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

Percentage Accurate: 68.2% → 88.4%

Time: 13.2s

Alternatives: 18

Speedup: 0.6×

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: 68.2% 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: 88.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+97}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e+97)
   (+ y (* (/ (- y x) t) (- a z)))
   (if (<= t 8e+53)
     (fma (- y x) (/ (- z t) (- a t)) x)
     (+ y (* (- y x) (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e+97) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t <= 8e+53) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e+97)
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (t <= 8e+53)
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e+97], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+53], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6e97

   1. Initial program 35.7%

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

   3. Taylor expanded in t around inf 66.0%

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

      1. associate--l+ 66.0%

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

      2. distribute-lft-out-- 66.0%

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

      3. div-sub 66.0%

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

      4. mul-1-neg 66.0%

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

      5. unsub-neg 66.0%

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

      6. div-sub 66.0%

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

      7. associate-/l* 79.0%

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

      8. associate-/l* 87.4%

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

      9. distribute-rgt-out-- 87.4%

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

   5. Simplified 87.4%

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

   if -2.6e97 < t < 7.9999999999999999e53

   1. Initial program 83.3%

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

      1. +-commutative 83.3%

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

      2. associate-/l* 94.1%

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

      3. fma-define 94.0%

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

   3. Simplified 94.0%

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

   if 7.9999999999999999e53 < t

   1. Initial program 41.1%

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

      1. +-commutative 41.1%

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

      2. associate-/l* 60.0%

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

      3. fma-define 60.0%

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

   3. Simplified 60.0%

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

      1. clear-num 59.9%

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

      2. inv-pow 59.9%

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

   6. Applied egg-rr 59.9%

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

      1. unpow-1 59.9%

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

   8. Simplified 59.9%

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

   9. Taylor expanded in t around inf 71.7%

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

       1. associate--l+ 71.7%

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

       2. associate-*r/ 71.7%

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

       3. associate-*r/ 71.7%

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

       4. mul-1-neg 71.7%

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

       5. distribute-lft-neg-out 71.7%

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

       6. div-sub 71.7%

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

       7. distribute-lft-neg-out 71.7%

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

       8. mul-1-neg 71.7%

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

       9. distribute-lft-out-- 71.7%

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

       10. distribute-rgt-out-- 71.7%

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

       11. associate-*r/ 71.7%

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

       12. distribute-rgt-out-- 71.7%

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

   11. Simplified 85.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+97}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 69.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;a \leq -5 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 10500000:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a)))))
   (if (<= a -5e-21)
     t_1
     (if (<= a -6.4e-50)
       (* x (/ (- z a) t))
       (if (<= a -2.3e-72)
         (* z (/ (- y x) (- a t)))
         (if (<= a -2.15e-136)
           (* y (/ (- z t) (- a t)))
           (if (<= a 10500000.0) (+ y (* (/ z t) (- x y))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -5e-21) {
		tmp = t_1;
	} else if (a <= -6.4e-50) {
		tmp = x * ((z - a) / t);
	} else if (a <= -2.3e-72) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= -2.15e-136) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 10500000.0) {
		tmp = y + ((z / t) * (x - y));
	} 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 + (z * ((y - x) / a))
    if (a <= (-5d-21)) then
        tmp = t_1
    else if (a <= (-6.4d-50)) then
        tmp = x * ((z - a) / t)
    else if (a <= (-2.3d-72)) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= (-2.15d-136)) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 10500000.0d0) then
        tmp = y + ((z / t) * (x - y))
    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 + (z * ((y - x) / a));
	double tmp;
	if (a <= -5e-21) {
		tmp = t_1;
	} else if (a <= -6.4e-50) {
		tmp = x * ((z - a) / t);
	} else if (a <= -2.3e-72) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= -2.15e-136) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 10500000.0) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	tmp = 0
	if a <= -5e-21:
		tmp = t_1
	elif a <= -6.4e-50:
		tmp = x * ((z - a) / t)
	elif a <= -2.3e-72:
		tmp = z * ((y - x) / (a - t))
	elif a <= -2.15e-136:
		tmp = y * ((z - t) / (a - t))
	elif a <= 10500000.0:
		tmp = y + ((z / t) * (x - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (a <= -5e-21)
		tmp = t_1;
	elseif (a <= -6.4e-50)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= -2.3e-72)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= -2.15e-136)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 10500000.0)
		tmp = Float64(y + Float64(Float64(z / t) * Float64(x - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (a <= -5e-21)
		tmp = t_1;
	elseif (a <= -6.4e-50)
		tmp = x * ((z - a) / t);
	elseif (a <= -2.3e-72)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= -2.15e-136)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 10500000.0)
		tmp = y + ((z / t) * (x - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e-21], t$95$1, If[LessEqual[a, -6.4e-50], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.3e-72], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.15e-136], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 10500000.0], N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.99999999999999973e-21 or 1.05e7 < a

