Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B

Percentage Accurate: 85.0% → 98.3%

Time: 8.8s

Alternatives: 10

Speedup: 1.0×

• could not determine a ground truth

  1. x = 4.8075542177846523e-225
  2. y = 5.252243818537559e-224
  3. z = 3.63444805291395e-179
  4. t = -6.085763140166005e+35
  5. a = 1.2613042169642747e-231

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{a - t}{z - t}} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.4%

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

   1. associate-/l* 99.6%

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

3. Simplified 99.6%

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

   1. clear-num 99.5%

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

   2. un-div-inv 99.7%

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

6. Applied egg-rr 99.7%

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

7. Final simplification 99.7%

   \[\leadsto x + \frac{y}{\frac{a - t}{z - t}} \]
8. Add Preprocessing

Alternative 2: 77.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{t - a}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-79}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -1.38 \cdot 10^{-111}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y (- t a))))))
   (if (<= t -1.15e+58)
     t_1
     (if (<= t -6e-79)
       (- x (/ y (/ t z)))
       (if (<= t -1.38e-111)
         (+ x y)
         (if (<= t 9.5e+57) (+ x (* y (/ z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / (t - a)));
	double tmp;
	if (t <= -1.15e+58) {
		tmp = t_1;
	} else if (t <= -6e-79) {
		tmp = x - (y / (t / z));
	} else if (t <= -1.38e-111) {
		tmp = x + y;
	} else if (t <= 9.5e+57) {
		tmp = x + (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / (t - a)))
    if (t <= (-1.15d+58)) then
        tmp = t_1
    else if (t <= (-6d-79)) then
        tmp = x - (y / (t / z))
    else if (t <= (-1.38d-111)) then
        tmp = x + y
    else if (t <= 9.5d+57) then
        tmp = x + (y * (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / (t - a)));
	double tmp;
	if (t <= -1.15e+58) {
		tmp = t_1;
	} else if (t <= -6e-79) {
		tmp = x - (y / (t / z));
	} else if (t <= -1.38e-111) {
		tmp = x + y;
	} else if (t <= 9.5e+57) {
		tmp = x + (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / (t - a)))
	tmp = 0
	if t <= -1.15e+58:
		tmp = t_1
	elif t <= -6e-79:
		tmp = x - (y / (t / z))
	elif t <= -1.38e-111:
		tmp = x + y
	elif t <= 9.5e+57:
		tmp = x + (y * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / Float64(t - a))))
	tmp = 0.0
	if (t <= -1.15e+58)
		tmp = t_1;
	elseif (t <= -6e-79)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	elseif (t <= -1.38e-111)
		tmp = Float64(x + y);
	elseif (t <= 9.5e+57)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / (t - a)));
	tmp = 0.0;
	if (t <= -1.15e+58)
		tmp = t_1;
	elseif (t <= -6e-79)
		tmp = x - (y / (t / z));
	elseif (t <= -1.38e-111)
		tmp = x + y;
	elseif (t <= 9.5e+57)
		tmp = x + (y * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+58], t$95$1, If[LessEqual[t, -6e-79], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.38e-111], N[(x + y), $MachinePrecision], If[LessEqual[t, 9.5e+57], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.15000000000000001e58 or 9.4999999999999997e57 < t

   1. Initial program 72.1%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 68.0%

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

      1. associate-*r/ 68.0%

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

      2. mul-1-neg 68.0%

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

      3. distribute-lft-neg-out 68.0%

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

      4. *-commutative 68.0%

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

      5. associate-/l* 91.3%

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

      6. distribute-neg-frac 91.3%

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

      7. distribute-neg-frac2 91.3%

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

      8. neg-sub0 91.3%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} \]

      9. associate--r- 91.3%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - a\right) + t}} \]

      10. neg-sub0 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in y around 0 68.0%

