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

Percentage Accurate: 77.2% → 90.4%

Time: 10.8s

Alternatives: 13

Speedup: 0.6×

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: 77.2% 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: 90.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+107}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+84}:\\ \;\;\;\;\left(x + y\right) + \frac{z - t}{\frac{t - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e+107)
   (+ (- x (* a (/ y t))) (* y (/ z t)))
   (if (<= t 2.8e+84)
     (+ (+ x y) (/ (- z t) (/ (- t a) y)))
     (- x (* y (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+107) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else if (t <= 2.8e+84) {
		tmp = (x + y) + ((z - t) / ((t - a) / y));
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4d+107)) then
        tmp = (x - (a * (y / t))) + (y * (z / t))
    else if (t <= 2.8d+84) then
        tmp = (x + y) + ((z - t) / ((t - a) / y))
    else
        tmp = x - (y * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+107) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else if (t <= 2.8e+84) {
		tmp = (x + y) + ((z - t) / ((t - a) / y));
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4e+107:
		tmp = (x - (a * (y / t))) + (y * (z / t))
	elif t <= 2.8e+84:
		tmp = (x + y) + ((z - t) / ((t - a) / y))
	else:
		tmp = x - (y * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e+107)
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	elseif (t <= 2.8e+84)
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) / Float64(Float64(t - a) / y)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4e+107)
		tmp = (x - (a * (y / t))) + (y * (z / t));
	elseif (t <= 2.8e+84)
		tmp = (x + y) + ((z - t) / ((t - a) / y));
	else
		tmp = x - (y * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e+107], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+84], N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.9999999999999999e107

