - x) / t) * (a - z))
	tmp = 0
	if t <= -2.2e+92:
		tmp = t_1
	elif t <= -2.7e-164:
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))))
	elif t <= 0.26:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	elif t <= 1.02e+145:
		tmp = y * ((((z / (a - t)) + (x / y)) + (x * ((t - z) / (y * (a - t))))) + (t / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)))
	tmp = 0.0
	if (t <= -2.2e+92)
		tmp = t_1;
	elseif (t <= -2.7e-164)
		tmp = Float64(x + Float64(x * Float64(Float64(Float64(z - t) / Float64(a - t)) * Float64(-1.0 + Float64(y / x)))));
	elseif (t <= 0.26)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	elseif (t <= 1.02e+145)
		tmp = Float64(y * Float64(Float64(Float64(Float64(z / Float64(a - t)) + Float64(x / y)) + Float64(x * Float64(Float64(t - z) / Float64(y * Float64(a - t))))) + Float64(t / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (((y - x) / t) * (a - z));
	tmp = 0.0;
	if (t <= -2.2e+92)
		tmp = t_1;
	elseif (t <= -2.7e-164)
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))));
	elseif (t <= 0.26)
		tmp = x + (((y - x) * (z - t)) / (a - t));
	elseif (t <= 1.02e+145)
		tmp = y * ((((z / (a - t)) + (x / y)) + (x * ((t - z) / (y * (a - t))))) + (t / (t - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+92], t$95$1, If[LessEqual[t, -2.7e-164], N[(x + N[(x * N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(-1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.26], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+145], N[(y * N[(N[(N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t - z), $MachinePrecision] / N[(y * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.19999999999999992e92 or 1.02e145 < t

   1. Initial program 37.5%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. associate--l+ 69.0%

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

      2. distribute-lft-out-- 69.0%

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

      3. div-sub 69.0%

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

      4. mul-1-neg 69.0%

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

      5. unsub-neg 69.0%

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

      6. div-sub 69.0%

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

      7. associate-/l* 82.0%

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

      8. associate-/l* 91.4%

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

      9. distribute-rgt-out-- 91.4%

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

   5. Simplified 91.4%

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

   if -2.19999999999999992e92 < t < -2.7000000000000001e-164

   1. Initial program 81.1%

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

   3. Taylor expanded in x around inf 77.5%

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

      1. times-frac 88.6%

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

      2. distribute-rgt-out 88.6%

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

   5. Simplified 88.6%

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

   if -2.7000000000000001e-164 < t < 0.26000000000000001

   1. Initial program 95.1%

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

   if 0.26000000000000001 < t < 1.02e145

   1. Initial program 63.4%

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

      1. clear-num 63.5%

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

      2. inv-pow 63.5%

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

      3. *-commutative 63.5%

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

      4. associate-/r* 82.9%

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

   4. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

      2. associate-/l/ 63.5%

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

      3. *-commutative 63.5%

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

   6. Simplified 63.5%

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

   7. Taylor expanded in y around inf 80.7%

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

      1. +-commutative 80.7%

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

      2. mul-1-neg 80.7%

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

      3. unsub-neg 80.7%

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

      4. +-commutative 80.7%

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

      5. associate-/l* 87.3%

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

   9. Simplified 87.3%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+92}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-164}:\\ \;\;\;\;x + x \cdot \left(\frac{z - t}{a - t} \cdot \left(-1 + \frac{y}{x}\right)\right)\\ \mathbf{elif}\;t \leq 0.26:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \left(\left(\left(\frac{z}{a - t} + \frac{x}{y}\right) + x \cdot \frac{t - z}{y \cdot \left(a - t\right)}\right) + \frac{t}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 39.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{-a}\\ t_2 := y \cdot \frac{z}{a}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+96}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+59}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z (- a)))) (t_2 (* y (/ z a))))
   (if (<= z -3.7e+178)
     t_2
     (if (<= z -4.5e+152)
       t_1
       (if (<= z -5e+124)
         t_2
         (if (<= z -1.95e+96)
           (+ y x)
           (if (<= z -2.85e+76) t_1 (if (<= z 5.6e+59) (+ y x) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / -a);
	double t_2 = y * (z / a);
	double tmp;
	if (z <= -3.7e+178) {
		tmp = t_2;
	} else if (z <= -4.5e+152) {
		tmp = t_1;
	} else if (z <= -5e+124) {
		tmp = t_2;
	} else if (z <= -1.95e+96) {
		tmp = y + x;
	} else if (z <= -2.85e+76) {
		tmp = t_1;
	} else if (z <= 5.6e+59) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z / -a)
    t_2 = y * (z / a)
    if (z <= (-3.7d+178)) then
        tmp = t_2
    else if (z <= (-4.5d+152)) then
        tmp = t_1
    else if (z <= (-5d+124)) then
        tmp = t_2
    else if (z <= (-1.95d+96)) then
        tmp = y + x
    else if (z <= (-2.85d+76)) then
        tmp = t_1
    else if (z <= 5.6d+59) then
        tmp = y + x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / -a);
	double t_2 = y * (z / a);
	double tmp;
	if (z <= -3.7e+178) {
		tmp = t_2;
	} else if (z <= -4.5e+152) {
		tmp = t_1;
	} else if (z <= -5e+124) {
		tmp = t_2;
	} else if (z <= -1.95e+96) {
		tmp = y + x;
	} else if (z <= -2.85e+76) {
		tmp = t_1;
	} else if (z <= 5.6e+59) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / -a)
	t_2 = y * (z / a)
	tmp = 0
	if z <= -3.7e+178:
		tmp = t_2
	elif z <= -4.5e+152:
		tmp = t_1
	elif z <= -5e+124:
		tmp = t_2
	elif z <= -1.95e+96:
		tmp = y + x
	elif z <= -2.85e+76:
		tmp = t_1
	elif z <= 5.6e+59:
		tmp = y + x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / Float64(-a)))
	t_2 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (z <= -3.7e+178)
		tmp = t_2;
	elseif (z <= -4.5e+152)
		tmp = t_1;
	elseif (z <= -5e+124)
		tmp = t_2;
	elseif (z <= -1.95e+96)
		tmp = Float64(y + x);
	elseif (z <= -2.85e+76)
		tmp = t_1;
	elseif (z <= 5.6e+59)
		tmp = Float64(y + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / -a);
	t_2 = y * (z / a);
	tmp = 0.0;
	if (z <= -3.7e+178)
		tmp = t_2;
	elseif (z <= -4.5e+152)
		tmp = t_1;
	elseif (z <= -5e+124)
		tmp = t_2;
	elseif (z <= -1.95e+96)
		tmp = y + x;
	elseif (z <= -2.85e+76)
		tmp = t_1;
	elseif (z <= 5.6e+59)
		tmp = y + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e+178], t$95$2, If[LessEqual[z, -4.5e+152], t$95$1, If[LessEqual[z, -5e+124], t$95$2, If[LessEqual[z, -1.95e+96], N[(y + x), $MachinePrecision], If[LessEqual[z, -2.85e+76], t$95$1, If[LessEqual[z, 5.6e+59], N[(y + x), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7000000000000002e178 or -4.5000000000000001e152 < z < -4.9999999999999996e124 or 5.5999999999999996e59 < z

