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

Percentage Accurate: 67.5% → 86.0%

Time: 23.7s

Alternatives: 19

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.5% 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: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+188}:\\ \;\;\;\;\frac{x}{\frac{t}{z}} - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+163}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.25e+188)
   (- (/ x (/ t z)) (/ y (/ t (- z t))))
   (if (<= t 1.06e+163)
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (/ a (/ t (- y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.25e+188) {
		tmp = (x / (t / z)) - (y / (t / (z - t)));
	} else if (t <= 1.06e+163) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.25d+188)) then
        tmp = (x / (t / z)) - (y / (t / (z - t)))
    else if (t <= 1.06d+163) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + (a / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.25e+188) {
		tmp = (x / (t / z)) - (y / (t / (z - t)));
	} else if (t <= 1.06e+163) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.25e+188:
		tmp = (x / (t / z)) - (y / (t / (z - t)))
	elif t <= 1.06e+163:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + (a / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.25e+188)
		tmp = Float64(Float64(x / Float64(t / z)) - Float64(y / Float64(t / Float64(z - t))));
	elseif (t <= 1.06e+163)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(a / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.25e+188)
		tmp = (x / (t / z)) - (y / (t / (z - t)));
	elseif (t <= 1.06e+163)
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + (a / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.25e+188], N[(N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision] - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e+163], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.25000000000000005e188

   1. Initial program 22.0%

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

      1. associate-*l/ 39.9%

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

   3. Simplified 39.9%

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

      1. associate-/r/ 47.3%

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

   6. Applied egg-rr 47.3%

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

   7. Taylor expanded in x around -inf 68.0%

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

      1. fma-def 68.0%

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

      2. *-commutative 68.0%

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

      3. associate-*r/ 74.2%

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

   9. Simplified 74.2%

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

   10. Taylor expanded in a around 0 52.2%

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

       1. +-commutative 52.2%

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

       2. mul-1-neg 52.2%

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

       3. unsub-neg 52.2%

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

       4. associate-/l* 67.9%

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

       5. associate-/l* 94.9%

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

   12. Simplified 94.9%

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

   if -2.25000000000000005e188 < t < 1.06e163

   1. Initial program 83.7%

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

      1. associate-*l/ 90.9%

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

   3. Simplified 90.9%

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

      1. associate-/r/ 92.6%

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

   6. Applied egg-rr 92.6%

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

   if 1.06e163 < t

   1. Initial program 31.7%

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

      1. associate-*l/ 42.0%

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

   3. Simplified 42.0%

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

   5. Taylor expanded in z around 0 28.4%

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

      1. +-commutative 28.4%

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

      2. associate-*r/ 28.4%

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

      3. mul-1-neg 28.4%

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

      4. distribute-lft-neg-out 28.4%

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

      5. associate-*r/ 42.0%

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

      6. *-commutative 42.0%

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

      7. fma-def 42.5%

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

   7. Simplified 42.5%

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

   8. Taylor expanded in t around inf 76.3%

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

      1. associate-/l* 89.7%

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

   10. Simplified 89.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+188}:\\ \;\;\;\;\frac{x}{\frac{t}{z}} - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+163}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.45 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+212}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -8.5e+80)
     t_1
     (if (<= t 5.5e-91)
       (+ x (/ (- y x) (/ a z)))
       (if (<= t 4.45e+74)
         t_1
         (if (<= t 2.3e+108)
           (+ x (/ z (/ a (- y x))))
           (if (<= t 1.15e+212) (+ y (/ a (/ t (- y x)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -8.5e+80) {
		tmp = t_1;
	} else if (t <= 5.5e-91) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 4.45e+74) {
		tmp = t_1;
	} else if (t <= 2.3e+108) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 1.15e+212) {
		tmp = y + (a / (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 = y * ((z - t) / (a - t))
    if (t <= (-8.5d+80)) then
        tmp = t_1
    else if (t <= 5.5d-91) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 4.45d+74) then
        tmp = t_1
    else if (t <= 2.3d+108) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 1.15d+212) then
        tmp = y + (a / (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 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -8.5e+80) {
		tmp = t_1;
	} else if (t <= 5.5e-91) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 4.45e+74) {
		tmp = t_1;
	} else if (t <= 2.3e+108) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 1.15e+212) {
		tmp = y + (a / (t / (y - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -8.5e+80:
		tmp = t_1
	elif t <= 5.5e-91:
		tmp = x + ((y - x) / (a / z))
	elif t <= 4.45e+74:
		tmp = t_1
	elif t <= 2.3e+108:
		tmp = x + (z / (a / (y - x)))
	elif t <= 1.15e+212:
		tmp = y + (a / (t / (y - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -8.5e+80)
		tmp = t_1;
	elseif (t <= 5.5e-91)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 4.45e+74)
		tmp = t_1;
	elseif (t <= 2.3e+108)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 1.15e+212)
		tmp = Float64(y + Float64(a / Float64(t / Float64(y - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -8.5e+80)
		tmp = t_1;
	elseif (t <= 5.5e-91)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 4.45e+74)
		tmp = t_1;
	elseif (t <= 2.3e+108)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 1.15e+212)
		tmp = y + (a / (t / (y - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+80], t$95$1, If[LessEqual[t, 5.5e-91], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.45e+74], t$95$1, If[LessEqual[t, 2.3e+108], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+212], N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.50000000000000007e80 or 5.49999999999999965e-91 < t < 4.4500000000000001e74 or 1.1499999999999999e212 < t

   1. Initial program 47.8%

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

      1. associate-*l/ 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in y around inf 70.8%