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

      1. associate-/l* 86.5%

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

   10. Simplified 86.5%

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

   if -1.15000000000000001e58 < t < -5.99999999999999999e-79

   1. Initial program 100.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf 94.6%

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

   8. Taylor expanded in a around 0 78.3%

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

      1. neg-mul-1 78.3%

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

      2. distribute-neg-frac2 78.3%

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

   10. Simplified 78.3%

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

   if -5.99999999999999999e-79 < t < -1.38000000000000004e-111

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

   if -1.38000000000000004e-111 < t < 9.4999999999999997e57

   1. Initial program 92.4%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around 0 79.6%

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

      1. associate-/l* 84.9%

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

   7. Simplified 84.9%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+58}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-79}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -1.38 \cdot 10^{-111}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+60}:\\ \;\;\;\;x + t \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-79}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-110} \lor \neg \left(t \leq 3.165 \cdot 10^{+60}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.15e+60)
   (+ x (* t (/ y t)))
   (if (<= t -4e-79)
     (- x (/ y (/ t z)))
     (if (or (<= t -4.2e-110) (not (<= t 3.165e+60)))
       (+ x y)
       (+ x (* y (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.15e+60) {
		tmp = x + (t * (y / t));
	} else if (t <= -4e-79) {
		tmp = x - (y / (t / z));
	} else if ((t <= -4.2e-110) || !(t <= 3.165e+60)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.15d+60)) then
        tmp = x + (t * (y / t))
    else if (t <= (-4d-79)) then
        tmp = x - (y / (t / z))
    else if ((t <= (-4.2d-110)) .or. (.not. (t <= 3.165d+60))) then
        tmp = x + y
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.15e+60) {
		tmp = x + (t * (y / t));
	} else if (t <= -4e-79) {
		tmp = x - (y / (t / z));
	} else if ((t <= -4.2e-110) || !(t <= 3.165e+60)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.15e+60:
		tmp = x + (t * (y / t))
	elif t <= -4e-79:
		tmp = x - (y / (t / z))
	elif (t <= -4.2e-110) or not (t <= 3.165e+60):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.15e+60)
		tmp = Float64(x + Float64(t * Float64(y / t)));
	elseif (t <= -4e-79)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	elseif ((t <= -4.2e-110) || !(t <= 3.165e+60))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.15e+60)
		tmp = x + (t * (y / t));
	elseif (t <= -4e-79)
		tmp = x - (y / (t / z));
	elseif ((t <= -4.2e-110) || ~((t <= 3.165e+60)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.15e+60], N[(x + N[(t * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4e-79], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -4.2e-110], N[Not[LessEqual[t, 3.165e+60]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.14999999999999986e60

   1. Initial program 68.6%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 65.2%

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

      1. associate-*r/ 65.2%

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

      2. mul-1-neg 65.2%

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

      3. distribute-lft-neg-out 65.2%

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

      4. *-commutative 65.2%

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

      5. associate-/l* 90.2%

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

      6. distribute-neg-frac 90.2%

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

      7. distribute-neg-frac2 90.2%

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

      8. neg-sub0 90.2%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} \]

      9. associate--r- 90.2%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - a\right) + t}} \]

      10. neg-sub0 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in y around 0 65.2%

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

      1. associate-/l* 83.9%

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

   10. Simplified 83.9%

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

   11. Taylor expanded in t around inf 78.9%

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

   if -2.14999999999999986e60 < t < -4e-79

   1. Initial program 100.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 89.6%

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

   8. Taylor expanded in a around 0 74.3%

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

      1. neg-mul-1 74.3%

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

      2. distribute-neg-frac2 74.3%

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

   10. Simplified 74.3%

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

   if -4e-79 < t < -4.20000000000000004e-110 or 3.165e60 < t

   1. Initial program 75.8%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 83.3%

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

   if -4.20000000000000004e-110 < t < 3.165e60

   1. Initial program 92.5%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around 0 79.9%

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

      1. associate-/l* 85.1%

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

   7. Simplified 85.1%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+60}:\\ \;\;\;\;x + t \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-79}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-110} \lor \neg \left(t \leq 3.165 \cdot 10^{+60}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+57} \lor \neg \left(t \leq 5.9 \cdot 10^{+82}\right):\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.5e+57) (not (<= t 5.9e+82)))
   (+ x (* t (/ y (- t a))))
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e+57) || !(t <= 5.9e+82)) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.5d+57)) .or. (.not. (t <= 5.9d+82))) then
        tmp = x + (t * (y / (t - a)))
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e+57) || !(t <= 5.9e+82)) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.5e+57) or not (t <= 5.9e+82):
		tmp = x + (t * (y / (t - a)))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.5e+57) || !(t <= 5.9e+82))
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.5e+57) || ~((t <= 5.9e+82)))
		tmp = x + (t * (y / (t - a)));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.5e+57], N[Not[LessEqual[t, 5.9e+82]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4999999999999997e57 or 5.8999999999999997e82 < t

