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

Percentage Accurate: 77.3% → 91.1%

Time: 11.9s

Alternatives: 13

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - a}{t}\\ t_2 := \left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-200}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+291}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{\left(\frac{z}{t - a} - \frac{t}{t - a}\right) + 1}{x} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z a) t))))
        (t_2 (+ (+ x y) (/ (* y (- z t)) (- t a)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -4e-200)
       t_2
       (if (<= t_2 1e-245)
         t_1
         (if (<= t_2 4e+291)
           t_2
           (*
            x
            (+ (* y (/ (+ (- (/ z (- t a)) (/ t (- t a))) 1.0) x)) 1.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - a) / t));
	double t_2 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -4e-200) {
		tmp = t_2;
	} else if (t_2 <= 1e-245) {
		tmp = t_1;
	} else if (t_2 <= 4e+291) {
		tmp = t_2;
	} else {
		tmp = x * ((y * ((((z / (t - a)) - (t / (t - a))) + 1.0) / x)) + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - a) / t));
	double t_2 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -4e-200) {
		tmp = t_2;
	} else if (t_2 <= 1e-245) {
		tmp = t_1;
	} else if (t_2 <= 4e+291) {
		tmp = t_2;
	} else {
		tmp = x * ((y * ((((z / (t - a)) - (t / (t - a))) + 1.0) / x)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - a) / t))
	t_2 = (x + y) + ((y * (z - t)) / (t - a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -4e-200:
		tmp = t_2
	elif t_2 <= 1e-245:
		tmp = t_1
	elif t_2 <= 4e+291:
		tmp = t_2
	else:
		tmp = x * ((y * ((((z / (t - a)) - (t / (t - a))) + 1.0) / x)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - a) / t)))
	t_2 = Float64(Float64(x + y) + Float64(Float64(y * Float64(z - t)) / Float64(t - a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -4e-200)
		tmp = t_2;
	elseif (t_2 <= 1e-245)
		tmp = t_1;
	elseif (t_2 <= 4e+291)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(Float64(y * Float64(Float64(Float64(Float64(z / Float64(t - a)) - Float64(t / Float64(t - a))) + 1.0) / x)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - a) / t));
	t_2 = (x + y) + ((y * (z - t)) / (t - a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -4e-200)
		tmp = t_2;
	elseif (t_2 <= 1e-245)
		tmp = t_1;
	elseif (t_2 <= 4e+291)
		tmp = t_2;
	else
		tmp = x * ((y * ((((z / (t - a)) - (t / (t - a))) + 1.0) / x)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -4e-200], t$95$2, If[LessEqual[t$95$2, 1e-245], t$95$1, If[LessEqual[t$95$2, 4e+291], t$95$2, N[(x * N[(N[(y * N[(N[(N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] - N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0 or -3.9999999999999999e-200 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.9999999999999993e-246

   1. Initial program 24.4%

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

   3. Taylor expanded in y around -inf 54.8%

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

      1. mul-1-neg 54.8%

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

      2. distribute-rgt-neg-in 54.8%

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

      3. mul-1-neg 54.8%

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

      4. distribute-neg-frac2 54.8%

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

      5. mul-1-neg 54.8%

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

      6. unsub-neg 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in t around inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. unsub-neg 77.2%

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

      3. associate-/l* 90.3%

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

      4. mul-1-neg 90.3%

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

      5. sub-neg 90.3%

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

   8. Simplified 90.3%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -3.9999999999999999e-200 or 9.9999999999999993e-246 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 3.9999999999999998e291

   1. Initial program 98.2%

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

   if 3.9999999999999998e291 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 61.0%

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

   3. Taylor expanded in y around -inf 91.9%

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

      1. mul-1-neg 91.9%

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

      2. distribute-rgt-neg-in 91.9%

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

      3. mul-1-neg 91.9%

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

      4. distribute-neg-frac2 91.9%

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

      5. mul-1-neg 91.9%

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

      6. unsub-neg 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in x around inf 94.5%

