Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B

Percentage Accurate: 74.6% → 91.7%

Time: 15.3s

Alternatives: 24

Speedup: 0.6×

• Rival profile vector overflowed, profile may not be complete

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 74.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 91.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + t\_1}\\ t_3 := 1 + \left(a + t\_1\right)\\ t_4 := z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{y}{t \cdot t\_3}\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-298}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+293}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;\frac{z - \frac{a}{b} \cdot \frac{z \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) t_1)))
        (t_3 (+ 1.0 (+ a t_1)))
        (t_4 (* z (+ (/ x (* z t_3)) (/ y (* t t_3))))))
   (if (<= t_2 (- INFINITY))
     t_4
     (if (<= t_2 -1e-298)
       t_2
       (if (<= t_2 0.0)
         (/ (+ x (/ y (/ t z))) (+ a (* y (/ b t))))
         (if (<= t_2 2e+293)
           t_2
           (if (<= t_2 INFINITY)
             t_4
             (/ (- z (* (/ a b) (/ (* z t) y))) b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double t_3 = 1.0 + (a + t_1);
	double t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_2 <= -1e-298) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (x + (y / (t / z))) / (a + (y * (b / t)));
	} else if (t_2 <= 2e+293) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = (z - ((a / b) * ((z * t) / y))) / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double t_3 = 1.0 + (a + t_1);
	double t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_2 <= -1e-298) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (x + (y / (t / z))) / (a + (y * (b / t)));
	} else if (t_2 <= 2e+293) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = (z - ((a / b) * ((z * t) / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1)
	t_3 = 1.0 + (a + t_1)
	t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_4
	elif t_2 <= -1e-298:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (x + (y / (t / z))) / (a + (y * (b / t)))
	elif t_2 <= 2e+293:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_4
	else:
		tmp = (z - ((a / b) * ((z * t) / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + t_1))
	t_3 = Float64(1.0 + Float64(a + t_1))
	t_4 = Float64(z * Float64(Float64(x / Float64(z * t_3)) + Float64(y / Float64(t * t_3))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_2 <= -1e-298)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(y * Float64(b / t))));
	elseif (t_2 <= 2e+293)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_4;
	else
		tmp = Float64(Float64(z - Float64(Float64(a / b) * Float64(Float64(z * t) / y))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	t_3 = 1.0 + (a + t_1);
	t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_4;
	elseif (t_2 <= -1e-298)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (x + (y / (t / z))) / (a + (y * (b / t)));
	elseif (t_2 <= 2e+293)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_4;
	else
		tmp = (z - ((a / b) * ((z * t) / y))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x / N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$4, If[LessEqual[t$95$2, -1e-298], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+293], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$4, N[(N[(z - N[(N[(a / b), $MachinePrecision] * N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or 1.9999999999999998e293 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 27.1%

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

      1. associate-/l* 61.6%

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

      2. associate-/l* 61.6%

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

   3. Simplified 61.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 95.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -9.99999999999999912e-299 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.9999999999999998e293

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   if -9.99999999999999912e-299 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 56.9%