   1. Initial program 61.4%

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

      1. associate-/l* 66.9%

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

      2. *-commutative 66.9%

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

   4. Applied egg-rr 66.9%

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

   5. Taylor expanded in t around inf 87.2%

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

      1. sub-neg 87.2%

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

      2. mul-1-neg 87.2%

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

      3. unsub-neg 87.2%

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

      4. associate-/l* 94.8%

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

      5. mul-1-neg 94.8%

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

      6. remove-double-neg 94.8%

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

      7. associate-/l* 97.3%

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

   7. Simplified 97.3%

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

   if -3.9999999999999999e107 < t < 2.79999999999999982e84

   1. Initial program 93.5%

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

      1. associate-/l* 93.9%

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

      2. *-commutative 93.9%

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

   4. Applied egg-rr 93.9%

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

      1. *-commutative 93.9%

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

      2. clear-num 93.9%

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

      3. un-div-inv 94.7%

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

   6. Applied egg-rr 94.7%

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

   if 2.79999999999999982e84 < t

   1. Initial program 62.9%

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

      1. associate-/l* 66.0%

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

      2. *-commutative 66.0%

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

   4. Applied egg-rr 66.0%

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

      1. *-commutative 66.0%

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

      2. clear-num 65.6%

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

      3. un-div-inv 65.8%

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

   6. Applied egg-rr 65.8%

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

   7. Taylor expanded in t around -inf 76.5%

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

      1. mul-1-neg 76.5%

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

      2. unsub-neg 76.5%

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

      3. *-commutative 76.5%

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

      4. cancel-sign-sub-inv 76.5%

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

      5. mul-1-neg 76.5%

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

      6. distribute-rgt-in 78.3%

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

      7. associate-/l* 87.1%

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

      8. mul-1-neg 87.1%

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

      9. sub-neg 87.1%

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

   9. Simplified 87.1%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+107}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+84}:\\ \;\;\;\;\left(x + y\right) + \frac{z - t}{\frac{t - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+24} \lor \neg \left(a \leq -3.8 \cdot 10^{-33}\right) \land \left(a \leq -4.1 \cdot 10^{-70} \lor \neg \left(a \leq 6.5 \cdot 10^{+83}\right)\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.12e+24)
         (and (not (<= a -3.8e-33)) (or (<= a -4.1e-70) (not (<= a 6.5e+83)))))
   (+ x y)
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.12e+24) || (!(a <= -3.8e-33) && ((a <= -4.1e-70) || !(a <= 6.5e+83)))) {
		tmp = x + y;
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.12d+24)) .or. (.not. (a <= (-3.8d-33))) .and. (a <= (-4.1d-70)) .or. (.not. (a <= 6.5d+83))) then
        tmp = x + y
    else
        tmp = x - ((y * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.12e+24) || (!(a <= -3.8e-33) && ((a <= -4.1e-70) || !(a <= 6.5e+83)))) {
		tmp = x + y;
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.12e+24) or (not (a <= -3.8e-33) and ((a <= -4.1e-70) or not (a <= 6.5e+83))):
		tmp = x + y
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.12e+24) || (!(a <= -3.8e-33) && ((a <= -4.1e-70) || !(a <= 6.5e+83))))
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.12e+24) || (~((a <= -3.8e-33)) && ((a <= -4.1e-70) || ~((a <= 6.5e+83)))))
		tmp = x + y;
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.12e+24], And[N[Not[LessEqual[a, -3.8e-33]], $MachinePrecision], Or[LessEqual[a, -4.1e-70], N[Not[LessEqual[a, 6.5e+83]], $MachinePrecision]]]], N[(x + y), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.12e24 or -3.79999999999999994e-33 < a < -4.09999999999999977e-70 or 6.5000000000000003e83 < a

   1. Initial program 87.2%

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

   3. Taylor expanded in a around inf 82.9%

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

      1. +-commutative 82.9%

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

   5. Simplified 82.9%

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

   if -1.12e24 < a < -3.79999999999999994e-33 or -4.09999999999999977e-70 < a < 6.5000000000000003e83

   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 t around inf 81.8%

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

      1. associate--l+ 81.8%

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

      2. distribute-lft-out-- 81.8%

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

      3. div-sub 81.9%

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

      4. mul-1-neg 81.9%

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

      5. unsub-neg 81.9%

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

      6. *-commutative 81.9%

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

      7. distribute-lft-out-- 81.9%

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

   5. Simplified 81.9%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+24} \lor \neg \left(a \leq -3.8 \cdot 10^{-33}\right) \land \left(a \leq -4.1 \cdot 10^{-70} \lor \neg \left(a \leq 6.5 \cdot 10^{+83}\right)\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{+23} \lor \neg \left(a \leq -1.08 \cdot 10^{-33} \lor \neg \left(a \leq -1.3 \cdot 10^{-68}\right) \land a \leq 8.5 \cdot 10^{+83}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.95e+23)
         (not
          (or (<= a -1.08e-33) (and (not (<= a -1.3e-68)) (<= a 8.5e+83)))))
   (+ x y)
   (- x (* y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.95e+23) || !((a <= -1.08e-33) || (!(a <= -1.3e-68) && (a <= 8.5e+83)))) {
		tmp = x + y;
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.95d+23)) .or. (.not. (a <= (-1.08d-33)) .or. (.not. (a <= (-1.3d-68))) .and. (a <= 8.5d+83))) then
        tmp = x + y
    else
        tmp = x - (y * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.95e+23) || !((a <= -1.08e-33) || (!(a <= -1.3e-68) && (a <= 8.5e+83)))) {
		tmp = x + y;
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.95e+23) or not ((a <= -1.08e-33) or (not (a <= -1.3e-68) and (a <= 8.5e+83))):
		tmp = x + y
	else:
		tmp = x - (y * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.95e+23) || !((a <= -1.08e-33) || (!(a <= -1.3e-68) && (a <= 8.5e+83))))
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.95e+23) || ~(((a <= -1.08e-33) || (~((a <= -1.3e-68)) && (a <= 8.5e+83)))))
		tmp = x + y;
	else
		tmp = x - (y * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.95e+23], N[Not[Or[LessEqual[a, -1.08e-33], And[N[Not[LessEqual[a, -1.3e-68]], $MachinePrecision], LessEqual[a, 8.5e+83]]]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.94999999999999994e23 or -1.08000000000000007e-33 < a < -1.2999999999999999e-68 or 8.4999999999999995e83 < a

   1. Initial program 87.2%

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

   3. Taylor expanded in a around inf 82.9%

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

      1. +-commutative 82.9%

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

   5. Simplified 82.9%

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

   if -2.94999999999999994e23 < a < -1.08000000000000007e-33 or -1.2999999999999999e-68 < a < 8.4999999999999995e83

