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

Percentage Accurate: 76.8% → 89.8%

Time: 18.0s

Alternatives: 12

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: 76.8% 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: 89.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x - \frac{-1}{\frac{\frac{t}{y}}{z - a}}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ (* y (- z t)) (- t a)))))
   (if (<= t_1 (- INFINITY))
     (- x (/ -1.0 (/ (/ t y) (- z a))))
     (if (<= t_1 -5e-242)
       t_1
       (if (<= t_1 0.0)
         (+ x (* y (/ (- z a) t)))
         (+ (+ x y) (* y (/ z (- t a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x - (-1.0 / ((t / y) / (z - a)));
	} else if (t_1 <= -5e-242) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = x + (y * ((z - a) / t));
	} else {
		tmp = (x + y) + (y * (z / (t - a)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x - (-1.0 / ((t / y) / (z - a)));
	} else if (t_1 <= -5e-242) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = x + (y * ((z - a) / t));
	} else {
		tmp = (x + y) + (y * (z / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) + ((y * (z - t)) / (t - a))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x - (-1.0 / ((t / y) / (z - a)))
	elif t_1 <= -5e-242:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = x + (y * ((z - a) / t))
	else:
		tmp = (x + y) + (y * (z / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(Float64(y * Float64(z - t)) / Float64(t - a)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x - Float64(-1.0 / Float64(Float64(t / y) / Float64(z - a))));
	elseif (t_1 <= -5e-242)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(x + Float64(y * Float64(Float64(z - a) / t)));
	else
		tmp = Float64(Float64(x + y) + Float64(y * Float64(z / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) + ((y * (z - t)) / (t - a));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x - (-1.0 / ((t / y) / (z - a)));
	elseif (t_1 <= -5e-242)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = x + (y * ((z - a) / t));
	else
		tmp = (x + y) + (y * (z / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x - N[(-1.0 / N[(N[(t / y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-242], t$95$1, If[LessEqual[t$95$1, 0.0], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0

   1. Initial program 36.2%

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

   3. Taylor expanded in t around inf 57.0%

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

      1. associate--l+ 57.0%

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

      2. distribute-lft-out-- 57.0%

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

      3. div-sub 57.0%

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

      4. mul-1-neg 57.0%

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

      5. unsub-neg 57.0%

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

      6. *-commutative 57.0%

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

      7. distribute-lft-out-- 57.2%

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

   5. Simplified 57.2%

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

      1. clear-num 57.2%

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

      2. inv-pow 57.2%

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

   7. Applied egg-rr 57.2%

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

      1. unpow-1 57.2%

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

      2. associate-/r* 75.3%

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

   9. Simplified 75.3%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.9999999999999998e-242

   1. Initial program 95.9%

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

   if -4.9999999999999998e-242 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 11.9%

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

   3. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. distribute-lft-out-- 99.6%

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

      3. div-sub 99.7%

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

      4. mul-1-neg 99.7%

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

      5. unsub-neg 99.7%

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

      6. *-commutative 99.7%

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

      7. distribute-lft-out-- 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in t around inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

      4. distribute-lft-neg-in 99.7%

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

      5. cancel-sign-sub-inv 99.7%

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

      6. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   if 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 83.2%