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

      1. associate-/l* 56.8%

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

      2. associate-/l* 78.5%

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

   3. Simplified 78.5%

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

      1. clear-num 78.5%

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

      2. un-div-inv 78.6%

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

   6. Applied egg-rr 78.6%

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

   7. Taylor expanded in a around inf 78.6%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0.0%

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

   4. Taylor expanded in x around 0 1.1%

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

   5. Taylor expanded in b around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

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

      3. times-frac 92.4%

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

   7. Simplified 92.4%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-298}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+293}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - \frac{a}{b} \cdot \frac{z \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + t\_1}\\ t_3 := a + t\_1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{y}{t \cdot t\_3}\right)\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-298}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+293}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) t_1)))
        (t_3 (+ a t_1)))
   (if (<= t_2 (- INFINITY))
     (* z (+ (/ x (* z t_3)) (/ y (* t t_3))))
     (if (<= t_2 -1e-298)
       t_2
       (if (<= t_2 0.0)
         (/ (+ x (/ y (/ t z))) (+ a (* y (/ b t))))
         (if (<= t_2 2e+293) t_2 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double t_3 = a + t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	} else if (t_2 <= -1e-298) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (x + (y / (t / z))) / (a + (y * (b / t)));
	} else if (t_2 <= 2e+293) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double t_3 = a + t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	} else if (t_2 <= -1e-298) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (x + (y / (t / z))) / (a + (y * (b / t)));
	} else if (t_2 <= 2e+293) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1)
	t_3 = a + t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)))
	elif t_2 <= -1e-298:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (x + (y / (t / z))) / (a + (y * (b / t)))
	elif t_2 <= 2e+293:
		tmp = t_2
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + t_1))
	t_3 = Float64(a + t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_3)) + Float64(y / Float64(t * t_3))));
	elseif (t_2 <= -1e-298)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(y * Float64(b / t))));
	elseif (t_2 <= 2e+293)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	t_3 = a + t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	elseif (t_2 <= -1e-298)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (x + (y / (t / z))) / (a + (y * (b / t)));
	elseif (t_2 <= 2e+293)
		tmp = t_2;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(N[(x / N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-298], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+293], t$95$2, N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0

   1. Initial program 27.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 16.7%

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

   4. Taylor expanded in z around inf 78.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -9.99999999999999912e-299 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.9999999999999998e293

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   if -9.99999999999999912e-299 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 56.9%

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

      1. associate-/l* 56.8%

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

      2. associate-/l* 78.5%

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

   3. Simplified 78.5%

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

      1. clear-num 78.5%

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

      2. un-div-inv 78.6%

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

   6. Applied egg-rr 78.6%

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

   7. Taylor expanded in a around inf 78.6%

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

   if 1.9999999999999998e293 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 13.3%

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

      1. associate-/l* 32.0%

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

      2. associate-/l* 39.4%

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

   3. Simplified 39.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 71.9%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(a + \frac{y \cdot b}{t}\right)} + \frac{y}{t \cdot \left(a + \frac{y \cdot b}{t}\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-298}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+293}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-307}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+293}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 2e-307)
     (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (/ y (/ t b))))
     (if (<= t_1 2e+293) t_1 (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= 2e-307) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	} else if (t_1 <= 2e+293) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
    if (t_1 <= 2d-307) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y / (t / b)))
    else if (t_1 <= 2d+293) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= 2e-307) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	} else if (t_1 <= 2e+293) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= 2e-307:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)))
	elif t_1 <= 2e+293:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= 2e-307)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t_1 <= 2e+293)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= 2e-307)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	elseif (t_1 <= 2e+293)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-307], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+293], t$95$1, N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.99999999999999982e-307

   1. Initial program 83.6%

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

      1. associate-/l* 82.3%

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

      2. associate-/l* 87.2%

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

   3. Simplified 87.2%

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

      1. clear-num 87.1%

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

      2. un-div-inv 87.3%

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

   6. Applied egg-rr 87.3%

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

   if 1.99999999999999982e-307 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.9999999999999998e293

   1. Initial program 99.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   if 1.9999999999999998e293 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 13.3%

