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

Percentage Accurate: 76.3% → 91.1%

Time: 11.1s

Alternatives: 13

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+83} \lor \neg \left(t \leq 1.12 \cdot 10^{+80}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{a - t}{y} \cdot \frac{-1}{t - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e+83) (not (<= t 1.12e+80)))
   (+ (- x (* a (/ y t))) (* y (/ z t)))
   (+ (+ x y) (/ -1.0 (* (/ (- a t) y) (/ -1.0 (- t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e+83) || !(t <= 1.12e+80)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = (x + y) + (-1.0 / (((a - t) / y) * (-1.0 / (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 <= (-1.2d+83)) .or. (.not. (t <= 1.12d+80))) then
        tmp = (x - (a * (y / t))) + (y * (z / t))
    else
        tmp = (x + y) + ((-1.0d0) / (((a - t) / y) * ((-1.0d0) / (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 <= -1.2e+83) || !(t <= 1.12e+80)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = (x + y) + (-1.0 / (((a - t) / y) * (-1.0 / (t - z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e+83) or not (t <= 1.12e+80):
		tmp = (x - (a * (y / t))) + (y * (z / t))
	else:
		tmp = (x + y) + (-1.0 / (((a - t) / y) * (-1.0 / (t - z))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e+83) || !(t <= 1.12e+80))
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(x + y) + Float64(-1.0 / Float64(Float64(Float64(a - t) / y) * Float64(-1.0 / Float64(t - z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.2e+83) || ~((t <= 1.12e+80)))
		tmp = (x - (a * (y / t))) + (y * (z / t));
	else
		tmp = (x + y) + (-1.0 / (((a - t) / y) * (-1.0 / (t - z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e+83], N[Not[LessEqual[t, 1.12e+80]], $MachinePrecision]], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(-1.0 / N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] * N[(-1.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.19999999999999996e83 or 1.12e80 < t

   1. Initial program 61.9%

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

   3. Taylor expanded in t around inf 88.4%

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

      1. sub-neg 88.4%

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

      2. mul-1-neg 88.4%

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

      3. unsub-neg 88.4%

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

      4. associate-/l* 87.6%

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

      5. mul-1-neg 87.6%

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

      6. remove-double-neg 87.6%

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

      7. associate-/l* 93.6%

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

   5. Simplified 93.6%

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

   if -1.19999999999999996e83 < t < 1.12e80

   1. Initial program 89.2%

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

      1. clear-num 89.2%

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

      2. inv-pow 89.2%

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

      3. *-commutative 89.2%

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

   4. Applied egg-rr 89.2%

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

      1. unpow-1 89.2%

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

      2. associate-/r* 93.9%

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

   6. Simplified 93.9%

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

      1. div-inv 94.0%

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

   8. Applied egg-rr 94.0%

      \[\leadsto \left(x + y\right) - \frac{1}{\color{blue}{\frac{a - t}{y} \cdot \frac{1}{z - t}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+83} \lor \neg \left(t \leq 1.12 \cdot 10^{+80}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{a - t}{y} \cdot \frac{-1}{t - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+83} \lor \neg \left(t \leq 9.5 \cdot 10^{+77}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{-1}{\frac{\frac{a - t}{y}}{t - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.4e+83) (not (<= t 9.5e+77)))
   (+ (- x (* a (/ y t))) (* y (/ z t)))
   (- (+ x y) (/ -1.0 (/ (/ (- a t) y) (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.4e+83) || !(t <= 9.5e+77)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = (x + y) - (-1.0 / (((a - t) / y) / (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 <= (-6.4d+83)) .or. (.not. (t <= 9.5d+77))) then
        tmp = (x - (a * (y / t))) + (y * (z / t))
    else
        tmp = (x + y) - ((-1.0d0) / (((a - t) / y) / (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 <= -6.4e+83) || !(t <= 9.5e+77)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = (x + y) - (-1.0 / (((a - t) / y) / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.4e+83) or not (t <= 9.5e+77):
		tmp = (x - (a * (y / t))) + (y * (z / t))
	else:
		tmp = (x + y) - (-1.0 / (((a - t) / y) / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.4e+83) || !(t <= 9.5e+77))
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(x + y) - Float64(-1.0 / Float64(Float64(Float64(a - t) / y) / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.4e+83) || ~((t <= 9.5e+77)))
		tmp = (x - (a * (y / t))) + (y * (z / t));
	else
		tmp = (x + y) - (-1.0 / (((a - t) / y) / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.4e+83], N[Not[LessEqual[t, 9.5e+77]], $MachinePrecision]], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(-1.0 / N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.3999999999999998e83 or 9.4999999999999998e77 < t

