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

Percentage Accurate: 84.9% → 98.3%

Time: 12.6s

Alternatives: 15

Speedup: 1.0×

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: 84.9% 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 89.3%

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

   1. associate-/l* 97.6%

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

3. Simplified 97.6%

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

5. Final simplification 97.6%

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

Alternative 2: 77.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2900000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+93}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.02e+24)
   (+ x y)
   (if (<= t -5.4e-8)
     (* y (/ z (- a t)))
     (if (<= t -3.5e-21)
       (+ x y)
       (if (<= t 2900000000000.0)
         (+ x (* z (/ y a)))
         (if (<= t 8.5e+93) (- x (* y (/ z t))) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e+24) {
		tmp = x + y;
	} else if (t <= -5.4e-8) {
		tmp = y * (z / (a - t));
	} else if (t <= -3.5e-21) {
		tmp = x + y;
	} else if (t <= 2900000000000.0) {
		tmp = x + (z * (y / a));
	} else if (t <= 8.5e+93) {
		tmp = x - (y * (z / t));
	} 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 <= (-1.02d+24)) then
        tmp = x + y
    else if (t <= (-5.4d-8)) then
        tmp = y * (z / (a - t))
    else if (t <= (-3.5d-21)) then
        tmp = x + y
    else if (t <= 2900000000000.0d0) then
        tmp = x + (z * (y / a))
    else if (t <= 8.5d+93) then
        tmp = x - (y * (z / t))
    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 <= -1.02e+24) {
		tmp = x + y;
	} else if (t <= -5.4e-8) {
		tmp = y * (z / (a - t));
	} else if (t <= -3.5e-21) {
		tmp = x + y;
	} else if (t <= 2900000000000.0) {
		tmp = x + (z * (y / a));
	} else if (t <= 8.5e+93) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.02e+24:
		tmp = x + y
	elif t <= -5.4e-8:
		tmp = y * (z / (a - t))
	elif t <= -3.5e-21:
		tmp = x + y
	elif t <= 2900000000000.0:
		tmp = x + (z * (y / a))
	elif t <= 8.5e+93:
		tmp = x - (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.02e+24)
		tmp = Float64(x + y);
	elseif (t <= -5.4e-8)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= -3.5e-21)
		tmp = Float64(x + y);
	elseif (t <= 2900000000000.0)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= 8.5e+93)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.02e+24)
		tmp = x + y;
	elseif (t <= -5.4e-8)
		tmp = y * (z / (a - t));
	elseif (t <= -3.5e-21)
		tmp = x + y;
	elseif (t <= 2900000000000.0)
		tmp = x + (z * (y / a));
	elseif (t <= 8.5e+93)
		tmp = x - (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.02e+24], N[(x + y), $MachinePrecision], If[LessEqual[t, -5.4e-8], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e-21], N[(x + y), $MachinePrecision], If[LessEqual[t, 2900000000000.0], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+93], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.02000000000000004e24 or -5.40000000000000005e-8 < t < -3.5000000000000003e-21 or 8.5000000000000005e93 < t