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

      1. associate-/l* 94.6%

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

      2. associate--l+ 94.6%

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

   8. Simplified 94.6%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -\infty:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -4 \cdot 10^{-200}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 10^{-245}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 4 \cdot 10^{+291}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{\left(\frac{z}{t - a} - \frac{t}{t - a}\right) + 1}{x} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - a}{t}\\ t_2 := \left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-200}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(\frac{z - t}{t - a} + 1\right) + \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z a) t))))
        (t_2 (+ (+ x y) (/ (* y (- z t)) (- t a)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -4e-200)
       t_2
       (if (<= t_2 1e-245)
         t_1
         (if (<= t_2 5e+304)
           t_2
           (* y (+ (+ (/ (- z t) (- t a)) 1.0) (/ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - a) / t));
	double t_2 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -4e-200) {
		tmp = t_2;
	} else if (t_2 <= 1e-245) {
		tmp = t_1;
	} else if (t_2 <= 5e+304) {
		tmp = t_2;
	} else {
		tmp = y * ((((z - t) / (t - a)) + 1.0) + (x / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - a) / t));
	double t_2 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -4e-200) {
		tmp = t_2;
	} else if (t_2 <= 1e-245) {
		tmp = t_1;
	} else if (t_2 <= 5e+304) {
		tmp = t_2;
	} else {
		tmp = y * ((((z - t) / (t - a)) + 1.0) + (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - a) / t))
	t_2 = (x + y) + ((y * (z - t)) / (t - a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -4e-200:
		tmp = t_2
	elif t_2 <= 1e-245:
		tmp = t_1
	elif t_2 <= 5e+304:
		tmp = t_2
	else:
		tmp = y * ((((z - t) / (t - a)) + 1.0) + (x / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - a) / t)))
	t_2 = Float64(Float64(x + y) + Float64(Float64(y * Float64(z - t)) / Float64(t - a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -4e-200)
		tmp = t_2;
	elseif (t_2 <= 1e-245)
		tmp = t_1;
	elseif (t_2 <= 5e+304)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0) + Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - a) / t));
	t_2 = (x + y) + ((y * (z - t)) / (t - a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -4e-200)
		tmp = t_2;
	elseif (t_2 <= 1e-245)
		tmp = t_1;
	elseif (t_2 <= 5e+304)
		tmp = t_2;
	else
		tmp = y * ((((z - t) / (t - a)) + 1.0) + (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -4e-200], t$95$2, If[LessEqual[t$95$2, 1e-245], t$95$1, If[LessEqual[t$95$2, 5e+304], t$95$2, N[(y * N[(N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0 or -3.9999999999999999e-200 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.9999999999999993e-246

   1. Initial program 24.4%

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

   3. Taylor expanded in y around -inf 54.8%

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

      1. mul-1-neg 54.8%

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

      2. distribute-rgt-neg-in 54.8%

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

      3. mul-1-neg 54.8%

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

      4. distribute-neg-frac2 54.8%

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

      5. mul-1-neg 54.8%

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

      6. unsub-neg 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in t around inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. unsub-neg 77.2%

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

      3. associate-/l* 90.3%

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

      4. mul-1-neg 90.3%

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

      5. sub-neg 90.3%

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

   8. Simplified 90.3%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -3.9999999999999999e-200 or 9.9999999999999993e-246 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 4.9999999999999997e304

   1. Initial program 98.2%

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

   if 4.9999999999999997e304 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a 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 y around -inf 94.0%