   1. Initial program 61.9%

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

   3. Taylor expanded in t around inf 88.4%

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

      1. sub-neg 88.4%

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

      2. mul-1-neg 88.4%

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

      3. unsub-neg 88.4%

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

      4. associate-/l* 87.6%

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

      5. mul-1-neg 87.6%

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

      6. remove-double-neg 87.6%

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

      7. associate-/l* 93.6%

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

   5. Simplified 93.6%

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

   if -6.3999999999999998e83 < t < 9.4999999999999998e77

   1. Initial program 89.2%

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

      1. clear-num 89.2%

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

      2. inv-pow 89.2%

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

      3. *-commutative 89.2%

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

   4. Applied egg-rr 89.2%

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

      1. unpow-1 89.2%

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

      2. associate-/r* 93.9%

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

   6. Simplified 93.9%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{1}{\frac{\frac{a - t}{y}}{z - t}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+83} \lor \neg \left(t \leq 9.5 \cdot 10^{+77}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{-1}{\frac{\frac{a - t}{y}}{t - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+46} \lor \neg \left(t \leq 4 \cdot 10^{+72}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.2e+46) (not (<= t 4e+72)))
   (+ (- x (* a (/ y t))) (* y (/ z t)))
   (- (+ x y) (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2e+46) || !(t <= 4e+72)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = (x + y) - (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 <= (-7.2d+46)) .or. (.not. (t <= 4d+72))) then
        tmp = (x - (a * (y / t))) + (y * (z / t))
    else
        tmp = (x + y) - (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 <= -7.2e+46) || !(t <= 4e+72)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = (x + y) - (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.2e+46) or not (t <= 4e+72):
		tmp = (x - (a * (y / t))) + (y * (z / t))
	else:
		tmp = (x + y) - (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.2e+46) || !(t <= 4e+72))
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(x + y) - Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.2e+46) || ~((t <= 4e+72)))
		tmp = (x - (a * (y / t))) + (y * (z / t));
	else
		tmp = (x + y) - (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.2e+46], N[Not[LessEqual[t, 4e+72]], $MachinePrecision]], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.1999999999999997e46 or 3.99999999999999978e72 < t

   1. Initial program 63.9%

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

   3. Taylor expanded in t around inf 88.0%

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

      1. sub-neg 88.0%

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

      2. mul-1-neg 88.0%

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

      3. unsub-neg 88.0%

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

      4. associate-/l* 88.2%

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

      5. mul-1-neg 88.2%

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

      6. remove-double-neg 88.2%

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

      7. associate-/l* 93.9%

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

   5. Simplified 93.9%

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

   if -7.1999999999999997e46 < t < 3.99999999999999978e72

   1. Initial program 88.9%

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

      1. clear-num 88.9%

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

      2. inv-pow 88.9%

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

      3. *-commutative 88.9%

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

   4. Applied egg-rr 88.9%

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

      1. unpow-1 88.9%

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

      2. associate-/r* 93.7%

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

   6. Simplified 93.7%

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

      1. div-inv 93.8%

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

   8. Applied egg-rr 93.8%

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

   9. Taylor expanded in t around 0 78.9%

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

       1. +-commutative 78.9%

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

       2. *-commutative 78.9%

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

       3. associate-*r/ 83.5%

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

   11. Simplified 83.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+46} \lor \neg \left(t \leq 4 \cdot 10^{+72}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+83} \lor \neg \left(t \leq 5 \cdot 10^{+79}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.02e+83) (not (<= t 5e+79)))
   (+ (- x (* a (/ y t))) (* y (/ z t)))
   (+ (+ x y) (* (- z t) (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.02e+83) || !(t <= 5e+79)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.02d+83)) .or. (.not. (t <= 5d+79))) then
        tmp = (x - (a * (y / t))) + (y * (z / t))
    else
        tmp = (x + y) + ((z - t) * (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.02e+83) || !(t <= 5e+79)) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.02e+83) or not (t <= 5e+79):
		tmp = (x - (a * (y / t))) + (y * (z / t))
	else:
		tmp = (x + y) + ((z - t) * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.02e+83) || !(t <= 5e+79))
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.02e+83) || ~((t <= 5e+79)))
		tmp = (x - (a * (y / t))) + (y * (z / t));
	else
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.02e+83], N[Not[LessEqual[t, 5e+79]], $MachinePrecision]], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0200000000000001e83 or 5e79 < t