   1. Initial program 77.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 82.1%

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

      1. +-commutative 82.1%

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

   7. Simplified 82.1%

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

   if -1.02000000000000004e24 < t < -5.40000000000000005e-8

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 77.5%

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

   6. Taylor expanded in x around 0 70.7%

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

      1. associate-*r/ 70.6%

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

   8. Simplified 70.6%

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

   if -3.5000000000000003e-21 < t < 2.9e12

   1. Initial program 97.1%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in t around 0 75.5%

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

      1. +-commutative 75.5%

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

      2. associate-/l* 75.7%

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

   7. Simplified 75.7%

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

      1. associate-/r/ 77.1%

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

   9. Applied egg-rr 77.1%

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

   if 2.9e12 < t < 8.5000000000000005e93

   1. Initial program 82.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 70.9%

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

   6. Taylor expanded in a around 0 65.0%

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

      1. mul-1-neg 65.0%

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

      2. unsub-neg 65.0%

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

      3. *-lft-identity 65.0%

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

      4. times-frac 76.5%

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

      5. /-rgt-identity 76.5%

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

   8. Simplified 76.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-21}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2900000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+93}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 15500000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+85}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.02e+24)
   (+ x y)
   (if (<= t -5.5e-8)
     (/ (* y z) (- a t))
     (if (<= t -9e-19)
       (+ x y)
       (if (<= t 15500000000000.0)
         (+ x (* z (/ y a)))
         (if (<= t 5.5e+85) (- x (* y (/ z t))) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e+24) {
		tmp = x + y;
	} else if (t <= -5.5e-8) {
		tmp = (y * z) / (a - t);
	} else if (t <= -9e-19) {
		tmp = x + y;
	} else if (t <= 15500000000000.0) {
		tmp = x + (z * (y / a));
	} else if (t <= 5.5e+85) {
		tmp = x - (y * (z / t));
	} 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 <= (-1.02d+24)) then
        tmp = x + y
    else if (t <= (-5.5d-8)) then
        tmp = (y * z) / (a - t)
    else if (t <= (-9d-19)) then
        tmp = x + y
    else if (t <= 15500000000000.0d0) then
        tmp = x + (z * (y / a))
    else if (t <= 5.5d+85) then
        tmp = x - (y * (z / t))
    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 <= -1.02e+24) {
		tmp = x + y;
	} else if (t <= -5.5e-8) {
		tmp = (y * z) / (a - t);
	} else if (t <= -9e-19) {
		tmp = x + y;
	} else if (t <= 15500000000000.0) {
		tmp = x + (z * (y / a));
	} else if (t <= 5.5e+85) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.02e+24:
		tmp = x + y
	elif t <= -5.5e-8:
		tmp = (y * z) / (a - t)
	elif t <= -9e-19:
		tmp = x + y
	elif t <= 15500000000000.0:
		tmp = x + (z * (y / a))
	elif t <= 5.5e+85:
		tmp = x - (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.02e+24)
		tmp = Float64(x + y);
	elseif (t <= -5.5e-8)
		tmp = Float64(Float64(y * z) / Float64(a - t));
	elseif (t <= -9e-19)
		tmp = Float64(x + y);
	elseif (t <= 15500000000000.0)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= 5.5e+85)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.02e+24)
		tmp = x + y;
	elseif (t <= -5.5e-8)
		tmp = (y * z) / (a - t);
	elseif (t <= -9e-19)
		tmp = x + y;
	elseif (t <= 15500000000000.0)
		tmp = x + (z * (y / a));
	elseif (t <= 5.5e+85)
		tmp = x - (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.02e+24], N[(x + y), $MachinePrecision], If[LessEqual[t, -5.5e-8], N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-19], N[(x + y), $MachinePrecision], If[LessEqual[t, 15500000000000.0], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+85], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.02000000000000004e24 or -5.5000000000000003e-8 < t < -9.00000000000000026e-19 or 5.50000000000000008e85 < t