   1. Initial program 71.5%

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

   3. Taylor expanded in t around 0 53.9%

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

   4. Taylor expanded in y around inf 43.8%

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

   5. Taylor expanded in x around 0 34.5%

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

      1. associate-*r/ 42.9%

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

   7. Simplified 42.9%

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

   if -3.7000000000000002e178 < z < -4.5000000000000001e152 or -1.95e96 < z < -2.85000000000000002e76

   1. Initial program 83.1%

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

   3. Taylor expanded in t around 0 70.5%

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

   4. Taylor expanded in y around 0 54.2%

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

      1. mul-1-neg 54.2%

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

      2. unsub-neg 54.2%

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

      3. associate-/l* 64.9%

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

   6. Simplified 64.9%

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

   7. Taylor expanded in z around inf 51.7%

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

      1. associate-*r/ 62.3%

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

      2. neg-mul-1 62.3%

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

      3. distribute-rgt-neg-in 62.3%

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

      4. distribute-neg-frac 62.3%

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

   9. Simplified 62.3%

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

   if -4.9999999999999996e124 < z < -1.95e96 or -2.85000000000000002e76 < z < 5.5999999999999996e59

   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 z around 0 60.3%

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

      1. mul-1-neg 60.3%

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

      2. unsub-neg 60.3%

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

      3. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in y around inf 64.8%

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

   7. Taylor expanded in t around inf 48.5%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   8. Step-by-step derivation

      1. mul-1-neg 48.5%

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

   9. Simplified 48.5%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+124}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+96}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+59}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+89}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+68} \lor \neg \left(t \leq -1.35 \cdot 10^{+33}\right) \land t \leq 1.9 \cdot 10^{+45}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e+89)
   (+ y (/ (* z (- x y)) t))
   (if (or (<= t -2.2e+68) (and (not (<= t -1.35e+33)) (<= t 1.9e+45)))
     (+ x (* z (/ (- y x) a)))
     (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+89) {
		tmp = y + ((z * (x - y)) / t);
	} else if ((t <= -2.2e+68) || (!(t <= -1.35e+33) && (t <= 1.9e+45))) {
		tmp = x + (z * ((y - x) / 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 (t <= (-6.2d+89)) then
        tmp = y + ((z * (x - y)) / t)
    else if ((t <= (-2.2d+68)) .or. (.not. (t <= (-1.35d+33))) .and. (t <= 1.9d+45)) then
        tmp = x + (z * ((y - x) / 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 (t <= -6.2e+89) {
		tmp = y + ((z * (x - y)) / t);
	} else if ((t <= -2.2e+68) || (!(t <= -1.35e+33) && (t <= 1.9e+45))) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.2e+89:
		tmp = y + ((z * (x - y)) / t)
	elif (t <= -2.2e+68) or (not (t <= -1.35e+33) and (t <= 1.9e+45)):
		tmp = x + (z * ((y - x) / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e+89)
		tmp = Float64(y + Float64(Float64(z * Float64(x - y)) / t));
	elseif ((t <= -2.2e+68) || (!(t <= -1.35e+33) && (t <= 1.9e+45)))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / 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 (t <= -6.2e+89)
		tmp = y + ((z * (x - y)) / t);
	elseif ((t <= -2.2e+68) || (~((t <= -1.35e+33)) && (t <= 1.9e+45)))
		tmp = x + (z * ((y - x) / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e+89], N[(y + N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.2e+68], And[N[Not[LessEqual[t, -1.35e+33]], $MachinePrecision], LessEqual[t, 1.9e+45]]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.2e89

   1. Initial program 40.7%

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

   3. Taylor expanded in t around inf 68.3%

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

      1. associate--l+ 68.3%

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

      2. distribute-lft-out-- 68.3%

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

      3. div-sub 68.3%

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

      4. mul-1-neg 68.3%

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

      5. unsub-neg 68.3%

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

      6. div-sub 68.3%

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

      7. associate-/l* 79.5%

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

      8. associate-/l* 86.4%

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

      9. distribute-rgt-out-- 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in z around inf 60.5%

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

   if -6.2e89 < t < -2.19999999999999987e68 or -1.34999999999999996e33 < t < 1.9000000000000001e45

   1. Initial program 87.6%

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

   3. Taylor expanded in t around 0 72.0%

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

      1. associate-/l* 75.7%

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

   5. Simplified 75.7%

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

   if -2.19999999999999987e68 < t < -1.34999999999999996e33 or 1.9000000000000001e45 < t

   1. Initial program 55.3%

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

   3. Taylor expanded in x around 0 63.3%

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

      1. +-commutative 63.3%

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

      2. +-commutative 63.3%

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

      3. distribute-lft-in 63.4%

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

      4. mul-1-neg 63.4%

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

      5. distribute-rgt-neg-in 63.4%

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

      6. associate-/l* 60.2%

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

      7. mul-1-neg 60.2%

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

      8. *-rgt-identity 60.2%

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

      9. associate-+l+ 55.3%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in y around inf 76.9%