   1. Initial program 72.1%

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

   3. Taylor expanded in t around 0 65.7%

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

      1. associate-/l* 74.9%

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

   5. Simplified 74.9%

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

   if -4.99999999999999973e-21 < a < -6.4e-50

   1. Initial program 51.9%

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

      1. +-commutative 51.9%

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

      2. associate-/l* 51.5%

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

      3. fma-define 51.5%

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

   3. Simplified 51.5%

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

      1. clear-num 51.5%

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

      2. inv-pow 51.5%

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

   6. Applied egg-rr 51.5%

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

      1. unpow-1 51.5%

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

   8. Simplified 51.5%

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

   9. Taylor expanded in t around inf 84.1%

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

       1. associate--l+ 84.1%

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

       2. associate-*r/ 84.1%

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

       3. associate-*r/ 84.1%

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

       4. mul-1-neg 84.1%

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

       5. distribute-lft-neg-out 84.1%

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

       6. div-sub 84.1%

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

       7. distribute-lft-neg-out 84.1%

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

       8. mul-1-neg 84.1%

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

       9. distribute-lft-out-- 84.1%

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

       10. distribute-rgt-out-- 84.1%

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

       11. associate-*r/ 84.1%

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

       12. distribute-rgt-out-- 84.1%

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

   11. Simplified 99.5%

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

   12. Taylor expanded in y around 0 84.1%

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

       1. associate-/l* 99.5%

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

   14. Simplified 99.5%

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

   if -6.4e-50 < a < -2.29999999999999995e-72

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around inf 100.0%

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

       1. div-sub 100.0%

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

   11. Simplified 100.0%

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

   if -2.29999999999999995e-72 < a < -2.15e-136

   1. Initial program 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-/l* 83.7%

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

      3. fma-define 83.7%

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

   3. Simplified 83.7%

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

      1. clear-num 83.7%

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

      2. inv-pow 83.7%

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

   6. Applied egg-rr 83.7%

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

      1. unpow-1 83.7%

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

   8. Simplified 83.7%

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

   9. Taylor expanded in y around inf 75.2%

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

       1. div-sub 75.3%

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

   11. Simplified 75.3%

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

   if -2.15e-136 < a < 1.05e7

   1. Initial program 60.3%

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

      1. +-commutative 60.3%

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

      2. associate-/l* 72.8%

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

      3. fma-define 72.8%

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

   3. Simplified 72.8%

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

      1. clear-num 72.7%

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

      2. inv-pow 72.7%

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

   6. Applied egg-rr 72.7%

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

      1. unpow-1 72.7%

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

   8. Simplified 72.7%

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

   9. Taylor expanded in t around inf 80.2%

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

       1. associate--l+ 80.2%

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

       2. associate-*r/ 80.2%

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

       3. associate-*r/ 80.2%

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

       4. mul-1-neg 80.2%

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

       5. distribute-lft-neg-out 80.2%

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

       6. div-sub 81.3%

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

       7. distribute-lft-neg-out 81.3%

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

       8. mul-1-neg 81.3%

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

       9. distribute-lft-out-- 81.3%

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

       10. distribute-rgt-out-- 81.3%

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

       11. associate-*r/ 81.3%

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

       12. distribute-rgt-out-- 81.3%

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

   11. Simplified 87.3%

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

   12. Taylor expanded in z around inf 84.7%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-21}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 10500000:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-102}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-135}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+96}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (<= a -1.2e-20)
     t_1
     (if (<= a -1.65e-102)
       (+ y (* (/ (- y x) t) (- a z)))
       (if (<= a -8.5e-135)
         (/ y (/ (- a t) (- z t)))
         (if (<= a 2.5e+96) (+ y (* (- y x) (/ (- a z) t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (a <= -1.2e-20) {
		tmp = t_1;
	} else if (a <= -1.65e-102) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (a <= -8.5e-135) {
		tmp = y / ((a - t) / (z - t));
	} else if (a <= 2.5e+96) {
		tmp = y + ((y - x) * ((a - z) / 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 = x + (y * ((z - t) / (a - t)))
    if (a <= (-1.2d-20)) then
        tmp = t_1
    else if (a <= (-1.65d-102)) then
        tmp = y + (((y - x) / t) * (a - z))
    else if (a <= (-8.5d-135)) then
        tmp = y / ((a - t) / (z - t))
    else if (a <= 2.5d+96) then
        tmp = y + ((y - x) * ((a - z) / 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 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (a <= -1.2e-20) {
		tmp = t_1;
	} else if (a <= -1.65e-102) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (a <= -8.5e-135) {
		tmp = y / ((a - t) / (z - t));
	} else if (a <= 2.5e+96) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if a <= -1.2e-20:
		tmp = t_1
	elif a <= -1.65e-102:
		tmp = y + (((y - x) / t) * (a - z))
	elif a <= -8.5e-135:
		tmp = y / ((a - t) / (z - t))
	elif a <= 2.5e+96:
		tmp = y + ((y - x) * ((a - z) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a <= -1.2e-20)
		tmp = t_1;
	elseif (a <= -1.65e-102)
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (a <= -8.5e-135)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (a <= 2.5e+96)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a <= -1.2e-20)
		tmp = t_1;
	elseif (a <= -1.65e-102)
		tmp = y + (((y - x) / t) * (a - z));
	elseif (a <= -8.5e-135)
		tmp = y / ((a - t) / (z - t));
	elseif (a <= 2.5e+96)
		tmp = y + ((y - x) * ((a - z) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e-20], t$95$1, If[LessEqual[a, -1.65e-102], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.5e-135], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+96], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.19999999999999996e-20 or 2.5000000000000002e96 < a

   1. Initial program 73.9%

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

   3. Taylor expanded in y around inf 77.4%

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

      1. associate-/l* 85.9%

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

   5. Simplified 85.9%

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

   if -1.19999999999999996e-20 < a < -1.65e-102

   1. Initial program 73.5%

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

   3. Taylor expanded in t around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. distribute-lft-out-- 77.5%

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

      3. div-sub 82.0%

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

      4. mul-1-neg 82.0%

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

      5. unsub-neg 82.0%

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

      6. div-sub 77.5%

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

      7. associate-/l* 81.6%

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

      8. associate-/l* 81.5%

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

      9. distribute-rgt-out-- 86.3%

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

   5. Simplified 86.3%

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

   if -1.65e-102 < a < -8.49999999999999942e-135

   1. Initial program 85.4%

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

      1. +-commutative 85.4%

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

      2. associate-/l* 92.3%

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

      3. fma-define 92.3%

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

   3. Simplified 92.3%

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

      1. clear-num 92.3%

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

      2. inv-pow 92.3%

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

   6. Applied egg-rr 92.3%

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

      1. unpow-1 92.3%

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

   8. Simplified 92.3%

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

   9. Taylor expanded in y around -inf 69.7%

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

       1. associate-/l* 84.2%

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

       2. clear-num 84.2%

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

       3. div-inv 84.2%

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

       4. add-cube-cbrt 83.2%

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

       5. *-un-lft-identity 83.2%

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

       6. times-frac 83.2%

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

       7. pow2 83.2%

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

   11. Applied egg-rr 83.2%

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

       1. /-rgt-identity 83.2%

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

       2. associate-*r/ 83.2%

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

       3. unpow2 83.2%

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

       4. rem-3cbrt-lft 84.2%

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

   13. Simplified 84.2%

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

   if -8.49999999999999942e-135 < a < 2.5000000000000002e96

   1. Initial program 60.4%

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

      1. +-commutative 60.4%

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

      2. associate-/l* 74.4%

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

      3. fma-define 74.4%

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

   3. Simplified 74.4%

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

      1. clear-num 74.3%

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

      2. inv-pow 74.3%

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

   6. Applied egg-rr 74.3%

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

      1. unpow-1 74.3%

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

   8. Simplified 74.3%

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

   9. Taylor expanded in t around inf 74.4%

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

       1. associate--l+ 74.4%

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

       2. associate-*r/ 74.4%

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

       3. associate-*r/ 74.4%

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

       4. mul-1-neg 74.4%

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

       5. distribute-lft-neg-out 74.4%

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

       6. div-sub 75.3%

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

       7. distribute-lft-neg-out 75.3%

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

       8. mul-1-neg 75.3%

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

       9. distribute-lft-out-- 75.3%

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

       10. distribute-rgt-out-- 75.3%

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

       11. associate-*r/ 75.3%

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

       12. distribute-rgt-out-- 75.3%

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

   11. Simplified 82.1%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-102}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-135}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+96}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(y - x\right) \cdot \frac{a - z}{t}\\ t_2 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-134}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- y x) (/ (- a z) t))))
        (t_2 (+ x (* y (/ (- z t) (- a t))))))
   (if (<= a -5.2e-21)
     t_2
     (if (<= a -6.8e-102)
       t_1
       (if (<= a -1.02e-134)
         (/ y (/ (- a t) (- z t)))
         (if (<= a 2.5e+96) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((y - x) * ((a - z) / t));
	double t_2 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (a <= -5.2e-21) {
		tmp = t_2;
	} else if (a <= -6.8e-102) {
		tmp = t_1;
	} else if (a <= -1.02e-134) {
		tmp = y / ((a - t) / (z - t));
	} else if (a <= 2.5e+96) {
		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 + ((y - x) * ((a - z) / t))
    t_2 = x + (y * ((z - t) / (a - t)))
    if (a <= (-5.2d-21)) then
        tmp = t_2
    else if (a <= (-6.8d-102)) then
        tmp = t_1
    else if (a <= (-1.02d-134)) then
        tmp = y / ((a - t) / (z - t))
    else if (a <= 2.5d+96) 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 + ((y - x) * ((a - z) / t));
	double t_2 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (a <= -5.2e-21) {
		tmp = t_2;
	} else if (a <= -6.8e-102) {
		tmp = t_1;
	} else if (a <= -1.02e-134) {
		tmp = y / ((a - t) / (z - t));
	} else if (a <= 2.5e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((y - x) * ((a - z) / t))
	t_2 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if a <= -5.2e-21:
		tmp = t_2
	elif a <= -6.8e-102:
		tmp = t_1
	elif a <= -1.02e-134:
		tmp = y / ((a - t) / (z - t))
	elif a <= 2.5e+96:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)))
	t_2 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a <= -5.2e-21)
		tmp = t_2;
	elseif (a <= -6.8e-102)
		tmp = t_1;
	elseif (a <= -1.02e-134)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (a <= 2.5e+96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((y - x) * ((a - z) / t));
	t_2 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a <= -5.2e-21)
		tmp = t_2;
	elseif (a <= -6.8e-102)
		tmp = t_1;
	elseif (a <= -1.02e-134)
		tmp = y / ((a - t) / (z - t));
	elseif (a <= 2.5e+96)
		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[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e-21], t$95$2, If[LessEqual[a, -6.8e-102], t$95$1, If[LessEqual[a, -1.02e-134], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+96], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.20000000000000035e-21 or 2.5000000000000002e96 < a