   1. Initial program 77.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 82.1%

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

      1. +-commutative 82.1%

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

   7. Simplified 82.1%

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

   if -1.02000000000000004e24 < t < -5.5000000000000003e-8

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 77.5%

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

   6. Taylor expanded in x around 0 70.7%

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

   if -9.00000000000000026e-19 < t < 1.55e13

   1. Initial program 97.1%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in t around 0 75.5%

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

      1. +-commutative 75.5%

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

      2. associate-/l* 75.7%

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

   7. Simplified 75.7%

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

      1. associate-/r/ 77.1%

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

   9. Applied egg-rr 77.1%

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

   if 1.55e13 < t < 5.50000000000000008e85

   1. Initial program 82.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 70.9%

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

   6. Taylor expanded in a around 0 65.0%

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

      1. mul-1-neg 65.0%

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

      2. unsub-neg 65.0%

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

      3. *-lft-identity 65.0%

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

      4. times-frac 76.5%

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

      5. /-rgt-identity 76.5%

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

   8. Simplified 76.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 15500000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+85}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-76} \lor \neg \left(t \leq 3.5 \cdot 10^{+42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.02e+24)
   (+ x y)
   (if (<= t -2.2e-8)
     (* y (/ z (- a t)))
     (if (or (<= t -1.62e-76) (not (<= t 3.5e+42)))
       (+ x y)
       (+ x (/ (* y z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e+24) {
		tmp = x + y;
	} else if (t <= -2.2e-8) {
		tmp = y * (z / (a - t));
	} else if ((t <= -1.62e-76) || !(t <= 3.5e+42)) {
		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 <= (-1.02d+24)) then
        tmp = x + y
    else if (t <= (-2.2d-8)) then
        tmp = y * (z / (a - t))
    else if ((t <= (-1.62d-76)) .or. (.not. (t <= 3.5d+42))) 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 <= -1.02e+24) {
		tmp = x + y;
	} else if (t <= -2.2e-8) {
		tmp = y * (z / (a - t));
	} else if ((t <= -1.62e-76) || !(t <= 3.5e+42)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.02e+24:
		tmp = x + y
	elif t <= -2.2e-8:
		tmp = y * (z / (a - t))
	elif (t <= -1.62e-76) or not (t <= 3.5e+42):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.02e+24)
		tmp = Float64(x + y);
	elseif (t <= -2.2e-8)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif ((t <= -1.62e-76) || !(t <= 3.5e+42))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.02e+24)
		tmp = x + y;
	elseif (t <= -2.2e-8)
		tmp = y * (z / (a - t));
	elseif ((t <= -1.62e-76) || ~((t <= 3.5e+42)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.02e+24], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.2e-8], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.62e-76], N[Not[LessEqual[t, 3.5e+42]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02000000000000004e24 or -2.1999999999999998e-8 < t < -1.62e-76 or 3.50000000000000023e42 < t

   1. Initial program 77.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 77.5%

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

      1. +-commutative 77.5%

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

   7. Simplified 77.5%

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

   if -1.02000000000000004e24 < t < -2.1999999999999998e-8

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 77.5%

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

   6. Taylor expanded in x around 0 70.7%

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

      1. associate-*r/ 70.6%

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

   8. Simplified 70.6%

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

   if -1.62e-76 < t < 3.50000000000000023e42

   1. Initial program 98.5%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in t around 0 76.4%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-76} \lor \neg \left(t \leq 3.5 \cdot 10^{+42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-16} \lor \neg \left(t \leq 7 \cdot 10^{+135}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.02e+24)
   (+ x y)
   (if (<= t -4.2e-8)
     (* y (/ z (- a t)))
     (if (or (<= t -2.25e-16) (not (<= t 7e+135)))
       (+ x y)
       (+ x (* z (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e+24) {
		tmp = x + y;
	} else if (t <= -4.2e-8) {
		tmp = y * (z / (a - t));
	} else if ((t <= -2.25e-16) || !(t <= 7e+135)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / 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 <= (-1.02d+24)) then
        tmp = x + y
    else if (t <= (-4.2d-8)) then
        tmp = y * (z / (a - t))
    else if ((t <= (-2.25d-16)) .or. (.not. (t <= 7d+135))) then
        tmp = x + y
    else
        tmp = x + (z * (y / 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 <= -1.02e+24) {
		tmp = x + y;
	} else if (t <= -4.2e-8) {
		tmp = y * (z / (a - t));
	} else if ((t <= -2.25e-16) || !(t <= 7e+135)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.02e+24:
		tmp = x + y
	elif t <= -4.2e-8:
		tmp = y * (z / (a - t))
	elif (t <= -2.25e-16) or not (t <= 7e+135):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.02e+24)
		tmp = Float64(x + y);
	elseif (t <= -4.2e-8)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif ((t <= -2.25e-16) || !(t <= 7e+135))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.02e+24)
		tmp = x + y;
	elseif (t <= -4.2e-8)
		tmp = y * (z / (a - t));
	elseif ((t <= -2.25e-16) || ~((t <= 7e+135)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.02e+24], N[(x + y), $MachinePrecision], If[LessEqual[t, -4.2e-8], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.25e-16], N[Not[LessEqual[t, 7e+135]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02000000000000004e24 or -4.19999999999999989e-8 < t < -2.2500000000000001e-16 or 7.0000000000000005e135 < t