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

      1. associate-/l* 32.0%

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

      2. associate-/l* 39.4%

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

   3. Simplified 39.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 71.9%

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

Alternative 4: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;a + 1 \leq -2000000000 \lor \neg \left(a + 1 \leq 2\right):\\ \;\;\;\;\frac{t\_1}{a + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{1 + \frac{y}{\frac{t}{b}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ t z)))))
   (if (or (<= (+ a 1.0) -2000000000.0) (not (<= (+ a 1.0) 2.0)))
     (/ t_1 (+ a (* y (/ b t))))
     (/ t_1 (+ 1.0 (/ y (/ t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y / (t / z));
	double tmp;
	if (((a + 1.0) <= -2000000000.0) || !((a + 1.0) <= 2.0)) {
		tmp = t_1 / (a + (y * (b / t)));
	} else {
		tmp = t_1 / (1.0 + (y / (t / b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (t / z))
    if (((a + 1.0d0) <= (-2000000000.0d0)) .or. (.not. ((a + 1.0d0) <= 2.0d0))) then
        tmp = t_1 / (a + (y * (b / t)))
    else
        tmp = t_1 / (1.0d0 + (y / (t / b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y / (t / z));
	double tmp;
	if (((a + 1.0) <= -2000000000.0) || !((a + 1.0) <= 2.0)) {
		tmp = t_1 / (a + (y * (b / t)));
	} else {
		tmp = t_1 / (1.0 + (y / (t / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y / (t / z))
	tmp = 0
	if ((a + 1.0) <= -2000000000.0) or not ((a + 1.0) <= 2.0):
		tmp = t_1 / (a + (y * (b / t)))
	else:
		tmp = t_1 / (1.0 + (y / (t / b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y / Float64(t / z)))
	tmp = 0.0
	if ((Float64(a + 1.0) <= -2000000000.0) || !(Float64(a + 1.0) <= 2.0))
		tmp = Float64(t_1 / Float64(a + Float64(y * Float64(b / t))));
	else
		tmp = Float64(t_1 / Float64(1.0 + Float64(y / Float64(t / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y / (t / z));
	tmp = 0.0;
	if (((a + 1.0) <= -2000000000.0) || ~(((a + 1.0) <= 2.0)))
		tmp = t_1 / (a + (y * (b / t)));
	else
		tmp = t_1 / (1.0 + (y / (t / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -2000000000.0], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 2.0]], $MachinePrecision]], N[(t$95$1 / N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -2e9 or 2 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 81.9%

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

      1. associate-/l* 80.5%

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

      2. associate-/l* 84.6%

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

   3. Simplified 84.6%

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

      1. clear-num 84.6%

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

      2. un-div-inv 85.8%

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

   6. Applied egg-rr 85.8%

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

   7. Taylor expanded in a around inf 84.5%

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

   if -2e9 < (+.f64 a #s(literal 1 binary64)) < 2

   1. Initial program 80.2%

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

      1. associate-/l* 79.4%

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

      2. associate-/l* 81.0%

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

   3. Simplified 81.0%

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

      1. clear-num 81.0%

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

      2. un-div-inv 81.1%

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

   6. Applied egg-rr 81.1%

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

      1. clear-num 81.0%

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

      2. un-div-inv 81.2%

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

   8. Applied egg-rr 81.3%

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

   9. Taylor expanded in a around 0 80.9%

      \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{1} + \frac{y}{\frac{t}{b}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -2000000000 \lor \neg \left(a + 1 \leq 2\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{1 + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -2000000000 \lor \neg \left(a + 1 \leq 1.1\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{1 + \frac{y}{\frac{t}{b}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ a 1.0) -2000000000.0) (not (<= (+ a 1.0) 1.1)))
   (/ (+ x (* y (/ z t))) (+ a (* y (/ b t))))
   (/ (+ x (/ y (/ t z))) (+ 1.0 (/ y (/ t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -2000000000.0) || !((a + 1.0) <= 1.1)) {
		tmp = (x + (y * (z / t))) / (a + (y * (b / t)));
	} else {
		tmp = (x + (y / (t / z))) / (1.0 + (y / (t / b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (((a + 1.0d0) <= (-2000000000.0d0)) .or. (.not. ((a + 1.0d0) <= 1.1d0))) then
        tmp = (x + (y * (z / t))) / (a + (y * (b / t)))
    else
        tmp = (x + (y / (t / z))) / (1.0d0 + (y / (t / b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -2000000000.0) || !((a + 1.0) <= 1.1)) {
		tmp = (x + (y * (z / t))) / (a + (y * (b / t)));
	} else {
		tmp = (x + (y / (t / z))) / (1.0 + (y / (t / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a + 1.0) <= -2000000000.0) or not ((a + 1.0) <= 1.1):
		tmp = (x + (y * (z / t))) / (a + (y * (b / t)))
	else:
		tmp = (x + (y / (t / z))) / (1.0 + (y / (t / b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a + 1.0) <= -2000000000.0) || !(Float64(a + 1.0) <= 1.1))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(1.0 + Float64(y / Float64(t / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a + 1.0) <= -2000000000.0) || ~(((a + 1.0) <= 1.1)))
		tmp = (x + (y * (z / t))) / (a + (y * (b / t)));
	else
		tmp = (x + (y / (t / z))) / (1.0 + (y / (t / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -2000000000.0], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 1.1]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -2e9 or 1.1000000000000001 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 82.0%