   1. Initial program 73.9%

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

   3. Taylor expanded in y around inf 77.4%

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

      1. associate-/l* 85.9%

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

   5. Simplified 85.9%

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

   if -5.20000000000000035e-21 < a < -6.80000000000000026e-102 or -1.02e-134 < a < 2.5000000000000002e96

   1. Initial program 62.7%

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

      1. +-commutative 62.7%

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

      2. associate-/l* 74.2%

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

      3. fma-define 74.2%

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

   3. Simplified 74.2%

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

      1. clear-num 74.1%

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

      2. inv-pow 74.1%

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

   6. Applied egg-rr 74.1%

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

      1. unpow-1 74.1%

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

   8. Simplified 74.1%

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

   9. Taylor expanded in t around inf 74.9%

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

       1. associate--l+ 74.9%

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

       2. associate-*r/ 74.9%

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

       3. associate-*r/ 74.9%

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

       4. mul-1-neg 74.9%

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

       5. distribute-lft-neg-out 74.9%

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

       6. div-sub 76.5%

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

       7. distribute-lft-neg-out 76.5%

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

       8. mul-1-neg 76.5%

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

       9. distribute-lft-out-- 76.5%

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

       10. distribute-rgt-out-- 76.5%

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

       11. associate-*r/ 76.5%

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

       12. distribute-rgt-out-- 76.5%

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

   11. Simplified 82.8%

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

   if -6.80000000000000026e-102 < a < -1.02e-134

   1. Initial program 85.4%

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

      1. +-commutative 85.4%

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

      2. associate-/l* 92.3%

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

      3. fma-define 92.3%

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

   3. Simplified 92.3%

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

      1. clear-num 92.3%

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

      2. inv-pow 92.3%

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

   6. Applied egg-rr 92.3%

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

      1. unpow-1 92.3%

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

   8. Simplified 92.3%

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

   9. Taylor expanded in y around -inf 69.7%

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

       1. associate-/l* 84.2%

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

       2. clear-num 84.2%

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

       3. div-inv 84.2%

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

       4. add-cube-cbrt 83.2%

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

       5. *-un-lft-identity 83.2%

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

       6. times-frac 83.2%

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

       7. pow2 83.2%

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

   11. Applied egg-rr 83.2%

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

       1. /-rgt-identity 83.2%

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

       2. associate-*r/ 83.2%

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

       3. unpow2 83.2%

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

       4. rem-3cbrt-lft 84.2%

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

   13. Simplified 84.2%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-21}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-134}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+96}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + t\_1\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-55}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x t_1)))
   (if (<= a -1.8e-23)
     t_2
     (if (<= a -1.2e-72)
       (* z (/ (- y x) (- a t)))
       (if (<= a -1.12e-135)
         t_1
         (if (<= a 1.45e-55) (+ y (* (/ z t) (- x y))) 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 + t_1;
	double tmp;
	if (a <= -1.8e-23) {
		tmp = t_2;
	} else if (a <= -1.2e-72) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= -1.12e-135) {
		tmp = t_1;
	} else if (a <= 1.45e-55) {
		tmp = y + ((z / t) * (x - y));
	} 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 + t_1
    if (a <= (-1.8d-23)) then
        tmp = t_2
    else if (a <= (-1.2d-72)) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= (-1.12d-135)) then
        tmp = t_1
    else if (a <= 1.45d-55) then
        tmp = y + ((z / t) * (x - y))
    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 + t_1;
	double tmp;
	if (a <= -1.8e-23) {
		tmp = t_2;
	} else if (a <= -1.2e-72) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= -1.12e-135) {
		tmp = t_1;
	} else if (a <= 1.45e-55) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + t_1
	tmp = 0
	if a <= -1.8e-23:
		tmp = t_2
	elif a <= -1.2e-72:
		tmp = z * ((y - x) / (a - t))
	elif a <= -1.12e-135:
		tmp = t_1
	elif a <= 1.45e-55:
		tmp = y + ((z / t) * (x - y))
	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 + t_1)
	tmp = 0.0
	if (a <= -1.8e-23)
		tmp = t_2;
	elseif (a <= -1.2e-72)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= -1.12e-135)
		tmp = t_1;
	elseif (a <= 1.45e-55)
		tmp = Float64(y + Float64(Float64(z / t) * Float64(x - y)));
	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 + t_1;
	tmp = 0.0;
	if (a <= -1.8e-23)
		tmp = t_2;
	elseif (a <= -1.2e-72)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= -1.12e-135)
		tmp = t_1;
	elseif (a <= 1.45e-55)
		tmp = y + ((z / t) * (x - y));
	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 + t$95$1), $MachinePrecision]}, If[LessEqual[a, -1.8e-23], t$95$2, If[LessEqual[a, -1.2e-72], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.12e-135], t$95$1, If[LessEqual[a, 1.45e-55], N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.7999999999999999e-23 or 1.45e-55 < a