   1. Initial program 61.9%

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

   3. Taylor expanded in t around inf 88.4%

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

      1. sub-neg 88.4%

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

      2. mul-1-neg 88.4%

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

      3. unsub-neg 88.4%

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

      4. associate-/l* 87.6%

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

      5. mul-1-neg 87.6%

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

      6. remove-double-neg 87.6%

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

      7. associate-/l* 93.6%

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

   5. Simplified 93.6%

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

   if -1.0200000000000001e83 < t < 5e79

   1. Initial program 89.2%

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

      1. associate-/l* 93.8%

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

      2. *-commutative 93.8%

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

   4. Applied egg-rr 93.8%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+83} \lor \neg \left(t \leq 5 \cdot 10^{+79}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-91}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 12000000000:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t}{y}}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6e-91)
   (- (+ x y) (* z (/ y a)))
   (if (<= a 12000000000.0)
     (+ x (/ -1.0 (/ (/ t y) (- a z))))
     (- (+ x y) (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e-91) {
		tmp = (x + y) - (z * (y / a));
	} else if (a <= 12000000000.0) {
		tmp = x + (-1.0 / ((t / y) / (a - z)));
	} else {
		tmp = (x + y) - (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 (a <= (-6d-91)) then
        tmp = (x + y) - (z * (y / a))
    else if (a <= 12000000000.0d0) then
        tmp = x + ((-1.0d0) / ((t / y) / (a - z)))
    else
        tmp = (x + y) - (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 (a <= -6e-91) {
		tmp = (x + y) - (z * (y / a));
	} else if (a <= 12000000000.0) {
		tmp = x + (-1.0 / ((t / y) / (a - z)));
	} else {
		tmp = (x + y) - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6e-91:
		tmp = (x + y) - (z * (y / a))
	elif a <= 12000000000.0:
		tmp = x + (-1.0 / ((t / y) / (a - z)))
	else:
		tmp = (x + y) - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6e-91)
		tmp = Float64(Float64(x + y) - Float64(z * Float64(y / a)));
	elseif (a <= 12000000000.0)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(t / y) / Float64(a - z))));
	else
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6e-91)
		tmp = (x + y) - (z * (y / a));
	elseif (a <= 12000000000.0)
		tmp = x + (-1.0 / ((t / y) / (a - z)));
	else
		tmp = (x + y) - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6e-91], N[(N[(x + y), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 12000000000.0], N[(x + N[(-1.0 / N[(N[(t / y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.0000000000000004e-91