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

      1. div-sub 76.9%

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

   8. Simplified 76.9%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+89}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+68} \lor \neg \left(t \leq -1.35 \cdot 10^{+33}\right) \land t \leq 1.9 \cdot 10^{+45}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+74}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* y (/ z a)))))
   (if (<= a -2.6e+89)
     t_2
     (if (<= a 6.3e-59)
       t_1
       (if (<= a 5.6e+74)
         (- x (* x (/ z a)))
         (if (<= a 3.25e+128) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (a <= -2.6e+89) {
		tmp = t_2;
	} else if (a <= 6.3e-59) {
		tmp = t_1;
	} else if (a <= 5.6e+74) {
		tmp = x - (x * (z / a));
	} else if (a <= 3.25e+128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (y * (z / a))
    if (a <= (-2.6d+89)) then
        tmp = t_2
    else if (a <= 6.3d-59) then
        tmp = t_1
    else if (a <= 5.6d+74) then
        tmp = x - (x * (z / a))
    else if (a <= 3.25d+128) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (a <= -2.6e+89) {
		tmp = t_2;
	} else if (a <= 6.3e-59) {
		tmp = t_1;
	} else if (a <= 5.6e+74) {
		tmp = x - (x * (z / a));
	} else if (a <= 3.25e+128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y * (z / a))
	tmp = 0
	if a <= -2.6e+89:
		tmp = t_2
	elif a <= 6.3e-59:
		tmp = t_1
	elif a <= 5.6e+74:
		tmp = x - (x * (z / a))
	elif a <= 3.25e+128:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -2.6e+89)
		tmp = t_2;
	elseif (a <= 6.3e-59)
		tmp = t_1;
	elseif (a <= 5.6e+74)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (a <= 3.25e+128)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (a <= -2.6e+89)
		tmp = t_2;
	elseif (a <= 6.3e-59)
		tmp = t_1;
	elseif (a <= 5.6e+74)
		tmp = x - (x * (z / a));
	elseif (a <= 3.25e+128)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+89], t$95$2, If[LessEqual[a, 6.3e-59], t$95$1, If[LessEqual[a, 5.6e+74], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.25e+128], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.6000000000000001e89 or 3.25000000000000015e128 < a

   1. Initial program 74.9%

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

   3. Taylor expanded in t around 0 69.3%

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

   4. Taylor expanded in y around inf 69.5%

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

      1. associate-/l* 77.2%

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

   6. Simplified 77.2%

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

   if -2.6000000000000001e89 < a < 6.3000000000000003e-59 or 5.60000000000000003e74 < a < 3.25000000000000015e128

   1. Initial program 70.4%

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

   3. Taylor expanded in x around 0 72.6%

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

      1. +-commutative 72.6%

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

      2. +-commutative 72.6%

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

      3. distribute-lft-in 72.7%

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

      4. mul-1-neg 72.7%

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

      5. distribute-rgt-neg-in 72.7%

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

      6. associate-/l* 73.1%

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

      7. mul-1-neg 73.1%

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

      8. *-rgt-identity 73.1%

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

      9. associate-+l+ 68.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in y around inf 68.0%

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

      1. div-sub 68.0%

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

   8. Simplified 68.0%

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

   if 6.3000000000000003e-59 < a < 5.60000000000000003e74

   1. Initial program 84.1%

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

   3. Taylor expanded in t around 0 64.0%

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

   4. Taylor expanded in y around 0 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

      3. associate-/l* 64.2%

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

   6. Simplified 64.2%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+89}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+74}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{+128}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-177}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* (/ x t) (- a z)))))
   (if (<= t -6.2e+90)
     t_1
     (if (<= t 4.5e-177)
       (+ x (* (- y x) (/ (- z t) a)))
       (if (<= t 1.8e+45)
         (+ x (/ (* (- y x) z) (- a t)))
         (if (<= t 2.5e+158) (* 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 <= -6.2e+90) {
		tmp = t_1;
	} else if (t <= 4.5e-177) {
		tmp = x + ((y - x) * ((z - t) / a));
	} else if (t <= 1.8e+45) {
		tmp = x + (((y - x) * z) / (a - t));
	} else if (t <= 2.5e+158) {
		tmp = 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 <= (-6.2d+90)) then
        tmp = t_1
    else if (t <= 4.5d-177) then
        tmp = x + ((y - x) * ((z - t) / a))
    else if (t <= 1.8d+45) then
        tmp = x + (((y - x) * z) / (a - t))
    else if (t <= 2.5d+158) then
        tmp = 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 <= -6.2e+90) {
		tmp = t_1;
	} else if (t <= 4.5e-177) {
		tmp = x + ((y - x) * ((z - t) / a));
	} else if (t <= 1.8e+45) {
		tmp = x + (((y - x) * z) / (a - t));
	} else if (t <= 2.5e+158) {
		tmp = 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 <= -6.2e+90:
		tmp = t_1
	elif t <= 4.5e-177:
		tmp = x + ((y - x) * ((z - t) / a))
	elif t <= 1.8e+45:
		tmp = x + (((y - x) * z) / (a - t))
	elif t <= 2.5e+158:
		tmp = 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 <= -6.2e+90)
		tmp = t_1;
	elseif (t <= 4.5e-177)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / a)));
	elseif (t <= 1.8e+45)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / Float64(a - t)));
	elseif (t <= 2.5e+158)
		tmp = 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 <= -6.2e+90)
		tmp = t_1;
	elseif (t <= 4.5e-177)
		tmp = x + ((y - x) * ((z - t) / a));
	elseif (t <= 1.8e+45)
		tmp = x + (((y - x) * z) / (a - t));
	elseif (t <= 2.5e+158)
		tmp = 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, -6.2e+90], t$95$1, If[LessEqual[t, 4.5e-177], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+45], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+158], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.19999999999999977e90 or 2.4999999999999998e158 < t