   1. Initial program 78.1%

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

      1. associate-/l* 76.7%

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

      2. *-commutative 76.7%

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

   4. Applied egg-rr 76.7%

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

      1. *-commutative 76.7%

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

      2. clear-num 76.4%

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

      3. un-div-inv 77.5%

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

   6. Applied egg-rr 77.5%

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

   7. Taylor expanded in t around -inf 81.9%

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

      1. mul-1-neg 81.9%

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

      2. unsub-neg 81.9%

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

      3. *-commutative 81.9%

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

      4. cancel-sign-sub-inv 81.9%

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

      5. mul-1-neg 81.9%

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

      6. distribute-rgt-in 81.9%

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

      7. associate-/l* 81.5%

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

      8. mul-1-neg 81.5%

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

      9. sub-neg 81.5%

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

   9. Simplified 81.5%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{+23} \lor \neg \left(a \leq -1.08 \cdot 10^{-33} \lor \neg \left(a \leq -1.3 \cdot 10^{-68}\right) \land a \leq 8.5 \cdot 10^{+83}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+106}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + t\_1\\ \mathbf{elif}\;t \leq -7.3 \cdot 10^{-23}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-58}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-28}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= t -9e+106)
     (+ (- x (* a (/ y t))) t_1)
     (if (<= t -7.3e-23)
       (+ x y)
       (if (<= t -5.8e-58)
         (+ x t_1)
         (if (<= t 3.6e-28)
           (- (+ x y) (* y (/ z a)))
           (- x (* y (/ (- a z) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / t);
	double tmp;
	if (t <= -9e+106) {
		tmp = (x - (a * (y / t))) + t_1;
	} else if (t <= -7.3e-23) {
		tmp = x + y;
	} else if (t <= -5.8e-58) {
		tmp = x + t_1;
	} else if (t <= 3.6e-28) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (t <= (-9d+106)) then
        tmp = (x - (a * (y / t))) + t_1
    else if (t <= (-7.3d-23)) then
        tmp = x + y
    else if (t <= (-5.8d-58)) then
        tmp = x + t_1
    else if (t <= 3.6d-28) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x - (y * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / t);
	double tmp;
	if (t <= -9e+106) {
		tmp = (x - (a * (y / t))) + t_1;
	} else if (t <= -7.3e-23) {
		tmp = x + y;
	} else if (t <= -5.8e-58) {
		tmp = x + t_1;
	} else if (t <= 3.6e-28) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / t)
	tmp = 0
	if t <= -9e+106:
		tmp = (x - (a * (y / t))) + t_1
	elif t <= -7.3e-23:
		tmp = x + y
	elif t <= -5.8e-58:
		tmp = x + t_1
	elif t <= 3.6e-28:
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x - (y * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (t <= -9e+106)
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + t_1);
	elseif (t <= -7.3e-23)
		tmp = Float64(x + y);
	elseif (t <= -5.8e-58)
		tmp = Float64(x + t_1);
	elseif (t <= 3.6e-28)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (t <= -9e+106)
		tmp = (x - (a * (y / t))) + t_1;
	elseif (t <= -7.3e-23)
		tmp = x + y;
	elseif (t <= -5.8e-58)
		tmp = x + t_1;
	elseif (t <= 3.6e-28)
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x - (y * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+106], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, -7.3e-23], N[(x + y), $MachinePrecision], If[LessEqual[t, -5.8e-58], N[(x + t$95$1), $MachinePrecision], If[LessEqual[t, 3.6e-28], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.9999999999999994e106