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

   3. Taylor expanded in z around inf 82.8%

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

      1. associate-/l* 94.4%

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

   5. Simplified 94.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -\infty:\\ \;\;\;\;x - \frac{-1}{\frac{\frac{t}{y}}{z - a}}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -5 \cdot 10^{-242}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 0:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+116}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-20}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-35} \lor \neg \left(a \leq 6000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.4e+116)
   (+ x y)
   (if (<= a -2.4e-20)
     (- x (* a (/ y t)))
     (if (or (<= a -1.85e-35) (not (<= a 6000000.0)))
       (+ x y)
       (+ x (/ (* y z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e+116) {
		tmp = x + y;
	} else if (a <= -2.4e-20) {
		tmp = x - (a * (y / t));
	} else if ((a <= -1.85e-35) || !(a <= 6000000.0)) {
		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 <= (-1.4d+116)) then
        tmp = x + y
    else if (a <= (-2.4d-20)) then
        tmp = x - (a * (y / t))
    else if ((a <= (-1.85d-35)) .or. (.not. (a <= 6000000.0d0))) 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 <= -1.4e+116) {
		tmp = x + y;
	} else if (a <= -2.4e-20) {
		tmp = x - (a * (y / t));
	} else if ((a <= -1.85e-35) || !(a <= 6000000.0)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.4e+116:
		tmp = x + y
	elif a <= -2.4e-20:
		tmp = x - (a * (y / t))
	elif (a <= -1.85e-35) or not (a <= 6000000.0):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.4e+116)
		tmp = Float64(x + y);
	elseif (a <= -2.4e-20)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif ((a <= -1.85e-35) || !(a <= 6000000.0))
		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 <= -1.4e+116)
		tmp = x + y;
	elseif (a <= -2.4e-20)
		tmp = x - (a * (y / t));
	elseif ((a <= -1.85e-35) || ~((a <= 6000000.0)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.4e+116], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.4e-20], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -1.85e-35], N[Not[LessEqual[a, 6000000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.40000000000000002e116 or -2.39999999999999993e-20 < a < -1.8499999999999999e-35 or 6e6 < a

   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 a around inf 81.9%

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

      1. +-commutative 81.9%

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

   5. Simplified 81.9%

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

   if -1.40000000000000002e116 < a < -2.39999999999999993e-20

   1. Initial program 62.1%

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

   3. Taylor expanded in t around inf 54.8%

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

      1. associate--l+ 54.8%

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

      2. distribute-lft-out-- 54.8%

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

      3. div-sub 54.8%

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

      4. mul-1-neg 54.8%

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

      5. unsub-neg 54.8%

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

      6. *-commutative 54.8%

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

      7. distribute-lft-out-- 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in a around inf 57.9%

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

      1. associate-/l* 64.2%

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

   8. Simplified 64.2%

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

   if -1.8499999999999999e-35 < a < 6e6

   1. Initial program 68.8%

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

   3. Taylor expanded in y around 0 68.8%

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

      1. associate-*l/ 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in a around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   8. Simplified 57.9%

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

   9. Taylor expanded in t around inf 76.3%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+116}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-20}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-35} \lor \neg \left(a \leq 6000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+144}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z a)))))
   (if (<= y -2.65e+193)
     t_1
     (if (<= y -1.9e+101)
       (* y (/ z (- t a)))
       (if (<= y 7e+144) (+ x y) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / a));
	double tmp;
	if (y <= -2.65e+193) {
		tmp = t_1;
	} else if (y <= -1.9e+101) {
		tmp = y * (z / (t - a));
	} else if (y <= 7e+144) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (1.0d0 - (z / a))
    if (y <= (-2.65d+193)) then
        tmp = t_1
    else if (y <= (-1.9d+101)) then
        tmp = y * (z / (t - a))
    else if (y <= 7d+144) then
        tmp = x + y
    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 * (1.0 - (z / a));
	double tmp;
	if (y <= -2.65e+193) {
		tmp = t_1;
	} else if (y <= -1.9e+101) {
		tmp = y * (z / (t - a));
	} else if (y <= 7e+144) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / a))
	tmp = 0
	if y <= -2.65e+193:
		tmp = t_1
	elif y <= -1.9e+101:
		tmp = y * (z / (t - a))
	elif y <= 7e+144:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (y <= -2.65e+193)
		tmp = t_1;
	elseif (y <= -1.9e+101)
		tmp = Float64(y * Float64(z / Float64(t - a)));
	elseif (y <= 7e+144)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / a));
	tmp = 0.0;
	if (y <= -2.65e+193)
		tmp = t_1;
	elseif (y <= -1.9e+101)
		tmp = y * (z / (t - a));
	elseif (y <= 7e+144)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.65e+193], t$95$1, If[LessEqual[y, -1.9e+101], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+144], N[(x + y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6499999999999999e193 or 6.9999999999999996e144 < y

   1. Initial program 46.5%

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

   3. Taylor expanded in t around 0 48.2%

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

      1. +-commutative 48.2%

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

      2. associate-/l* 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in y around inf 56.1%