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

      1. div-sub 70.8%

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

   7. Simplified 70.8%

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

   if -8.50000000000000007e80 < t < 5.49999999999999965e-91

   1. Initial program 92.4%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

      1. associate-/r/ 95.3%

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

   6. Applied egg-rr 95.3%

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

   7. Taylor expanded in t around 0 75.9%

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

   if 4.4500000000000001e74 < t < 2.2999999999999999e108

   1. Initial program 84.4%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 68.1%

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

      1. associate-/l* 68.1%

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

   7. Simplified 68.1%

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

   if 2.2999999999999999e108 < t < 1.1499999999999999e212

   1. Initial program 66.2%

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

      1. associate-*l/ 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in z around 0 48.9%

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

      1. +-commutative 48.9%

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

      2. associate-*r/ 48.9%

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

      3. mul-1-neg 48.9%

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

      4. distribute-lft-neg-out 48.9%

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

      5. associate-*r/ 53.5%

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

      6. *-commutative 53.5%

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

      7. fma-def 54.6%

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

   7. Simplified 54.6%

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

   8. Taylor expanded in t around inf 62.0%

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

      1. associate-/l* 70.1%

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

   10. Simplified 70.1%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.45 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+212}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (* (- y x) (- a z)) t))))
   (if (<= t -1.95e+151)
     (* y (/ (- z t) (- a t)))
     (if (<= t -1.25e+79)
       t_1
       (if (<= t 4e+14)
         (+ x (/ (- y x) (/ a (- z t))))
         (if (<= t 2.7e+164) t_1 (+ y (/ a (/ t (- y x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) * (a - z)) / t);
	double tmp;
	if (t <= -1.95e+151) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -1.25e+79) {
		tmp = t_1;
	} else if (t <= 4e+14) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else if (t <= 2.7e+164) {
		tmp = t_1;
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (((y - x) * (a - z)) / t)
    if (t <= (-1.95d+151)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= (-1.25d+79)) then
        tmp = t_1
    else if (t <= 4d+14) then
        tmp = x + ((y - x) / (a / (z - t)))
    else if (t <= 2.7d+164) then
        tmp = t_1
    else
        tmp = y + (a / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) * (a - z)) / t);
	double tmp;
	if (t <= -1.95e+151) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -1.25e+79) {
		tmp = t_1;
	} else if (t <= 4e+14) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else if (t <= 2.7e+164) {
		tmp = t_1;
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (((y - x) * (a - z)) / t)
	tmp = 0
	if t <= -1.95e+151:
		tmp = y * ((z - t) / (a - t))
	elif t <= -1.25e+79:
		tmp = t_1
	elif t <= 4e+14:
		tmp = x + ((y - x) / (a / (z - t)))
	elif t <= 2.7e+164:
		tmp = t_1
	else:
		tmp = y + (a / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t))
	tmp = 0.0
	if (t <= -1.95e+151)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= -1.25e+79)
		tmp = t_1;
	elseif (t <= 4e+14)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))));
	elseif (t <= 2.7e+164)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(a / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (((y - x) * (a - z)) / t);
	tmp = 0.0;
	if (t <= -1.95e+151)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= -1.25e+79)
		tmp = t_1;
	elseif (t <= 4e+14)
		tmp = x + ((y - x) / (a / (z - t)));
	elseif (t <= 2.7e+164)
		tmp = t_1;
	else
		tmp = y + (a / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.95e+151], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.25e+79], t$95$1, If[LessEqual[t, 4e+14], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+164], t$95$1, N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.94999999999999988e151