   1. Initial program 37.5%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. associate--l+ 69.0%

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

      2. distribute-lft-out-- 69.0%

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

      3. div-sub 69.0%

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

      4. mul-1-neg 69.0%

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

      5. unsub-neg 69.0%

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

      6. div-sub 69.0%

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

      7. associate-/l* 81.2%

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

      8. associate-/l* 91.0%

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

      9. distribute-rgt-out-- 91.0%

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

   5. Simplified 91.0%

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

   6. Taylor expanded in y around 0 81.2%

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

      1. associate-*r/ 81.2%

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

      2. neg-mul-1 81.2%

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

   8. Simplified 81.2%

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

   if -6.19999999999999977e90 < t < 4.5000000000000003e-177

   1. Initial program 88.4%

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

   3. Taylor expanded in a around inf 77.8%

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

      1. associate-/l* 84.7%

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

   5. Simplified 84.7%

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

   if 4.5000000000000003e-177 < t < 1.8e45

   1. Initial program 86.9%

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

   3. Taylor expanded in z around inf 82.2%

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

   if 1.8e45 < t < 2.4999999999999998e158

   1. Initial program 62.9%

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

   3. Taylor expanded in x around 0 68.3%

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

      1. +-commutative 68.3%

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

      2. +-commutative 68.3%

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

      3. distribute-lft-in 68.3%

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

      4. mul-1-neg 68.3%

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

      5. distribute-rgt-neg-in 68.3%

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

      6. associate-/l* 68.2%

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

      7. mul-1-neg 68.2%

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

      8. *-rgt-identity 68.2%

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

      9. associate-+l+ 62.8%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in y around inf 76.4%

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

      1. div-sub 76.4%

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

   8. Simplified 76.4%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+90}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-177}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-160}:\\ \;\;\;\;x + x \cdot \left(\frac{z - t}{a - t} \cdot \left(-1 + \frac{y}{x}\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (/ (- y x) t) (- a z)))))
   (if (<= t -2.7e+93)
     t_1
     (if (<= t -2e-160)
       (+ x (* x (* (/ (- z t) (- a t)) (+ -1.0 (/ y x)))))
       (if (<= t 1.1e+83) (+ x (/ (* (- y x) (- z t)) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) / t) * (a - z));
	double tmp;
	if (t <= -2.7e+93) {
		tmp = t_1;
	} else if (t <= -2e-160) {
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))));
	} else if (t <= 1.1e+83) {
		tmp = x + (((y - x) * (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 + (((y - x) / t) * (a - z))
    if (t <= (-2.7d+93)) then
        tmp = t_1
    else if (t <= (-2d-160)) then
        tmp = x + (x * (((z - t) / (a - t)) * ((-1.0d0) + (y / x))))
    else if (t <= 1.1d+83) then
        tmp = x + (((y - x) * (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 + (((y - x) / t) * (a - z));
	double tmp;
	if (t <= -2.7e+93) {
		tmp = t_1;
	} else if (t <= -2e-160) {
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))));
	} else if (t <= 1.1e+83) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (((y - x) / t) * (a - z))
	tmp = 0
	if t <= -2.7e+93:
		tmp = t_1
	elif t <= -2e-160:
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))))
	elif t <= 1.1e+83:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)))
	tmp = 0.0
	if (t <= -2.7e+93)
		tmp = t_1;
	elseif (t <= -2e-160)
		tmp = Float64(x + Float64(x * Float64(Float64(Float64(z - t) / Float64(a - t)) * Float64(-1.0 + Float64(y / x)))));
	elseif (t <= 1.1e+83)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * 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 + (((y - x) / t) * (a - z));
	tmp = 0.0;
	if (t <= -2.7e+93)
		tmp = t_1;
	elseif (t <= -2e-160)
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))));
	elseif (t <= 1.1e+83)
		tmp = x + (((y - x) * (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[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+93], t$95$1, If[LessEqual[t, -2e-160], N[(x + N[(x * N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(-1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+83], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6999999999999999e93 or 1.09999999999999999e83 < t

   1. Initial program 38.2%

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

   3. Taylor expanded in t around inf 68.8%

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

      1. associate--l+ 68.8%

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

      2. distribute-lft-out-- 68.8%

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

      3. div-sub 68.8%

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

      4. mul-1-neg 68.8%

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

      5. unsub-neg 68.8%

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

      6. div-sub 68.8%

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

      7. associate-/l* 80.3%

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

      8. associate-/l* 89.8%

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

      9. distribute-rgt-out-- 89.8%

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

   5. Simplified 89.8%

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

   if -2.6999999999999999e93 < t < -2e-160

   1. Initial program 81.1%

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

   3. Taylor expanded in x around inf 77.5%

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

      1. times-frac 88.6%

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

      2. distribute-rgt-out 88.6%

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

   5. Simplified 88.6%

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

   if -2e-160 < t < 1.09999999999999999e83

   1. Initial program 91.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+93}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-160}:\\ \;\;\;\;x + x \cdot \left(\frac{z - t}{a - t} \cdot \left(-1 + \frac{y}{x}\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 44.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+123} \lor \neg \left(z \leq -6.4 \cdot 10^{+95} \lor \neg \left(z \leq -1.2 \cdot 10^{+26}\right) \land z \leq 2.2 \cdot 10^{+52}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.8e+123)
         (not (or (<= z -6.4e+95) (and (not (<= z -1.2e+26)) (<= z 2.2e+52)))))
   (* z (/ (- y x) a))
   (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.8e+123) || !((z <= -6.4e+95) || (!(z <= -1.2e+26) && (z <= 2.2e+52)))) {
		tmp = z * ((y - x) / 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 <= (-9.8d+123)) .or. (.not. (z <= (-6.4d+95)) .or. (.not. (z <= (-1.2d+26))) .and. (z <= 2.2d+52))) then
        tmp = z * ((y - x) / 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 <= -9.8e+123) || !((z <= -6.4e+95) || (!(z <= -1.2e+26) && (z <= 2.2e+52)))) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.8e+123) or not ((z <= -6.4e+95) or (not (z <= -1.2e+26) and (z <= 2.2e+52))):
		tmp = z * ((y - x) / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.8e+123) || !((z <= -6.4e+95) || (!(z <= -1.2e+26) && (z <= 2.2e+52))))
		tmp = Float64(z * Float64(Float64(y - x) / 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 <= -9.8e+123) || ~(((z <= -6.4e+95) || (~((z <= -1.2e+26)) && (z <= 2.2e+52)))))
		tmp = z * ((y - x) / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.8e+123], N[Not[Or[LessEqual[z, -6.4e+95], And[N[Not[LessEqual[z, -1.2e+26]], $MachinePrecision], LessEqual[z, 2.2e+52]]]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.79999999999999952e123 or -6.4000000000000001e95 < z < -1.20000000000000002e26 or 2.2e52 < z

