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

Percentage Accurate: 85.5% → 99.5%

Time: 13.2s

Alternatives: 21

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+277}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+257}:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 -5e+277)
     (fma y (/ (- z t) (- z a)) x)
     (if (<= t_1 2e+257) (+ t_1 x) (+ x (/ y (/ (- z a) (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -5e+277) {
		tmp = fma(y, ((z - t) / (z - a)), x);
	} else if (t_1 <= 2e+257) {
		tmp = t_1 + x;
	} else {
		tmp = x + (y / ((z - a) / (z - t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+277)
		tmp = fma(y, Float64(Float64(z - t) / Float64(z - a)), x);
	elseif (t_1 <= 2e+257)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / Float64(z - t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+277], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2e+257], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -4.99999999999999982e277

   1. Initial program 49.5%

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

      1. +-commutative 49.5%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   if -4.99999999999999982e277 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.00000000000000006e257

   1. Initial program 99.9%

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

   if 2.00000000000000006e257 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 40.8%

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

      1. +-commutative 40.8%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-/l* 40.8%

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

      3. div-inv 40.8%

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

      4. *-commutative 40.8%

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

      5. associate-*r* 99.7%

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

      6. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. div-inv 99.7%

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

      3. associate-*r* 99.7%

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

      4. associate-/r/ 99.9%

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

      5. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -5 \cdot 10^{+277}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+257}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+257}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+257)))
     (+ x (/ y (/ (- z a) (- z t))))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+257)) {
		tmp = x + (y / ((z - a) / (z - t)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+257)) {
		tmp = x + (y / ((z - a) / (z - t)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+257):
		tmp = x + (y / ((z - a) / (z - t)))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+257))
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / Float64(z - t))));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+257)))
		tmp = x + (y / ((z - a) / (z - t)));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+257]], $MachinePrecision]], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 2.00000000000000006e257 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 43.0%

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

      1. +-commutative 43.0%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-/l* 43.0%

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

      3. div-inv 43.0%

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

      4. *-commutative 43.0%

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

      5. associate-*r* 99.7%

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

      6. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. div-inv 99.7%

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

      3. associate-*r* 99.7%

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

      4. associate-/r/ 99.9%

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

      5. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.00000000000000006e257

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+257}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+212}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+212)))
     (+ x (* (- z t) (/ y (- z a))))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+212)) {
		tmp = x + ((z - t) * (y / (z - a)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+212)) {
		tmp = x + ((z - t) * (y / (z - a)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+212):
		tmp = x + ((z - t) * (y / (z - a)))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+212))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(z - a))));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+212)))
		tmp = x + ((z - t) * (y / (z - a)));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+212]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 1.9999999999999998e212 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 46.1%

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

      1. +-commutative 46.1%

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

      2. associate-/l* 96.4%

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

      3. fma-define 96.4%

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

   3. Simplified 96.4%

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

      1. fma-undefine 96.4%

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

      2. associate-/l* 46.1%

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

      3. div-inv 46.1%

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

      4. *-commutative 46.1%

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

      5. associate-*r* 99.7%

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

      6. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 1.9999999999999998e212

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+212}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+277} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+257}\right):\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 -5e+277) (not (<= t_1 2e+257)))
     (* y (/ (- z t) (- z a)))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -5e+277) || !(t_1 <= 2e+257)) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = t_1 + 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) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / (z - a)
    if ((t_1 <= (-5d+277)) .or. (.not. (t_1 <= 2d+257))) then
        tmp = y * ((z - t) / (z - a))
    else
        tmp = t_1 + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -5e+277) || !(t_1 <= 2e+257)) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -5e+277) or not (t_1 <= 2e+257):
		tmp = y * ((z - t) / (z - a))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= -5e+277) || !(t_1 <= 2e+257))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -5e+277) || ~((t_1 <= 2e+257)))
		tmp = y * ((z - t) / (z - a));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+277], N[Not[LessEqual[t$95$1, 2e+257]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -4.99999999999999982e277 or 2.00000000000000006e257 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 45.1%

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

      1. +-commutative 45.1%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around inf 95.0%

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

       1. div-sub 95.0%

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

   11. Simplified 95.0%

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

   if -4.99999999999999982e277 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.00000000000000006e257

   1. Initial program 99.9%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -5 \cdot 10^{+277} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+257}\right):\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+257}:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (- z t) (/ (- z a) y)))
     (if (<= t_1 2e+257) (+ t_1 x) (+ x (/ y (/ (- z a) (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else if (t_1 <= 2e+257) {
		tmp = t_1 + x;
	} else {
		tmp = x + (y / ((z - a) / (z - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else if (t_1 <= 2e+257) {
		tmp = t_1 + x;
	} else {
		tmp = x + (y / ((z - a) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((z - t) / ((z - a) / y))
	elif t_1 <= 2e+257:
		tmp = t_1 + x
	else:
		tmp = x + (y / ((z - a) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	elseif (t_1 <= 2e+257)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((z - t) / ((z - a) / y));
	elseif (t_1 <= 2e+257)
		tmp = t_1 + x;
	else
		tmp = x + (y / ((z - a) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+257], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 45.4%

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

      1. +-commutative 45.4%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-/l* 45.4%