   1. Initial program 61.4%

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

      1. associate-/l* 66.9%

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

      2. *-commutative 66.9%

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

   4. Applied egg-rr 66.9%

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

   5. Taylor expanded in t around inf 87.2%

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

      1. sub-neg 87.2%

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

      2. mul-1-neg 87.2%

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

      3. unsub-neg 87.2%

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

      4. associate-/l* 94.8%

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

      5. mul-1-neg 94.8%

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

      6. remove-double-neg 94.8%

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

      7. associate-/l* 97.3%

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

   7. Simplified 97.3%

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

   if -8.9999999999999994e106 < t < -7.30000000000000005e-23

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf 86.9%

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

      1. +-commutative 86.9%

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

   5. Simplified 86.9%

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

   if -7.30000000000000005e-23 < t < -5.7999999999999998e-58

   1. Initial program 96.5%

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

      1. associate-/l* 96.5%

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

      2. *-commutative 96.5%

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

   4. Applied egg-rr 96.5%

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

      1. *-commutative 96.5%

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

      2. clear-num 96.5%

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

      3. un-div-inv 96.8%

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

   6. Applied egg-rr 96.8%

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

      1. div-sub 96.8%

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

   8. Applied egg-rr 96.8%

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

   9. Taylor expanded in a around 0 99.7%

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

       1. sub-neg 99.7%

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

       2. distribute-rgt1-in 99.7%

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

       3. metadata-eval 99.7%

          \[\leadsto \left(x + \color{blue}{0} \cdot y\right) + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]

       4. mul0-lft 99.7%

          \[\leadsto \left(x + \color{blue}{0}\right) + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]

       5. +-rgt-identity 99.7%

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

       6. mul-1-neg 99.7%

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

       7. remove-double-neg 99.7%

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

       8. associate-/l* 100.0%

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

   11. Simplified 100.0%

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

   if -5.7999999999999998e-58 < t < 3.5999999999999999e-28

   1. Initial program 95.3%

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

   3. Taylor expanded in t around 0 86.2%

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

      1. +-commutative 86.2%

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

      2. associate-/l* 87.3%

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

   5. Simplified 87.3%

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

   if 3.5999999999999999e-28 < t

   1. Initial program 68.3%

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

      1. associate-/l* 71.8%

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

      2. *-commutative 71.8%

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

   4. Applied egg-rr 71.8%

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

      1. *-commutative 71.8%

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

      2. clear-num 71.6%

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

      3. un-div-inv 71.6%

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

   6. Applied egg-rr 71.6%

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

   7. Taylor expanded in t around -inf 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

      3. *-commutative 75.9%

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

      4. cancel-sign-sub-inv 75.9%

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

      5. mul-1-neg 75.9%

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

      6. distribute-rgt-in 77.2%

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

      7. associate-/l* 83.8%

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

      8. mul-1-neg 83.8%

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

      9. sub-neg 83.8%

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

   9. Simplified 83.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+106}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -7.3 \cdot 10^{-23}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-58}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-28}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-18}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-57}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-29}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- a z) t)))))
   (if (<= t -1.6e+105)
     t_1
     (if (<= t -6e-18)
       (+ x y)
       (if (<= t -1.5e-57)
         (+ x (* y (/ z t)))
         (if (<= t 1.8e-29) (- (+ x y) (* y (/ z a))) 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 (t <= -1.6e+105) {
		tmp = t_1;
	} else if (t <= -6e-18) {
		tmp = x + y;
	} else if (t <= -1.5e-57) {
		tmp = x + (y * (z / t));
	} else if (t <= 1.8e-29) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * ((a - z) / t))
    if (t <= (-1.6d+105)) then
        tmp = t_1
    else if (t <= (-6d-18)) then
        tmp = x + y
    else if (t <= (-1.5d-57)) then
        tmp = x + (y * (z / t))
    else if (t <= 1.8d-29) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((a - z) / t));
	double tmp;
	if (t <= -1.6e+105) {
		tmp = t_1;
	} else if (t <= -6e-18) {
		tmp = x + y;
	} else if (t <= -1.5e-57) {
		tmp = x + (y * (z / t));
	} else if (t <= 1.8e-29) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((a - z) / t))
	tmp = 0
	if t <= -1.6e+105:
		tmp = t_1
	elif t <= -6e-18:
		tmp = x + y
	elif t <= -1.5e-57:
		tmp = x + (y * (z / t))
	elif t <= 1.8e-29:
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -1.6e+105)
		tmp = t_1;
	elseif (t <= -6e-18)
		tmp = Float64(x + y);
	elseif (t <= -1.5e-57)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 1.8e-29)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((a - z) / t));
	tmp = 0.0;
	if (t <= -1.6e+105)
		tmp = t_1;
	elseif (t <= -6e-18)
		tmp = x + y;
	elseif (t <= -1.5e-57)
		tmp = x + (y * (z / t));
	elseif (t <= 1.8e-29)
		tmp = (x + y) - (y * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+105], t$95$1, If[LessEqual[t, -6e-18], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.5e-57], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-29], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.6e105 or 1.79999999999999987e-29 < t