   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 t around 0 55.3%

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

   4. Taylor expanded in z around inf 53.4%

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

      1. div-sub 54.3%

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

   6. Simplified 54.3%

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

   if -9.79999999999999952e123 < z < -6.4000000000000001e95 or -1.20000000000000002e26 < z < 2.2e52

   1. Initial program 73.3%

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

   3. Taylor expanded in z around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. unsub-neg 63.9%

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

      3. associate-/l* 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in y around inf 67.4%

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

   7. Taylor expanded in t around inf 49.8%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   8. Step-by-step derivation

      1. mul-1-neg 49.8%

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

   9. Simplified 49.8%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+123} \lor \neg \left(z \leq -6.4 \cdot 10^{+95} \lor \neg \left(z \leq -1.2 \cdot 10^{+26}\right) \land z \leq 2.2 \cdot 10^{+52}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;z \leq -1.96 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{+95}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+55}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (<= z -1.96e+124)
     t_1
     (if (<= z -1.32e+95)
       (+ y x)
       (if (<= z -8.4e+68)
         (* x (/ z (- a)))
         (if (<= z 2.5e+55) (+ y x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (z <= -1.96e+124) {
		tmp = t_1;
	} else if (z <= -1.32e+95) {
		tmp = y + x;
	} else if (z <= -8.4e+68) {
		tmp = x * (z / -a);
	} else if (z <= 2.5e+55) {
		tmp = 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 = y * (z / (a - t))
    if (z <= (-1.96d+124)) then
        tmp = t_1
    else if (z <= (-1.32d+95)) then
        tmp = y + x
    else if (z <= (-8.4d+68)) then
        tmp = x * (z / -a)
    else if (z <= 2.5d+55) then
        tmp = 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 = y * (z / (a - t));
	double tmp;
	if (z <= -1.96e+124) {
		tmp = t_1;
	} else if (z <= -1.32e+95) {
		tmp = y + x;
	} else if (z <= -8.4e+68) {
		tmp = x * (z / -a);
	} else if (z <= 2.5e+55) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if z <= -1.96e+124:
		tmp = t_1
	elif z <= -1.32e+95:
		tmp = y + x
	elif z <= -8.4e+68:
		tmp = x * (z / -a)
	elif z <= 2.5e+55:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (z <= -1.96e+124)
		tmp = t_1;
	elseif (z <= -1.32e+95)
		tmp = Float64(y + x);
	elseif (z <= -8.4e+68)
		tmp = Float64(x * Float64(z / Float64(-a)));
	elseif (z <= 2.5e+55)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if (z <= -1.96e+124)
		tmp = t_1;
	elseif (z <= -1.32e+95)
		tmp = y + x;
	elseif (z <= -8.4e+68)
		tmp = x * (z / -a);
	elseif (z <= 2.5e+55)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.96e+124], t$95$1, If[LessEqual[z, -1.32e+95], N[(y + x), $MachinePrecision], If[LessEqual[z, -8.4e+68], N[(x * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+55], N[(y + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9599999999999999e124 or 2.50000000000000023e55 < z

   1. Initial program 72.8%

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

   3. Taylor expanded in x around inf 62.9%

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

      1. times-frac 77.6%

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

      2. distribute-rgt-out 84.8%

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

   5. Simplified 84.8%

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

   6. Taylor expanded in z around inf 52.4%

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

      1. associate-/l* 58.1%

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

      2. associate-/l* 69.4%

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

      3. sub-neg 69.4%

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

      4. metadata-eval 69.4%

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

      5. +-commutative 69.4%

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

   8. Simplified 69.4%

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

   9. Taylor expanded in x around 0 41.9%

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

       1. associate-/l* 51.6%

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

   11. Simplified 51.6%

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

   if -1.9599999999999999e124 < z < -1.32e95 or -8.40000000000000003e68 < z < 2.50000000000000023e55

   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 z around 0 60.3%

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

      1. mul-1-neg 60.3%

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

      2. unsub-neg 60.3%

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

      3. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in y around inf 64.8%

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

   7. Taylor expanded in t around inf 48.5%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   8. Step-by-step derivation