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

   if -2.6499999999999999e193 < y < -1.8999999999999999e101

   1. Initial program 46.4%

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

      1. sub-neg 46.4%

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

      2. +-commutative 46.4%

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

      3. distribute-frac-neg 46.4%

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

      4. distribute-rgt-neg-out 46.4%

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

      5. associate-/l* 75.8%

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

      6. fma-define 76.3%

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

      7. distribute-frac-neg 76.3%

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

      8. distribute-neg-frac2 76.3%

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

      9. sub-neg 76.3%

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

      10. distribute-neg-in 76.3%

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

      11. remove-double-neg 76.3%

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

      12. +-commutative 76.3%

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

      13. sub-neg 76.3%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in z around inf 46.3%

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

      1. associate-/l* 68.3%

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

   7. Simplified 68.3%

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

   if -1.8999999999999999e101 < y < 6.9999999999999996e144

   1. Initial program 86.9%

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

   3. Taylor expanded in a around inf 72.6%

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

      1. +-commutative 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+193}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+144}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+29}:\\ \;\;\;\;x - \frac{-1}{\frac{\frac{t}{y}}{z - a}}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+120}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.5e+29)
   (- x (/ -1.0 (/ (/ t y) (- z a))))
   (if (<= t 5.6e+120)
     (+ (+ x y) (* y (/ z (- t a))))
     (+ x (* y (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+29) {
		tmp = x - (-1.0 / ((t / y) / (z - a)));
	} else if (t <= 5.6e+120) {
		tmp = (x + y) + (y * (z / (t - a)));
	} else {
		tmp = x + (y * ((z - a) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.5d+29)) then
        tmp = x - ((-1.0d0) / ((t / y) / (z - a)))
    else if (t <= 5.6d+120) then
        tmp = (x + y) + (y * (z / (t - a)))
    else
        tmp = x + (y * ((z - a) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+29) {
		tmp = x - (-1.0 / ((t / y) / (z - a)));
	} else if (t <= 5.6e+120) {
		tmp = (x + y) + (y * (z / (t - a)));
	} else {
		tmp = x + (y * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.5e+29:
		tmp = x - (-1.0 / ((t / y) / (z - a)))
	elif t <= 5.6e+120:
		tmp = (x + y) + (y * (z / (t - a)))
	else:
		tmp = x + (y * ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.5e+29)
		tmp = Float64(x - Float64(-1.0 / Float64(Float64(t / y) / Float64(z - a))));
	elseif (t <= 5.6e+120)
		tmp = Float64(Float64(x + y) + Float64(y * Float64(z / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.5e+29)
		tmp = x - (-1.0 / ((t / y) / (z - a)));
	elseif (t <= 5.6e+120)
		tmp = (x + y) + (y * (z / (t - a)));
	else
		tmp = x + (y * ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.5e+29], N[(x - N[(-1.0 / N[(N[(t / y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+120], N[(N[(x + y), $MachinePrecision] + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5e29

   1. Initial program 58.1%

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

   3. Taylor expanded in t around inf 74.5%

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

      1. associate--l+ 74.5%

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

      2. distribute-lft-out-- 74.5%

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

      3. div-sub 74.5%

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

      4. mul-1-neg 74.5%

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

      5. unsub-neg 74.5%

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

      6. *-commutative 74.5%

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

      7. distribute-lft-out-- 74.5%

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

   5. Simplified 74.5%

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

      1. clear-num 74.5%

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

      2. inv-pow 74.5%

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

   7. Applied egg-rr 74.5%

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

      1. unpow-1 74.5%

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

      2. associate-/r* 90.3%

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

   9. Simplified 90.3%

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

   if -2.5e29 < t < 5.6000000000000001e120

   1. Initial program 85.1%

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

   3. Taylor expanded in z around inf 83.9%

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

      1. associate-/l* 90.5%

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

   5. Simplified 90.5%

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

   if 5.6000000000000001e120 < t

   1. Initial program 54.0%

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

   3. Taylor expanded in t around inf 81.5%

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

      1. associate--l+ 81.5%

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

      2. distribute-lft-out-- 81.5%

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

      3. div-sub 81.5%

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

      4. mul-1-neg 81.5%

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

      5. unsub-neg 81.5%

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

      6. *-commutative 81.5%

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

      7. distribute-lft-out-- 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in t around inf 81.5%