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

      1. associate-/l* 79.9%

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

      2. associate-/l* 84.1%

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

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 82.7%

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

   if -2e9 < (+.f64 a #s(literal 1 binary64)) < 1.1000000000000001

   1. Initial program 80.0%

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

      1. associate-/l* 80.0%

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

      2. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

      1. clear-num 81.7%

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

      2. un-div-inv 81.8%

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

   6. Applied egg-rr 81.8%

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

      1. clear-num 81.7%

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

      2. un-div-inv 81.9%

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

   8. Applied egg-rr 81.9%

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

   9. Taylor expanded in a around 0 81.5%

      \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{1} + \frac{y}{\frac{t}{b}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -2000000000 \lor \neg \left(a + 1 \leq 1.1\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{1 + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{t}\\ \mathbf{if}\;a + 1 \leq -2000000000 \lor \neg \left(a + 1 \leq 1.1\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{1 + t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (/ b t))))
   (if (or (<= (+ a 1.0) -2000000000.0) (not (<= (+ a 1.0) 1.1)))
     (/ (+ x (* y (/ z t))) (+ a t_1))
     (/ (+ x (/ y (/ t z))) (+ 1.0 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / t);
	double tmp;
	if (((a + 1.0) <= -2000000000.0) || !((a + 1.0) <= 1.1)) {
		tmp = (x + (y * (z / t))) / (a + t_1);
	} else {
		tmp = (x + (y / (t / z))) / (1.0 + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b / t)
    if (((a + 1.0d0) <= (-2000000000.0d0)) .or. (.not. ((a + 1.0d0) <= 1.1d0))) then
        tmp = (x + (y * (z / t))) / (a + t_1)
    else
        tmp = (x + (y / (t / z))) / (1.0d0 + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / t);
	double tmp;
	if (((a + 1.0) <= -2000000000.0) || !((a + 1.0) <= 1.1)) {
		tmp = (x + (y * (z / t))) / (a + t_1);
	} else {
		tmp = (x + (y / (t / z))) / (1.0 + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b / t)
	tmp = 0
	if ((a + 1.0) <= -2000000000.0) or not ((a + 1.0) <= 1.1):
		tmp = (x + (y * (z / t))) / (a + t_1)
	else:
		tmp = (x + (y / (t / z))) / (1.0 + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b / t))
	tmp = 0.0
	if ((Float64(a + 1.0) <= -2000000000.0) || !(Float64(a + 1.0) <= 1.1))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + t_1));
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(1.0 + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b / t);
	tmp = 0.0;
	if (((a + 1.0) <= -2000000000.0) || ~(((a + 1.0) <= 1.1)))
		tmp = (x + (y * (z / t))) / (a + t_1);
	else
		tmp = (x + (y / (t / z))) / (1.0 + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -2000000000.0], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 1.1]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -2e9 or 1.1000000000000001 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 82.0%