      1. mul-1-neg 48.5%

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

   9. Simplified 48.5%

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

   if -1.32e95 < z < -8.40000000000000003e68

   1. Initial program 78.5%

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

   3. Taylor expanded in t around 0 66.4%

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

   4. Taylor expanded in y around 0 44.7%

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

      1. mul-1-neg 44.7%

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

      2. unsub-neg 44.7%

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

      3. associate-/l* 55.2%

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

   6. Simplified 55.2%

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

   7. Taylor expanded in z around inf 39.8%

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

      1. associate-*r/ 50.3%

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

      2. neg-mul-1 50.3%

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

      3. distribute-rgt-neg-in 50.3%

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

      4. distribute-neg-frac 50.3%

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

   9. Simplified 50.3%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.96 \cdot 10^{+124}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{+95}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+55}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+181}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+91}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+46}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.6e+181)
   y
   (if (<= t -2.4e+101)
     (* x (/ (- z a) t))
     (if (<= t -4.2e+91) y (if (<= t 3.1e+46) (+ x (* y (/ z a))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.6e+181) {
		tmp = y;
	} else if (t <= -2.4e+101) {
		tmp = x * ((z - a) / t);
	} else if (t <= -4.2e+91) {
		tmp = y;
	} else if (t <= 3.1e+46) {
		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 <= (-8.6d+181)) then
        tmp = y
    else if (t <= (-2.4d+101)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-4.2d+91)) then
        tmp = y
    else if (t <= 3.1d+46) 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 <= -8.6e+181) {
		tmp = y;
	} else if (t <= -2.4e+101) {
		tmp = x * ((z - a) / t);
	} else if (t <= -4.2e+91) {
		tmp = y;
	} else if (t <= 3.1e+46) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.6e+181:
		tmp = y
	elif t <= -2.4e+101:
		tmp = x * ((z - a) / t)
	elif t <= -4.2e+91:
		tmp = y
	elif t <= 3.1e+46:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.6e+181)
		tmp = y;
	elseif (t <= -2.4e+101)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -4.2e+91)
		tmp = y;
	elseif (t <= 3.1e+46)
		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 <= -8.6e+181)
		tmp = y;
	elseif (t <= -2.4e+101)
		tmp = x * ((z - a) / t);
	elseif (t <= -4.2e+91)
		tmp = y;
	elseif (t <= 3.1e+46)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.6e+181], y, If[LessEqual[t, -2.4e+101], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.2e+91], y, If[LessEqual[t, 3.1e+46], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.59999999999999943e181 or -2.39999999999999988e101 < t < -4.20000000000000015e91 or 3.09999999999999975e46 < t

   1. Initial program 43.3%

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

   3. Taylor expanded in t around inf 60.1%

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

   if -8.59999999999999943e181 < t < -2.39999999999999988e101

   1. Initial program 42.1%

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

   3. Taylor expanded in x around -inf 53.5%

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

      1. associate-*r* 53.5%

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

      2. neg-mul-1 53.5%

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

      3. +-commutative 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in t around -inf 52.3%

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

      1. associate-/l* 56.3%

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

   8. Simplified 56.3%

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

   if -4.20000000000000015e91 < t < 3.09999999999999975e46

   1. Initial program 88.1%

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

   3. Taylor expanded in t around 0 69.8%

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

   4. Taylor expanded in y around inf 57.8%

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

      1. associate-/l* 61.7%

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

   6. Simplified 61.7%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+181}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+91}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+46}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+181}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.38 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+89}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+46}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e+181)
   y
   (if (<= t -1.38e+101)
     (* z (/ (- x y) t))
     (if (<= t -7.5e+89) y (if (<= t 2.6e+46) (+ x (* y (/ z a))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+181) {
		tmp = y;
	} else if (t <= -1.38e+101) {
		tmp = z * ((x - y) / t);
	} else if (t <= -7.5e+89) {
		tmp = y;
	} else if (t <= 2.6e+46) {
		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 <= (-7d+181)) then
        tmp = y
    else if (t <= (-1.38d+101)) then
        tmp = z * ((x - y) / t)
    else if (t <= (-7.5d+89)) then
        tmp = y
    else if (t <= 2.6d+46) 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 <= -7e+181) {
		tmp = y;
	} else if (t <= -1.38e+101) {
		tmp = z * ((x - y) / t);
	} else if (t <= -7.5e+89) {
		tmp = y;
	} else if (t <= 2.6e+46) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7e+181:
		tmp = y
	elif t <= -1.38e+101:
		tmp = z * ((x - y) / t)
	elif t <= -7.5e+89:
		tmp = y
	elif t <= 2.6e+46:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e+181)
		tmp = y;
	elseif (t <= -1.38e+101)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (t <= -7.5e+89)
		tmp = y;
	elseif (t <= 2.6e+46)
		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 <= -7e+181)
		tmp = y;
	elseif (t <= -1.38e+101)
		tmp = z * ((x - y) / t);
	elseif (t <= -7.5e+89)
		tmp = y;
	elseif (t <= 2.6e+46)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e+181], y, If[LessEqual[t, -1.38e+101], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.5e+89], y, If[LessEqual[t, 2.6e+46], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.00000000000000016e181 or -1.38e101 < t < -7.49999999999999947e89 or 2.60000000000000013e46 < t

   1. Initial program 43.3%

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

   3. Taylor expanded in t around inf 60.1%

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

   if -7.00000000000000016e181 < t < -1.38e101

   1. Initial program 42.1%

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

   3. Taylor expanded in t around inf 63.1%

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

      1. associate--l+ 63.1%

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

      2. distribute-lft-out-- 63.1%

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

      3. div-sub 63.1%

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

      4. mul-1-neg 63.1%

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

      5. unsub-neg 63.1%

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

      6. div-sub 63.1%

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

      7. associate-/l* 79.8%

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

      8. associate-/l* 79.8%

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

      9. distribute-rgt-out-- 79.8%

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

   5. Simplified 79.8%

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

   6. Taylor expanded in z around -inf 47.4%

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

      1. mul-1-neg 47.4%

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

      2. associate-/l* 64.1%

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

      3. distribute-rgt-neg-in 64.1%

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

      4. distribute-neg-frac2 64.1%

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

   8. Simplified 64.1%

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

   if -7.49999999999999947e89 < t < 2.60000000000000013e46

   1. Initial program 88.1%

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

   3. Taylor expanded in t around 0 69.8%

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

   4. Taylor expanded in y around inf 57.8%

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

      1. associate-/l* 61.7%

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

   6. Simplified 61.7%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+181}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.38 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+89}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+46}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+90} \lor \neg \left(t \leq 9.2 \cdot 10^{+81}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.4e+90) (not (<= t 9.2e+81)))
   (+ y (* (/ (- y x) t) (- a z)))
   (+ x (/ (* (- y x) (- z t)) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.4e+90) || !(t <= 9.2e+81)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x + (((y - x) * (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 ((t <= (-1.4d+90)) .or. (.not. (t <= 9.2d+81))) then
        tmp = y + (((y - x) / t) * (a - z))
    else
        tmp = x + (((y - x) * (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 ((t <= -1.4e+90) || !(t <= 9.2e+81)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.4e+90) or not (t <= 9.2e+81):
		tmp = y + (((y - x) / t) * (a - z))
	else:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.4e+90) || !(t <= 9.2e+81))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.4e+90) || ~((t <= 9.2e+81)))
		tmp = y + (((y - x) / t) * (a - z));
	else
		tmp = x + (((y - x) * (z - t)) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.4e+90], N[Not[LessEqual[t, 9.2e+81]], $MachinePrecision]], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4e90 or 9.1999999999999995e81 < t