   1. Initial program 18.2%

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

      1. associate-*l/ 54.7%

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

   3. Simplified 54.7%

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

   5. Taylor expanded in y around inf 82.1%

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

      1. div-sub 82.1%

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

   7. Simplified 82.1%

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

   if -1.94999999999999988e151 < t < -1.25e79 or 4e14 < t < 2.70000000000000006e164

   1. Initial program 63.9%

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

      1. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in t around inf 74.1%

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

      1. associate--l+ 74.1%

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

      2. distribute-lft-out-- 74.1%

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

      3. div-sub 74.1%

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

      4. mul-1-neg 74.1%

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

      5. unsub-neg 74.1%

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

      6. distribute-rgt-out-- 74.1%

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

   7. Simplified 74.1%

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

   if -1.25e79 < t < 4e14

   1. Initial program 92.4%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in a around inf 74.2%

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

      1. associate-/l* 77.4%

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

   7. Simplified 77.4%

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

   if 2.70000000000000006e164 < t

   1. Initial program 31.7%

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

      1. associate-*l/ 42.0%

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

   3. Simplified 42.0%

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

   5. Taylor expanded in z around 0 28.4%

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

      1. +-commutative 28.4%

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

      2. associate-*r/ 28.4%

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

      3. mul-1-neg 28.4%

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

      4. distribute-lft-neg-out 28.4%

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

      5. associate-*r/ 42.0%

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

      6. *-commutative 42.0%

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

      7. fma-def 42.5%

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

   7. Simplified 42.5%

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

   8. Taylor expanded in t around inf 76.3%

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

      1. associate-/l* 89.7%

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

   10. Simplified 89.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+79}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+164}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.38 \cdot 10^{+78}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y a))))
   (if (<= t -1.38e+78)
     y
     (if (<= t 1.1e-294)
       x
       (if (<= t 5.8e-229)
         t_1
         (if (<= t 1.86e-113) x (if (<= t 2.35e-16) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / a);
	double tmp;
	if (t <= -1.38e+78) {
		tmp = y;
	} else if (t <= 1.1e-294) {
		tmp = x;
	} else if (t <= 5.8e-229) {
		tmp = t_1;
	} else if (t <= 1.86e-113) {
		tmp = x;
	} else if (t <= 2.35e-16) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * (y / a)
    if (t <= (-1.38d+78)) then
        tmp = y
    else if (t <= 1.1d-294) then
        tmp = x
    else if (t <= 5.8d-229) then
        tmp = t_1
    else if (t <= 1.86d-113) then
        tmp = x
    else if (t <= 2.35d-16) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / a);
	double tmp;
	if (t <= -1.38e+78) {
		tmp = y;
	} else if (t <= 1.1e-294) {
		tmp = x;
	} else if (t <= 5.8e-229) {
		tmp = t_1;
	} else if (t <= 1.86e-113) {
		tmp = x;
	} else if (t <= 2.35e-16) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * (y / a)
	tmp = 0
	if t <= -1.38e+78:
		tmp = y
	elif t <= 1.1e-294:
		tmp = x
	elif t <= 5.8e-229:
		tmp = t_1
	elif t <= 1.86e-113:
		tmp = x
	elif t <= 2.35e-16:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / a))
	tmp = 0.0
	if (t <= -1.38e+78)
		tmp = y;
	elseif (t <= 1.1e-294)
		tmp = x;
	elseif (t <= 5.8e-229)
		tmp = t_1;
	elseif (t <= 1.86e-113)
		tmp = x;
	elseif (t <= 2.35e-16)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * (y / a);
	tmp = 0.0;
	if (t <= -1.38e+78)
		tmp = y;
	elseif (t <= 1.1e-294)
		tmp = x;
	elseif (t <= 5.8e-229)
		tmp = t_1;
	elseif (t <= 1.86e-113)
		tmp = x;
	elseif (t <= 2.35e-16)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.38e+78], y, If[LessEqual[t, 1.1e-294], x, If[LessEqual[t, 5.8e-229], t$95$1, If[LessEqual[t, 1.86e-113], x, If[LessEqual[t, 2.35e-16], t$95$1, y]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.37999999999999992e78 or 2.35000000000000022e-16 < t

   1. Initial program 48.3%

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

      1. associate-*l/ 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in t around inf 54.9%

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

   if -1.37999999999999992e78 < t < 1.1e-294 or 5.7999999999999999e-229 < t < 1.86000000000000013e-113

   1. Initial program 91.7%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in a around inf 38.4%

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

   if 1.1e-294 < t < 5.7999999999999999e-229 or 1.86000000000000013e-113 < t < 2.35000000000000022e-16

   1. Initial program 94.7%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in x around 0 61.2%

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

   6. Taylor expanded in a around inf 47.3%

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

      1. *-commutative 47.3%

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

      2. *-un-lft-identity 47.3%

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

      3. times-frac 49.8%

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

      4. /-rgt-identity 49.8%

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

   8. Applied egg-rr 49.8%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.38 \cdot 10^{+78}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-229}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-16}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-292}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-225}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.95e+77)
   y
   (if (<= t 1.95e-292)
     x
     (if (<= t 4.2e-225)
       (* (- z t) (/ y a))
       (if (<= t 1.55e-113) x (if (<= t 2.2e-16) (/ y (/ a (- z t))) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e+77) {
		tmp = y;
	} else if (t <= 1.95e-292) {
		tmp = x;
	} else if (t <= 4.2e-225) {
		tmp = (z - t) * (y / a);
	} else if (t <= 1.55e-113) {
		tmp = x;
	} else if (t <= 2.2e-16) {
		tmp = y / (a / (z - t));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.95d+77)) then
        tmp = y
    else if (t <= 1.95d-292) then
        tmp = x
    else if (t <= 4.2d-225) then
        tmp = (z - t) * (y / a)
    else if (t <= 1.55d-113) then
        tmp = x
    else if (t <= 2.2d-16) then
        tmp = y / (a / (z - t))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e+77) {
		tmp = y;
	} else if (t <= 1.95e-292) {
		tmp = x;
	} else if (t <= 4.2e-225) {
		tmp = (z - t) * (y / a);
	} else if (t <= 1.55e-113) {
		tmp = x;
	} else if (t <= 2.2e-16) {
		tmp = y / (a / (z - t));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.95e+77:
		tmp = y
	elif t <= 1.95e-292:
		tmp = x
	elif t <= 4.2e-225:
		tmp = (z - t) * (y / a)
	elif t <= 1.55e-113:
		tmp = x
	elif t <= 2.2e-16:
		tmp = y / (a / (z - t))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.95e+77)
		tmp = y;
	elseif (t <= 1.95e-292)
		tmp = x;
	elseif (t <= 4.2e-225)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	elseif (t <= 1.55e-113)
		tmp = x;
	elseif (t <= 2.2e-16)
		tmp = Float64(y / Float64(a / Float64(z - t)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.95e+77)
		tmp = y;
	elseif (t <= 1.95e-292)
		tmp = x;
	elseif (t <= 4.2e-225)
		tmp = (z - t) * (y / a);
	elseif (t <= 1.55e-113)
		tmp = x;
	elseif (t <= 2.2e-16)
		tmp = y / (a / (z - t));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.95e+77], y, If[LessEqual[t, 1.95e-292], x, If[LessEqual[t, 4.2e-225], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e-113], x, If[LessEqual[t, 2.2e-16], N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.9499999999999999e77 or 2.2e-16 < t

   1. Initial program 48.3%

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

      1. associate-*l/ 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in t around inf 54.9%

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

   if -1.9499999999999999e77 < t < 1.95e-292 or 4.20000000000000001e-225 < t < 1.55000000000000006e-113