   1. Initial program 70.7%

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

   3. Taylor expanded in y around inf 70.3%

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

      1. associate-/l* 78.9%

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

   5. Simplified 78.9%

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

   if -1.7999999999999999e-23 < a < -1.2e-72

   1. Initial program 90.1%

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

      1. +-commutative 90.1%

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

      2. associate-/l* 90.2%

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

      3. fma-define 90.2%

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

   3. Simplified 90.2%

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

      1. clear-num 90.2%

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

      2. inv-pow 90.2%

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

   6. Applied egg-rr 90.2%

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

      1. unpow-1 90.2%

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

   8. Simplified 90.2%

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

   9. Taylor expanded in z around inf 99.8%

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

       1. div-sub 99.8%

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

   11. Simplified 99.8%

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

   if -1.2e-72 < a < -1.12e-135

   1. Initial program 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-/l* 83.7%

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

      3. fma-define 83.7%

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

   3. Simplified 83.7%

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

      1. clear-num 83.7%

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

      2. inv-pow 83.7%

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

   6. Applied egg-rr 83.7%

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

      1. unpow-1 83.7%

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

   8. Simplified 83.7%

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

   9. Taylor expanded in y around inf 75.2%

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

       1. div-sub 75.3%

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

   11. Simplified 75.3%

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

   if -1.12e-135 < a < 1.45e-55

   1. Initial program 59.3%

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

      1. +-commutative 59.3%

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

      2. associate-/l* 71.5%

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

      3. fma-define 71.4%

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

   3. Simplified 71.4%

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

      1. clear-num 71.3%

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

      2. inv-pow 71.3%

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

   6. Applied egg-rr 71.3%

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

      1. unpow-1 71.3%

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

   8. Simplified 71.3%

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

   9. Taylor expanded in t around inf 84.3%

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

       1. associate--l+ 84.3%

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

       2. associate-*r/ 84.3%

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

       3. associate-*r/ 84.3%

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

       4. mul-1-neg 84.3%

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

       5. distribute-lft-neg-out 84.3%

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

       6. div-sub 85.6%

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

       7. distribute-lft-neg-out 85.6%

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

       8. mul-1-neg 85.6%

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

       9. distribute-lft-out-- 85.6%

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

       10. distribute-rgt-out-- 85.6%

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

       11. associate-*r/ 85.6%

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

       12. distribute-rgt-out-- 85.6%

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

   11. Simplified 90.3%

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

   12. Taylor expanded in z around inf 88.6%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-23}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-55}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 0.00125:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a)))))
   (if (<= a -2.25e-20)
     t_1
     (if (<= a -9.8e-51)
       (* x (/ (- z a) t))
       (if (<= a -2.8e-72)
         (* z (/ (- y x) (- a t)))
         (if (<= a 0.00125) (* y (/ (- z t) (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -2.25e-20) {
		tmp = t_1;
	} else if (a <= -9.8e-51) {
		tmp = x * ((z - a) / t);
	} else if (a <= -2.8e-72) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 0.00125) {
		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 = x + (z * ((y - x) / a))
    if (a <= (-2.25d-20)) then
        tmp = t_1
    else if (a <= (-9.8d-51)) then
        tmp = x * ((z - a) / t)
    else if (a <= (-2.8d-72)) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 0.00125d0) 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 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -2.25e-20) {
		tmp = t_1;
	} else if (a <= -9.8e-51) {
		tmp = x * ((z - a) / t);
	} else if (a <= -2.8e-72) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 0.00125) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	tmp = 0
	if a <= -2.25e-20:
		tmp = t_1
	elif a <= -9.8e-51:
		tmp = x * ((z - a) / t)
	elif a <= -2.8e-72:
		tmp = z * ((y - x) / (a - t))
	elif a <= 0.00125:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (a <= -2.25e-20)
		tmp = t_1;
	elseif (a <= -9.8e-51)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= -2.8e-72)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 0.00125)
		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 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (a <= -2.25e-20)
		tmp = t_1;
	elseif (a <= -9.8e-51)
		tmp = x * ((z - a) / t);
	elseif (a <= -2.8e-72)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 0.00125)
		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[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.25e-20], t$95$1, If[LessEqual[a, -9.8e-51], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.8e-72], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.00125], 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 a < -2.2500000000000001e-20 or 0.00125000000000000003 < a

   1. Initial program 71.4%

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

   3. Taylor expanded in t around 0 65.0%

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

      1. associate-/l* 74.0%

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

   5. Simplified 74.0%

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

   if -2.2500000000000001e-20 < a < -9.79999999999999948e-51

   1. Initial program 51.9%

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

      1. +-commutative 51.9%

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

      2. associate-/l* 51.5%

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

      3. fma-define 51.5%

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

   3. Simplified 51.5%

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

      1. clear-num 51.5%

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

      2. inv-pow 51.5%

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

   6. Applied egg-rr 51.5%

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

      1. unpow-1 51.5%

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

   8. Simplified 51.5%

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

   9. Taylor expanded in t around inf 84.1%

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

       1. associate--l+ 84.1%

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

       2. associate-*r/ 84.1%

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

       3. associate-*r/ 84.1%

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

       4. mul-1-neg 84.1%

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

       5. distribute-lft-neg-out 84.1%

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

       6. div-sub 84.1%

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

       7. distribute-lft-neg-out 84.1%

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

       8. mul-1-neg 84.1%

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

       9. distribute-lft-out-- 84.1%

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

       10. distribute-rgt-out-- 84.1%

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

       11. associate-*r/ 84.1%

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

       12. distribute-rgt-out-- 84.1%

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

   11. Simplified 99.5%

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

   12. Taylor expanded in y around 0 84.1%

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

       1. associate-/l* 99.5%

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

   14. Simplified 99.5%

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

   if -9.79999999999999948e-51 < a < -2.7999999999999998e-72

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around inf 100.0%

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

       1. div-sub 100.0%

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

   11. Simplified 100.0%

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

   if -2.7999999999999998e-72 < a < 0.00125000000000000003

   1. Initial program 65.1%

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

      1. +-commutative 65.1%

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

      2. associate-/l* 75.3%

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

      3. fma-define 75.3%

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

   3. Simplified 75.3%

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

      1. clear-num 75.2%

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

      2. inv-pow 75.2%

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

   6. Applied egg-rr 75.2%

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

      1. unpow-1 75.2%

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

   8. Simplified 75.2%

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

   9. Taylor expanded in y around inf 72.1%

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

       1. div-sub 72.2%

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

   11. Simplified 72.2%

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

Alternative 7: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -4 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 15:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t)))) (t_2 (+ x (* y (/ z a)))))
   (if (<= a -4e-7)
     t_2
     (if (<= a -1.6e-72)
       t_1
       (if (<= a 15.0)
         (* y (/ (- z t) (- a t)))
         (if (<= a 2.6e+111) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (a <= -4e-7) {
		tmp = t_2;
	} else if (a <= -1.6e-72) {
		tmp = t_1;
	} else if (a <= 15.0) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 2.6e+111) {
		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 = z * ((y - x) / (a - t))
    t_2 = x + (y * (z / a))
    if (a <= (-4d-7)) then
        tmp = t_2
    else if (a <= (-1.6d-72)) then
        tmp = t_1
    else if (a <= 15.0d0) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 2.6d+111) 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 = z * ((y - x) / (a - t));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (a <= -4e-7) {
		tmp = t_2;
	} else if (a <= -1.6e-72) {
		tmp = t_1;
	} else if (a <= 15.0) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 2.6e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	t_2 = x + (y * (z / a))
	tmp = 0
	if a <= -4e-7:
		tmp = t_2
	elif a <= -1.6e-72:
		tmp = t_1
	elif a <= 15.0:
		tmp = y * ((z - t) / (a - t))
	elif a <= 2.6e+111:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -4e-7)
		tmp = t_2;
	elseif (a <= -1.6e-72)
		tmp = t_1;
	elseif (a <= 15.0)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 2.6e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (a <= -4e-7)
		tmp = t_2;
	elseif (a <= -1.6e-72)
		tmp = t_1;
	elseif (a <= 15.0)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 2.6e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e-7], t$95$2, If[LessEqual[a, -1.6e-72], t$95$1, If[LessEqual[a, 15.0], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+111], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.9999999999999998e-7 or 2.5999999999999999e111 < a

   1. Initial program 74.5%

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

   3. Taylor expanded in t around 0 70.2%

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

   4. Taylor expanded in y around inf 72.8%

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

      1. associate-/l* 77.4%

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

   6. Simplified 77.4%

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

   if -3.9999999999999998e-7 < a < -1.6e-72 or 15 < a < 2.5999999999999999e111

   1. Initial program 65.2%

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

      1. +-commutative 65.2%

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

      2. associate-/l* 79.3%

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

      3. fma-define 79.3%

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

   3. Simplified 79.3%

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

      1. clear-num 79.3%

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

      2. inv-pow 79.3%

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

   6. Applied egg-rr 79.3%

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

      1. unpow-1 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in z around inf 64.6%