   1. Initial program 70.7%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 67.2%

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

      1. associate-*r/ 67.2%

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

      2. mul-1-neg 67.2%

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

      3. distribute-lft-neg-out 67.2%

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

      4. *-commutative 67.2%

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

      5. associate-/l* 91.5%

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

      6. distribute-neg-frac 91.5%

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

      7. distribute-neg-frac2 91.5%

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

      8. neg-sub0 91.5%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} \]

      9. associate--r- 91.5%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - a\right) + t}} \]

      10. neg-sub0 91.5%

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

   7. Simplified 91.5%

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

   8. Taylor expanded in y around 0 67.2%

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

      1. associate-/l* 86.3%

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

   10. Simplified 86.3%

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

   if -3.4999999999999997e57 < t < 5.8999999999999997e82

   1. Initial program 93.3%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around inf 88.8%

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

      1. associate-/l* 94.0%

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

   7. Simplified 94.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+57} \lor \neg \left(t \leq 5.9 \cdot 10^{+82}\right):\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+57} \lor \neg \left(t \leq 3.1 \cdot 10^{+97}\right):\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.2e+57) (not (<= t 3.1e+97)))
   (+ x (* t (/ y (- t a))))
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.2e+57) || !(t <= 3.1e+97)) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5.2d+57)) .or. (.not. (t <= 3.1d+97))) then
        tmp = x + (t * (y / (t - a)))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.2e+57) || !(t <= 3.1e+97)) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.2e+57) or not (t <= 3.1e+97):
		tmp = x + (t * (y / (t - a)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.2e+57) || !(t <= 3.1e+97))
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.2e+57) || ~((t <= 3.1e+97)))
		tmp = x + (t * (y / (t - a)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.2e+57], N[Not[LessEqual[t, 3.1e+97]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2e57 or 3.09999999999999981e97 < t

   1. Initial program 70.7%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 67.2%

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

      1. associate-*r/ 67.2%

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

      2. mul-1-neg 67.2%

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

      3. distribute-lft-neg-out 67.2%

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

      4. *-commutative 67.2%

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

      5. associate-/l* 91.5%

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

      6. distribute-neg-frac 91.5%

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

      7. distribute-neg-frac2 91.5%

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

      8. neg-sub0 91.5%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} \]

      9. associate--r- 91.5%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - a\right) + t}} \]

      10. neg-sub0 91.5%

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

   7. Simplified 91.5%

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

   8. Taylor expanded in y around 0 67.2%

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

      1. associate-/l* 86.3%

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

   10. Simplified 86.3%

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

   if -5.2e57 < t < 3.09999999999999981e97

   1. Initial program 93.3%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

      1. clear-num 99.2%

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

      2. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in z around inf 94.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+57} \lor \neg \left(t \leq 3.1 \cdot 10^{+97}\right):\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+57} \lor \neg \left(t \leq 1.1 \cdot 10^{+82}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9e+57) (not (<= t 1.1e+82)))
   (+ x (* y (/ t (- t a))))
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9e+57) || !(t <= 1.1e+82)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-9d+57)) .or. (.not. (t <= 1.1d+82))) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9e+57) || !(t <= 1.1e+82)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9e+57) or not (t <= 1.1e+82):
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9e+57) || !(t <= 1.1e+82))
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9e+57) || ~((t <= 1.1e+82)))
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9e+57], N[Not[LessEqual[t, 1.1e+82]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.99999999999999991e57 or 1.1000000000000001e82 < t