   1. Initial program 91.7%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in a around inf 38.4%

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

   if 1.95e-292 < t < 4.20000000000000001e-225

   1. Initial program 90.6%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 62.2%

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

   6. Taylor expanded in a around inf 53.3%

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

      1. *-commutative 53.3%

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

      2. *-un-lft-identity 53.3%

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

      3. times-frac 62.7%

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

      4. /-rgt-identity 62.7%

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

   8. Applied egg-rr 62.7%

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

   if 1.55000000000000006e-113 < t < 2.2e-16

   1. Initial program 96.2%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around 0 60.8%

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

   6. Taylor expanded in a around inf 45.0%

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

      1. associate-/l* 45.2%

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

   8. Simplified 45.2%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-292}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-225}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a - t}{z}}\\ \mathbf{if}\;t \leq -1.04 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ (- a t) z))))
   (if (<= t -1.04e+77)
     y
     (if (<= t 4.8e-275)
       x
       (if (<= t 4.5e-227)
         t_1
         (if (<= t 2.35e-132) x (if (<= t 2.35e-16) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / ((a - t) / z);
	double tmp;
	if (t <= -1.04e+77) {
		tmp = y;
	} else if (t <= 4.8e-275) {
		tmp = x;
	} else if (t <= 4.5e-227) {
		tmp = t_1;
	} else if (t <= 2.35e-132) {
		tmp = x;
	} else if (t <= 2.35e-16) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / ((a - t) / z)
    if (t <= (-1.04d+77)) then
        tmp = y
    else if (t <= 4.8d-275) then
        tmp = x
    else if (t <= 4.5d-227) then
        tmp = t_1
    else if (t <= 2.35d-132) then
        tmp = x
    else if (t <= 2.35d-16) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / ((a - t) / z);
	double tmp;
	if (t <= -1.04e+77) {
		tmp = y;
	} else if (t <= 4.8e-275) {
		tmp = x;
	} else if (t <= 4.5e-227) {
		tmp = t_1;
	} else if (t <= 2.35e-132) {
		tmp = x;
	} else if (t <= 2.35e-16) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / ((a - t) / z)
	tmp = 0
	if t <= -1.04e+77:
		tmp = y
	elif t <= 4.8e-275:
		tmp = x
	elif t <= 4.5e-227:
		tmp = t_1
	elif t <= 2.35e-132:
		tmp = x
	elif t <= 2.35e-16:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(Float64(a - t) / z))
	tmp = 0.0
	if (t <= -1.04e+77)
		tmp = y;
	elseif (t <= 4.8e-275)
		tmp = x;
	elseif (t <= 4.5e-227)
		tmp = t_1;
	elseif (t <= 2.35e-132)
		tmp = x;
	elseif (t <= 2.35e-16)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / ((a - t) / z);
	tmp = 0.0;
	if (t <= -1.04e+77)
		tmp = y;
	elseif (t <= 4.8e-275)
		tmp = x;
	elseif (t <= 4.5e-227)
		tmp = t_1;
	elseif (t <= 2.35e-132)
		tmp = x;
	elseif (t <= 2.35e-16)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.04e+77], y, If[LessEqual[t, 4.8e-275], x, If[LessEqual[t, 4.5e-227], t$95$1, If[LessEqual[t, 2.35e-132], x, If[LessEqual[t, 2.35e-16], t$95$1, y]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.04e77 or 2.35000000000000022e-16 < t

   1. Initial program 48.3%

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

      1. associate-*l/ 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in t around inf 54.9%

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

   if -1.04e77 < t < 4.79999999999999981e-275 or 4.49999999999999993e-227 < t < 2.3500000000000001e-132

   1. Initial program 91.6%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in a around inf 37.8%

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

   if 4.79999999999999981e-275 < t < 4.49999999999999993e-227 or 2.3500000000000001e-132 < t < 2.35000000000000022e-16

   1. Initial program 94.8%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in x around 0 62.1%

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

   6. Taylor expanded in z around inf 53.4%

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

      1. associate-/l* 56.0%

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

   8. Simplified 56.0%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.04 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-227}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-16}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+196}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+164}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.1e+196)
   y
   (if (<= t 3.1e+164)
     (+ x (* (- z t) (/ (- y x) (- a t))))
     (+ y (/ a (/ t (- y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+196) {
		tmp = y;
	} else if (t <= 3.1e+164) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.1d+196)) then
        tmp = y
    else if (t <= 3.1d+164) then
        tmp = x + ((z - t) * ((y - x) / (a - t)))
    else
        tmp = y + (a / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+196) {
		tmp = y;
	} else if (t <= 3.1e+164) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.1e+196:
		tmp = y
	elif t <= 3.1e+164:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	else:
		tmp = y + (a / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.1e+196)
		tmp = y;
	elseif (t <= 3.1e+164)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(a / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.1e+196)
		tmp = y;
	elseif (t <= 3.1e+164)
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	else
		tmp = y + (a / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.1e+196], y, If[LessEqual[t, 3.1e+164], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.09999999999999999e196

   1. Initial program 23.3%

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

      1. associate-*l/ 38.0%

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

   3. Simplified 38.0%

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

   5. Taylor expanded in t around inf 80.8%

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

   if -1.09999999999999999e196 < t < 3.1000000000000002e164

   1. Initial program 83.3%

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

      1. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   if 3.1000000000000002e164 < t

   1. Initial program 31.7%

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

      1. associate-*l/ 42.0%

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

   3. Simplified 42.0%

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

   5. Taylor expanded in z around 0 28.4%

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

      1. +-commutative 28.4%

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

      2. associate-*r/ 28.4%

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

      3. mul-1-neg 28.4%

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

      4. distribute-lft-neg-out 28.4%

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

      5. associate-*r/ 42.0%

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

      6. *-commutative 42.0%

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

      7. fma-def 42.5%

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

   7. Simplified 42.5%

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

   8. Taylor expanded in t around inf 76.3%

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

      1. associate-/l* 89.7%

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

   10. Simplified 89.7%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+196}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+164}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+196}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+164}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.4e+196)
   y
   (if (<= t 2.7e+164)
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (/ a (/ t (- y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e+196) {
		tmp = y;
	} else if (t <= 2.7e+164) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.4d+196)) then
        tmp = y
    else if (t <= 2.7d+164) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + (a / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e+196) {
		tmp = y;
	} else if (t <= 2.7e+164) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.4e+196:
		tmp = y
	elif t <= 2.7e+164:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + (a / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.4e+196)
		tmp = y;
	elseif (t <= 2.7e+164)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(a / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.4e+196)
		tmp = y;
	elseif (t <= 2.7e+164)
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + (a / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.4e+196], y, If[LessEqual[t, 2.7e+164], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4e196