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

       1. div-sub 64.6%

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

   11. Simplified 64.6%

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

   if -1.6e-72 < a < 15

   1. Initial program 64.8%

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

      1. +-commutative 64.8%

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

      2. associate-/l* 74.9%

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

      3. fma-define 74.9%

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

   3. Simplified 74.9%

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

      1. clear-num 74.8%

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

      2. inv-pow 74.8%

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

   6. Applied egg-rr 74.8%

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

      1. unpow-1 74.8%

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

   8. Simplified 74.8%

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

   9. Taylor expanded in y around inf 71.8%

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

       1. div-sub 71.8%

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

   11. Simplified 71.8%

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

Alternative 8: 56.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-72}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 0.00156:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= a -3.2e-20)
     t_1
     (if (<= a -4e-52)
       (* x (/ (- z a) t))
       (if (<= a -1.2e-72)
         (* (- y x) (/ z a))
         (if (<= a 0.00156) (* y (- 1.0 (/ z t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (a <= -3.2e-20) {
		tmp = t_1;
	} else if (a <= -4e-52) {
		tmp = x * ((z - a) / t);
	} else if (a <= -1.2e-72) {
		tmp = (y - x) * (z / a);
	} else if (a <= 0.00156) {
		tmp = y * (1.0 - (z / 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 = x + (y * (z / a))
    if (a <= (-3.2d-20)) then
        tmp = t_1
    else if (a <= (-4d-52)) then
        tmp = x * ((z - a) / t)
    else if (a <= (-1.2d-72)) then
        tmp = (y - x) * (z / a)
    else if (a <= 0.00156d0) then
        tmp = y * (1.0d0 - (z / 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 = x + (y * (z / a));
	double tmp;
	if (a <= -3.2e-20) {
		tmp = t_1;
	} else if (a <= -4e-52) {
		tmp = x * ((z - a) / t);
	} else if (a <= -1.2e-72) {
		tmp = (y - x) * (z / a);
	} else if (a <= 0.00156) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if a <= -3.2e-20:
		tmp = t_1
	elif a <= -4e-52:
		tmp = x * ((z - a) / t)
	elif a <= -1.2e-72:
		tmp = (y - x) * (z / a)
	elif a <= 0.00156:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -3.2e-20)
		tmp = t_1;
	elseif (a <= -4e-52)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= -1.2e-72)
		tmp = Float64(Float64(y - x) * Float64(z / a));
	elseif (a <= 0.00156)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (a <= -3.2e-20)
		tmp = t_1;
	elseif (a <= -4e-52)
		tmp = x * ((z - a) / t);
	elseif (a <= -1.2e-72)
		tmp = (y - x) * (z / a);
	elseif (a <= 0.00156)
		tmp = y * (1.0 - (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e-20], t$95$1, If[LessEqual[a, -4e-52], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.2e-72], N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.00156], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.1999999999999997e-20 or 0.00155999999999999997 < a

   1. Initial program 71.4%

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

   3. Taylor expanded in t around 0 65.0%

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

   4. Taylor expanded in y around inf 64.0%

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

      1. associate-/l* 68.3%

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

   6. Simplified 68.3%

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

   if -3.1999999999999997e-20 < a < -4e-52

   1. Initial program 51.9%

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

      1. +-commutative 51.9%

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

      2. associate-/l* 51.5%

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

      3. fma-define 51.5%

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

   3. Simplified 51.5%

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

      1. clear-num 51.5%

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

      2. inv-pow 51.5%

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

   6. Applied egg-rr 51.5%

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

      1. unpow-1 51.5%

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

   8. Simplified 51.5%

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

   9. Taylor expanded in t around inf 84.1%

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

       1. associate--l+ 84.1%

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

       2. associate-*r/ 84.1%

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

       3. associate-*r/ 84.1%

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

       4. mul-1-neg 84.1%

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

       5. distribute-lft-neg-out 84.1%

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

       6. div-sub 84.1%

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

       7. distribute-lft-neg-out 84.1%

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

       8. mul-1-neg 84.1%

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

       9. distribute-lft-out-- 84.1%

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

       10. distribute-rgt-out-- 84.1%

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

       11. associate-*r/ 84.1%

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

       12. distribute-rgt-out-- 84.1%

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

   11. Simplified 99.5%

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

   12. Taylor expanded in y around 0 84.1%

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

       1. associate-/l* 99.5%

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

   14. Simplified 99.5%

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

   if -4e-52 < a < -1.2e-72

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0 82.9%

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

   4. Taylor expanded in z around inf 83.4%

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

      1. div-sub 83.4%

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

      2. associate-*r/ 82.9%

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

      3. *-commutative 82.9%

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

      4. associate-*r/ 83.4%

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

   6. Simplified 83.4%

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

   if -1.2e-72 < a < 0.00155999999999999997

   1. Initial program 65.1%

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

   3. Taylor expanded in a around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. unsub-neg 50.4%

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

      3. associate-/l* 59.7%

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

      4. div-sub 59.7%

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

      5. sub-neg 59.7%

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

      6. *-inverses 59.7%

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

      7. metadata-eval 59.7%

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

   5. Simplified 59.7%

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

   6. Taylor expanded in x around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. sub-neg 63.7%

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

      3. metadata-eval 63.7%

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

      4. *-commutative 63.7%

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

      5. distribute-lft-neg-in 63.7%

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

      6. distribute-neg-in 63.7%

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

      7. mul-1-neg 63.7%

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

      8. metadata-eval 63.7%

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

      9. +-commutative 63.7%

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

      10. mul-1-neg 63.7%

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

      11. sub-neg 63.7%

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

      12. *-commutative 63.7%

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

   8. Simplified 63.7%

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

Alternative 9: 38.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - a}{t}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 0.0017:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- z a) t))))
   (if (<= a -1.15e-6)
     x
     (if (<= a -1.7e-77) t_1 (if (<= a 0.0017) y (if (<= a 2.5e+96) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (a <= -1.15e-6) {
		tmp = x;
	} else if (a <= -1.7e-77) {
		tmp = t_1;
	} else if (a <= 0.0017) {
		tmp = y;
	} else if (a <= 2.5e+96) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - a) / t)
    if (a <= (-1.15d-6)) then
        tmp = x
    else if (a <= (-1.7d-77)) then
        tmp = t_1
    else if (a <= 0.0017d0) then
        tmp = y
    else if (a <= 2.5d+96) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (a <= -1.15e-6) {
		tmp = x;
	} else if (a <= -1.7e-77) {
		tmp = t_1;
	} else if (a <= 0.0017) {
		tmp = y;
	} else if (a <= 2.5e+96) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((z - a) / t)
	tmp = 0
	if a <= -1.15e-6:
		tmp = x
	elif a <= -1.7e-77:
		tmp = t_1
	elif a <= 0.0017:
		tmp = y
	elif a <= 2.5e+96:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(z - a) / t))
	tmp = 0.0
	if (a <= -1.15e-6)
		tmp = x;
	elseif (a <= -1.7e-77)
		tmp = t_1;
	elseif (a <= 0.0017)
		tmp = y;
	elseif (a <= 2.5e+96)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((z - a) / t);
	tmp = 0.0;
	if (a <= -1.15e-6)
		tmp = x;
	elseif (a <= -1.7e-77)
		tmp = t_1;
	elseif (a <= 0.0017)
		tmp = y;
	elseif (a <= 2.5e+96)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e-6], x, If[LessEqual[a, -1.7e-77], t$95$1, If[LessEqual[a, 0.0017], y, If[LessEqual[a, 2.5e+96], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.15e-6 or 2.5000000000000002e96 < a