   1. Initial program 76.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 82.7%

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

      1. +-commutative 82.7%

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

   7. Simplified 82.7%

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

   if -1.02000000000000004e24 < t < -4.19999999999999989e-8

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 77.5%

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

   6. Taylor expanded in x around 0 70.7%

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

      1. associate-*r/ 70.6%

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

   8. Simplified 70.6%

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

   if -2.2500000000000001e-16 < t < 7.0000000000000005e135

   1. Initial program 95.2%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around 0 72.5%

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

      1. +-commutative 72.5%

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

      2. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

      1. associate-/r/ 74.5%

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

   9. Applied egg-rr 74.5%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-16} \lor \neg \left(t \leq 7 \cdot 10^{+135}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+205}:\\ \;\;\;\;x + \left(y + \frac{a}{\frac{t}{y}}\right)\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+237}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e+205)
   (+ x (+ y (/ a (/ t y))))
   (if (<= t -1.08e-16)
     (+ x (/ (- t z) (/ t y)))
     (if (<= t 3.6e+237) (+ x (* z (/ y (- a t)))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+205) {
		tmp = x + (y + (a / (t / y)));
	} else if (t <= -1.08e-16) {
		tmp = x + ((t - z) / (t / y));
	} else if (t <= 3.6e+237) {
		tmp = x + (z * (y / (a - t)));
	} 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 <= (-3.8d+205)) then
        tmp = x + (y + (a / (t / y)))
    else if (t <= (-1.08d-16)) then
        tmp = x + ((t - z) / (t / y))
    else if (t <= 3.6d+237) then
        tmp = x + (z * (y / (a - t)))
    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 <= -3.8e+205) {
		tmp = x + (y + (a / (t / y)));
	} else if (t <= -1.08e-16) {
		tmp = x + ((t - z) / (t / y));
	} else if (t <= 3.6e+237) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e+205:
		tmp = x + (y + (a / (t / y)))
	elif t <= -1.08e-16:
		tmp = x + ((t - z) / (t / y))
	elif t <= 3.6e+237:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e+205)
		tmp = Float64(x + Float64(y + Float64(a / Float64(t / y))));
	elseif (t <= -1.08e-16)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(t / y)));
	elseif (t <= 3.6e+237)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e+205)
		tmp = x + (y + (a / (t / y)));
	elseif (t <= -1.08e-16)
		tmp = x + ((t - z) / (t / y));
	elseif (t <= 3.6e+237)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e+205], N[(x + N[(y + N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.08e-16], N[(x + N[(N[(t - z), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+237], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.8e205

   1. Initial program 61.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. *-commutative 53.3%

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

      4. associate-*l/ 73.9%

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

      5. distribute-rgt-neg-out 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in a around 0 82.7%