   1. Initial program 80.4%

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

      1. clear-num 80.3%

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

      2. inv-pow 80.3%

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

      3. *-commutative 80.3%

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

   4. Applied egg-rr 80.3%

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

      1. unpow-1 80.3%

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

      2. associate-/r* 87.5%

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

   6. Simplified 87.5%

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

      1. div-inv 87.5%

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

   8. Applied egg-rr 87.5%

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

   9. Taylor expanded in t around 0 79.5%

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

       1. +-commutative 79.5%

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

       2. *-commutative 79.5%

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

       3. associate-*r/ 85.0%

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

   11. Simplified 85.0%

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

   if -6.0000000000000004e-91 < a < 1.2e10

   1. Initial program 76.4%

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

   3. Taylor expanded in t around -inf 85.9%

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

      1. mul-1-neg 85.9%

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

      2. unsub-neg 85.9%

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

      3. *-commutative 85.9%

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

   5. Simplified 85.9%

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

      1. clear-num 85.9%

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

      2. inv-pow 85.9%

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

      3. distribute-lft-out-- 85.9%

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

   7. Applied egg-rr 85.9%

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

      1. unpow-1 85.9%

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

      2. associate-/r* 87.1%

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

   9. Simplified 87.1%

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

   if 1.2e10 < a

   1. Initial program 82.9%

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

   3. Taylor expanded in t around 0 82.3%

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

      1. +-commutative 82.3%

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

      2. associate-/l* 89.4%

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

   5. Simplified 89.4%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-91}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 12000000000:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t}{y}}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+65} \lor \neg \left(a \leq 70000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.6e+65) (not (<= a 70000000000.0)))
   (+ x y)
   (+ x (/ (* y (- z a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.6e+65) || !(a <= 70000000000.0)) {
		tmp = x + y;
	} 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 ((a <= (-7.6d+65)) .or. (.not. (a <= 70000000000.0d0))) then
        tmp = x + y
    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 ((a <= -7.6e+65) || !(a <= 70000000000.0)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.6e+65) or not (a <= 70000000000.0):
		tmp = x + y
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.6e+65) || !(a <= 70000000000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.6e+65) || ~((a <= 70000000000.0)))
		tmp = x + y;
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.6e+65], N[Not[LessEqual[a, 70000000000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.60000000000000022e65 or 7e10 < a

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 79.7%

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

      1. +-commutative 79.7%

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

   5. Simplified 79.7%

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

   if -7.60000000000000022e65 < a < 7e10

   1. Initial program 77.9%

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

   3. Taylor expanded in t around -inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. unsub-neg 83.3%

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

      3. *-commutative 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in y around 0 83.3%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+65} \lor \neg \left(a \leq 70000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-17} \lor \neg \left(a \leq 55000000000000\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.5e-17) (not (<= a 55000000000000.0)))
   (- (+ x y) (* y (/ z a)))
   (+ x (/ (* y (- z a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.5e-17) || !(a <= 55000000000000.0)) {
		tmp = (x + y) - (y * (z / 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 ((a <= (-1.5d-17)) .or. (.not. (a <= 55000000000000.0d0))) then
        tmp = (x + y) - (y * (z / 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 ((a <= -1.5e-17) || !(a <= 55000000000000.0)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.5e-17) or not (a <= 55000000000000.0):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.5e-17) || !(a <= 55000000000000.0))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.5e-17) || ~((a <= 55000000000000.0)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.5e-17], N[Not[LessEqual[a, 55000000000000.0]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.50000000000000003e-17 or 5.5e13 < a

   1. Initial program 79.9%

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

   3. Taylor expanded in t around 0 79.5%

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

      1. +-commutative 79.5%

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

      2. associate-/l* 87.0%

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

   5. Simplified 87.0%

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

   if -1.50000000000000003e-17 < a < 5.5e13

   1. Initial program 78.8%

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

   3. Taylor expanded in t around -inf 85.9%

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

      1. mul-1-neg 85.9%

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

      2. unsub-neg 85.9%

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

      3. *-commutative 85.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in y around 0 85.9%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-17} \lor \neg \left(a \leq 55000000000000\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-92}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 85000000000:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e-92)
   (- (+ x y) (* z (/ y a)))
   (if (<= a 85000000000.0)
     (+ x (/ (* y (- z a)) t))
     (- (+ x y) (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e-92) {
		tmp = (x + y) - (z * (y / a));
	} else if (a <= 85000000000.0) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) - (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 (a <= (-9.5d-92)) then
        tmp = (x + y) - (z * (y / a))
    else if (a <= 85000000000.0d0) then
        tmp = x + ((y * (z - a)) / t)
    else
        tmp = (x + y) - (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 (a <= -9.5e-92) {
		tmp = (x + y) - (z * (y / a));
	} else if (a <= 85000000000.0) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e-92:
		tmp = (x + y) - (z * (y / a))
	elif a <= 85000000000.0:
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = (x + y) - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e-92)
		tmp = Float64(Float64(x + y) - Float64(z * Float64(y / a)));
	elseif (a <= 85000000000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e-92)
		tmp = (x + y) - (z * (y / a));
	elseif (a <= 85000000000.0)
		tmp = x + ((y * (z - a)) / t);
	else
		tmp = (x + y) - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e-92], N[(N[(x + y), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 85000000000.0], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.49999999999999946e-92