   1. Initial program 73.6%

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

   3. Taylor expanded in a around inf 61.4%

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

   if -1.15e-6 < a < -1.69999999999999991e-77 or 0.00169999999999999991 < a < 2.5000000000000002e96

   1. Initial program 66.9%

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

      1. +-commutative 66.9%

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

      2. associate-/l* 78.8%

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

      3. fma-define 78.8%

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

   3. Simplified 78.8%

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

      1. clear-num 78.8%

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

      2. inv-pow 78.8%

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

   6. Applied egg-rr 78.8%

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

      1. unpow-1 78.8%

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

   8. Simplified 78.8%

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

   9. Taylor expanded in t around inf 53.4%

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

       1. associate--l+ 53.4%

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

       2. associate-*r/ 53.4%

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

       3. associate-*r/ 53.4%

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

       4. mul-1-neg 53.4%

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

       5. distribute-lft-neg-out 53.4%

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

       6. div-sub 56.1%

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

       7. distribute-lft-neg-out 56.1%

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

       8. mul-1-neg 56.1%

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

       9. distribute-lft-out-- 56.1%

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

       10. distribute-rgt-out-- 56.1%

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

       11. associate-*r/ 56.1%

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

       12. distribute-rgt-out-- 56.1%

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

   11. Simplified 68.2%

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

   12. Taylor expanded in y around 0 37.7%

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

       1. associate-/l* 47.0%

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

   14. Simplified 47.0%

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

   if -1.69999999999999991e-77 < a < 0.00169999999999999991

   1. Initial program 64.8%

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

   3. Taylor expanded in t around inf 39.9%

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

Alternative 10: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -1 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= a -1e-20)
     t_1
     (if (<= a -6.2e-50)
       (* x (/ (- z a) t))
       (if (<= a 7e+86) (* y (/ (- z t) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (a <= -1e-20) {
		tmp = t_1;
	} else if (a <= -6.2e-50) {
		tmp = x * ((z - a) / t);
	} else if (a <= 7e+86) {
		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 = x + (y * (z / a))
    if (a <= (-1d-20)) then
        tmp = t_1
    else if (a <= (-6.2d-50)) then
        tmp = x * ((z - a) / t)
    else if (a <= 7d+86) 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 = x + (y * (z / a));
	double tmp;
	if (a <= -1e-20) {
		tmp = t_1;
	} else if (a <= -6.2e-50) {
		tmp = x * ((z - a) / t);
	} else if (a <= 7e+86) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if a <= -1e-20:
		tmp = t_1
	elif a <= -6.2e-50:
		tmp = x * ((z - a) / t)
	elif a <= 7e+86:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -1e-20)
		tmp = t_1;
	elseif (a <= -6.2e-50)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= 7e+86)
		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 = x + (y * (z / a));
	tmp = 0.0;
	if (a <= -1e-20)
		tmp = t_1;
	elseif (a <= -6.2e-50)
		tmp = x * ((z - a) / t);
	elseif (a <= 7e+86)
		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[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e-20], t$95$1, If[LessEqual[a, -6.2e-50], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+86], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.99999999999999945e-21 or 7.00000000000000038e86 < a

   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 0 67.9%

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

   4. Taylor expanded in y around inf 69.4%

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

      1. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   if -9.99999999999999945e-21 < a < -6.2000000000000004e-50

   1. Initial program 51.9%

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

      1. +-commutative 51.9%

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

      2. associate-/l* 51.5%

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

      3. fma-define 51.5%

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

   3. Simplified 51.5%

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

      1. clear-num 51.5%

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

      2. inv-pow 51.5%

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

   6. Applied egg-rr 51.5%

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

      1. unpow-1 51.5%

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

   8. Simplified 51.5%

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

   9. Taylor expanded in t around inf 84.1%

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

       1. associate--l+ 84.1%

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

       2. associate-*r/ 84.1%

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

       3. associate-*r/ 84.1%

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

       4. mul-1-neg 84.1%

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

       5. distribute-lft-neg-out 84.1%

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

       6. div-sub 84.1%

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

       7. distribute-lft-neg-out 84.1%

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

       8. mul-1-neg 84.1%

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

       9. distribute-lft-out-- 84.1%

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

       10. distribute-rgt-out-- 84.1%

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

       11. associate-*r/ 84.1%

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

       12. distribute-rgt-out-- 84.1%

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

   11. Simplified 99.5%

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

   12. Taylor expanded in y around 0 84.1%

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

       1. associate-/l* 99.5%

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

   14. Simplified 99.5%

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

   if -6.2000000000000004e-50 < a < 7.00000000000000038e86

   1. Initial program 65.8%

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

      1. +-commutative 65.8%

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

      2. associate-/l* 77.5%

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

      3. fma-define 77.5%

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

   3. Simplified 77.5%

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

      1. clear-num 77.4%

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

      2. inv-pow 77.4%

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

   6. Applied egg-rr 77.4%

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

      1. unpow-1 77.4%

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

   8. Simplified 77.4%

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

   9. Taylor expanded in y around inf 67.1%

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

       1. div-sub 67.1%

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

   11. Simplified 67.1%

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

Alternative 11: 88.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+100}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e+100)
   (+ y (* (/ (- y x) t) (- a z)))
   (if (<= t 8e+53)
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (* (- y x) (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+100) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t <= 8e+53) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7d+100)) then
        tmp = y + (((y - x) / t) * (a - z))
    else if (t <= 8d+53) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + ((y - x) * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+100) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t <= 8e+53) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7e+100:
		tmp = y + (((y - x) / t) * (a - z))
	elif t <= 8e+53:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + ((y - x) * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e+100)
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (t <= 8e+53)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7e+100)
		tmp = y + (((y - x) / t) * (a - z));
	elseif (t <= 8e+53)
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + ((y - x) * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e+100], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+53], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.99999999999999953e100