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

      1. associate-/l* 87.3%

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

   10. Simplified 87.3%

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

   if -3.8e205 < t < -1.08e-16

   1. Initial program 90.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. frac-2neg 99.8%

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

      3. associate-*r/ 90.1%

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

      4. sub-neg 90.1%

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

      5. distribute-neg-in 90.1%

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

      6. add-sqr-sqrt 90.0%

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

      7. sqrt-unprod 75.3%

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

      8. sqr-neg 75.3%

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

      9. sqrt-unprod 0.0%

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

      10. add-sqr-sqrt 65.2%

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

      11. add-sqr-sqrt 65.2%

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

      12. sqrt-unprod 58.9%

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

      13. sqr-neg 58.9%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 90.1%

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

      16. sub-neg 90.1%

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

      17. distribute-neg-in 90.1%

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

      18. add-sqr-sqrt 89.9%

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

      19. sqrt-unprod 81.7%

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

      20. sqr-neg 81.7%

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

      21. sqrt-unprod 0.0%

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

      22. add-sqr-sqrt 57.0%

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

   8. Applied egg-rr 90.1%

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

      1. *-commutative 90.1%

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

      2. associate-/l* 95.8%

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

      3. +-commutative 95.8%

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

      4. unsub-neg 95.8%

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

      5. +-commutative 95.8%

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

      6. unsub-neg 95.8%

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

   10. Simplified 95.8%

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

   11. Taylor expanded in t around inf 82.1%

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

   if -1.08e-16 < t < 3.60000000000000015e237

   1. Initial program 94.9%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around inf 80.9%

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

      1. associate-*l/ 83.7%

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

      2. *-commutative 83.7%

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

   7. Simplified 83.7%

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

   if 3.60000000000000015e237 < t

   1. Initial program 62.5%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 97.1%

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

      1. +-commutative 97.1%

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

   7. Simplified 97.1%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+205}:\\ \;\;\;\;x + \left(y + \frac{a}{\frac{t}{y}}\right)\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+237}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-196}:\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- z t))))))
   (if (<= a -2e+21)
     t_1
     (if (<= a -5.3e-196)
       (+ x (/ (- t z) (/ t y)))
       (if (<= a 1.2e-73) (+ x (/ (* y (- t z)) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (z - t)));
	double tmp;
	if (a <= -2e+21) {
		tmp = t_1;
	} else if (a <= -5.3e-196) {
		tmp = x + ((t - z) / (t / y));
	} else if (a <= 1.2e-73) {
		tmp = x + ((y * (t - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / (z - t)))
    if (a <= (-2d+21)) then
        tmp = t_1
    else if (a <= (-5.3d-196)) then
        tmp = x + ((t - z) / (t / y))
    else if (a <= 1.2d-73) then
        tmp = x + ((y * (t - z)) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (z - t)));
	double tmp;
	if (a <= -2e+21) {
		tmp = t_1;
	} else if (a <= -5.3e-196) {
		tmp = x + ((t - z) / (t / y));
	} else if (a <= 1.2e-73) {
		tmp = x + ((y * (t - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (z - t)))
	tmp = 0
	if a <= -2e+21:
		tmp = t_1
	elif a <= -5.3e-196:
		tmp = x + ((t - z) / (t / y))
	elif a <= 1.2e-73:
		tmp = x + ((y * (t - z)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -2e+21)
		tmp = t_1;
	elseif (a <= -5.3e-196)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(t / y)));
	elseif (a <= 1.2e-73)
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (z - t)));
	tmp = 0.0;
	if (a <= -2e+21)
		tmp = t_1;
	elseif (a <= -5.3e-196)
		tmp = x + ((t - z) / (t / y));
	elseif (a <= 1.2e-73)
		tmp = x + ((y * (t - z)) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+21], t$95$1, If[LessEqual[a, -5.3e-196], N[(x + N[(N[(t - z), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-73], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2e21 or 1.20000000000000003e-73 < a