   1. Initial program 23.3%

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

      1. associate-*l/ 38.0%

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

   3. Simplified 38.0%

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

   5. Taylor expanded in t around inf 80.8%

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

   if -2.4e196 < t < 2.70000000000000006e164

   1. Initial program 83.3%

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

      1. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

      1. associate-/r/ 92.5%

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

   6. Applied egg-rr 92.5%

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

   if 2.70000000000000006e164 < t

   1. Initial program 31.7%

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

      1. associate-*l/ 42.0%

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

   3. Simplified 42.0%

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

   5. Taylor expanded in z around 0 28.4%

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

      1. +-commutative 28.4%

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

      2. associate-*r/ 28.4%

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

      3. mul-1-neg 28.4%

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

      4. distribute-lft-neg-out 28.4%

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

      5. associate-*r/ 42.0%

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

      6. *-commutative 42.0%

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

      7. fma-def 42.5%

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

   7. Simplified 42.5%

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

   8. Taylor expanded in t around inf 76.3%

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

      1. associate-/l* 89.7%

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

   10. Simplified 89.7%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+196}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+164}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+195}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+77}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+195)
   x
   (if (<= a -7.4e+56)
     (/ y (/ a (- z t)))
     (if (<= a -5.3e+14) x (if (<= a 7.2e+77) (/ (- y) (/ t (- z t))) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+195) {
		tmp = x;
	} else if (a <= -7.4e+56) {
		tmp = y / (a / (z - t));
	} else if (a <= -5.3e+14) {
		tmp = x;
	} else if (a <= 7.2e+77) {
		tmp = -y / (t / (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 <= (-1.9d+195)) then
        tmp = x
    else if (a <= (-7.4d+56)) then
        tmp = y / (a / (z - t))
    else if (a <= (-5.3d+14)) then
        tmp = x
    else if (a <= 7.2d+77) then
        tmp = -y / (t / (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 <= -1.9e+195) {
		tmp = x;
	} else if (a <= -7.4e+56) {
		tmp = y / (a / (z - t));
	} else if (a <= -5.3e+14) {
		tmp = x;
	} else if (a <= 7.2e+77) {
		tmp = -y / (t / (z - t));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+195:
		tmp = x
	elif a <= -7.4e+56:
		tmp = y / (a / (z - t))
	elif a <= -5.3e+14:
		tmp = x
	elif a <= 7.2e+77:
		tmp = -y / (t / (z - t))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+195)
		tmp = x;
	elseif (a <= -7.4e+56)
		tmp = Float64(y / Float64(a / Float64(z - t)));
	elseif (a <= -5.3e+14)
		tmp = x;
	elseif (a <= 7.2e+77)
		tmp = Float64(Float64(-y) / Float64(t / 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 <= -1.9e+195)
		tmp = x;
	elseif (a <= -7.4e+56)
		tmp = y / (a / (z - t));
	elseif (a <= -5.3e+14)
		tmp = x;
	elseif (a <= 7.2e+77)
		tmp = -y / (t / (z - t));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+195], x, If[LessEqual[a, -7.4e+56], N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.3e+14], x, If[LessEqual[a, 7.2e+77], N[((-y) / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9e195 or -7.39999999999999994e56 < a < -5.3e14 or 7.1999999999999996e77 < a

   1. Initial program 76.0%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in a around inf 56.6%

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

   if -1.9e195 < a < -7.39999999999999994e56

   1. Initial program 66.3%

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

      1. associate-*l/ 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in x around 0 44.7%

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

   6. Taylor expanded in a around inf 40.8%

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

      1. associate-/l* 44.2%

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

   8. Simplified 44.2%

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

   if -5.3e14 < a < 7.1999999999999996e77

   1. Initial program 73.9%

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

      1. associate-*l/ 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in x around 0 50.0%