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

      1. mul-1-neg 94.0%

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

      2. distribute-rgt-neg-in 94.0%

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

      3. mul-1-neg 94.0%

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

      4. distribute-neg-frac2 94.0%

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

      5. mul-1-neg 94.0%

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

      6. unsub-neg 94.0%

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

   5. Simplified 94.0%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -\infty:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -4 \cdot 10^{-200}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 10^{-245}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(\frac{z - t}{t - a} + 1\right) + \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - a}{t}\\ t_2 := \left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-200}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z a) t))))
        (t_2 (+ (+ x y) (/ (* y (- z t)) (- t a)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -4e-200)
       t_2
       (if (<= t_2 1e-245) t_1 (+ (+ x y) (* (- z t) (/ y (- t a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - a) / t));
	double t_2 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -4e-200) {
		tmp = t_2;
	} else if (t_2 <= 1e-245) {
		tmp = t_1;
	} else {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - a) / t));
	double t_2 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -4e-200) {
		tmp = t_2;
	} else if (t_2 <= 1e-245) {
		tmp = t_1;
	} else {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - a) / t))
	t_2 = (x + y) + ((y * (z - t)) / (t - a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -4e-200:
		tmp = t_2
	elif t_2 <= 1e-245:
		tmp = t_1
	else:
		tmp = (x + y) + ((z - t) * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - a) / t)))
	t_2 = Float64(Float64(x + y) + Float64(Float64(y * Float64(z - t)) / Float64(t - a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -4e-200)
		tmp = t_2;
	elseif (t_2 <= 1e-245)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - a) / t));
	t_2 = (x + y) + ((y * (z - t)) / (t - a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -4e-200)
		tmp = t_2;
	elseif (t_2 <= 1e-245)
		tmp = t_1;
	else
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -4e-200], t$95$2, If[LessEqual[t$95$2, 1e-245], t$95$1, N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0 or -3.9999999999999999e-200 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.9999999999999993e-246

   1. Initial program 24.4%

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

   3. Taylor expanded in y around -inf 54.8%

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

      1. mul-1-neg 54.8%

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

      2. distribute-rgt-neg-in 54.8%

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

      3. mul-1-neg 54.8%

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

      4. distribute-neg-frac2 54.8%

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

      5. mul-1-neg 54.8%

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

      6. unsub-neg 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in t around inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. unsub-neg 77.2%

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

      3. associate-/l* 90.3%

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

      4. mul-1-neg 90.3%

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

      5. sub-neg 90.3%

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

   8. Simplified 90.3%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -3.9999999999999999e-200

   1. Initial program 96.6%

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

   if 9.9999999999999993e-246 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 88.8%

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

      1. associate-/l* 93.5%

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

      2. *-commutative 93.5%

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

   4. Applied egg-rr 93.5%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -\infty:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -4 \cdot 10^{-200}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 10^{-245}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+51}:\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-123}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(\frac{y \cdot \left(\left(1 - \frac{t}{t - a}\right) + \frac{z}{t - a}\right)}{x} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6e+51)
   (+ x (- (* y (/ z t)) (* a (/ y t))))
   (if (<= t 5.5e-123)
     (+ (+ x y) (/ (* y (- z t)) (- t a)))
     (if (<= t 1.4e+178)
       (* x (+ (/ (* y (+ (- 1.0 (/ t (- t a))) (/ z (- t a)))) x) 1.0))
       (+ x (* y (/ (- z a) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e+51) {
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	} else if (t <= 5.5e-123) {
		tmp = (x + y) + ((y * (z - t)) / (t - a));
	} else if (t <= 1.4e+178) {
		tmp = x * (((y * ((1.0 - (t / (t - a))) + (z / (t - a)))) / x) + 1.0);
	} 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 <= (-6d+51)) then
        tmp = x + ((y * (z / t)) - (a * (y / t)))
    else if (t <= 5.5d-123) then
        tmp = (x + y) + ((y * (z - t)) / (t - a))
    else if (t <= 1.4d+178) then
        tmp = x * (((y * ((1.0d0 - (t / (t - a))) + (z / (t - a)))) / x) + 1.0d0)
    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 <= -6e+51) {
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	} else if (t <= 5.5e-123) {
		tmp = (x + y) + ((y * (z - t)) / (t - a));
	} else if (t <= 1.4e+178) {
		tmp = x * (((y * ((1.0 - (t / (t - a))) + (z / (t - a)))) / x) + 1.0);
	} else {
		tmp = x + (y * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6e+51:
		tmp = x + ((y * (z / t)) - (a * (y / t)))
	elif t <= 5.5e-123:
		tmp = (x + y) + ((y * (z - t)) / (t - a))
	elif t <= 1.4e+178:
		tmp = x * (((y * ((1.0 - (t / (t - a))) + (z / (t - a)))) / x) + 1.0)
	else:
		tmp = x + (y * ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6e+51)
		tmp = Float64(x + Float64(Float64(y * Float64(z / t)) - Float64(a * Float64(y / t))));
	elseif (t <= 5.5e-123)
		tmp = Float64(Float64(x + y) + Float64(Float64(y * Float64(z - t)) / Float64(t - a)));
	elseif (t <= 1.4e+178)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(1.0 - Float64(t / Float64(t - a))) + Float64(z / Float64(t - a)))) / x) + 1.0));
	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 <= -6e+51)
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	elseif (t <= 5.5e-123)
		tmp = (x + y) + ((y * (z - t)) / (t - a));
	elseif (t <= 1.4e+178)
		tmp = x * (((y * ((1.0 - (t / (t - a))) + (z / (t - a)))) / x) + 1.0);
	else
		tmp = x + (y * ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6e+51], N[(x + N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-123], N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+178], N[(x * N[(N[(N[(y * N[(N[(1.0 - N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6e51