   1. Initial program 35.7%

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

   3. Taylor expanded in t around inf 66.0%

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

      1. associate--l+ 66.0%

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

      2. distribute-lft-out-- 66.0%

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

      3. div-sub 66.0%

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

      4. mul-1-neg 66.0%

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

      5. unsub-neg 66.0%

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

      6. div-sub 66.0%

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

      7. associate-/l* 79.0%

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

      8. associate-/l* 87.4%

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

      9. distribute-rgt-out-- 87.4%

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

   5. Simplified 87.4%

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

   if -6.99999999999999953e100 < t < 7.9999999999999999e53

   1. Initial program 83.3%

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

      1. clear-num 83.2%

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

      2. inv-pow 83.2%

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

      3. *-commutative 83.2%

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

      4. associate-/r* 94.0%

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

   4. Applied egg-rr 94.0%

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

      1. *-un-lft-identity 94.0%

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

      2. unpow-1 94.0%

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

      3. clear-num 94.0%

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

   6. Applied egg-rr 94.0%

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

      1. *-lft-identity 94.0%

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

   8. Simplified 94.0%

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

   if 7.9999999999999999e53 < t

   1. Initial program 41.1%

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

      1. +-commutative 41.1%

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

      2. associate-/l* 60.0%

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

      3. fma-define 60.0%

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

   3. Simplified 60.0%

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

      1. clear-num 59.9%

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

      2. inv-pow 59.9%

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

   6. Applied egg-rr 59.9%

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

      1. unpow-1 59.9%

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

   8. Simplified 59.9%

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

   9. Taylor expanded in t around inf 71.7%

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

       1. associate--l+ 71.7%

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

       2. associate-*r/ 71.7%

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

       3. associate-*r/ 71.7%

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

       4. mul-1-neg 71.7%

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

       5. distribute-lft-neg-out 71.7%

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

       6. div-sub 71.7%

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

       7. distribute-lft-neg-out 71.7%

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

       8. mul-1-neg 71.7%

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

       9. distribute-lft-out-- 71.7%

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

       10. distribute-rgt-out-- 71.7%

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

       11. associate-*r/ 71.7%

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

       12. distribute-rgt-out-- 71.7%

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

   11. Simplified 85.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+100}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+71}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.85e+71)
   (+ y (* (/ (- y x) t) (- a z)))
   (if (<= t 6.8e+53)
     (+ x (/ (* (- y x) (- z t)) (- a t)))
     (+ y (* (- y x) (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.85e+71) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t <= 6.8e+53) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.85d+71)) then
        tmp = y + (((y - x) / t) * (a - z))
    else if (t <= 6.8d+53) then
        tmp = x + (((y - x) * (z - t)) / (a - t))
    else
        tmp = y + ((y - x) * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.85e+71) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t <= 6.8e+53) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.85e+71:
		tmp = y + (((y - x) / t) * (a - z))
	elif t <= 6.8e+53:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	else:
		tmp = y + ((y - x) * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.85e+71)
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (t <= 6.8e+53)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.85e+71)
		tmp = y + (((y - x) / t) * (a - z));
	elseif (t <= 6.8e+53)
		tmp = x + (((y - x) * (z - t)) / (a - t));
	else
		tmp = y + ((y - x) * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.85e+71], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+53], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.85e71

   1. Initial program 38.3%

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

   3. Taylor expanded in t around inf 66.3%

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

      1. associate--l+ 66.3%

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

      2. distribute-lft-out-- 66.3%

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

      3. div-sub 66.3%

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

      4. mul-1-neg 66.3%

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

      5. unsub-neg 66.3%

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

      6. div-sub 66.3%

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

      7. associate-/l* 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* 88.3%

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

      9. distribute-rgt-out-- 88.3%

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

   5. Simplified 88.3%

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

   if -1.85e71 < t < 6.79999999999999995e53

   1. Initial program 83.5%

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

   if 6.79999999999999995e53 < t

   1. Initial program 41.1%

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

      1. +-commutative 41.1%

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

      2. associate-/l* 60.0%

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

      3. fma-define 60.0%

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

   3. Simplified 60.0%

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

      1. clear-num 59.9%

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

      2. inv-pow 59.9%

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

   6. Applied egg-rr 59.9%

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

      1. unpow-1 59.9%

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

   8. Simplified 59.9%

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

   9. Taylor expanded in t around inf 71.7%

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

       1. associate--l+ 71.7%

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

       2. associate-*r/ 71.7%

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

       3. associate-*r/ 71.7%

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

       4. mul-1-neg 71.7%

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

       5. distribute-lft-neg-out 71.7%

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

       6. div-sub 71.7%

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

       7. distribute-lft-neg-out 71.7%

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

       8. mul-1-neg 71.7%

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

       9. distribute-lft-out-- 71.7%

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

       10. distribute-rgt-out-- 71.7%

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

       11. associate-*r/ 71.7%

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

       12. distribute-rgt-out-- 71.7%

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

   11. Simplified 85.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+71}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e+32)
   x
   (if (<= a -3.4e-72)
     (* z (/ (- x y) t))
     (if (<= a 2.4e+84) (* y (- 1.0 (/ z t))) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+32) {
		tmp = x;
	} else if (a <= -3.4e-72) {
		tmp = z * ((x - y) / t);
	} else if (a <= 2.4e+84) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.2d+32)) then
        tmp = x
    else if (a <= (-3.4d-72)) then
        tmp = z * ((x - y) / t)
    else if (a <= 2.4d+84) then
        tmp = y * (1.0d0 - (z / t))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+32) {
		tmp = x;
	} else if (a <= -3.4e-72) {
		tmp = z * ((x - y) / t);
	} else if (a <= 2.4e+84) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e+32:
		tmp = x
	elif a <= -3.4e-72:
		tmp = z * ((x - y) / t)
	elif a <= 2.4e+84:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e+32)
		tmp = x;
	elseif (a <= -3.4e-72)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (a <= 2.4e+84)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e+32)
		tmp = x;
	elseif (a <= -3.4e-72)
		tmp = z * ((x - y) / t);
	elseif (a <= 2.4e+84)
		tmp = y * (1.0 - (z / t));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e+32], x, If[LessEqual[a, -3.4e-72], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+84], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.19999999999999996e32 or 2.4e84 < a

   1. Initial program 74.0%

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

   3. Taylor expanded in a around inf 61.7%

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

   if -1.19999999999999996e32 < a < -3.3999999999999998e-72

   1. Initial program 71.0%

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

   3. Taylor expanded in a around 0 42.3%

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

      1. mul-1-neg 42.3%

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

      2. unsub-neg 42.3%

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

      3. associate-/l* 44.2%

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

      4. div-sub 44.2%

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

      5. sub-neg 44.2%

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

      6. *-inverses 44.2%

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

      7. metadata-eval 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in z around inf 51.2%

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

      1. div-sub 51.6%

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

   8. Simplified 51.6%

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

   if -3.3999999999999998e-72 < a < 2.4e84

   1. Initial program 64.3%

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

   3. Taylor expanded in a around 0 47.1%

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

      1. mul-1-neg 47.1%

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

      2. unsub-neg 47.1%

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

      3. associate-/l* 57.2%

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

      4. div-sub 57.2%

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

      5. sub-neg 57.2%

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

      6. *-inverses 57.2%

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

      7. metadata-eval 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in x around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. sub-neg 58.3%

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

      3. metadata-eval 58.3%

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

      4. *-commutative 58.3%

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

      5. distribute-lft-neg-in 58.3%

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

      6. distribute-neg-in 58.3%

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

      7. mul-1-neg 58.3%

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

      8. metadata-eval 58.3%

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

      9. +-commutative 58.3%

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

      10. mul-1-neg 58.3%

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

      11. sub-neg 58.3%

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

      12. *-commutative 58.3%

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

   8. Simplified 58.3%

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

Alternative 14: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.02 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.85e-6)
   x
   (if (<= a -2.02e-50)
     (* x (/ (- z a) t))
     (if (<= a 2.9e+90) (* y (- 1.0 (/ z t))) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.85e-6) {
		tmp = x;
	} else if (a <= -2.02e-50) {
		tmp = x * ((z - a) / t);
	} else if (a <= 2.9e+90) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.85d-6)) then
        tmp = x
    else if (a <= (-2.02d-50)) then
        tmp = x * ((z - a) / t)
    else if (a <= 2.9d+90) then
        tmp = y * (1.0d0 - (z / t))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.85e-6) {
		tmp = x;
	} else if (a <= -2.02e-50) {
		tmp = x * ((z - a) / t);
	} else if (a <= 2.9e+90) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.85e-6:
		tmp = x
	elif a <= -2.02e-50:
		tmp = x * ((z - a) / t)
	elif a <= 2.9e+90:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.85e-6)
		tmp = x;
	elseif (a <= -2.02e-50)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= 2.9e+90)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.85e-6)
		tmp = x;
	elseif (a <= -2.02e-50)
		tmp = x * ((z - a) / t);
	elseif (a <= 2.9e+90)
		tmp = y * (1.0 - (z / t));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.85e-6], x, If[LessEqual[a, -2.02e-50], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+90], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8500000000000001e-6 or 2.9000000000000001e90 < 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 60.9%