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

      1. mul-1-neg 81.5%

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

      2. associate-*r/ 92.8%

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

      3. *-commutative 92.8%

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

      4. distribute-lft-neg-in 92.8%

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

      5. cancel-sign-sub-inv 92.8%

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

      6. *-commutative 92.8%

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

   8. Simplified 92.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+29}:\\ \;\;\;\;x - \frac{-1}{\frac{\frac{t}{y}}{z - a}}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+120}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+116} \lor \neg \left(a \leq 15000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.4e+116) (not (<= a 15000000000.0)))
   (+ x y)
   (+ x (* y (/ (- z a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.4e+116) || !(a <= 15000000000.0)) {
		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 <= (-1.4d+116)) .or. (.not. (a <= 15000000000.0d0))) 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 <= -1.4e+116) || !(a <= 15000000000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.4e+116) or not (a <= 15000000000.0):
		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 <= -1.4e+116) || !(a <= 15000000000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.4e+116) || ~((a <= 15000000000.0)))
		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, -1.4e+116], N[Not[LessEqual[a, 15000000000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.40000000000000002e116 or 1.5e10 < a

   1. Initial program 81.0%

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

   3. Taylor expanded in a around inf 82.8%

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

      1. +-commutative 82.8%

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

   5. Simplified 82.8%

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

   if -1.40000000000000002e116 < a < 1.5e10

   1. Initial program 68.9%

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

   3. Taylor expanded in t around inf 73.6%

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

      1. associate--l+ 73.6%

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

      2. distribute-lft-out-- 73.6%

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

      3. div-sub 73.6%

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

      4. mul-1-neg 73.6%

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

      5. unsub-neg 73.6%

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

      6. *-commutative 73.6%

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

      7. distribute-lft-out-- 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in t around inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. associate-*r/ 78.9%

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

      3. *-commutative 78.9%

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

      4. distribute-lft-neg-in 78.9%

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

      5. cancel-sign-sub-inv 78.9%

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

      6. *-commutative 78.9%

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

   8. Simplified 78.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+116} \lor \neg \left(a \leq 15000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-58} \lor \neg \left(t \leq 2700\right):\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.6e-58) (not (<= t 2700.0)))
   (+ 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 ((t <= -4.6e-58) || !(t <= 2700.0)) {
		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 ((t <= (-4.6d-58)) .or. (.not. (t <= 2700.0d0))) 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 ((t <= -4.6e-58) || !(t <= 2700.0)) {
		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 (t <= -4.6e-58) or not (t <= 2700.0):
		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 ((t <= -4.6e-58) || !(t <= 2700.0))
		tmp = Float64(x + Float64(y * Float64(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 ((t <= -4.6e-58) || ~((t <= 2700.0)))
		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[Or[LessEqual[t, -4.6e-58], N[Not[LessEqual[t, 2700.0]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5999999999999998e-58 or 2700 < t

   1. Initial program 59.2%

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

   3. Taylor expanded in t around inf 73.0%

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

      1. associate--l+ 73.0%

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

      2. distribute-lft-out-- 73.0%

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

      3. div-sub 73.0%

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

      4. mul-1-neg 73.0%

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

      5. unsub-neg 73.0%

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

      6. *-commutative 73.0%

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

      7. distribute-lft-out-- 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in t around inf 73.0%