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

      3. div-inv 45.4%

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

      4. *-commutative 45.4%

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

      5. associate-*r* 99.7%

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

      6. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.00000000000000006e257

   1. Initial program 99.9%

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

   if 2.00000000000000006e257 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 40.8%

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

      1. +-commutative 40.8%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-/l* 40.8%

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

      3. div-inv 40.8%

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

      4. *-commutative 40.8%

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

      5. associate-*r* 99.7%

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

      6. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. div-inv 99.7%

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

      3. associate-*r* 99.7%

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

      4. associate-/r/ 99.9%

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

      5. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+257}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+95}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))))
   (if (<= z -1.22e+95)
     (+ x (/ y (/ z (- z t))))
     (if (<= z -4e-88)
       t_1
       (if (<= z 5.5e-60)
         (+ x (/ t (/ a y)))
         (if (<= z 1.9e-13)
           (* y (/ (- z t) (- z a)))
           (if (<= z 1.1e+124) t_1 (+ x (* y (- 1.0 (/ t z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -1.22e+95) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= -4e-88) {
		tmp = t_1;
	} else if (z <= 5.5e-60) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.9e-13) {
		tmp = y * ((z - t) / (z - a));
	} else if (z <= 1.1e+124) {
		tmp = t_1;
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / (z - a)))
    if (z <= (-1.22d+95)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= (-4d-88)) then
        tmp = t_1
    else if (z <= 5.5d-60) then
        tmp = x + (t / (a / y))
    else if (z <= 1.9d-13) then
        tmp = y * ((z - t) / (z - a))
    else if (z <= 1.1d+124) then
        tmp = t_1
    else
        tmp = x + (y * (1.0d0 - (t / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double tmp;
	if (z <= -1.22e+95) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= -4e-88) {
		tmp = t_1;
	} else if (z <= 5.5e-60) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.9e-13) {
		tmp = y * ((z - t) / (z - a));
	} else if (z <= 1.1e+124) {
		tmp = t_1;
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	tmp = 0
	if z <= -1.22e+95:
		tmp = x + (y / (z / (z - t)))
	elif z <= -4e-88:
		tmp = t_1
	elif z <= 5.5e-60:
		tmp = x + (t / (a / y))
	elif z <= 1.9e-13:
		tmp = y * ((z - t) / (z - a))
	elif z <= 1.1e+124:
		tmp = t_1
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(z - a))))
	tmp = 0.0
	if (z <= -1.22e+95)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= -4e-88)
		tmp = t_1;
	elseif (z <= 5.5e-60)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 1.9e-13)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	elseif (z <= 1.1e+124)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (z - a)));
	tmp = 0.0;
	if (z <= -1.22e+95)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= -4e-88)
		tmp = t_1;
	elseif (z <= 5.5e-60)
		tmp = x + (t / (a / y));
	elseif (z <= 1.9e-13)
		tmp = y * ((z - t) / (z - a));
	elseif (z <= 1.1e+124)
		tmp = t_1;
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.22e+95], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-88], t$95$1, If[LessEqual[z, 5.5e-60], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-13], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+124], t$95$1, N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.22000000000000007e95

   1. Initial program 78.4%

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

      1. +-commutative 78.4%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-/l* 78.4%

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

      3. div-inv 78.4%

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

      4. *-commutative 78.4%

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

      5. associate-*r* 92.0%

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

      6. div-inv 92.1%

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

   6. Applied egg-rr 92.1%

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

      1. *-commutative 92.1%

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

      2. div-inv 92.0%

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

      3. associate-*r* 99.8%

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

      4. associate-/r/ 99.9%

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

      5. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in a around 0 97.9%

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

   if -1.22000000000000007e95 < z < -3.99999999999999974e-88 or 1.9e-13 < z < 1.1e124

   1. Initial program 89.4%

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

   3. Taylor expanded in t around 0 71.4%

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

      1. +-commutative 71.4%

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

      2. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

   if -3.99999999999999974e-88 < z < 5.4999999999999997e-60

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0 82.2%

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

      1. +-commutative 82.2%

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

      2. associate-/l* 83.1%

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

   5. Simplified 83.1%

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

      1. clear-num 83.1%

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

      2. un-div-inv 84.3%

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

   7. Applied egg-rr 84.3%

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

   if 5.4999999999999997e-60 < z < 1.9e-13

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. inv-pow 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. unpow-1 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in y around inf 99.7%