   1. Initial program 89.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-/l* 88.5%

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

   7. Simplified 88.5%

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

   if -2e21 < a < -5.3000000000000001e-196

   1. Initial program 79.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 97.7%

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

      3. clear-num 97.8%

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

   6. Applied egg-rr 97.8%

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

      1. *-commutative 97.8%

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

      2. frac-2neg 97.8%

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

      3. associate-*r/ 79.7%

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

      4. sub-neg 79.7%

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

      5. distribute-neg-in 79.7%

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

      6. add-sqr-sqrt 39.7%

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

      7. sqrt-unprod 59.9%

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

      8. sqr-neg 59.9%

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

      9. sqrt-unprod 30.8%

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

      10. add-sqr-sqrt 63.4%

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

      11. add-sqr-sqrt 32.7%

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

      12. sqrt-unprod 58.3%

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

      13. sqr-neg 58.3%

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

      14. sqrt-unprod 39.9%

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

      15. add-sqr-sqrt 79.7%

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

      16. sub-neg 79.7%

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

      17. distribute-neg-in 79.7%

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

      18. add-sqr-sqrt 39.6%

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

      19. sqrt-unprod 62.5%

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

      20. sqr-neg 62.5%

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

      21. sqrt-unprod 25.5%

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

      22. add-sqr-sqrt 51.8%

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

   8. Applied egg-rr 79.7%

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

      1. *-commutative 79.7%

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

      2. associate-/l* 97.8%

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

      3. +-commutative 97.8%

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

      4. unsub-neg 97.8%

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

      5. +-commutative 97.8%

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

      6. unsub-neg 97.8%

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

   10. Simplified 97.8%

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

   11. Taylor expanded in t around inf 79.0%

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

   if -5.3000000000000001e-196 < a < 1.20000000000000003e-73

   1. Initial program 94.9%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

      1. clear-num 92.1%

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

      2. associate-/r/ 92.3%

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

      3. clear-num 92.3%

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

   6. Applied egg-rr 92.3%

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

      1. *-commutative 92.3%

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

      2. frac-2neg 92.3%

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

      3. associate-*r/ 94.9%

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

      4. sub-neg 94.9%

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

      5. distribute-neg-in 94.9%

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

      6. add-sqr-sqrt 41.4%

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

      7. sqrt-unprod 64.6%

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

      8. sqr-neg 64.6%

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

      9. sqrt-unprod 39.9%

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

      10. add-sqr-sqrt 65.9%

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

      11. add-sqr-sqrt 26.0%

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

      12. sqrt-unprod 63.4%

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

      13. sqr-neg 63.4%

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

      14. sqrt-unprod 53.2%

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

      15. add-sqr-sqrt 94.9%

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

      16. sub-neg 94.9%

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

      17. distribute-neg-in 94.9%

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

      18. add-sqr-sqrt 41.4%

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

      19. sqrt-unprod 67.1%

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

      20. sqr-neg 67.1%

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

      21. sqrt-unprod 34.4%

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

      22. add-sqr-sqrt 48.7%

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

   8. Applied egg-rr 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-/l* 84.1%

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

      3. +-commutative 84.1%

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

      4. unsub-neg 84.1%

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

      5. +-commutative 84.1%

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

      6. unsub-neg 84.1%

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

   10. Simplified 84.1%

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

   11. Taylor expanded in a around 0 79.6%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-196}:\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-190}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;x - \frac{y \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- z t))))))
   (if (<= a -2e+21)
     t_1
     (if (<= a 3e-190)
       (- x (/ y (/ t (- z t))))
       (if (<= a 1.2e-73) (- x (/ (* y t) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (z - t)));
	double tmp;
	if (a <= -2e+21) {
		tmp = t_1;
	} else if (a <= 3e-190) {
		tmp = x - (y / (t / (z - t)));
	} else if (a <= 1.2e-73) {
		tmp = x - ((y * t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / (z - t)))
    if (a <= (-2d+21)) then
        tmp = t_1
    else if (a <= 3d-190) then
        tmp = x - (y / (t / (z - t)))
    else if (a <= 1.2d-73) then
        tmp = x - ((y * t) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (z - t)));
	double tmp;
	if (a <= -2e+21) {
		tmp = t_1;
	} else if (a <= 3e-190) {
		tmp = x - (y / (t / (z - t)));
	} else if (a <= 1.2e-73) {
		tmp = x - ((y * t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (z - t)))
	tmp = 0
	if a <= -2e+21:
		tmp = t_1
	elif a <= 3e-190:
		tmp = x - (y / (t / (z - t)))
	elif a <= 1.2e-73:
		tmp = x - ((y * t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -2e+21)
		tmp = t_1;
	elseif (a <= 3e-190)
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	elseif (a <= 1.2e-73)
		tmp = Float64(x - Float64(Float64(y * t) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (z - t)));
	tmp = 0.0;
	if (a <= -2e+21)
		tmp = t_1;
	elseif (a <= 3e-190)
		tmp = x - (y / (t / (z - t)));
	elseif (a <= 1.2e-73)
		tmp = x - ((y * t) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+21], t$95$1, If[LessEqual[a, 3e-190], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-73], N[(x - N[(N[(y * t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2e21 or 1.20000000000000003e-73 < a

   1. Initial program 89.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-/l* 88.5%

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

   7. Simplified 88.5%

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

   if -2e21 < a < 2.9999999999999998e-190

   1. Initial program 87.6%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in a around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. unsub-neg 75.2%