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

   6. Taylor expanded in a around 0 43.1%

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

      1. mul-1-neg 43.1%

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

      2. associate-/l* 56.4%

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

   8. Simplified 56.4%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+195}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+77}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+76}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= t -5.5e+76)
     y
     (if (<= t 1.6e-275)
       x
       (if (<= t 4.9e-227)
         t_1
         (if (<= t 1.55e-113)
           x
           (if (<= t 9.5e-6) t_1 (if (<= t 2.4e+78) x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (t <= -5.5e+76) {
		tmp = y;
	} else if (t <= 1.6e-275) {
		tmp = x;
	} else if (t <= 4.9e-227) {
		tmp = t_1;
	} else if (t <= 1.55e-113) {
		tmp = x;
	} else if (t <= 9.5e-6) {
		tmp = t_1;
	} else if (t <= 2.4e+78) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / a)
    if (t <= (-5.5d+76)) then
        tmp = y
    else if (t <= 1.6d-275) then
        tmp = x
    else if (t <= 4.9d-227) then
        tmp = t_1
    else if (t <= 1.55d-113) then
        tmp = x
    else if (t <= 9.5d-6) then
        tmp = t_1
    else if (t <= 2.4d+78) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (t <= -5.5e+76) {
		tmp = y;
	} else if (t <= 1.6e-275) {
		tmp = x;
	} else if (t <= 4.9e-227) {
		tmp = t_1;
	} else if (t <= 1.55e-113) {
		tmp = x;
	} else if (t <= 9.5e-6) {
		tmp = t_1;
	} else if (t <= 2.4e+78) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if t <= -5.5e+76:
		tmp = y
	elif t <= 1.6e-275:
		tmp = x
	elif t <= 4.9e-227:
		tmp = t_1
	elif t <= 1.55e-113:
		tmp = x
	elif t <= 9.5e-6:
		tmp = t_1
	elif t <= 2.4e+78:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (t <= -5.5e+76)
		tmp = y;
	elseif (t <= 1.6e-275)
		tmp = x;
	elseif (t <= 4.9e-227)
		tmp = t_1;
	elseif (t <= 1.55e-113)
		tmp = x;
	elseif (t <= 9.5e-6)
		tmp = t_1;
	elseif (t <= 2.4e+78)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (t <= -5.5e+76)
		tmp = y;
	elseif (t <= 1.6e-275)
		tmp = x;
	elseif (t <= 4.9e-227)
		tmp = t_1;
	elseif (t <= 1.55e-113)
		tmp = x;
	elseif (t <= 9.5e-6)
		tmp = t_1;
	elseif (t <= 2.4e+78)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+76], y, If[LessEqual[t, 1.6e-275], x, If[LessEqual[t, 4.9e-227], t$95$1, If[LessEqual[t, 1.55e-113], x, If[LessEqual[t, 9.5e-6], t$95$1, If[LessEqual[t, 2.4e+78], x, y]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5000000000000001e76 or 2.3999999999999999e78 < t

   1. Initial program 42.3%

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

      1. associate-*l/ 60.6%

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

   3. Simplified 60.6%

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

   5. Taylor expanded in t around inf 61.4%

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

   if -5.5000000000000001e76 < t < 1.6e-275 or 4.9000000000000002e-227 < t < 1.55000000000000006e-113 or 9.5000000000000005e-6 < t < 2.3999999999999999e78

   1. Initial program 87.6%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in a around inf 39.1%

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

   if 1.6e-275 < t < 4.9000000000000002e-227 or 1.55000000000000006e-113 < t < 9.5000000000000005e-6

   1. Initial program 95.0%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around inf 69.2%

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

      1. div-sub 69.2%

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

   7. Simplified 69.2%

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

   8. Taylor expanded in t around 0 42.1%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+76}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.3e+77)
   y
   (if (<= t 7e-275)
     x
     (if (<= t 2e-228)
       (* y (/ z a))
       (if (<= t 2.1e-113)
         x
         (if (<= t 8.5e-5) (/ y (/ a z)) (if (<= t 1.16e+76) x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e+77) {
		tmp = y;
	} else if (t <= 7e-275) {
		tmp = x;
	} else if (t <= 2e-228) {
		tmp = y * (z / a);
	} else if (t <= 2.1e-113) {
		tmp = x;
	} else if (t <= 8.5e-5) {
		tmp = y / (a / z);
	} else if (t <= 1.16e+76) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.3d+77)) then
        tmp = y
    else if (t <= 7d-275) then
        tmp = x
    else if (t <= 2d-228) then
        tmp = y * (z / a)
    else if (t <= 2.1d-113) then
        tmp = x
    else if (t <= 8.5d-5) then
        tmp = y / (a / z)
    else if (t <= 1.16d+76) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e+77) {
		tmp = y;
	} else if (t <= 7e-275) {
		tmp = x;
	} else if (t <= 2e-228) {
		tmp = y * (z / a);
	} else if (t <= 2.1e-113) {
		tmp = x;
	} else if (t <= 8.5e-5) {
		tmp = y / (a / z);
	} else if (t <= 1.16e+76) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.3e+77:
		tmp = y
	elif t <= 7e-275:
		tmp = x
	elif t <= 2e-228:
		tmp = y * (z / a)
	elif t <= 2.1e-113:
		tmp = x
	elif t <= 8.5e-5:
		tmp = y / (a / z)
	elif t <= 1.16e+76:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.3e+77)
		tmp = y;
	elseif (t <= 7e-275)
		tmp = x;
	elseif (t <= 2e-228)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 2.1e-113)
		tmp = x;
	elseif (t <= 8.5e-5)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 1.16e+76)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.3e+77)
		tmp = y;
	elseif (t <= 7e-275)
		tmp = x;
	elseif (t <= 2e-228)
		tmp = y * (z / a);
	elseif (t <= 2.1e-113)
		tmp = x;
	elseif (t <= 8.5e-5)
		tmp = y / (a / z);
	elseif (t <= 1.16e+76)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.3e+77], y, If[LessEqual[t, 7e-275], x, If[LessEqual[t, 2e-228], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-113], x, If[LessEqual[t, 8.5e-5], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.16e+76], x, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.2999999999999998e77 or 1.1599999999999999e76 < t

   1. Initial program 42.3%

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

      1. associate-*l/ 60.6%

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

   3. Simplified 60.6%

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

   5. Taylor expanded in t around inf 61.4%

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

   if -3.2999999999999998e77 < t < 6.99999999999999938e-275 or 2.00000000000000007e-228 < t < 2.1e-113 or 8.500000000000001e-5 < t < 1.1599999999999999e76

   1. Initial program 87.6%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in a around inf 39.1%

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

   if 6.99999999999999938e-275 < t < 2.00000000000000007e-228

   1. Initial program 86.5%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 85.8%

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

      1. div-sub 85.8%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in t around 0 73.1%