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

       1. div-sub 99.7%

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

   11. Simplified 99.7%

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

   if 1.1e124 < z

   1. Initial program 78.0%

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

   3. Taylor expanded in a around 0 77.4%

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

      1. associate-/l* 94.4%

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

      2. div-sub 94.5%

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

      3. *-inverses 94.5%

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

   5. Simplified 94.5%

      \[\leadsto x + \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+95}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-88}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+124}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ t_2 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))) (t_2 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -2.3e+94)
     t_2
     (if (<= z -1.46e-86)
       t_1
       (if (<= z 6.2e-60)
         (+ x (/ t (/ a y)))
         (if (<= z 2.8e-13)
           (* y (/ (- z t) (- z a)))
           (if (<= z 1.3e+125) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double t_2 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -2.3e+94) {
		tmp = t_2;
	} else if (z <= -1.46e-86) {
		tmp = t_1;
	} else if (z <= 6.2e-60) {
		tmp = x + (t / (a / y));
	} else if (z <= 2.8e-13) {
		tmp = y * ((z - t) / (z - a));
	} else if (z <= 1.3e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = x + (y * (z / (z - a)))
    t_2 = x + (y * (1.0d0 - (t / z)))
    if (z <= (-2.3d+94)) then
        tmp = t_2
    else if (z <= (-1.46d-86)) then
        tmp = t_1
    else if (z <= 6.2d-60) then
        tmp = x + (t / (a / y))
    else if (z <= 2.8d-13) then
        tmp = y * ((z - t) / (z - a))
    else if (z <= 1.3d+125) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double t_2 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -2.3e+94) {
		tmp = t_2;
	} else if (z <= -1.46e-86) {
		tmp = t_1;
	} else if (z <= 6.2e-60) {
		tmp = x + (t / (a / y));
	} else if (z <= 2.8e-13) {
		tmp = y * ((z - t) / (z - a));
	} else if (z <= 1.3e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	t_2 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if z <= -2.3e+94:
		tmp = t_2
	elif z <= -1.46e-86:
		tmp = t_1
	elif z <= 6.2e-60:
		tmp = x + (t / (a / y))
	elif z <= 2.8e-13:
		tmp = y * ((z - t) / (z - a))
	elif z <= 1.3e+125:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(z - a))))
	t_2 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (z <= -2.3e+94)
		tmp = t_2;
	elseif (z <= -1.46e-86)
		tmp = t_1;
	elseif (z <= 6.2e-60)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 2.8e-13)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(z - a)));
	elseif (z <= 1.3e+125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (z - a)));
	t_2 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (z <= -2.3e+94)
		tmp = t_2;
	elseif (z <= -1.46e-86)
		tmp = t_1;
	elseif (z <= 6.2e-60)
		tmp = x + (t / (a / y));
	elseif (z <= 2.8e-13)
		tmp = y * ((z - t) / (z - a));
	elseif (z <= 1.3e+125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+94], t$95$2, If[LessEqual[z, -1.46e-86], t$95$1, If[LessEqual[z, 6.2e-60], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-13], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+125], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3e94 or 1.30000000000000002e125 < z

   1. Initial program 78.2%

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

   3. Taylor expanded in a around 0 77.9%

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

      1. associate-/l* 96.3%

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

      2. div-sub 96.3%

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

      3. *-inverses 96.3%

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

   5. Simplified 96.3%

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

   if -2.3e94 < z < -1.45999999999999993e-86 or 2.8000000000000002e-13 < z < 1.30000000000000002e125

   1. Initial program 89.4%

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

   3. Taylor expanded in t around 0 71.4%

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

      1. +-commutative 71.4%

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

      2. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

   if -1.45999999999999993e-86 < z < 6.19999999999999976e-60

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0 82.2%

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

      1. +-commutative 82.2%

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

      2. associate-/l* 83.1%

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

   5. Simplified 83.1%

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

      1. clear-num 83.1%

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

      2. un-div-inv 84.3%

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

   7. Applied egg-rr 84.3%

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

   if 6.19999999999999976e-60 < z < 2.8000000000000002e-13

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. inv-pow 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. unpow-1 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in y around inf 99.7%

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

       1. div-sub 99.7%

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

   11. Simplified 99.7%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-86}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-170}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.1e+52)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 8.6e-170)
     (+ x (* y (/ (- t z) a)))
     (if (<= z 3.5e-13)
       (/ (* y (- z t)) (- z a))
       (if (<= z 1.95e+125)
         (+ x (* y (/ z (- z a))))
         (+ x (* y (- 1.0 (/ t z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+52) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 8.6e-170) {
		tmp = x + (y * ((t - z) / a));
	} else if (z <= 3.5e-13) {
		tmp = (y * (z - t)) / (z - a);
	} else if (z <= 1.95e+125) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.1d+52)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 8.6d-170) then
        tmp = x + (y * ((t - z) / a))
    else if (z <= 3.5d-13) then
        tmp = (y * (z - t)) / (z - a)
    else if (z <= 1.95d+125) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (y * (1.0d0 - (t / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+52) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 8.6e-170) {
		tmp = x + (y * ((t - z) / a));
	} else if (z <= 3.5e-13) {
		tmp = (y * (z - t)) / (z - a);
	} else if (z <= 1.95e+125) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.1e+52:
		tmp = x + (y / (z / (z - t)))
	elif z <= 8.6e-170:
		tmp = x + (y * ((t - z) / a))
	elif z <= 3.5e-13:
		tmp = (y * (z - t)) / (z - a)
	elif z <= 1.95e+125:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.1e+52)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 8.6e-170)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	elseif (z <= 3.5e-13)
		tmp = Float64(Float64(y * Float64(z - t)) / Float64(z - a));
	elseif (z <= 1.95e+125)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.1e+52)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 8.6e-170)
		tmp = x + (y * ((t - z) / a));
	elseif (z <= 3.5e-13)
		tmp = (y * (z - t)) / (z - a);
	elseif (z <= 1.95e+125)
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.1e+52], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e-170], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-13], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+125], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.1e52