   1. Initial program 55.6%

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

      1. sub-neg 55.6%

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

      2. +-commutative 55.6%

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

      3. distribute-frac-neg 55.6%

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

      4. distribute-rgt-neg-out 55.6%

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

      5. associate-/l* 66.2%

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

      6. fma-define 66.2%

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

      7. distribute-frac-neg 66.2%

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

      8. distribute-neg-frac2 66.2%

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

      9. sub-neg 66.2%

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

      10. distribute-neg-in 66.2%

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

      11. remove-double-neg 66.2%

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

      12. +-commutative 66.2%

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

      13. sub-neg 66.2%

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

   3. Simplified 66.2%

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

   5. Taylor expanded in t around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. associate-+r+ 79.0%

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

      3. distribute-rgt1-in 79.0%

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

      4. metadata-eval 79.0%

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

      5. mul0-lft 79.0%

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

      6. associate-/l* 85.2%

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

      7. associate-/l* 89.5%

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

   7. Simplified 89.5%

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

   if -6e51 < t < 5.5e-123

   1. Initial program 96.1%

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

   if 5.5e-123 < t < 1.39999999999999997e178

   1. Initial program 74.4%

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

   3. Taylor expanded in y around -inf 75.9%

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

      1. mul-1-neg 75.9%

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

      2. distribute-rgt-neg-in 75.9%

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

      3. mul-1-neg 75.9%

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

      4. distribute-neg-frac2 75.9%

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

      5. mul-1-neg 75.9%

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

      6. unsub-neg 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in x around inf 94.9%

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

   if 1.39999999999999997e178 < t

   1. Initial program 43.9%

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

   3. Taylor expanded in y around -inf 66.2%

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

      1. mul-1-neg 66.2%

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

      2. distribute-rgt-neg-in 66.2%

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

      3. mul-1-neg 66.2%

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

      4. distribute-neg-frac2 66.2%

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

      5. mul-1-neg 66.2%

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

      6. unsub-neg 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in t around inf 88.0%