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

      1. associate-/l* 79.9%

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

      2. associate-/l* 84.1%

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

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 82.7%

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

   if -2e9 < (+.f64 a #s(literal 1 binary64)) < 1.1000000000000001

   1. Initial program 80.0%

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

      1. associate-/l* 80.0%

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

      2. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

      1. clear-num 81.7%

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

      2. un-div-inv 81.8%

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

   6. Applied egg-rr 81.8%

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

   7. Taylor expanded in a around 0 81.3%

      \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{1} + y \cdot \frac{b}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -2000000000 \lor \neg \left(a + 1 \leq 1.1\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{1 + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ t_2 := y \cdot \frac{b}{t}\\ \mathbf{if}\;a + 1 \leq -2000000000 \lor \neg \left(a + 1 \leq 1.1\right):\\ \;\;\;\;\frac{t\_1}{a + t\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{1 + t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))) (t_2 (* y (/ b t))))
   (if (or (<= (+ a 1.0) -2000000000.0) (not (<= (+ a 1.0) 1.1)))
     (/ t_1 (+ a t_2))
     (/ t_1 (+ 1.0 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double t_2 = y * (b / t);
	double tmp;
	if (((a + 1.0) <= -2000000000.0) || !((a + 1.0) <= 1.1)) {
		tmp = t_1 / (a + t_2);
	} else {
		tmp = t_1 / (1.0 + t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    t_2 = y * (b / t)
    if (((a + 1.0d0) <= (-2000000000.0d0)) .or. (.not. ((a + 1.0d0) <= 1.1d0))) then
        tmp = t_1 / (a + t_2)
    else
        tmp = t_1 / (1.0d0 + t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double t_2 = y * (b / t);
	double tmp;
	if (((a + 1.0) <= -2000000000.0) || !((a + 1.0) <= 1.1)) {
		tmp = t_1 / (a + t_2);
	} else {
		tmp = t_1 / (1.0 + t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	t_2 = y * (b / t)
	tmp = 0
	if ((a + 1.0) <= -2000000000.0) or not ((a + 1.0) <= 1.1):
		tmp = t_1 / (a + t_2)
	else:
		tmp = t_1 / (1.0 + t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	t_2 = Float64(y * Float64(b / t))
	tmp = 0.0
	if ((Float64(a + 1.0) <= -2000000000.0) || !(Float64(a + 1.0) <= 1.1))
		tmp = Float64(t_1 / Float64(a + t_2));
	else
		tmp = Float64(t_1 / Float64(1.0 + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	t_2 = y * (b / t);
	tmp = 0.0;
	if (((a + 1.0) <= -2000000000.0) || ~(((a + 1.0) <= 1.1)))
		tmp = t_1 / (a + t_2);
	else
		tmp = t_1 / (1.0 + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -2000000000.0], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 1.1]], $MachinePrecision]], N[(t$95$1 / N[(a + t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(1.0 + t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -2e9 or 1.1000000000000001 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 82.0%

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

      1. associate-/l* 79.9%

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

      2. associate-/l* 84.1%

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

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 82.7%

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

   if -2e9 < (+.f64 a #s(literal 1 binary64)) < 1.1000000000000001

   1. Initial program 80.0%

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

      1. associate-/l* 80.0%

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

      2. associate-/l* 81.7%

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

   3. Simplified 81.7%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 81.3%

      \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\color{blue}{1} + y \cdot \frac{b}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -2000000000 \lor \neg \left(a + 1 \leq 1.1\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -2000000000 \lor \neg \left(a + 1 \leq 1\right):\\ \;\;\;\;\frac{x + z \cdot \left(y \cdot \frac{1}{t}\right)}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ a 1.0) -2000000000.0) (not (<= (+ a 1.0) 1.0)))
   (/ (+ x (* z (* y (/ 1.0 t)))) (+ a 1.0))
   (/ (+ x (* y (/ z t))) (+ 1.0 (* y (/ b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -2000000000.0) || !((a + 1.0) <= 1.0)) {
		tmp = (x + (z * (y * (1.0 / t)))) / (a + 1.0);
	} else {
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (((a + 1.0d0) <= (-2000000000.0d0)) .or. (.not. ((a + 1.0d0) <= 1.0d0))) then
        tmp = (x + (z * (y * (1.0d0 / t)))) / (a + 1.0d0)
    else
        tmp = (x + (y * (z / t))) / (1.0d0 + (y * (b / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -2000000000.0) || !((a + 1.0) <= 1.0)) {
		tmp = (x + (z * (y * (1.0 / t)))) / (a + 1.0);
	} else {
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a + 1.0) <= -2000000000.0) or not ((a + 1.0) <= 1.0):
		tmp = (x + (z * (y * (1.0 / t)))) / (a + 1.0)
	else:
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a + 1.0) <= -2000000000.0) || !(Float64(a + 1.0) <= 1.0))
		tmp = Float64(Float64(x + Float64(z * Float64(y * Float64(1.0 / t)))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(1.0 + Float64(y * Float64(b / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a + 1.0) <= -2000000000.0) || ~(((a + 1.0) <= 1.0)))
		tmp = (x + (z * (y * (1.0 / t)))) / (a + 1.0);
	else
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -2000000000.0], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 1.0]], $MachinePrecision]], N[(N[(x + N[(z * N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -2e9 or 1 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 82.1%