   1. Initial program 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-/l* 78.3%

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

      3. div-inv 78.3%

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

      4. *-commutative 78.3%

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

      5. associate-*r* 92.7%

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

      6. div-inv 92.7%

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

   6. Applied egg-rr 92.7%

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

      1. *-commutative 92.7%

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

      2. div-inv 92.7%

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

      3. associate-*r* 99.8%

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

      4. associate-/r/ 99.9%

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

      5. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in a around 0 96.3%

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

   if -3.1e52 < z < 8.5999999999999997e-170

   1. Initial program 97.9%

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

   3. Taylor expanded in a around inf 90.4%

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

      1. mul-1-neg 90.4%

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

      2. unsub-neg 90.4%

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

      3. associate-/l* 90.3%

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

   5. Simplified 90.3%

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

   if 8.5999999999999997e-170 < z < 3.5000000000000002e-13

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 75.1%

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

   if 3.5000000000000002e-13 < z < 1.9500000000000001e125

   1. Initial program 83.4%

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

   3. Taylor expanded in t around 0 70.6%

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

      1. +-commutative 70.6%

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

      2. associate-/l* 82.3%

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

   5. Simplified 82.3%

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

   if 1.9500000000000001e125 < z

   1. Initial program 78.0%

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

   3. Taylor expanded in a around 0 77.4%

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

      1. associate-/l* 94.4%

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

      2. div-sub 94.5%

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

      3. *-inverses 94.5%

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

   5. Simplified 94.5%

      \[\leadsto x + \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-170}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-143}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+52)
   (+ x (/ y (/ z (- z t))))
   (if (<= z -2e-143)
     (+ x (* y (/ (- t z) a)))
     (if (<= z 2.75e+66)
       (+ x (/ (* y t) (- a z)))
       (+ x (* y (- 1.0 (/ t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+52) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= -2e-143) {
		tmp = x + (y * ((t - z) / a));
	} else if (z <= 2.75e+66) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.95d+52)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= (-2d-143)) then
        tmp = x + (y * ((t - z) / a))
    else if (z <= 2.75d+66) then
        tmp = x + ((y * t) / (a - z))
    else
        tmp = x + (y * (1.0d0 - (t / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+52) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= -2e-143) {
		tmp = x + (y * ((t - z) / a));
	} else if (z <= 2.75e+66) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e+52:
		tmp = x + (y / (z / (z - t)))
	elif z <= -2e-143:
		tmp = x + (y * ((t - z) / a))
	elif z <= 2.75e+66:
		tmp = x + ((y * t) / (a - z))
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+52)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= -2e-143)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	elseif (z <= 2.75e+66)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.95e+52)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= -2e-143)
		tmp = x + (y * ((t - z) / a));
	elseif (z <= 2.75e+66)
		tmp = x + ((y * t) / (a - z));
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+52], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-143], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.75e+66], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.95e52

   1. Initial program 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-/l* 78.3%

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

      3. div-inv 78.3%

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

      4. *-commutative 78.3%

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

      5. associate-*r* 92.7%

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

      6. div-inv 92.7%

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

   6. Applied egg-rr 92.7%

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

      1. *-commutative 92.7%

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

      2. div-inv 92.7%

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

      3. associate-*r* 99.8%

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

      4. associate-/r/ 99.9%

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

      5. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in a around 0 96.3%

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

   if -1.95e52 < z < -1.9999999999999999e-143

   1. Initial program 95.4%

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

   3. Taylor expanded in a around inf 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

      3. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

   if -1.9999999999999999e-143 < z < 2.75e66

   1. Initial program 98.1%

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

   3. Taylor expanded in t around inf 88.1%

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

      1. associate-*r/ 88.1%

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

      2. mul-1-neg 88.1%

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

      3. distribute-lft-neg-out 88.1%

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

      4. *-commutative 88.1%

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

   5. Simplified 88.1%

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

   if 2.75e66 < z

   1. Initial program 75.3%

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

   3. Taylor expanded in a around 0 70.4%

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

      1. associate-/l* 86.7%

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

      2. div-sub 86.7%

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

      3. *-inverses 86.7%

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

   5. Simplified 86.7%

      \[\leadsto x + \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-143}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+124}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- z a)))))
   (if (<= y -5.5e+18)
     t_1
     (if (<= y 7.5e-62)
       (+ x (/ (* y t) a))
       (if (<= y 6.6e+124) (- x (/ y (/ z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (z - a));
	double tmp;
	if (y <= -5.5e+18) {
		tmp = t_1;
	} else if (y <= 7.5e-62) {
		tmp = x + ((y * t) / a);
	} else if (y <= 6.6e+124) {
		tmp = x - (y / (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (z - a))
    if (y <= (-5.5d+18)) then
        tmp = t_1
    else if (y <= 7.5d-62) then
        tmp = x + ((y * t) / a)
    else if (y <= 6.6d+124) then
        tmp = x - (y / (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (z - a));
	double tmp;
	if (y <= -5.5e+18) {
		tmp = t_1;
	} else if (y <= 7.5e-62) {
		tmp = x + ((y * t) / a);
	} else if (y <= 6.6e+124) {
		tmp = x - (y / (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (z - a))
	tmp = 0
	if y <= -5.5e+18:
		tmp = t_1
	elif y <= 7.5e-62:
		tmp = x + ((y * t) / a)
	elif y <= 6.6e+124:
		tmp = x - (y / (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(z - a)))
	tmp = 0.0
	if (y <= -5.5e+18)
		tmp = t_1;
	elseif (y <= 7.5e-62)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (y <= 6.6e+124)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (z - a));
	tmp = 0.0;
	if (y <= -5.5e+18)
		tmp = t_1;
	elseif (y <= 7.5e-62)
		tmp = x + ((y * t) / a);
	elseif (y <= 6.6e+124)
		tmp = x - (y / (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+18], t$95$1, If[LessEqual[y, 7.5e-62], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+124], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5e18 or 6.60000000000000029e124 < y