   1. Initial program 80.4%

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

      1. clear-num 80.3%

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

      2. inv-pow 80.3%

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

      3. *-commutative 80.3%

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

   4. Applied egg-rr 80.3%

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

      1. unpow-1 80.3%

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

      2. associate-/r* 87.5%

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

   6. Simplified 87.5%

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

      1. div-inv 87.5%

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

   8. Applied egg-rr 87.5%

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

   9. Taylor expanded in t around 0 79.5%

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

       1. +-commutative 79.5%

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

       2. *-commutative 79.5%

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

       3. associate-*r/ 85.0%

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

   11. Simplified 85.0%

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

   if -9.49999999999999946e-92 < a < 8.5e10

   1. Initial program 76.4%

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

   3. Taylor expanded in t around -inf 85.9%

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

      1. mul-1-neg 85.9%

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

      2. unsub-neg 85.9%

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

      3. *-commutative 85.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in y around 0 85.9%

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

   if 8.5e10 < a

   1. Initial program 82.9%

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

   3. Taylor expanded in t around 0 82.3%

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

      1. +-commutative 82.3%

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

      2. associate-/l* 89.4%

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

   5. Simplified 89.4%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-92}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 85000000000:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+237} \lor \neg \left(z \leq 5.2 \cdot 10^{+139}\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e+237) (not (<= z 5.2e+139))) (* y (/ z (- t a))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+237) || !(z <= 5.2e+139)) {
		tmp = y * (z / (t - 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 ((z <= (-5.2d+237)) .or. (.not. (z <= 5.2d+139))) then
        tmp = y * (z / (t - 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 ((z <= -5.2e+237) || !(z <= 5.2e+139)) {
		tmp = y * (z / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e+237) or not (z <= 5.2e+139):
		tmp = y * (z / (t - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e+237) || !(z <= 5.2e+139))
		tmp = Float64(y * Float64(z / Float64(t - a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.2e+237) || ~((z <= 5.2e+139)))
		tmp = y * (z / (t - a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.2e+237], N[Not[LessEqual[z, 5.2e+139]], $MachinePrecision]], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000005e237 or 5.20000000000000044e139 < z

   1. Initial program 83.6%

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

      1. sub-neg 83.6%

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

      2. +-commutative 83.6%

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

      3. distribute-frac-neg 83.6%

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

      4. distribute-rgt-neg-out 83.6%

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

      5. associate-/l* 91.1%

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

      6. fma-define 91.2%

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

      7. distribute-frac-neg 91.2%

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

      8. distribute-neg-frac2 91.2%

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

      9. sub-neg 91.2%

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

      10. distribute-neg-in 91.2%

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

      11. remove-double-neg 91.2%

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

      12. +-commutative 91.2%

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

      13. sub-neg 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in z around inf 61.4%

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

      1. associate-/l* 63.3%

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

   7. Applied egg-rr 63.3%

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

   if -5.20000000000000005e237 < z < 5.20000000000000044e139

   1. Initial program 78.4%

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

   3. Taylor expanded in a around inf 71.5%

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

      1. +-commutative 71.5%

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

   5. Simplified 71.5%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+237} \lor \neg \left(z \leq 5.2 \cdot 10^{+139}\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+86} \lor \neg \left(a \leq 3.5 \cdot 10^{+16}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.3e+86) (not (<= a 3.5e+16))) (+ x y) (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.3e+86) || !(a <= 3.5e+16)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.3d+86)) .or. (.not. (a <= 3.5d+16))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.3e+86) || !(a <= 3.5e+16)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.3e+86) or not (a <= 3.5e+16):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.3e+86) || !(a <= 3.5e+16))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.3e+86) || ~((a <= 3.5e+16)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.3e+86], N[Not[LessEqual[a, 3.5e+16]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2999999999999999e86 or 3.5e16 < a

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 79.8%

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

      1. +-commutative 79.8%

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

   5. Simplified 79.8%

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

   if -2.2999999999999999e86 < a < 3.5e16

   1. Initial program 77.9%

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

   3. Taylor expanded in t around -inf 82.6%

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

      1. mul-1-neg 82.6%

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

      2. unsub-neg 82.6%

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

      3. *-commutative 82.6%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in a around 0 79.4%