   1. Initial program 39.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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* 80.6%

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

      8. associate-/l* 90.0%

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

      9. distribute-rgt-out-- 90.0%

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

   5. Simplified 90.0%

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

   if -1.4e90 < t < 9.1999999999999995e81

   1. Initial program 87.6%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+90} \lor \neg \left(t \leq 9.2 \cdot 10^{+81}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+90} \lor \neg \left(t \leq 4200000000000\right):\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.6e+90) (not (<= t 4200000000000.0)))
   (- y (* (/ x t) (- a z)))
   (+ x (* (- y x) (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.6e+90) || !(t <= 4200000000000.0)) {
		tmp = y - ((x / t) * (a - z));
	} else {
		tmp = x + ((y - x) * ((z - t) / 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 <= (-7.6d+90)) .or. (.not. (t <= 4200000000000.0d0))) then
        tmp = y - ((x / t) * (a - z))
    else
        tmp = x + ((y - x) * ((z - t) / 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 <= -7.6e+90) || !(t <= 4200000000000.0)) {
		tmp = y - ((x / t) * (a - z));
	} else {
		tmp = x + ((y - x) * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.6e+90) or not (t <= 4200000000000.0):
		tmp = y - ((x / t) * (a - z))
	else:
		tmp = x + ((y - x) * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.6e+90) || !(t <= 4200000000000.0))
		tmp = Float64(y - Float64(Float64(x / t) * Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.6e+90) || ~((t <= 4200000000000.0)))
		tmp = y - ((x / t) * (a - z));
	else
		tmp = x + ((y - x) * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.6e+90], N[Not[LessEqual[t, 4200000000000.0]], $MachinePrecision]], N[(y - N[(N[(x / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.6000000000000002e90 or 4.2e12 < t

   1. Initial program 46.1%

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

   3. Taylor expanded in t around inf 67.4%

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

      1. associate--l+ 67.4%

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

      2. distribute-lft-out-- 67.4%

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

      3. div-sub 67.4%

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

      4. mul-1-neg 67.4%

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

      5. unsub-neg 67.4%

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

      6. div-sub 67.4%

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

      7. associate-/l* 76.4%

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

      8. associate-/l* 85.0%

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

      9. distribute-rgt-out-- 85.0%

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

   5. Simplified 85.0%

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

   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. associate-*r/ 75.7%

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

      2. neg-mul-1 75.7%

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

   8. Simplified 75.7%

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

   if -7.6000000000000002e90 < t < 4.2e12

   1. Initial program 89.2%

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

   3. Taylor expanded in a around inf 76.8%

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

      1. associate-/l* 83.4%

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

   5. Simplified 83.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+90} \lor \neg \left(t \leq 4200000000000\right):\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+89} \lor \neg \left(t \leq 330000000000\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.5e+89) (not (<= t 330000000000.0)))
   (+ y (* (/ (- y x) t) (- a z)))
   (+ x (* (- y x) (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e+89) || !(t <= 330000000000.0)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x + ((y - x) * ((z - t) / 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 <= (-8.5d+89)) .or. (.not. (t <= 330000000000.0d0))) then
        tmp = y + (((y - x) / t) * (a - z))
    else
        tmp = x + ((y - x) * ((z - t) / 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 <= -8.5e+89) || !(t <= 330000000000.0)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x + ((y - x) * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.5e+89) or not (t <= 330000000000.0):
		tmp = y + (((y - x) / t) * (a - z))
	else:
		tmp = x + ((y - x) * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.5e+89) || !(t <= 330000000000.0))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.5e+89) || ~((t <= 330000000000.0)))
		tmp = y + (((y - x) / t) * (a - z));
	else
		tmp = x + ((y - x) * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.5e+89], N[Not[LessEqual[t, 330000000000.0]], $MachinePrecision]], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000045e89 or 3.3e11 < t

   1. Initial program 46.1%

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

   3. Taylor expanded in t around inf 67.4%

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

      1. associate--l+ 67.4%

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

      2. distribute-lft-out-- 67.4%

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

      3. div-sub 67.4%

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

      4. mul-1-neg 67.4%

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

      5. unsub-neg 67.4%

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

      6. div-sub 67.4%

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

      7. associate-/l* 76.4%

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

      8. associate-/l* 85.0%

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

      9. distribute-rgt-out-- 85.0%

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

   5. Simplified 85.0%

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

   if -8.50000000000000045e89 < t < 3.3e11

   1. Initial program 89.2%

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

   3. Taylor expanded in a around inf 76.8%

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

      1. associate-/l* 83.4%

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

   5. Simplified 83.4%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+89} \lor \neg \left(t \leq 330000000000\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+33} \lor \neg \left(t \leq 1.18 \cdot 10^{+44}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1e+33) (not (<= t 1.18e+44)))
   (* 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 <= -1e+33) || !(t <= 1.18e+44)) {
		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 <= (-1d+33)) .or. (.not. (t <= 1.18d+44))) 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 <= -1e+33) || !(t <= 1.18e+44)) {
		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 <= -1e+33) or not (t <= 1.18e+44):
		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 <= -1e+33) || !(t <= 1.18e+44))
		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 <= -1e+33) || ~((t <= 1.18e+44)))
		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, -1e+33], N[Not[LessEqual[t, 1.18e+44]], $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 < -9.9999999999999995e32 or 1.17999999999999997e44 < t