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

   if 2.1e-113 < t < 8.500000000000001e-5

   1. Initial program 96.8%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around 0 63.8%

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

   6. Taylor expanded in t around 0 35.3%

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

      1. associate-/l* 35.4%

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

   8. Simplified 35.4%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-240}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= y -5.5e-42)
     t_1
     (if (<= y 3e-240) (/ (- x) (/ (- a t) z)) (if (<= y 2.9e-91) x t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -5.5e-42) {
		tmp = t_1;
	} else if (y <= 3e-240) {
		tmp = -x / ((a - t) / z);
	} else if (y <= 2.9e-91) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (y <= (-5.5d-42)) then
        tmp = t_1
    else if (y <= 3d-240) then
        tmp = -x / ((a - t) / z)
    else if (y <= 2.9d-91) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -5.5e-42) {
		tmp = t_1;
	} else if (y <= 3e-240) {
		tmp = -x / ((a - t) / z);
	} else if (y <= 2.9e-91) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -5.5e-42:
		tmp = t_1
	elif y <= 3e-240:
		tmp = -x / ((a - t) / z)
	elif y <= 2.9e-91:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -5.5e-42)
		tmp = t_1;
	elseif (y <= 3e-240)
		tmp = Float64(Float64(-x) / Float64(Float64(a - t) / z));
	elseif (y <= 2.9e-91)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -5.5e-42)
		tmp = t_1;
	elseif (y <= 3e-240)
		tmp = -x / ((a - t) / z);
	elseif (y <= 2.9e-91)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e-42], t$95$1, If[LessEqual[y, 3e-240], N[((-x) / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-91], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5e-42 or 2.9000000000000001e-91 < y

   1. Initial program 73.8%

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

      1. associate-*l/ 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in y around inf 70.8%

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

      1. div-sub 70.8%

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

   7. Simplified 70.8%

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

   if -5.5e-42 < y < 2.99999999999999991e-240

   1. Initial program 73.3%

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

      1. associate-*l/ 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in z around -inf 49.2%

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

   6. Taylor expanded in y around 0 46.1%

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

      1. mul-1-neg 46.1%

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

      2. associate-/l* 49.2%

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

      3. distribute-neg-frac 49.2%

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

   8. Simplified 49.2%

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

   if 2.99999999999999991e-240 < y < 2.9000000000000001e-91

   1. Initial program 73.7%

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

      1. associate-*l/ 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in a around inf 48.2%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-240}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-241}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= y -1.55e-41)
     t_1
     (if (<= y 1.9e-241)
       (* z (/ (- y x) (- a t)))
       (if (<= y 1.95e-93) x t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -1.55e-41) {
		tmp = t_1;
	} else if (y <= 1.9e-241) {
		tmp = z * ((y - x) / (a - t));
	} else if (y <= 1.95e-93) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (y <= (-1.55d-41)) then
        tmp = t_1
    else if (y <= 1.9d-241) then
        tmp = z * ((y - x) / (a - t))
    else if (y <= 1.95d-93) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (y <= -1.55e-41) {
		tmp = t_1;
	} else if (y <= 1.9e-241) {
		tmp = z * ((y - x) / (a - t));
	} else if (y <= 1.95e-93) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if y <= -1.55e-41:
		tmp = t_1
	elif y <= 1.9e-241:
		tmp = z * ((y - x) / (a - t))
	elif y <= 1.95e-93:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (y <= -1.55e-41)
		tmp = t_1;
	elseif (y <= 1.9e-241)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (y <= 1.95e-93)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (y <= -1.55e-41)
		tmp = t_1;
	elseif (y <= 1.9e-241)
		tmp = z * ((y - x) / (a - t));
	elseif (y <= 1.95e-93)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e-41], t$95$1, If[LessEqual[y, 1.9e-241], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-93], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55e-41 or 1.95000000000000009e-93 < y

   1. Initial program 73.8%

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

      1. associate-*l/ 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in y around inf 70.8%

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

      1. div-sub 70.8%

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

   7. Simplified 70.8%

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

   if -1.55e-41 < y < 1.8999999999999999e-241

   1. Initial program 73.3%

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

      1. associate-*l/ 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in z around inf 50.8%

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

      1. div-sub 50.8%

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

   7. Simplified 50.8%

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

   if 1.8999999999999999e-241 < y < 1.95000000000000009e-93

   1. Initial program 73.7%

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

      1. associate-*l/ 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in a around inf 48.2%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-241}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+79)
   (* y (/ (- z t) (- a t)))
   (if (<= t 6.6e+108)
     (+ x (/ (- y x) (/ a (- z t))))
     (+ y (/ a (/ t (- y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+79) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 6.6e+108) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.7d+79)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 6.6d+108) then
        tmp = x + ((y - x) / (a / (z - t)))
    else
        tmp = y + (a / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+79) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 6.6e+108) {
		tmp = x + ((y - x) / (a / (z - t)));
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+79:
		tmp = y * ((z - t) / (a - t))
	elif t <= 6.6e+108:
		tmp = x + ((y - x) / (a / (z - t)))
	else:
		tmp = y + (a / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+79)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 6.6e+108)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / Float64(z - t))));
	else
		tmp = Float64(y + Float64(a / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+79)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 6.6e+108)
		tmp = x + ((y - x) / (a / (z - t)));
	else
		tmp = y + (a / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+79], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+108], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7e79

   1. Initial program 28.2%

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

      1. associate-*l/ 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in y around inf 71.5%