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

      3. associate-/l* 85.5%

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

   7. Simplified 85.5%

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

   if 2.9999999999999998e-190 < a < 1.20000000000000003e-73

   1. Initial program 95.7%

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

      1. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

      1. clear-num 90.8%

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

      2. associate-/r/ 91.0%

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

      3. clear-num 91.1%

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

   6. Applied egg-rr 91.1%

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

   7. Taylor expanded in z around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. unsub-neg 81.7%

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

   9. Simplified 81.7%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-190}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;x - \frac{y \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-152} \lor \neg \left(t \leq 3.5 \cdot 10^{-104}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.02e+24)
   (+ x y)
   (if (<= t -5.5e-8)
     (/ (* y (- z)) t)
     (if (or (<= t -1.5e-152) (not (<= t 3.5e-104))) (+ x y) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e+24) {
		tmp = x + y;
	} else if (t <= -5.5e-8) {
		tmp = (y * -z) / t;
	} else if ((t <= -1.5e-152) || !(t <= 3.5e-104)) {
		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 (t <= (-1.02d+24)) then
        tmp = x + y
    else if (t <= (-5.5d-8)) then
        tmp = (y * -z) / t
    else if ((t <= (-1.5d-152)) .or. (.not. (t <= 3.5d-104))) 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 (t <= -1.02e+24) {
		tmp = x + y;
	} else if (t <= -5.5e-8) {
		tmp = (y * -z) / t;
	} else if ((t <= -1.5e-152) || !(t <= 3.5e-104)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.02e+24:
		tmp = x + y
	elif t <= -5.5e-8:
		tmp = (y * -z) / t
	elif (t <= -1.5e-152) or not (t <= 3.5e-104):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.02e+24)
		tmp = Float64(x + y);
	elseif (t <= -5.5e-8)
		tmp = Float64(Float64(y * Float64(-z)) / t);
	elseif ((t <= -1.5e-152) || !(t <= 3.5e-104))
		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 (t <= -1.02e+24)
		tmp = x + y;
	elseif (t <= -5.5e-8)
		tmp = (y * -z) / t;
	elseif ((t <= -1.5e-152) || ~((t <= 3.5e-104)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.02e+24], N[(x + y), $MachinePrecision], If[LessEqual[t, -5.5e-8], N[(N[(y * (-z)), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[t, -1.5e-152], N[Not[LessEqual[t, 3.5e-104]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02000000000000004e24 or -5.5000000000000003e-8 < t < -1.5e-152 or 3.50000000000000029e-104 < t

   1. Initial program 84.9%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t around inf 68.2%

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

      1. +-commutative 68.2%

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

   7. Simplified 68.2%

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

   if -1.02000000000000004e24 < t < -5.5000000000000003e-8

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 77.5%

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

   6. Taylor expanded in x around 0 70.7%

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

   7. Taylor expanded in a around 0 61.7%

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

      1. associate-*r/ 61.7%

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

      2. associate-*r* 61.7%

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

      3. neg-mul-1 61.7%

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

      4. *-commutative 61.7%

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

   9. Simplified 61.7%

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

   if -1.5e-152 < t < 3.50000000000000029e-104

   1. Initial program 97.4%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in x around inf 61.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-152} \lor \neg \left(t \leq 3.5 \cdot 10^{-104}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+50} \lor \neg \left(t \leq 3.6 \cdot 10^{+237}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.3e+50) (not (<= t 3.6e+237)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.3e+50) || !(t <= 3.6e+237)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (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 <= (-3.3d+50)) .or. (.not. (t <= 3.6d+237))) then
        tmp = x + y
    else
        tmp = x + (z * (y / (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 <= -3.3e+50) || !(t <= 3.6e+237)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.3e+50) or not (t <= 3.6e+237):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.3e+50) || !(t <= 3.6e+237))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.3e+50) || ~((t <= 3.6e+237)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.3e+50], N[Not[LessEqual[t, 3.6e+237]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3e50 or 3.60000000000000015e237 < t

   1. Initial program 71.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 82.4%

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

      1. +-commutative 82.4%

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

   7. Simplified 82.4%

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

   if -3.3e50 < t < 3.60000000000000015e237

   1. Initial program 95.4%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around inf 80.5%

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

      1. associate-*l/ 83.1%

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

      2. *-commutative 83.1%

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

   7. Simplified 83.1%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+50} \lor \neg \left(t \leq 3.6 \cdot 10^{+237}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-17} \lor \neg \left(t \leq 6 \cdot 10^{+192}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.7e-17) (not (<= t 6e+192)))
   (- x (/ y (/ t (- z t))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.7e-17) || !(t <= 6e+192)) {
		tmp = x - (y / (t / (z - t)));
	} else {
		tmp = x + (z * (y / (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 <= (-2.7d-17)) .or. (.not. (t <= 6d+192))) then
        tmp = x - (y / (t / (z - t)))
    else
        tmp = x + (z * (y / (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 <= -2.7e-17) || !(t <= 6e+192)) {
		tmp = x - (y / (t / (z - t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.7e-17) or not (t <= 6e+192):
		tmp = x - (y / (t / (z - t)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.7e-17) || !(t <= 6e+192))
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.7e-17) || ~((t <= 6e+192)))
		tmp = x - (y / (t / (z - t)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.7e-17], N[Not[LessEqual[t, 6e+192]], $MachinePrecision]], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7000000000000001e-17 or 6e192 < t