   1. Initial program 73.5%

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

      1. +-commutative 73.5%

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

      2. associate-/l* 98.0%

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

      3. fma-define 98.0%

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

   3. Simplified 98.0%

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

      1. clear-num 97.9%

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

      2. inv-pow 97.9%

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

   6. Applied egg-rr 97.9%

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

      1. unpow-1 97.9%

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

   8. Simplified 97.9%

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

   9. Taylor expanded in y around inf 81.6%

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

       1. div-sub 81.6%

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

   11. Simplified 81.6%

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

   if -5.5e18 < y < 7.5000000000000003e-62

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.6%

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

   if 7.5000000000000003e-62 < y < 6.60000000000000029e124

   1. Initial program 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-/l* 97.0%

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

      3. fma-define 97.0%

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

   3. Simplified 97.0%

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

      1. fma-undefine 97.0%

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

      2. associate-/l* 90.7%

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

      3. div-inv 90.5%

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

      4. *-commutative 90.5%

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

      5. associate-*r* 99.6%

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

      6. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. div-inv 99.6%

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

      3. associate-*r* 96.8%

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

      4. associate-/r/ 96.9%

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

      5. un-div-inv 96.9%

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

   8. Applied egg-rr 96.9%

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

   9. Taylor expanded in a around 0 76.0%

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

   10. Taylor expanded in z around 0 70.1%

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

       1. associate-*r/ 70.1%

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

       2. neg-mul-1 70.1%

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

   12. Simplified 70.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+124}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+65}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+65)
   (+ y x)
   (if (<= z 6.8e-81)
     (+ x (/ (* y t) a))
     (if (<= z 2.1e+50) (- x (/ y (/ z t))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+65) {
		tmp = y + x;
	} else if (z <= 6.8e-81) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.1e+50) {
		tmp = x - (y / (z / t));
	} else {
		tmp = y + 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 (z <= (-1d+65)) then
        tmp = y + x
    else if (z <= 6.8d-81) then
        tmp = x + ((y * t) / a)
    else if (z <= 2.1d+50) then
        tmp = x - (y / (z / t))
    else
        tmp = y + 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 (z <= -1e+65) {
		tmp = y + x;
	} else if (z <= 6.8e-81) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.1e+50) {
		tmp = x - (y / (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+65:
		tmp = y + x
	elif z <= 6.8e-81:
		tmp = x + ((y * t) / a)
	elif z <= 2.1e+50:
		tmp = x - (y / (z / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+65)
		tmp = Float64(y + x);
	elseif (z <= 6.8e-81)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 2.1e+50)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e+65)
		tmp = y + x;
	elseif (z <= 6.8e-81)
		tmp = x + ((y * t) / a);
	elseif (z <= 2.1e+50)
		tmp = x - (y / (z / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+65], N[(y + x), $MachinePrecision], If[LessEqual[z, 6.8e-81], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+50], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.9999999999999999e64 or 2.1e50 < z

   1. Initial program 77.3%

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

   3. Taylor expanded in z around inf 76.6%

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

      1. +-commutative 76.6%

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

   5. Simplified 76.6%

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

   if -9.9999999999999999e64 < z < 6.7999999999999997e-81

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 78.6%

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

   if 6.7999999999999997e-81 < z < 2.1e50

   1. Initial program 97.0%

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

      1. +-commutative 97.0%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-/l* 97.0%

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

      3. div-inv 96.7%

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

      4. *-commutative 96.7%

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

      5. associate-*r* 99.8%

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

      6. div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. *-commutative 99.9%

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

      2. div-inv 99.8%

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

      3. associate-*r* 99.7%

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

      4. associate-/r/ 99.7%

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

      5. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in a around 0 68.1%

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

   10. Taylor expanded in z around 0 68.3%

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

       1. associate-*r/ 68.3%

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

       2. neg-mul-1 68.3%

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

   12. Simplified 68.3%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+65}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+53}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+41}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+53)
   (+ y x)
   (if (<= z 3.3e-31)
     (+ x (/ (* y t) a))
     (if (<= z 4e+41) (- x (* z (/ y a))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+53) {
		tmp = y + x;
	} else if (z <= 3.3e-31) {
		tmp = x + ((y * t) / a);
	} else if (z <= 4e+41) {
		tmp = x - (z * (y / a));
	} else {
		tmp = y + 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 (z <= (-1.05d+53)) then
        tmp = y + x
    else if (z <= 3.3d-31) then
        tmp = x + ((y * t) / a)
    else if (z <= 4d+41) then
        tmp = x - (z * (y / a))
    else
        tmp = y + 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 (z <= -1.05e+53) {
		tmp = y + x;
	} else if (z <= 3.3e-31) {
		tmp = x + ((y * t) / a);
	} else if (z <= 4e+41) {
		tmp = x - (z * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+53:
		tmp = y + x
	elif z <= 3.3e-31:
		tmp = x + ((y * t) / a)
	elif z <= 4e+41:
		tmp = x - (z * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+53)
		tmp = Float64(y + x);
	elseif (z <= 3.3e-31)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 4e+41)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+53)
		tmp = y + x;
	elseif (z <= 3.3e-31)
		tmp = x + ((y * t) / a);
	elseif (z <= 4e+41)
		tmp = x - (z * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+53], N[(y + x), $MachinePrecision], If[LessEqual[z, 3.3e-31], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+41], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0500000000000001e53 or 4.00000000000000002e41 < z