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

      1. mul-1-neg 88.0%

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

      2. unsub-neg 88.0%

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

      3. associate-/l* 96.3%

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

      4. mul-1-neg 96.3%

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

      5. sub-neg 96.3%

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

   8. Simplified 96.3%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+51}:\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-123}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(\frac{y \cdot \left(\left(1 - \frac{t}{t - a}\right) + \frac{z}{t - a}\right)}{x} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+152} \lor \neg \left(z \leq -2.4 \cdot 10^{+123}\right) \land \left(z \leq -2.9 \cdot 10^{+82} \lor \neg \left(z \leq 9.6 \cdot 10^{+176}\right)\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+152)
         (and (not (<= z -2.4e+123))
              (or (<= z -2.9e+82) (not (<= z 9.6e+176)))))
   (* y (/ z (- t a)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+152) || (!(z <= -2.4e+123) && ((z <= -2.9e+82) || !(z <= 9.6e+176)))) {
		tmp = y * (z / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.35d+152)) .or. (.not. (z <= (-2.4d+123))) .and. (z <= (-2.9d+82)) .or. (.not. (z <= 9.6d+176))) then
        tmp = y * (z / (t - a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+152) || (!(z <= -2.4e+123) && ((z <= -2.9e+82) || !(z <= 9.6e+176)))) {
		tmp = y * (z / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+152) or (not (z <= -2.4e+123) and ((z <= -2.9e+82) or not (z <= 9.6e+176))):
		tmp = y * (z / (t - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+152) || (!(z <= -2.4e+123) && ((z <= -2.9e+82) || !(z <= 9.6e+176))))
		tmp = Float64(y * Float64(z / Float64(t - a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.35e+152) || (~((z <= -2.4e+123)) && ((z <= -2.9e+82) || ~((z <= 9.6e+176)))))
		tmp = y * (z / (t - a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+152], And[N[Not[LessEqual[z, -2.4e+123]], $MachinePrecision], Or[LessEqual[z, -2.9e+82], N[Not[LessEqual[z, 9.6e+176]], $MachinePrecision]]]], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000007e152 or -2.39999999999999989e123 < z < -2.9000000000000001e82 or 9.6000000000000005e176 < z

   1. Initial program 80.3%

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

      1. sub-neg 80.3%

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

      2. +-commutative 80.3%

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

      3. distribute-frac-neg 80.3%

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

      4. distribute-rgt-neg-out 80.3%

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

      5. associate-/l* 87.6%

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

      6. fma-define 87.7%

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

      7. distribute-frac-neg 87.7%

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

      8. distribute-neg-frac2 87.7%

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

      9. sub-neg 87.7%

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

      10. distribute-neg-in 87.7%

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

      11. remove-double-neg 87.7%

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

      12. +-commutative 87.7%

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

      13. sub-neg 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in z around inf 61.7%

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

      1. associate-/l* 69.6%

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

   7. Simplified 69.6%

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

   if -1.35000000000000007e152 < z < -2.39999999999999989e123 or -2.9000000000000001e82 < z < 9.6000000000000005e176

   1. Initial program 77.8%

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

   3. Taylor expanded in a around inf 67.7%

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

      1. +-commutative 67.7%

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

   5. Simplified 67.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+152} \lor \neg \left(z \leq -2.4 \cdot 10^{+123}\right) \land \left(z \leq -2.9 \cdot 10^{+82} \lor \neg \left(z \leq 9.6 \cdot 10^{+176}\right)\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+51} \lor \neg \left(t \leq 5.6 \cdot 10^{+32}\right):\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.2e+51) (not (<= t 5.6e+32)))
   (+ 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 tmp;
	if ((t <= -3.2e+51) || !(t <= 5.6e+32)) {
		tmp = x + (y * ((z - a) / t));
	} else {
		tmp = (x + y) + (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 ((t <= (-3.2d+51)) .or. (.not. (t <= 5.6d+32))) then
        tmp = x + (y * ((z - a) / t))
    else
        tmp = (x + y) + (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 ((t <= -3.2e+51) || !(t <= 5.6e+32)) {
		tmp = x + (y * ((z - a) / t));
	} else {
		tmp = (x + y) + (y * (z / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.2e+51) or not (t <= 5.6e+32):
		tmp = x + (y * ((z - a) / t))
	else:
		tmp = (x + y) + (y * (z / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.2e+51) || !(t <= 5.6e+32))
		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)
	tmp = 0.0;
	if ((t <= -3.2e+51) || ~((t <= 5.6e+32)))
		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_] := If[Or[LessEqual[t, -3.2e+51], N[Not[LessEqual[t, 5.6e+32]], $MachinePrecision]], 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 2 regimes

2. if t < -3.2000000000000002e51 or 5.6e32 < t

   1. Initial program 54.9%

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

   3. Taylor expanded in y around -inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. distribute-rgt-neg-in 66.1%

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

      3. mul-1-neg 66.1%

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

      4. distribute-neg-frac2 66.1%

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

      5. mul-1-neg 66.1%

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

      6. unsub-neg 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in t around inf 79.9%