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

      1. mul-1-neg 73.0%

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

      2. associate-*r/ 83.8%

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

      3. *-commutative 83.8%

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

      4. distribute-lft-neg-in 83.8%

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

      5. cancel-sign-sub-inv 83.8%

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

      6. *-commutative 83.8%

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

   8. Simplified 83.8%

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

   if -4.5999999999999998e-58 < t < 2700

   1. Initial program 90.9%

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

   3. Taylor expanded in t around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 85.7%

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

   5. Simplified 85.7%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-58} \lor \neg \left(t \leq 2700\right):\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{-58}:\\ \;\;\;\;x - \frac{-1}{\frac{\frac{t}{y}}{z - a}}\\ \mathbf{elif}\;t \leq 116:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.45e-58)
   (- x (/ -1.0 (/ (/ t y) (- z a))))
   (if (<= t 116.0) (- (+ 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 (t <= -2.45e-58) {
		tmp = x - (-1.0 / ((t / y) / (z - a)));
	} else if (t <= 116.0) {
		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 (t <= (-2.45d-58)) then
        tmp = x - ((-1.0d0) / ((t / y) / (z - a)))
    else if (t <= 116.0d0) 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 (t <= -2.45e-58) {
		tmp = x - (-1.0 / ((t / y) / (z - a)));
	} else if (t <= 116.0) {
		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 t <= -2.45e-58:
		tmp = x - (-1.0 / ((t / y) / (z - a)))
	elif t <= 116.0:
		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 (t <= -2.45e-58)
		tmp = Float64(x - Float64(-1.0 / Float64(Float64(t / y) / Float64(z - a))));
	elseif (t <= 116.0)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.45e-58)
		tmp = x - (-1.0 / ((t / y) / (z - a)));
	elseif (t <= 116.0)
		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[LessEqual[t, -2.45e-58], N[(x - N[(-1.0 / N[(N[(t / y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 116.0], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.45000000000000015e-58

   1. Initial program 60.8%

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

   3. Taylor expanded in t around inf 71.5%

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

      1. associate--l+ 71.5%

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

      2. distribute-lft-out-- 71.5%

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

      3. div-sub 71.5%

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

      4. mul-1-neg 71.5%

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

      5. unsub-neg 71.5%

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

      6. *-commutative 71.5%

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

      7. distribute-lft-out-- 71.5%

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

   5. Simplified 71.5%

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

      1. clear-num 71.5%

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

      2. inv-pow 71.5%

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

   7. Applied egg-rr 71.5%

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

      1. unpow-1 71.5%

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

      2. associate-/r* 83.4%

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

   9. Simplified 83.4%

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

   if -2.45000000000000015e-58 < t < 116

   1. Initial program 90.9%

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

   3. Taylor expanded in t around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 85.7%

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

   5. Simplified 85.7%

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

   if 116 < t

   1. Initial program 57.3%

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

   3. Taylor expanded in t around inf 74.7%

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

      1. associate--l+ 74.7%

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

      2. distribute-lft-out-- 74.7%

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

      3. div-sub 74.7%

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

      4. mul-1-neg 74.7%

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

      5. unsub-neg 74.7%

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

      6. *-commutative 74.7%

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

      7. distribute-lft-out-- 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in t around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. associate-*r/ 84.9%

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

      3. *-commutative 84.9%

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

      4. distribute-lft-neg-in 84.9%

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

      5. cancel-sign-sub-inv 84.9%

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

      6. *-commutative 84.9%

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

   8. Simplified 84.9%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{-58}:\\ \;\;\;\;x - \frac{-1}{\frac{\frac{t}{y}}{z - a}}\\ \mathbf{elif}\;t \leq 116:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+107} \lor \neg \left(y \leq 1.7 \cdot 10^{+145}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.5e+107) (not (<= y 1.7e+145)))
   (* y (- 1.0 (/ z a)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.5e+107) || !(y <= 1.7e+145)) {
		tmp = y * (1.0 - (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.5d+107)) .or. (.not. (y <= 1.7d+145))) then
        tmp = y * (1.0d0 - (z / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.5e+107) || !(y <= 1.7e+145)) {
		tmp = y * (1.0 - (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.5e+107) or not (y <= 1.7e+145):
		tmp = y * (1.0 - (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.5e+107) || !(y <= 1.7e+145))
		tmp = Float64(y * Float64(1.0 - Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.5e+107) || ~((y <= 1.7e+145)))
		tmp = y * (1.0 - (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.5e+107], N[Not[LessEqual[y, 1.7e+145]], $MachinePrecision]], N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000012e107 or 1.7e145 < y

   1. Initial program 47.5%

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

   3. Taylor expanded in t around 0 46.3%

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

      1. +-commutative 46.3%

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

      2. associate-/l* 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in y around inf 52.9%