   1. Initial program 78.3%

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

   3. Taylor expanded in z around inf 76.7%

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

      1. +-commutative 76.7%

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

   5. Simplified 76.7%

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

   if -1.0500000000000001e53 < z < 3.2999999999999999e-31

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0 76.6%

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

   if 3.2999999999999999e-31 < z < 4.00000000000000002e41

   1. Initial program 94.2%

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

   3. Taylor expanded in a around inf 53.8%

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

      1. mul-1-neg 53.8%

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

      2. unsub-neg 53.8%

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

      3. associate-/l* 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in z around inf 59.4%

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

      1. div-inv 59.3%

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

      2. *-commutative 59.3%

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

      3. associate-*l* 65.0%

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

      4. div-inv 65.1%

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

   8. Applied egg-rr 65.1%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+53}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+41}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+55}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;\frac{-t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e+55)
   (+ y x)
   (if (<= z 4.4e-141) x (if (<= z 1.9e-13) (/ (- t) (/ z y)) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+55) {
		tmp = y + x;
	} else if (z <= 4.4e-141) {
		tmp = x;
	} else if (z <= 1.9e-13) {
		tmp = -t / (z / y);
	} else {
		tmp = y + 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 (z <= (-4d+55)) then
        tmp = y + x
    else if (z <= 4.4d-141) then
        tmp = x
    else if (z <= 1.9d-13) then
        tmp = -t / (z / y)
    else
        tmp = y + 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 (z <= -4e+55) {
		tmp = y + x;
	} else if (z <= 4.4e-141) {
		tmp = x;
	} else if (z <= 1.9e-13) {
		tmp = -t / (z / y);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e+55:
		tmp = y + x
	elif z <= 4.4e-141:
		tmp = x
	elif z <= 1.9e-13:
		tmp = -t / (z / y)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e+55)
		tmp = Float64(y + x);
	elseif (z <= 4.4e-141)
		tmp = x;
	elseif (z <= 1.9e-13)
		tmp = Float64(Float64(-t) / Float64(z / y));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4e+55)
		tmp = y + x;
	elseif (z <= 4.4e-141)
		tmp = x;
	elseif (z <= 1.9e-13)
		tmp = -t / (z / y);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e+55], N[(y + x), $MachinePrecision], If[LessEqual[z, 4.4e-141], x, If[LessEqual[z, 1.9e-13], N[((-t) / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.00000000000000004e55 or 1.9e-13 < z

   1. Initial program 79.7%

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

   3. Taylor expanded in z around inf 74.3%

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

      1. +-commutative 74.3%

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

   5. Simplified 74.3%

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

   if -4.00000000000000004e55 < z < 4.40000000000000018e-141

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 52.9%

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

   if 4.40000000000000018e-141 < z < 1.9e-13

   1. Initial program 96.5%

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

      1. +-commutative 96.5%

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

      2. associate-/l* 86.8%

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

      3. fma-define 86.8%

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

   3. Simplified 86.8%

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

      1. clear-num 86.7%

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

      2. inv-pow 86.7%

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

   6. Applied egg-rr 86.7%

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

      1. unpow-1 86.7%

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

   8. Simplified 86.7%

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

   9. Taylor expanded in t around inf 53.7%

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

       1. mul-1-neg 53.7%

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

       2. associate-/l* 56.9%

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

       3. distribute-lft-neg-out 56.9%

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

       4. *-commutative 56.9%

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

   11. Simplified 56.9%

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

   12. Taylor expanded in z around inf 41.2%

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

       1. distribute-rgt-neg-out 41.2%

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

       2. neg-sub0 41.2%

          \[\leadsto \color{blue}{0 - \frac{y}{z} \cdot t} \]

       3. add-sqr-sqrt 22.2%

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

       4. sqrt-unprod 22.7%

          \[\leadsto 0 - \frac{y}{z} \cdot \color{blue}{\sqrt{t \cdot t}} \]

       5. sqr-neg 22.7%

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

       6. sqrt-unprod 0.6%

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

       7. add-sqr-sqrt 1.7%

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

       8. *-commutative 1.7%

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

       9. clear-num 1.7%

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

       10. un-div-inv 1.7%

           \[\leadsto 0 - \color{blue}{\frac{-t}{\frac{z}{y}}} \]

       11. add-sqr-sqrt 0.6%

           \[\leadsto 0 - \frac{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}}{\frac{z}{y}} \]

       12. sqrt-unprod 22.7%

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

       13. sqr-neg 22.7%

           \[\leadsto 0 - \frac{\sqrt{\color{blue}{t \cdot t}}}{\frac{z}{y}} \]