   1. Initial program 65.9%

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

      1. associate-/l* 70.1%

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

      2. *-commutative 70.1%

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

   4. Applied egg-rr 70.1%

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

      1. *-commutative 70.1%

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

      2. clear-num 69.9%

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

      3. un-div-inv 70.0%

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

   6. Applied egg-rr 70.0%

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

   7. Taylor expanded in t around -inf 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

      3. *-commutative 79.8%

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

      4. cancel-sign-sub-inv 79.8%

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

      5. mul-1-neg 79.8%

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

      6. distribute-rgt-in 80.7%

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

      7. associate-/l* 87.6%

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

      8. mul-1-neg 87.6%

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

      9. sub-neg 87.6%

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

   9. Simplified 87.6%

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

   if -1.6e105 < t < -5.99999999999999966e-18

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf 86.9%

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

      1. +-commutative 86.9%

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

   5. Simplified 86.9%

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

   if -5.99999999999999966e-18 < t < -1.5e-57

   1. Initial program 96.5%

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

      1. associate-/l* 96.5%

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

      2. *-commutative 96.5%

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

   4. Applied egg-rr 96.5%

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

      1. *-commutative 96.5%

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

      2. clear-num 96.5%

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

      3. un-div-inv 96.8%

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

   6. Applied egg-rr 96.8%

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

      1. div-sub 96.8%

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

   8. Applied egg-rr 96.8%

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

   9. Taylor expanded in a around 0 99.7%

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

       1. sub-neg 99.7%

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

       2. distribute-rgt1-in 99.7%

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

       3. metadata-eval 99.7%

          \[\leadsto \left(x + \color{blue}{0} \cdot y\right) + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]

       4. mul0-lft 99.7%

          \[\leadsto \left(x + \color{blue}{0}\right) + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]

       5. +-rgt-identity 99.7%

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

       6. mul-1-neg 99.7%

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

       7. remove-double-neg 99.7%

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

       8. associate-/l* 100.0%

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

   11. Simplified 100.0%

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

   if -1.5e-57 < t < 1.79999999999999987e-29

   1. Initial program 95.3%

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

   3. Taylor expanded in t around 0 86.2%

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

      1. +-commutative 86.2%

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

      2. associate-/l* 87.3%

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

   5. Simplified 87.3%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+105}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-18}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-57}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-29}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-256}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.2e+112)
   x
   (if (<= t -4.4e-256)
     (+ x y)
     (if (<= t 8e-279) (* y (- 1.0 (/ z a))) (if (<= t 7.7e+84) (+ x y) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.2e+112) {
		tmp = x;
	} else if (t <= -4.4e-256) {
		tmp = x + y;
	} else if (t <= 8e-279) {
		tmp = y * (1.0 - (z / a));
	} else if (t <= 7.7e+84) {
		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 <= (-8.2d+112)) then
        tmp = x
    else if (t <= (-4.4d-256)) then
        tmp = x + y
    else if (t <= 8d-279) then
        tmp = y * (1.0d0 - (z / a))
    else if (t <= 7.7d+84) 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 <= -8.2e+112) {
		tmp = x;
	} else if (t <= -4.4e-256) {
		tmp = x + y;
	} else if (t <= 8e-279) {
		tmp = y * (1.0 - (z / a));
	} else if (t <= 7.7e+84) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.2e+112:
		tmp = x
	elif t <= -4.4e-256:
		tmp = x + y
	elif t <= 8e-279:
		tmp = y * (1.0 - (z / a))
	elif t <= 7.7e+84:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.2e+112)
		tmp = x;
	elseif (t <= -4.4e-256)
		tmp = Float64(x + y);
	elseif (t <= 8e-279)
		tmp = Float64(y * Float64(1.0 - Float64(z / a)));
	elseif (t <= 7.7e+84)
		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 <= -8.2e+112)
		tmp = x;
	elseif (t <= -4.4e-256)
		tmp = x + y;
	elseif (t <= 8e-279)
		tmp = y * (1.0 - (z / a));
	elseif (t <= 7.7e+84)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.2e+112], x, If[LessEqual[t, -4.4e-256], N[(x + y), $MachinePrecision], If[LessEqual[t, 8e-279], N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.7e+84], N[(x + y), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.19999999999999951e112 or 7.7000000000000003e84 < t