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

      1. mul-1-neg 79.9%

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

      2. unsub-neg 79.9%

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

      3. associate-/l* 89.7%

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

      4. mul-1-neg 89.7%

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

      5. sub-neg 89.7%

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

   8. Simplified 89.7%

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

   if -3.2000000000000002e51 < t < 5.6e32

   1. Initial program 93.0%

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

   3. Taylor expanded in z around inf 91.6%

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

      1. associate-/l* 93.5%

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

   5. Simplified 93.5%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+51} \lor \neg \left(t \leq 5.6 \cdot 10^{+32}\right):\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-132}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-261}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.05e-132)
   (+ x y)
   (if (<= a 7.8e-261) x (if (<= a 9.5e-120) (* z (/ y t)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e-132) {
		tmp = x + y;
	} else if (a <= 7.8e-261) {
		tmp = x;
	} else if (a <= 9.5e-120) {
		tmp = z * (y / 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 (a <= (-2.05d-132)) then
        tmp = x + y
    else if (a <= 7.8d-261) then
        tmp = x
    else if (a <= 9.5d-120) then
        tmp = z * (y / 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 <= -2.05e-132) {
		tmp = x + y;
	} else if (a <= 7.8e-261) {
		tmp = x;
	} else if (a <= 9.5e-120) {
		tmp = z * (y / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.05e-132:
		tmp = x + y
	elif a <= 7.8e-261:
		tmp = x
	elif a <= 9.5e-120:
		tmp = z * (y / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.05e-132)
		tmp = Float64(x + y);
	elseif (a <= 7.8e-261)
		tmp = x;
	elseif (a <= 9.5e-120)
		tmp = Float64(z * Float64(y / 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 <= -2.05e-132)
		tmp = x + y;
	elseif (a <= 7.8e-261)
		tmp = x;
	elseif (a <= 9.5e-120)
		tmp = z * (y / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.05e-132], N[(x + y), $MachinePrecision], If[LessEqual[a, 7.8e-261], x, If[LessEqual[a, 9.5e-120], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.05000000000000003e-132 or 9.49999999999999937e-120 < a

   1. Initial program 82.5%

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

   3. Taylor expanded in a around inf 69.8%

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

      1. +-commutative 69.8%

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

   5. Simplified 69.8%

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

   if -2.05000000000000003e-132 < a < 7.80000000000000035e-261

   1. Initial program 66.4%

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

   3. Taylor expanded in x around inf 54.5%

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

   if 7.80000000000000035e-261 < a < 9.49999999999999937e-120

   1. Initial program 76.7%

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

      1. sub-neg 76.7%

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

      2. +-commutative 76.7%

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

      3. distribute-frac-neg 76.7%

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

      4. distribute-rgt-neg-out 76.7%

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

      5. associate-/l* 76.8%

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

      6. fma-define 76.7%

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

      7. distribute-frac-neg 76.7%

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

      8. distribute-neg-frac2 76.7%

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

      9. sub-neg 76.7%

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

      10. distribute-neg-in 76.7%

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

      11. remove-double-neg 76.7%

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

      12. +-commutative 76.7%

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

      13. sub-neg 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in z around inf 61.5%