       14. sqrt-unprod 22.3%

           \[\leadsto 0 - \frac{\color{blue}{\sqrt{t} \cdot \sqrt{t}}}{\frac{z}{y}} \]

       15. add-sqr-sqrt 41.3%

           \[\leadsto 0 - \frac{\color{blue}{t}}{\frac{z}{y}} \]

   14. Applied egg-rr 41.3%

       \[\leadsto \color{blue}{0 - \frac{t}{\frac{z}{y}}} \]
   15. Step-by-step derivation

       1. neg-sub0 41.3%

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

       2. distribute-frac-neg 41.3%

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

   16. Simplified 41.3%

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

Alternative 14: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+51}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+51)
   (+ y x)
   (if (<= z 4.4e-141) x (if (<= z 1.9e-13) (* (- t) (/ y z)) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+51) {
		tmp = y + x;
	} else if (z <= 4.4e-141) {
		tmp = x;
	} else if (z <= 1.9e-13) {
		tmp = -t * (y / z);
	} else {
		tmp = y + 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 (z <= (-2.4d+51)) then
        tmp = y + x
    else if (z <= 4.4d-141) then
        tmp = x
    else if (z <= 1.9d-13) then
        tmp = -t * (y / z)
    else
        tmp = y + 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 (z <= -2.4e+51) {
		tmp = y + x;
	} else if (z <= 4.4e-141) {
		tmp = x;
	} else if (z <= 1.9e-13) {
		tmp = -t * (y / z);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+51:
		tmp = y + x
	elif z <= 4.4e-141:
		tmp = x
	elif z <= 1.9e-13:
		tmp = -t * (y / z)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+51)
		tmp = Float64(y + x);
	elseif (z <= 4.4e-141)
		tmp = x;
	elseif (z <= 1.9e-13)
		tmp = Float64(Float64(-t) * Float64(y / z));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+51)
		tmp = y + x;
	elseif (z <= 4.4e-141)
		tmp = x;
	elseif (z <= 1.9e-13)
		tmp = -t * (y / z);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+51], N[(y + x), $MachinePrecision], If[LessEqual[z, 4.4e-141], x, If[LessEqual[z, 1.9e-13], N[((-t) * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3999999999999999e51 or 1.9e-13 < z

   1. Initial program 79.7%

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

   3. Taylor expanded in z around inf 74.3%

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

      1. +-commutative 74.3%

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

   5. Simplified 74.3%

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

   if -2.3999999999999999e51 < z < 4.40000000000000018e-141

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 52.9%

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

   if 4.40000000000000018e-141 < z < 1.9e-13

   1. Initial program 96.5%

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

      1. +-commutative 96.5%

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

      2. associate-/l* 86.8%

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

      3. fma-define 86.8%

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

   3. Simplified 86.8%

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

      1. clear-num 86.7%

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

      2. inv-pow 86.7%

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

   6. Applied egg-rr 86.7%

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

      1. unpow-1 86.7%

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

   8. Simplified 86.7%

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

   9. Taylor expanded in t around inf 53.7%

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

       1. mul-1-neg 53.7%

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

       2. associate-/l* 56.9%

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

       3. distribute-lft-neg-out 56.9%

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

       4. *-commutative 56.9%

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

   11. Simplified 56.9%

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

   12. Taylor expanded in z around inf 41.2%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+51}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \lor \neg \left(t \leq 8.8 \cdot 10^{-58}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.9) (not (<= t 8.8e-58)))
   (+ x (* t (/ y (- a z))))
   (+ x (* y (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.9) || !(t <= 8.8e-58)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (z / (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 <= (-2.9d0)) .or. (.not. (t <= 8.8d-58))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (y * (z / (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 <= -2.9) || !(t <= 8.8e-58)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.9) or not (t <= 8.8e-58):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.9) || !(t <= 8.8e-58))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.9) || ~((t <= 8.8e-58)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.9], N[Not[LessEqual[t, 8.8e-58]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.89999999999999991 or 8.80000000000000023e-58 < t

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-/l* 95.6%

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

      3. fma-define 95.6%

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

   3. Simplified 95.6%

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

      1. fma-undefine 95.6%

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

      2. associate-/l* 88.1%

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

      3. div-inv 88.0%

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

      4. *-commutative 88.0%

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

      5. associate-*r* 97.6%

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

      6. div-inv 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in z around 0 86.7%

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

      1. neg-mul-1 86.7%

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

   9. Simplified 86.7%

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

   if -2.89999999999999991 < t < 8.80000000000000023e-58

   1. Initial program 89.0%

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

   3. Taylor expanded in t around 0 84.4%

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

      1. +-commutative 84.4%

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

      2. associate-/l* 93.0%

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

   5. Simplified 93.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \lor \neg \left(t \leq 8.8 \cdot 10^{-58}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 81.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+51} \lor \neg \left(z \leq 1.16 \cdot 10^{-61}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.1e+51) (not (<= z 1.16e-61)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+51) || !(z <= 1.16e-61)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.1d+51)) .or. (.not. (z <= 1.16d-61))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+51) || !(z <= 1.16e-61)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.1e+51) or not (z <= 1.16e-61):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.1e+51) || !(z <= 1.16e-61))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.1e+51) || ~((z <= 1.16e-61)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.1e+51], N[Not[LessEqual[z, 1.16e-61]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1000000000000001e51 or 1.15999999999999994e-61 < z