   1. Initial program 70.7%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 67.2%

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

      1. associate-*r/ 67.2%

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

      2. mul-1-neg 67.2%

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

      3. distribute-lft-neg-out 67.2%

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

      4. *-commutative 67.2%

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

      5. associate-/l* 91.5%

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

      6. distribute-neg-frac 91.5%

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

      7. distribute-neg-frac2 91.5%

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

      8. neg-sub0 91.5%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} \]

      9. associate--r- 91.5%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - a\right) + t}} \]

      10. neg-sub0 91.5%

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

   7. Simplified 91.5%

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

   if -8.99999999999999991e57 < t < 1.1000000000000001e82

   1. Initial program 93.3%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

      1. clear-num 99.2%

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

      2. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in z around inf 94.4%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+57} \lor \neg \left(t \leq 1.1 \cdot 10^{+82}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-110}:\\ \;\;\;\;x + t \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 3.165 \cdot 10^{+60}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e-110)
   (+ x (* t (/ y t)))
   (if (<= t 3.165e+60) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e-110) {
		tmp = x + (t * (y / t));
	} else if (t <= 3.165e+60) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + 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 <= (-4.2d-110)) then
        tmp = x + (t * (y / t))
    else if (t <= 3.165d+60) then
        tmp = x + (y * (z / a))
    else
        tmp = x + 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 <= -4.2e-110) {
		tmp = x + (t * (y / t));
	} else if (t <= 3.165e+60) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e-110:
		tmp = x + (t * (y / t))
	elif t <= 3.165e+60:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e-110)
		tmp = Float64(x + Float64(t * Float64(y / t)));
	elseif (t <= 3.165e+60)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.2e-110)
		tmp = x + (t * (y / t));
	elseif (t <= 3.165e+60)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e-110], N[(x + N[(t * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.165e+60], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.20000000000000004e-110

   1. Initial program 77.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 65.4%

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

      1. associate-*r/ 65.4%

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

      2. mul-1-neg 65.4%

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

      3. distribute-lft-neg-out 65.4%

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

      4. *-commutative 65.4%

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

      5. associate-/l* 83.4%

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

      6. distribute-neg-frac 83.4%

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

      7. distribute-neg-frac2 83.4%

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

      8. neg-sub0 83.4%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} \]

      9. associate--r- 83.4%

         \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - a\right) + t}} \]

      10. neg-sub0 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in y around 0 65.4%

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

      1. associate-/l* 78.9%

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

   10. Simplified 78.9%

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

   11. Taylor expanded in t around inf 73.0%

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

   if -4.20000000000000004e-110 < t < 3.165e60

   1. Initial program 92.5%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around 0 79.9%

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

      1. associate-/l* 85.1%

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

   7. Simplified 85.1%

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

   if 3.165e60 < t

   1. Initial program 74.1%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 82.2%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-110}:\\ \;\;\;\;x + t \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 3.165 \cdot 10^{+60}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-36}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.35e+147) x (if (<= a 8.2e-36) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e+147) {
		tmp = x;
	} else if (a <= 8.2e-36) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.35d+147)) then
        tmp = x
    else if (a <= 8.2d-36) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e+147) {
		tmp = x;
	} else if (a <= 8.2e-36) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.35e+147:
		tmp = x
	elif a <= 8.2e-36:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.35e+147)
		tmp = x;
	elseif (a <= 8.2e-36)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.35e+147)
		tmp = x;
	elseif (a <= 8.2e-36)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.35e+147], x, If[LessEqual[a, 8.2e-36], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.34999999999999999e147 or 8.20000000000000025e-36 < a

   1. Initial program 80.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 77.4%

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

   6. Taylor expanded in x around inf 74.0%

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

   if -1.34999999999999999e147 < a < 8.20000000000000025e-36

   1. Initial program 85.9%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in t around inf 61.4%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-36}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.4%

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

   1. associate-/l* 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

   \[\leadsto x + y \cdot \frac{z - t}{a - t} \]
6. Add Preprocessing

Alternative 10: 50.1% accurate, 11.0× 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 83.4%

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

   1. associate-/l* 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in t around 0 64.5%

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

6. Taylor expanded in x around inf 55.1%

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

7. Final simplification 55.1%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{a - t}{z - t}} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024073 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (+ x (/ y (/ (- a t) (- z t))))

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