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

      1. div-sub 71.5%

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

   7. Simplified 71.5%

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

   if -2.7e79 < t < 6.60000000000000038e108

   1. Initial program 89.6%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in a around inf 70.7%

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

      1. associate-/l* 74.2%

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

   7. Simplified 74.2%

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

   if 6.60000000000000038e108 < t

   1. Initial program 46.8%

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

      1. associate-*l/ 59.6%

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

   3. Simplified 59.6%

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

   5. Taylor expanded in z around 0 35.9%

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

      1. +-commutative 35.9%

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

      2. associate-*r/ 35.9%

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

      3. mul-1-neg 35.9%

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

      4. distribute-lft-neg-out 35.9%

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

      5. associate-*r/ 48.7%

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

      6. *-commutative 48.7%

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

      7. fma-def 49.2%

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

   7. Simplified 49.2%

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

   8. Taylor expanded in t around inf 70.0%

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

      1. associate-/l* 78.4%

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

   10. Simplified 78.4%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+76}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.8e+76)
   y
   (if (<= t -5.4e-68) x (if (<= t 2.3e-16) (/ z (/ a (- y x))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.8e+76) {
		tmp = y;
	} else if (t <= -5.4e-68) {
		tmp = x;
	} else if (t <= 2.3e-16) {
		tmp = z / (a / (y - x));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.8d+76)) then
        tmp = y
    else if (t <= (-5.4d-68)) then
        tmp = x
    else if (t <= 2.3d-16) then
        tmp = z / (a / (y - x))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.8e+76) {
		tmp = y;
	} else if (t <= -5.4e-68) {
		tmp = x;
	} else if (t <= 2.3e-16) {
		tmp = z / (a / (y - x));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.8e+76:
		tmp = y
	elif t <= -5.4e-68:
		tmp = x
	elif t <= 2.3e-16:
		tmp = z / (a / (y - x))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.8e+76)
		tmp = y;
	elseif (t <= -5.4e-68)
		tmp = x;
	elseif (t <= 2.3e-16)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.8e+76)
		tmp = y;
	elseif (t <= -5.4e-68)
		tmp = x;
	elseif (t <= 2.3e-16)
		tmp = z / (a / (y - x));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.8e+76], y, If[LessEqual[t, -5.4e-68], x, If[LessEqual[t, 2.3e-16], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.8000000000000003e76 or 2.2999999999999999e-16 < t

   1. Initial program 48.3%

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

      1. associate-*l/ 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in t around inf 54.9%

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

   if -5.8000000000000003e76 < t < -5.4000000000000003e-68

   1. Initial program 83.8%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in a around inf 42.9%

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

   if -5.4000000000000003e-68 < t < 2.2999999999999999e-16

   1. Initial program 94.1%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around -inf 55.8%

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

   6. Taylor expanded in a around inf 44.5%

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

      1. associate-/l* 45.6%

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

   8. Simplified 45.6%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+76}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 65.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+79} \lor \neg \left(t \leq 8.5 \cdot 10^{-91}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.25e+79) (not (<= t 8.5e-91)))
   (* y (/ (- z t) (- a t)))
   (+ x (/ z (/ a (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.25e+79) || !(t <= 8.5e-91)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.25d+79)) .or. (.not. (t <= 8.5d-91))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z / (a / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.25e+79) || !(t <= 8.5e-91)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.25e+79) or not (t <= 8.5e-91):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z / (a / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.25e+79) || !(t <= 8.5e-91))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.25e+79) || ~((t <= 8.5e-91)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z / (a / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.25e+79], N[Not[LessEqual[t, 8.5e-91]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25e79 or 8.49999999999999985e-91 < t

   1. Initial program 53.0%

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

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in y around inf 67.1%

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

      1. div-sub 67.1%

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

   7. Simplified 67.1%

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

   if -1.25e79 < t < 8.49999999999999985e-91

   1. Initial program 92.4%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in t around 0 72.7%

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

      1. associate-/l* 75.6%

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

   7. Simplified 75.6%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+79} \lor \neg \left(t \leq 8.5 \cdot 10^{-91}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 65.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+79} \lor \neg \left(t \leq 8.5 \cdot 10^{-91}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.4e+79) (not (<= t 8.5e-91)))
   (* y (/ (- z t) (- a t)))
   (+ x (/ (- y x) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.4e+79) || !(t <= 8.5e-91)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.4d+79)) .or. (.not. (t <= 8.5d-91))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + ((y - x) / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.4e+79) || !(t <= 8.5e-91)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.4e+79) or not (t <= 8.5e-91):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.4e+79) || !(t <= 8.5e-91))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.4e+79) || ~((t <= 8.5e-91)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.4e+79], N[Not[LessEqual[t, 8.5e-91]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4000000000000001e79 or 8.49999999999999985e-91 < t

   1. Initial program 53.0%

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

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in y around inf 67.1%

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

      1. div-sub 67.1%

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

   7. Simplified 67.1%

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

   if -1.4000000000000001e79 < t < 8.49999999999999985e-91

   1. Initial program 92.4%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

      1. associate-/r/ 95.3%

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

   6. Applied egg-rr 95.3%

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

   7. Taylor expanded in t around 0 75.9%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+79} \lor \neg \left(t \leq 8.5 \cdot 10^{-91}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+78}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.25e+78) y (if (<= t 2.4e+78) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+78) {
		tmp = y;
	} else if (t <= 2.4e+78) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.25d+78)) then
        tmp = y
    else if (t <= 2.4d+78) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+78) {
		tmp = y;
	} else if (t <= 2.4e+78) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.25e+78:
		tmp = y
	elif t <= 2.4e+78:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.25e+78)
		tmp = y;
	elseif (t <= 2.4e+78)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.25e+78)
		tmp = y;
	elseif (t <= 2.4e+78)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.25e+78], y, If[LessEqual[t, 2.4e+78], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.24999999999999996e78 or 2.3999999999999999e78 < t

   1. Initial program 42.3%

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

      1. associate-*l/ 60.6%

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

   3. Simplified 60.6%

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

   5. Taylor expanded in t around inf 61.4%

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

   if -1.24999999999999996e78 < t < 2.3999999999999999e78

   1. Initial program 89.3%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in a around inf 33.8%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+78}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.7%

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

   1. associate-*l/ 82.0%

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

3. Simplified 82.0%

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

5. Taylor expanded in a around inf 24.8%

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

6. Final simplification 24.8%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 86.2% accurate, 0.7× 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 2024019 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (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))))