   1. Initial program 62.3%

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

   3. Taylor expanded in x around inf 68.1%

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

   if -8.19999999999999951e112 < t < -4.4000000000000002e-256 or 8.00000000000000044e-279 < t < 7.7000000000000003e84

   1. Initial program 93.4%

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

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

   if -4.4000000000000002e-256 < t < 8.00000000000000044e-279

   1. Initial program 94.5%

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

   3. Taylor expanded in t around 0 94.5%

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

      1. +-commutative 94.5%

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

      2. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf 77.0%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-256}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+105}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+45}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.05e+105)
   (+ (- x (* a (/ y t))) (* y (/ z t)))
   (if (<= t 8.8e+45)
     (+ (+ x y) (* (- z t) (/ y (- t a))))
     (- x (* y (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+105) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else if (t <= 8.8e+45) {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.05d+105)) then
        tmp = (x - (a * (y / t))) + (y * (z / t))
    else if (t <= 8.8d+45) then
        tmp = (x + y) + ((z - t) * (y / (t - a)))
    else
        tmp = x - (y * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+105) {
		tmp = (x - (a * (y / t))) + (y * (z / t));
	} else if (t <= 8.8e+45) {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	} else {
		tmp = x - (y * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.05e+105:
		tmp = (x - (a * (y / t))) + (y * (z / t))
	elif t <= 8.8e+45:
		tmp = (x + y) + ((z - t) * (y / (t - a)))
	else:
		tmp = x - (y * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.05e+105)
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(y * Float64(z / t)));
	elseif (t <= 8.8e+45)
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) * Float64(y / Float64(t - a))));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.05e+105)
		tmp = (x - (a * (y / t))) + (y * (z / t));
	elseif (t <= 8.8e+45)
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	else
		tmp = x - (y * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.05e+105], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e+45], N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05000000000000005e105