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

   6. Taylor expanded in t around inf 51.7%

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

      1. associate-/l* 57.7%

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

   8. Simplified 57.7%

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

   9. Taylor expanded in y around 0 51.7%

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

       1. *-commutative 51.7%

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

       2. associate-/l* 57.8%

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

   11. Simplified 57.8%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-132}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-261}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-132}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-262}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.8e-132)
   (+ x y)
   (if (<= a 2.5e-262) x (if (<= a 5.4e-120) (* y (/ z t)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e-132) {
		tmp = x + y;
	} else if (a <= 2.5e-262) {
		tmp = x;
	} else if (a <= 5.4e-120) {
		tmp = 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 (a <= (-3.8d-132)) then
        tmp = x + y
    else if (a <= 2.5d-262) then
        tmp = x
    else if (a <= 5.4d-120) then
        tmp = 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 <= -3.8e-132) {
		tmp = x + y;
	} else if (a <= 2.5e-262) {
		tmp = x;
	} else if (a <= 5.4e-120) {
		tmp = y * (z / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.8e-132:
		tmp = x + y
	elif a <= 2.5e-262:
		tmp = x
	elif a <= 5.4e-120:
		tmp = y * (z / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.8e-132)
		tmp = Float64(x + y);
	elseif (a <= 2.5e-262)
		tmp = x;
	elseif (a <= 5.4e-120)
		tmp = 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 <= -3.8e-132)
		tmp = x + y;
	elseif (a <= 2.5e-262)
		tmp = x;
	elseif (a <= 5.4e-120)
		tmp = y * (z / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.8e-132], N[(x + y), $MachinePrecision], If[LessEqual[a, 2.5e-262], x, If[LessEqual[a, 5.4e-120], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.7999999999999997e-132 or 5.3999999999999997e-120 < a

   1. Initial program 82.5%

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

   3. Taylor expanded in a around inf 69.8%

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

      1. +-commutative 69.8%

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

   5. Simplified 69.8%

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

   if -3.7999999999999997e-132 < a < 2.49999999999999996e-262

   1. Initial program 66.4%

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

   3. Taylor expanded in x around inf 54.5%

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

   if 2.49999999999999996e-262 < a < 5.3999999999999997e-120

   1. Initial program 76.7%

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

      1. sub-neg 76.7%

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

      2. +-commutative 76.7%

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

      3. distribute-frac-neg 76.7%

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

      4. distribute-rgt-neg-out 76.7%

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

      5. associate-/l* 76.8%

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

      6. fma-define 76.7%

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

      7. distribute-frac-neg 76.7%

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

      8. distribute-neg-frac2 76.7%

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

      9. sub-neg 76.7%

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

      10. distribute-neg-in 76.7%

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

      11. remove-double-neg 76.7%

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

      12. +-commutative 76.7%

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

      13. sub-neg 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in z around inf 61.5%

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

   6. Taylor expanded in t around inf 51.7%

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

      1. associate-/l* 57.7%

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

   8. Simplified 57.7%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-132}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-262}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00013 \lor \neg \left(a \leq 1.7 \cdot 10^{+42}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.00013) (not (<= a 1.7e+42)))
   (- (+ x y) (* y (/ z a)))
   (+ x (* y (/ (- z a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.00013) || !(a <= 1.7e+42)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + (y * ((z - a) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-0.00013d0)) .or. (.not. (a <= 1.7d+42))) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x + (y * ((z - a) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.00013) || !(a <= 1.7e+42)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + (y * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.00013) or not (a <= 1.7e+42):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x + (y * ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.00013) || !(a <= 1.7e+42))
		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 ((a <= -0.00013) || ~((a <= 1.7e+42)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x + (y * ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.00013], N[Not[LessEqual[a, 1.7e+42]], $MachinePrecision]], 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 2 regimes

2. if a < -1.29999999999999989e-4 or 1.69999999999999988e42 < a

   1. Initial program 85.7%

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

   3. Taylor expanded in t around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-/l* 89.9%

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

   5. Simplified 89.9%

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

   if -1.29999999999999989e-4 < a < 1.69999999999999988e42

   1. Initial program 73.4%

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

   3. Taylor expanded in y around -inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. distribute-rgt-neg-in 76.2%

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

      3. mul-1-neg 76.2%

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

      4. distribute-neg-frac2 76.2%

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

      5. mul-1-neg 76.2%

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

      6. unsub-neg 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in t around inf 80.8%

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

      1. mul-1-neg 80.8%

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

      2. unsub-neg 80.8%

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

      3. associate-/l* 84.3%

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

      4. mul-1-neg 84.3%

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

      5. sub-neg 84.3%

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

   8. Simplified 84.3%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00013 \lor \neg \left(a \leq 1.7 \cdot 10^{+42}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.012 \lor \neg \left(a \leq 5 \cdot 10^{+61}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.012) (not (<= a 5e+61))) (+ x y) (+ x (* y (/ (- z a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.012) || !(a <= 5e+61)) {
		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 <= (-0.012d0)) .or. (.not. (a <= 5d+61))) 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 <= -0.012) || !(a <= 5e+61)) {
		tmp = x + y;
	} else {
		tmp = x + (y * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.012) or not (a <= 5e+61):
		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 <= -0.012) || !(a <= 5e+61))
		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 <= -0.012) || ~((a <= 5e+61)))
		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, -0.012], N[Not[LessEqual[a, 5e+61]], $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 < -0.012 or 5.00000000000000018e61 < a