   1. Initial program 50.8%

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

   3. Taylor expanded in x around 0 59.7%

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

      1. +-commutative 59.7%

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

      2. +-commutative 59.7%

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

      3. distribute-lft-in 59.7%

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

      4. mul-1-neg 59.7%

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

      5. distribute-rgt-neg-in 59.7%

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

      6. associate-/l* 55.5%

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

      7. mul-1-neg 55.5%

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

      8. *-rgt-identity 55.5%

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

      9. associate-+l+ 50.6%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in y around inf 67.1%

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

      1. div-sub 67.1%

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

   8. Simplified 67.1%

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

   if -9.9999999999999995e32 < t < 1.17999999999999997e44

   1. Initial program 88.5%

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

   3. Taylor expanded in t around 0 72.3%

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

      1. associate-/l* 74.9%

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

   5. Simplified 74.9%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+33} \lor \neg \left(t \leq 1.18 \cdot 10^{+44}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+89} \lor \neg \left(t \leq 300000000000\right):\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.5e+89) (not (<= t 300000000000.0)))
   (- y (* (/ x t) (- a z)))
   (+ x (* z (/ (- y x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.5e+89) || !(t <= 300000000000.0)) {
		tmp = y - ((x / t) * (a - z));
	} 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 <= (-6.5d+89)) .or. (.not. (t <= 300000000000.0d0))) then
        tmp = y - ((x / t) * (a - z))
    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 <= -6.5e+89) || !(t <= 300000000000.0)) {
		tmp = y - ((x / t) * (a - z));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.5e+89) or not (t <= 300000000000.0):
		tmp = y - ((x / t) * (a - z))
	else:
		tmp = x + (z * ((y - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.5e+89) || !(t <= 300000000000.0))
		tmp = Float64(y - Float64(Float64(x / t) * Float64(a - z)));
	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 <= -6.5e+89) || ~((t <= 300000000000.0)))
		tmp = y - ((x / t) * (a - z));
	else
		tmp = x + (z * ((y - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.5e+89], N[Not[LessEqual[t, 300000000000.0]], $MachinePrecision]], N[(y - N[(N[(x / t), $MachinePrecision] * N[(a - z), $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 < -6.4999999999999996e89 or 3e11 < t

   1. Initial program 46.1%

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

   3. Taylor expanded in t around inf 67.4%

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

      1. associate--l+ 67.4%

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

      2. distribute-lft-out-- 67.4%

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

      3. div-sub 67.4%

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

      4. mul-1-neg 67.4%

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

      5. unsub-neg 67.4%

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

      6. div-sub 67.4%

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

      7. associate-/l* 76.4%

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

      8. associate-/l* 85.0%

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

      9. distribute-rgt-out-- 85.0%

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

   5. Simplified 85.0%

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

   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. associate-*r/ 75.7%

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

      2. neg-mul-1 75.7%

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

   8. Simplified 75.7%

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

   if -6.4999999999999996e89 < t < 3e11

   1. Initial program 89.2%

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

   3. Taylor expanded in t around 0 71.5%

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

      1. associate-/l* 75.2%

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

   5. Simplified 75.2%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+89} \lor \neg \left(t \leq 300000000000\right):\\ \;\;\;\;y - \frac{x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+124} \lor \neg \left(z \leq 8.5 \cdot 10^{+60}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+124) (not (<= z 8.5e+60))) (* y (/ z a)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+124) || !(z <= 8.5e+60)) {
		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 <= (-1.35d+124)) .or. (.not. (z <= 8.5d+60))) 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 <= -1.35e+124) || !(z <= 8.5e+60)) {
		tmp = y * (z / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+124) or not (z <= 8.5e+60):
		tmp = y * (z / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+124) || !(z <= 8.5e+60))
		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 <= -1.35e+124) || ~((z <= 8.5e+60)))
		tmp = y * (z / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+124], N[Not[LessEqual[z, 8.5e+60]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.34999999999999989e124 or 8.50000000000000064e60 < z

   1. Initial program 72.8%

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

   3. Taylor expanded in t around 0 55.7%

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

   4. Taylor expanded in y around inf 42.3%

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

   5. Taylor expanded in x around 0 33.8%

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

      1. associate-*r/ 41.5%

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

   7. Simplified 41.5%

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

   if -1.34999999999999989e124 < z < 8.50000000000000064e60

   1. Initial program 73.4%

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

   3. Taylor expanded in z around 0 57.2%

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

      1. mul-1-neg 57.2%

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

      2. unsub-neg 57.2%

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

      3. associate-/l* 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in y around inf 61.4%

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

   7. Taylor expanded in t around inf 46.0%

      \[\leadsto x - \color{blue}{-1 \cdot y} \]
   8. Step-by-step derivation

      1. mul-1-neg 46.0%

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

   9. Simplified 46.0%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+124} \lor \neg \left(z \leq 8.5 \cdot 10^{+60}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.45e+89) x (if (<= a 4.5e-25) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.45e+89) {
		tmp = x;
	} else if (a <= 4.5e-25) {
		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 <= (-2.45d+89)) then
        tmp = x
    else if (a <= 4.5d-25) 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 <= -2.45e+89) {
		tmp = x;
	} else if (a <= 4.5e-25) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.45e+89:
		tmp = x
	elif a <= 4.5e-25:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.45e+89)
		tmp = x;
	elseif (a <= 4.5e-25)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.45e+89)
		tmp = x;
	elseif (a <= 4.5e-25)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.45e+89], x, If[LessEqual[a, 4.5e-25], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.44999999999999998e89 or 4.5000000000000001e-25 < a

   1. Initial program 73.0%

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

   3. Taylor expanded in a around inf 48.7%

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

   if -2.44999999999999998e89 < a < 4.5000000000000001e-25

   1. Initial program 73.3%

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

   3. Taylor expanded in t around inf 34.0%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.5% 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 73.2%

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

3. Taylor expanded in a around inf 26.8%

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

4. Final simplification 26.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 87.7% 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 2024078 
(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))))