   1. Initial program 61.4%

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

      1. associate-/l* 66.9%

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

      2. *-commutative 66.9%

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

   4. Applied egg-rr 66.9%

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

   5. Taylor expanded in t around inf 87.2%

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

      1. sub-neg 87.2%

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

      2. mul-1-neg 87.2%

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

      3. unsub-neg 87.2%

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

      4. associate-/l* 94.8%

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

      5. mul-1-neg 94.8%

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

      6. remove-double-neg 94.8%

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

      7. associate-/l* 97.3%

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

   7. Simplified 97.3%

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

   if -1.05000000000000005e105 < t < 8.8000000000000001e45

   1. Initial program 93.8%

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

      1. associate-/l* 94.2%

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

      2. *-commutative 94.2%

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

   4. Applied egg-rr 94.2%

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

   if 8.8000000000000001e45 < t

   1. Initial program 65.6%

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

      1. associate-/l* 68.3%

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

      2. *-commutative 68.3%

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

   4. Applied egg-rr 68.3%

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

      1. *-commutative 68.3%

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

      2. clear-num 68.1%

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

      3. un-div-inv 68.1%

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

   6. Applied egg-rr 68.1%

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

   7. Taylor expanded in t around -inf 77.6%

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

      1. mul-1-neg 77.6%

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

      2. unsub-neg 77.6%

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

      3. *-commutative 77.6%

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

      4. cancel-sign-sub-inv 77.6%

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

      5. mul-1-neg 77.6%

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

      6. distribute-rgt-in 79.3%

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

      7. associate-/l* 87.0%

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

      8. mul-1-neg 87.0%

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

      9. sub-neg 87.0%

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

   9. Simplified 87.0%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+105}:\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+45}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\neg \left(a \leq -1.3 \cdot 10^{-68}\right) \land a \leq 3.4 \cdot 10^{-30}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (and (not (<= a -1.3e-68)) (<= a 3.4e-30)) (+ x (* y (/ z t))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (!(a <= -1.3e-68) && (a <= 3.4e-30)) {
		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 ((.not. (a <= (-1.3d-68))) .and. (a <= 3.4d-30)) 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 (!(a <= -1.3e-68) && (a <= 3.4e-30)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if not (a <= -1.3e-68) and (a <= 3.4e-30):
		tmp = x + (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (!(a <= -1.3e-68) && (a <= 3.4e-30))
		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 (~((a <= -1.3e-68)) && (a <= 3.4e-30))
		tmp = x + (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[And[N[Not[LessEqual[a, -1.3e-68]], $MachinePrecision], LessEqual[a, 3.4e-30]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.2999999999999999e-68 or 3.4000000000000003e-30 < a

   1. Initial program 81.9%

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

   3. Taylor expanded in a around inf 74.4%

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

      1. +-commutative 74.4%

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

   5. Simplified 74.4%

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

   if -1.2999999999999999e-68 < a < 3.4000000000000003e-30

   1. Initial program 82.9%

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

      1. associate-/l* 80.1%

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

      2. *-commutative 80.1%

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

   4. Applied egg-rr 80.1%

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

      1. *-commutative 80.1%

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

      2. clear-num 79.7%

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

      3. un-div-inv 81.2%

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

   6. Applied egg-rr 81.2%

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

      1. div-sub 80.3%

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

   8. Applied egg-rr 80.3%

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

   9. Taylor expanded in a around 0 84.5%

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

       1. sub-neg 84.5%

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

       2. distribute-rgt1-in 84.5%

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

       3. metadata-eval 84.5%

          \[\leadsto \left(x + \color{blue}{0} \cdot y\right) + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]

       4. mul0-lft 84.5%

          \[\leadsto \left(x + \color{blue}{0}\right) + \left(--1 \cdot \frac{y \cdot z}{t}\right) \]

       5. +-rgt-identity 84.5%

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

       6. mul-1-neg 84.5%

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

       7. remove-double-neg 84.5%

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

       8. associate-/l* 84.9%

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

   11. Simplified 84.9%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\neg \left(a \leq -1.3 \cdot 10^{-68}\right) \land a \leq 3.4 \cdot 10^{-30}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+241} \lor \neg \left(z \leq 8.5 \cdot 10^{+223}\right):\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e+241) (not (<= z 8.5e+223))) (* z (/ y (- t a))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+241) || !(z <= 8.5e+223)) {
		tmp = z * (y / (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 <= (-4.5d+241)) .or. (.not. (z <= 8.5d+223))) then
        tmp = z * (y / (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 <= -4.5e+241) || !(z <= 8.5e+223)) {
		tmp = z * (y / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e+241) or not (z <= 8.5e+223):
		tmp = z * (y / (t - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e+241) || !(z <= 8.5e+223))
		tmp = Float64(z * Float64(y / 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 <= -4.5e+241) || ~((z <= 8.5e+223)))
		tmp = z * (y / (t - a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e+241], N[Not[LessEqual[z, 8.5e+223]], $MachinePrecision]], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999993e241 or 8.5000000000000005e223 < z

   1. Initial program 89.3%

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

      1. sub-neg 89.3%

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

      2. +-commutative 89.3%

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

      3. distribute-frac-neg 89.3%

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

      4. distribute-rgt-neg-out 89.3%

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

      5. associate-/l* 96.8%

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

      6. fma-define 96.8%

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

      7. distribute-frac-neg 96.8%

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

      8. distribute-neg-frac2 96.8%

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

      9. sub-neg 96.8%

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

      10. distribute-neg-in 96.8%

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

      11. remove-double-neg 96.8%

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

      12. +-commutative 96.8%

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

      13. sub-neg 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around inf 67.1%