   1. Initial program 81.4%

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

   3. Taylor expanded in a around 0 72.7%

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

      1. associate-/l* 86.5%

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

      2. div-sub 86.5%

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

      3. *-inverses 86.5%

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

   5. Simplified 86.5%

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

   if -2.1000000000000001e51 < z < 1.15999999999999994e-61

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 78.4%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+51} \lor \neg \left(z \leq 1.16 \cdot 10^{-61}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 82.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-35}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+66)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 4.7e-35) (+ x (* y (/ (- t z) a))) (+ x (* y (- 1.0 (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+66) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 4.7e-35) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.5d+66)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 4.7d-35) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + (y * (1.0d0 - (t / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+66) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 4.7e-35) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+66:
		tmp = x + (y / (z / (z - t)))
	elif z <= 4.7e-35:
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+66)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 4.7e-35)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+66)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 4.7e-35)
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+66], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e-35], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5000000000000001e66

   1. Initial program 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-/l* 78.3%

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

      3. div-inv 78.3%

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

      4. *-commutative 78.3%

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

      5. associate-*r* 92.7%

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

      6. div-inv 92.7%

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

   6. Applied egg-rr 92.7%

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

      1. *-commutative 92.7%

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

      2. div-inv 92.7%

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

      3. associate-*r* 99.8%

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

      4. associate-/r/ 99.9%

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

      5. un-div-inv 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in a around 0 96.3%

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

   if -6.5000000000000001e66 < z < 4.7e-35

   1. Initial program 97.6%

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

   3. Taylor expanded in a around inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

      3. associate-/l* 82.2%

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

   5. Simplified 82.2%

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

   if 4.7e-35 < z

   1. Initial program 82.0%

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

   3. Taylor expanded in a around 0 71.9%

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

      1. associate-/l* 82.9%

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

      2. div-sub 83.0%

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

      3. *-inverses 83.0%

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

   5. Simplified 83.0%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-35}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+52} \lor \neg \left(z \leq 3 \cdot 10^{+68}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e+52) (not (<= z 3e+68))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+52) || !(z <= 3e+68)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.6d+52)) .or. (.not. (z <= 3d+68))) then
        tmp = y + x
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+52) || !(z <= 3e+68)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.6e+52) or not (z <= 3e+68):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e+52) || !(z <= 3e+68))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.6e+52) || ~((z <= 3e+68)))
		tmp = y + x;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e+52], N[Not[LessEqual[z, 3e+68]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e52 or 3.0000000000000002e68 < z

   1. Initial program 76.7%

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

   3. Taylor expanded in z around inf 76.8%

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

      1. +-commutative 76.8%

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

   5. Simplified 76.8%

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

   if -1.6e52 < z < 3.0000000000000002e68

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0 72.5%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+52} \lor \neg \left(z \leq 3 \cdot 10^{+68}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 64.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51} \lor \neg \left(z \leq 5.5 \cdot 10^{-63}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.4e+51) (not (<= z 5.5e-63))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e+51) || !(z <= 5.5e-63)) {
		tmp = y + x;
	} 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 ((z <= (-4.4d+51)) .or. (.not. (z <= 5.5d-63))) then
        tmp = y + x
    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 ((z <= -4.4e+51) || !(z <= 5.5e-63)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.4e+51) or not (z <= 5.5e-63):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.4e+51) || !(z <= 5.5e-63))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.4e+51) || ~((z <= 5.5e-63)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.4e+51], N[Not[LessEqual[z, 5.5e-63]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.39999999999999984e51 or 5.50000000000000043e-63 < z

   1. Initial program 81.4%

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

   3. Taylor expanded in z around inf 70.1%

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

      1. +-commutative 70.1%

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

   5. Simplified 70.1%

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

   if -4.39999999999999984e51 < z < 5.50000000000000043e-63

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf 49.3%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51} \lor \neg \left(z \leq 5.5 \cdot 10^{-63}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 54.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+213}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.02e+213) y (if (<= y 2.9e+131) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.02e+213) {
		tmp = y;
	} else if (y <= 2.9e+131) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.02d+213)) then
        tmp = y
    else if (y <= 2.9d+131) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.02e+213) {
		tmp = y;
	} else if (y <= 2.9e+131) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.02e+213:
		tmp = y
	elif y <= 2.9e+131:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.02e+213)
		tmp = y;
	elseif (y <= 2.9e+131)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.02e+213)
		tmp = y;
	elseif (y <= 2.9e+131)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.02e+213], y, If[LessEqual[y, 2.9e+131], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e213 or 2.9000000000000001e131 < y

   1. Initial program 65.8%

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

   3. Taylor expanded in z around inf 34.8%

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

      1. +-commutative 34.8%

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

   5. Simplified 34.8%

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

   6. Taylor expanded in y around inf 34.8%

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

      1. +-commutative 34.8%

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

   8. Simplified 34.8%

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

   9. Taylor expanded in x around 0 30.5%

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

   if -1.02e213 < y < 2.9000000000000001e131

   1. Initial program 95.5%

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

   3. Taylor expanded in x around inf 61.0%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+213}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 52.2% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.6%

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

3. Taylor expanded in x around inf 49.2%

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

Developer Target 1: 98.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{z - a}{z - t}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024135 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- z a) (- z t)))))

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