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

   if -1.50000000000000012e107 < y < 1.7e145

   1. Initial program 86.0%

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

   3. Taylor expanded in a around inf 72.3%

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

      1. +-commutative 72.3%

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

   5. Simplified 72.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+107} \lor \neg \left(y \leq 1.7 \cdot 10^{+145}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+93} \lor \neg \left(a \leq 185000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.35e+93) (not (<= a 185000.0))) (+ x y) (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.35e+93) || !(a <= 185000.0)) {
		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 <= (-1.35d+93)) .or. (.not. (a <= 185000.0d0))) 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 <= -1.35e+93) || !(a <= 185000.0)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.35e+93) or not (a <= 185000.0):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.35e+93) || !(a <= 185000.0))
		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 <= -1.35e+93) || ~((a <= 185000.0)))
		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, -1.35e+93], N[Not[LessEqual[a, 185000.0]], $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 < -1.35e93 or 185000 < a

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 80.4%

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

      1. +-commutative 80.4%

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

   5. Simplified 80.4%

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

   if -1.35e93 < a < 185000

   1. Initial program 70.0%

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

   3. Taylor expanded in y around 0 70.0%

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

      1. associate-*l/ 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in a around 0 57.2%

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

      1. associate-*r/ 57.2%

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

      2. neg-mul-1 57.2%

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

   8. Simplified 57.2%

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

   9. Taylor expanded in t around inf 72.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+93} \lor \neg \left(a \leq 185000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+199}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+187}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.55e+199) x (if (<= t 1.2e+187) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.55e+199) {
		tmp = x;
	} else if (t <= 1.2e+187) {
		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 <= (-1.55d+199)) then
        tmp = x
    else if (t <= 1.2d+187) 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 <= -1.55e+199) {
		tmp = x;
	} else if (t <= 1.2e+187) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.55e+199:
		tmp = x
	elif t <= 1.2e+187:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.55e+199)
		tmp = x;
	elseif (t <= 1.2e+187)
		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 <= -1.55e+199)
		tmp = x;
	elseif (t <= 1.2e+187)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.55e+199], x, If[LessEqual[t, 1.2e+187], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.54999999999999993e199 or 1.19999999999999993e187 < t

   1. Initial program 53.3%

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

   3. Taylor expanded in x around inf 75.2%

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

   if -1.54999999999999993e199 < t < 1.19999999999999993e187

   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 61.9%

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

      1. +-commutative 61.9%

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

   5. Simplified 61.9%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+199}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+187}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.65 \cdot 10^{+193}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 2.65e+193) (+ x y) (* y (/ z t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 2.65e+193) {
		tmp = x + y;
	} else {
		tmp = 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 (z <= 2.65d+193) then
        tmp = x + y
    else
        tmp = 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 (z <= 2.65e+193) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 2.65e+193:
		tmp = x + y
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 2.65e+193)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 2.65e+193)
		tmp = x + y;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 2.65e+193], N[(x + y), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.6499999999999999e193

   1. Initial program 73.7%

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

   3. Taylor expanded in a around inf 62.5%

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

      1. +-commutative 62.5%

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

   5. Simplified 62.5%

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

   if 2.6499999999999999e193 < z

   1. Initial program 73.2%

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

      1. sub-neg 73.2%

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

      2. +-commutative 73.2%

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

      3. distribute-frac-neg 73.2%

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

      4. distribute-rgt-neg-out 73.2%

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

      5. associate-/l* 73.8%

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

      6. fma-define 74.0%

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

      7. distribute-frac-neg 74.0%

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

      8. distribute-neg-frac2 74.0%

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

      9. sub-neg 74.0%

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

      10. distribute-neg-in 74.0%

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

      11. remove-double-neg 74.0%

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

      12. +-commutative 74.0%

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

      13. sub-neg 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in z around inf 49.6%

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

   6. Taylor expanded in t around inf 36.2%

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

      1. associate-/l* 55.0%

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

   8. Simplified 55.0%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.65 \cdot 10^{+193}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.7%

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

3. Taylor expanded in x around inf 51.2%

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

4. Final simplification 51.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 87.6% 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 2024076 
(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))))