   1. Initial program 85.4%

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

   3. Taylor expanded in a around inf 81.5%

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

      1. +-commutative 81.5%

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

   5. Simplified 81.5%

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

   if -0.012 < a < 5.00000000000000018e61

   1. Initial program 73.8%

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

   3. Taylor expanded in y around -inf 76.5%

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

      1. mul-1-neg 76.5%

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

      2. distribute-rgt-neg-in 76.5%

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

      3. mul-1-neg 76.5%

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

      4. distribute-neg-frac2 76.5%

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

      5. mul-1-neg 76.5%

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

      6. unsub-neg 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in t around inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

      3. associate-/l* 83.9%

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

      4. mul-1-neg 83.9%

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

      5. sub-neg 83.9%

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

   8. Simplified 83.9%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.012 \lor \neg \left(a \leq 5 \cdot 10^{+61}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1850 \lor \neg \left(a \leq 1.8 \cdot 10^{+59}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1850.0) (not (<= a 1.8e+59))) (+ x y) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1850.0) || !(a <= 1.8e+59)) {
		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 <= (-1850.0d0)) .or. (.not. (a <= 1.8d+59))) 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 <= -1850.0) || !(a <= 1.8e+59)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1850.0) or not (a <= 1.8e+59):
		tmp = x + y
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1850.0) || !(a <= 1.8e+59))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1850.0) || ~((a <= 1.8e+59)))
		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, -1850.0], N[Not[LessEqual[a, 1.8e+59]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1850 or 1.7999999999999999e59 < a

   1. Initial program 85.4%

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

   3. Taylor expanded in a around inf 81.5%

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

      1. +-commutative 81.5%

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

   5. Simplified 81.5%

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

   if -1850 < a < 1.7999999999999999e59

   1. Initial program 73.8%

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

   3. Taylor expanded in y around -inf 76.5%

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

      1. mul-1-neg 76.5%

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

      2. distribute-rgt-neg-in 76.5%

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

      3. mul-1-neg 76.5%

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

      4. distribute-neg-frac2 76.5%

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

      5. mul-1-neg 76.5%

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

      6. unsub-neg 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in a around 0 71.0%

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

      1. associate-*r* 71.0%

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

      2. mul-1-neg 71.0%

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

      3. mul-1-neg 71.0%

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

      4. unsub-neg 71.0%

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

      5. associate-*r/ 71.0%

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

      6. neg-mul-1 71.0%

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

   8. Simplified 71.0%

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

   9. Taylor expanded in y around 0 76.8%

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

       1. associate-/l* 80.2%

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

   11. Simplified 80.2%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1850 \lor \neg \left(a \leq 1.8 \cdot 10^{+59}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-132} \lor \neg \left(a \leq 1.7 \cdot 10^{+42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.8e-132) (not (<= a 1.7e+42))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.8e-132) || !(a <= 1.7e+42)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.8d-132)) .or. (.not. (a <= 1.7d+42))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.8e-132) || !(a <= 1.7e+42)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.8e-132) or not (a <= 1.7e+42):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.8e-132) || !(a <= 1.7e+42))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.8e-132) || ~((a <= 1.7e+42)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.8e-132], N[Not[LessEqual[a, 1.7e+42]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -3.7999999999999997e-132 or 1.69999999999999988e42 < a

   1. Initial program 84.2%

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

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

   if -3.7999999999999997e-132 < a < 1.69999999999999988e42

   1. Initial program 72.3%

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

   3. Taylor expanded in x around inf 52.4%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-132} \lor \neg \left(a \leq 1.7 \cdot 10^{+42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.7% 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 78.4%

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

3. Taylor expanded in x around inf 50.3%

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

Developer target: 88.0% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024119 
(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))))