   1. Initial program 79.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. unsub-neg 72.9%

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

      3. associate-/l* 90.4%

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

   7. Simplified 90.4%

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

   if -2.7000000000000001e-17 < t < 6e192

   1. Initial program 94.8%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 81.1%

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

      1. associate-*l/ 84.2%

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

      2. *-commutative 84.2%

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

   7. Simplified 84.2%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-17} \lor \neg \left(t \leq 6 \cdot 10^{+192}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+59} \lor \neg \left(z \leq 2.4 \cdot 10^{+222}\right):\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.7e+59) (not (<= z 2.4e+222))) (* y (/ z (- a t))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.7e+59) || !(z <= 2.4e+222)) {
		tmp = y * (z / (a - t));
	} 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 ((z <= (-3.7d+59)) .or. (.not. (z <= 2.4d+222))) then
        tmp = y * (z / (a - t))
    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 ((z <= -3.7e+59) || !(z <= 2.4e+222)) {
		tmp = y * (z / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.7e+59) or not (z <= 2.4e+222):
		tmp = y * (z / (a - t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.7e+59) || !(z <= 2.4e+222))
		tmp = Float64(y * Float64(z / Float64(a - t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.7e+59) || ~((z <= 2.4e+222)))
		tmp = y * (z / (a - t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.7e+59], N[Not[LessEqual[z, 2.4e+222]], $MachinePrecision]], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.69999999999999997e59 or 2.4000000000000001e222 < z

   1. Initial program 85.7%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in z around inf 78.9%

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

   6. Taylor expanded in x around 0 50.7%

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

      1. associate-*r/ 56.2%

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

   8. Simplified 56.2%

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

   if -3.69999999999999997e59 < z < 2.4000000000000001e222

   1. Initial program 90.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 67.1%

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

      1. +-commutative 67.1%

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

   7. Simplified 67.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+59} \lor \neg \left(z \leq 2.4 \cdot 10^{+222}\right):\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-152} \lor \neg \left(t \leq 2.9 \cdot 10^{-102}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45e-152) (not (<= t 2.9e-102))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e-152) || !(t <= 2.9e-102)) {
		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 ((t <= (-1.45d-152)) .or. (.not. (t <= 2.9d-102))) 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 ((t <= -1.45e-152) || !(t <= 2.9e-102)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.45e-152) or not (t <= 2.9e-102):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.45e-152) || !(t <= 2.9e-102))
		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 ((t <= -1.45e-152) || ~((t <= 2.9e-102)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.45e-152], N[Not[LessEqual[t, 2.9e-102]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.4500000000000001e-152 or 2.89999999999999986e-102 < t

   1. Initial program 85.8%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around inf 65.1%

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

      1. +-commutative 65.1%

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

   7. Simplified 65.1%

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

   if -1.4500000000000001e-152 < t < 2.89999999999999986e-102

   1. Initial program 97.4%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in x around inf 61.3%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-152} \lor \neg \left(t \leq 2.9 \cdot 10^{-102}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 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 89.3%

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

   1. associate-/l* 97.6%

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

3. Simplified 97.6%

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

   1. clear-num 97.5%

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

   2. associate-/r/ 97.2%

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

   3. clear-num 97.3%

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

6. Applied egg-rr 97.3%

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

7. Final simplification 97.3%

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

Alternative 15: 49.6% 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 89.3%

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

   1. associate-/l* 97.6%

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

3. Simplified 97.6%

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

5. Taylor expanded in x around inf 49.6%

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

6. Final simplification 49.6%

   \[\leadsto x \]
7. 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 2024031 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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