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

   if -1.8500000000000001e-6 < a < -2.02000000000000007e-50

   1. Initial program 64.9%

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

      1. +-commutative 64.9%

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

      2. associate-/l* 64.4%

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

      3. fma-define 64.4%

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

   3. Simplified 64.4%

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

      1. clear-num 64.4%

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

      2. inv-pow 64.4%

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

   6. Applied egg-rr 64.4%

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

      1. unpow-1 64.4%

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

   8. Simplified 64.4%

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

   9. Taylor expanded in t around inf 56.6%

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

       1. associate--l+ 56.6%

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

       2. associate-*r/ 56.6%

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

       3. associate-*r/ 56.6%

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

       4. mul-1-neg 56.6%

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

       5. distribute-lft-neg-out 56.6%

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

       6. div-sub 56.6%

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

       7. distribute-lft-neg-out 56.6%

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

       8. mul-1-neg 56.6%

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

       9. distribute-lft-out-- 56.6%

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

       10. distribute-rgt-out-- 56.6%

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

       11. associate-*r/ 56.6%

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

       12. distribute-rgt-out-- 56.6%

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

   11. Simplified 73.7%

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

   12. Taylor expanded in y around 0 48.0%

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

       1. associate-/l* 65.1%

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

   14. Simplified 65.1%

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

   if -2.02000000000000007e-50 < a < 2.9000000000000001e90

   1. Initial program 65.8%

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

   3. Taylor expanded in a around 0 47.9%

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

      1. mul-1-neg 47.9%

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

      2. unsub-neg 47.9%

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

      3. associate-/l* 57.5%

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

      4. div-sub 57.5%

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

      5. sub-neg 57.5%

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

      6. *-inverses 57.5%

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

      7. metadata-eval 57.5%

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

   5. Simplified 57.5%

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

   6. Taylor expanded in x around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. sub-neg 57.3%

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

      3. metadata-eval 57.3%

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

      4. *-commutative 57.3%

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

      5. distribute-lft-neg-in 57.3%

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

      6. distribute-neg-in 57.3%

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

      7. mul-1-neg 57.3%

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

      8. metadata-eval 57.3%

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

      9. +-commutative 57.3%

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

      10. mul-1-neg 57.3%

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

      11. sub-neg 57.3%

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

      12. *-commutative 57.3%

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

   8. Simplified 57.3%

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

Alternative 15: 38.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 7.7 \cdot 10^{+84}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e-17)
   x
   (if (<= a -1.1e-62) (* y (/ z a)) (if (<= a 7.7e+84) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e-17) {
		tmp = x;
	} else if (a <= -1.1e-62) {
		tmp = y * (z / a);
	} else if (a <= 7.7e+84) {
		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 <= (-9.5d-17)) then
        tmp = x
    else if (a <= (-1.1d-62)) then
        tmp = y * (z / a)
    else if (a <= 7.7d+84) 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 <= -9.5e-17) {
		tmp = x;
	} else if (a <= -1.1e-62) {
		tmp = y * (z / a);
	} else if (a <= 7.7e+84) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e-17:
		tmp = x
	elif a <= -1.1e-62:
		tmp = y * (z / a)
	elif a <= 7.7e+84:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e-17)
		tmp = x;
	elseif (a <= -1.1e-62)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= 7.7e+84)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e-17)
		tmp = x;
	elseif (a <= -1.1e-62)
		tmp = y * (z / a);
	elseif (a <= 7.7e+84)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e-17], x, If[LessEqual[a, -1.1e-62], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.7e+84], y, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.50000000000000029e-17 or 7.7000000000000003e84 < a

   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 a around inf 60.2%

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

   if -9.50000000000000029e-17 < a < -1.10000000000000009e-62

   1. Initial program 77.3%

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

   3. Taylor expanded in t around 0 47.8%

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

   4. Taylor expanded in z around inf 48.2%

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

      1. div-sub 48.2%

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

      2. associate-*r/ 48.0%

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

      3. *-commutative 48.0%

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

      4. associate-*r/ 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in y around inf 48.8%

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

      1. associate-/l* 49.1%

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

   9. Simplified 49.1%

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

   if -1.10000000000000009e-62 < a < 7.7000000000000003e84

   1. Initial program 64.5%

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

   3. Taylor expanded in t around inf 36.9%

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

Alternative 16: 38.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+84}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.46e+32)
   x
   (if (<= a -5.1e-77) (* x (/ z t)) (if (<= a 1.45e+84) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.46e+32) {
		tmp = x;
	} else if (a <= -5.1e-77) {
		tmp = x * (z / t);
	} else if (a <= 1.45e+84) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.46d+32)) then
        tmp = x
    else if (a <= (-5.1d-77)) then
        tmp = x * (z / t)
    else if (a <= 1.45d+84) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.46e+32) {
		tmp = x;
	} else if (a <= -5.1e-77) {
		tmp = x * (z / t);
	} else if (a <= 1.45e+84) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.46e+32:
		tmp = x
	elif a <= -5.1e-77:
		tmp = x * (z / t)
	elif a <= 1.45e+84:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.46e+32)
		tmp = x;
	elseif (a <= -5.1e-77)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 1.45e+84)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.46e+32)
		tmp = x;
	elseif (a <= -5.1e-77)
		tmp = x * (z / t);
	elseif (a <= 1.45e+84)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.46e+32], x, If[LessEqual[a, -5.1e-77], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+84], y, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.46000000000000005e32 or 1.44999999999999994e84 < a

   1. Initial program 74.0%

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

   3. Taylor expanded in a around inf 61.7%

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

   if -1.46000000000000005e32 < a < -5.10000000000000032e-77

   1. Initial program 73.7%

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

   3. Taylor expanded in a around 0 47.5%

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

      1. mul-1-neg 47.5%

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

      2. unsub-neg 47.5%

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

      3. associate-/l* 49.3%

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

      4. div-sub 49.3%

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

      5. sub-neg 49.3%

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

      6. *-inverses 49.3%

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

      7. metadata-eval 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in x around -inf 33.7%

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

      1. associate-/l* 42.3%

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

   8. Simplified 42.3%

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

   if -5.10000000000000032e-77 < a < 1.44999999999999994e84

   1. Initial program 63.7%

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

   3. Taylor expanded in t around inf 37.0%

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

Alternative 17: 38.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+84}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.65e-52) x (if (<= a 1.4e+84) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e-52) {
		tmp = x;
	} else if (a <= 1.4e+84) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.65d-52)) then
        tmp = x
    else if (a <= 1.4d+84) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e-52) {
		tmp = x;
	} else if (a <= 1.4e+84) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.65e-52:
		tmp = x
	elif a <= 1.4e+84:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.65e-52)
		tmp = x;
	elseif (a <= 1.4e+84)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.65e-52)
		tmp = x;
	elseif (a <= 1.4e+84)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.65e-52], x, If[LessEqual[a, 1.4e+84], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.64999999999999998e-52 or 1.39999999999999991e84 < a

   1. Initial program 72.5%

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

   3. Taylor expanded in a around inf 55.9%

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

   if -1.64999999999999998e-52 < a < 1.39999999999999991e84

   1. Initial program 65.6%

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

   3. Taylor expanded in t around inf 36.0%

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

Alternative 18: 26.0% 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 68.8%

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

3. Taylor expanded in a around inf 29.8%

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

Developer target: 87.1% 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 2024091 
(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))))