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

      1. associate-/l* 61.4%

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

   7. Simplified 61.4%

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

      1. clear-num 61.3%

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

      2. un-div-inv 61.4%

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

   9. Applied egg-rr 61.4%

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

       1. associate-/r/ 71.0%

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

   11. Simplified 71.0%

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

   if -4.49999999999999993e241 < z < 8.5000000000000005e223

   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 68.4%

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

      1. +-commutative 68.4%

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

   5. Simplified 68.4%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+241} \lor \neg \left(z \leq 8.5 \cdot 10^{+223}\right):\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.85e+112) x (if (<= t 1.95e+84) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.85e+112) {
		tmp = x;
	} else if (t <= 1.95e+84) {
		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 <= (-1.85d+112)) then
        tmp = x
    else if (t <= 1.95d+84) 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 <= -1.85e+112) {
		tmp = x;
	} else if (t <= 1.95e+84) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.85e+112:
		tmp = x
	elif t <= 1.95e+84:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.85e+112)
		tmp = x;
	elseif (t <= 1.95e+84)
		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 <= -1.85e+112)
		tmp = x;
	elseif (t <= 1.95e+84)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.85e+112], x, If[LessEqual[t, 1.95e+84], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.85000000000000002e112 or 1.95000000000000008e84 < t

   1. Initial program 62.3%

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

   3. Taylor expanded in x around inf 68.1%

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

   if -1.85000000000000002e112 < t < 1.95000000000000008e84

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf 68.6%

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

      1. +-commutative 68.6%

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

   5. Simplified 68.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 8.7 \cdot 10^{+223}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 8.7e+223) (+ x y) (* y (/ z (- t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 8.7e+223) {
		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 <= 8.7d+223) 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 <= 8.7e+223) {
		tmp = x + y;
	} else {
		tmp = y * (z / (t - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 8.7e+223:
		tmp = x + y
	else:
		tmp = y * (z / (t - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 8.7e+223)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / Float64(t - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 8.7e+223)
		tmp = x + y;
	else
		tmp = y * (z / (t - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 8.7e+223], N[(x + y), $MachinePrecision], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.7000000000000001e223

   1. Initial program 81.2%

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

   3. Taylor expanded in a around inf 66.7%

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

      1. +-commutative 66.7%

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

   5. Simplified 66.7%

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

   if 8.7000000000000001e223 < z

   1. Initial program 93.4%

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

      1. sub-neg 93.4%

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

      2. +-commutative 93.4%

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

      3. distribute-frac-neg 93.4%

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

      4. distribute-rgt-neg-out 93.4%

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

      5. associate-/l* 95.6%

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

      6. fma-define 95.6%

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

      7. distribute-frac-neg 95.6%

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

      8. distribute-neg-frac2 95.6%

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

      9. sub-neg 95.6%

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

      10. distribute-neg-in 95.6%

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

      11. remove-double-neg 95.6%

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

      12. +-commutative 95.6%

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

      13. sub-neg 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in z around inf 66.8%

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

      1. associate-/l* 62.9%

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

   7. Simplified 62.9%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.7 \cdot 10^{+223}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+124}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+214}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.8e+124) y (if (<= y 1.15e+214) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.8e+124) {
		tmp = y;
	} else if (y <= 1.15e+214) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.8d+124)) then
        tmp = y
    else if (y <= 1.15d+214) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.8e+124) {
		tmp = y;
	} else if (y <= 1.15e+214) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.8e+124:
		tmp = y
	elif y <= 1.15e+214:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.8e+124)
		tmp = y;
	elseif (y <= 1.15e+214)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.8e+124)
		tmp = y;
	elseif (y <= 1.15e+214)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.8e+124], y, If[LessEqual[y, 1.15e+214], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999993e124 or 1.15e214 < y

   1. Initial program 66.2%

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

   3. Taylor expanded in x around 0 59.4%

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

      1. associate-*r/ 68.3%

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

      2. sub-neg 68.3%

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

      3. *-rgt-identity 68.3%

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

      4. distribute-rgt-neg-in 68.3%

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

      5. mul-1-neg 68.3%

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

      6. distribute-lft-in 68.4%

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

      7. mul-1-neg 68.4%

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

      8. unsub-neg 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in a around inf 48.2%

      \[\leadsto y \cdot \color{blue}{1} \]

   if -1.79999999999999993e124 < y < 1.15e214

   1. Initial program 86.6%

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

   3. Taylor expanded in x around inf 62.8%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+124}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+214}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.2% 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 82.3%

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

3. Taylor expanded in x around inf 53.1%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 88.1% 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 2024087 
(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))))