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

      1. mul-1-neg 79.4%

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

      2. distribute-rgt-neg-out 79.4%

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

   8. Simplified 79.4%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+86} \lor \neg \left(a \leq 3.5 \cdot 10^{+16}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+238}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+99}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+238)
   (* y (/ z (- t a)))
   (if (<= z 7.8e+99) (+ x y) (/ (* y z) (- t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+238) {
		tmp = y * (z / (t - a));
	} else if (z <= 7.8e+99) {
		tmp = x + y;
	} else {
		tmp = (y * z) / (t - a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.2d+238)) then
        tmp = y * (z / (t - a))
    else if (z <= 7.8d+99) then
        tmp = x + y
    else
        tmp = (y * z) / (t - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+238) {
		tmp = y * (z / (t - a));
	} else if (z <= 7.8e+99) {
		tmp = x + y;
	} else {
		tmp = (y * z) / (t - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+238:
		tmp = y * (z / (t - a))
	elif z <= 7.8e+99:
		tmp = x + y
	else:
		tmp = (y * z) / (t - a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+238)
		tmp = Float64(y * Float64(z / Float64(t - a)));
	elseif (z <= 7.8e+99)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(y * z) / Float64(t - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e+238)
		tmp = y * (z / (t - a));
	elseif (z <= 7.8e+99)
		tmp = x + y;
	else
		tmp = (y * z) / (t - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+238], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+99], N[(x + y), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999999e238

   1. Initial program 77.6%

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

      1. sub-neg 77.6%

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

      2. +-commutative 77.6%

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

      3. distribute-frac-neg 77.6%

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

      4. distribute-rgt-neg-out 77.6%

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

      5. associate-/l* 97.7%

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

      6. fma-define 98.2%

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

      7. distribute-frac-neg 98.2%

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

      8. distribute-neg-frac2 98.2%

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

      9. sub-neg 98.2%

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

      10. distribute-neg-in 98.2%

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

      11. remove-double-neg 98.2%

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

      12. +-commutative 98.2%

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

      13. sub-neg 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in z around inf 54.7%

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

      1. associate-/l* 65.7%

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

   7. Applied egg-rr 65.7%

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

   if -5.1999999999999999e238 < z < 7.79999999999999989e99

   1. Initial program 78.1%

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

   3. Taylor expanded in a around inf 72.4%

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

      1. +-commutative 72.4%

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

   5. Simplified 72.4%

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

   if 7.79999999999999989e99 < z

   1. Initial program 86.7%

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

      1. sub-neg 86.7%

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

      2. +-commutative 86.7%

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

      3. distribute-frac-neg 86.7%

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

      4. distribute-rgt-neg-out 86.7%

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

      5. associate-/l* 87.5%

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

      6. fma-define 87.4%

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

      7. distribute-frac-neg 87.4%

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

      8. distribute-neg-frac2 87.4%

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

      9. sub-neg 87.4%

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

      10. distribute-neg-in 87.4%

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

      11. remove-double-neg 87.4%

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

      12. +-commutative 87.4%

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

      13. sub-neg 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in z around inf 61.5%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+238}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+99}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+86} \lor \neg \left(a \leq 72000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.4e+86) (not (<= a 72000000000.0))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.4e+86) || !(a <= 72000000000.0)) {
		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 <= (-1.4d+86)) .or. (.not. (a <= 72000000000.0d0))) 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 <= -1.4e+86) || !(a <= 72000000000.0)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.4e+86) or not (a <= 72000000000.0):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.4e+86) || !(a <= 72000000000.0))
		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 <= -1.4e+86) || ~((a <= 72000000000.0)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.4e+86], N[Not[LessEqual[a, 72000000000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.40000000000000002e86 or 7.2e10 < a

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 79.8%

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

      1. +-commutative 79.8%

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

   5. Simplified 79.8%

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

   if -1.40000000000000002e86 < a < 7.2e10

   1. Initial program 77.9%

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

   3. Taylor expanded in x around inf 57.8%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+86} \lor \neg \left(a \leq 72000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.8% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.4%

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

3. Taylor expanded in x around inf 53.3%

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

4. Final simplification 53.3%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * 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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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