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

      1. associate-/l* 80.1%

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

      2. associate-/l* 84.2%

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

   3. Simplified 84.2%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 74.0%

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

      1. associate-*r/ 74.6%

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

      2. *-commutative 74.6%

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

      3. div-inv 74.7%

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

      4. associate-*l* 75.3%

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

   7. Applied egg-rr 75.3%

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

   if -2e9 < (+.f64 a #s(literal 1 binary64)) < 1

   1. Initial program 79.8%

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

      1. associate-/l* 79.9%

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

      2. associate-/l* 81.5%

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

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 81.4%

      \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\color{blue}{1} + y \cdot \frac{b}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -2000000000 \lor \neg \left(a + 1 \leq 1\right):\\ \;\;\;\;\frac{x + z \cdot \left(y \cdot \frac{1}{t}\right)}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-230} \lor \neg \left(t \leq 1.75 \cdot 10^{-154}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.1e-230) (not (<= t 1.75e-154)))
   (/ (+ x (/ y (/ t z))) (+ (+ a 1.0) (* y (/ b t))))
   (/ (* y z) (+ (* y b) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.1e-230) || !(t <= 1.75e-154)) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (y * z) / ((y * b) + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3.1d-230)) .or. (.not. (t <= 1.75d-154))) then
        tmp = (x + (y / (t / z))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (y * z) / ((y * b) + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.1e-230) || !(t <= 1.75e-154)) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (y * z) / ((y * b) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.1e-230) or not (t <= 1.75e-154):
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (y * z) / ((y * b) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.1e-230) || !(t <= 1.75e-154))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.1e-230) || ~((t <= 1.75e-154)))
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (y * z) / ((y * b) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.1e-230], N[Not[LessEqual[t, 1.75e-154]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1e-230 or 1.75e-154 < t

   1. Initial program 83.4%

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

      1. associate-/l* 84.2%

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

      2. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

      1. clear-num 88.9%

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

      2. un-div-inv 89.4%

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

   6. Applied egg-rr 89.4%

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

   if -3.1e-230 < t < 1.75e-154

   1. Initial program 63.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 56.2%

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

   4. Taylor expanded in x around 0 56.5%

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

   5. Taylor expanded in t around 0 79.4%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-230} \lor \neg \left(t \leq 1.75 \cdot 10^{-154}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-230} \lor \neg \left(t \leq 2.3 \cdot 10^{-157}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.1e-230) (not (<= t 2.3e-157)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (/ (* y z) (+ (* y b) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.1e-230) || !(t <= 2.3e-157)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (y * z) / ((y * b) + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3.1d-230)) .or. (.not. (t <= 2.3d-157))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (y * z) / ((y * b) + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.1e-230) || !(t <= 2.3e-157)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (y * z) / ((y * b) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.1e-230) or not (t <= 2.3e-157):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (y * z) / ((y * b) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.1e-230) || !(t <= 2.3e-157))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.1e-230) || ~((t <= 2.3e-157)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (y * z) / ((y * b) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.1e-230], N[Not[LessEqual[t, 2.3e-157]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1e-230 or 2.29999999999999989e-157 < t

   1. Initial program 83.4%

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

      1. associate-/l* 84.2%

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

      2. associate-/l* 88.9%

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

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   if -3.1e-230 < t < 2.29999999999999989e-157

   1. Initial program 63.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 56.2%

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

   4. Taylor expanded in x around 0 56.5%

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

   5. Taylor expanded in t around 0 79.4%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-230} \lor \neg \left(t \leq 2.3 \cdot 10^{-157}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-230}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-157}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= t -2.9e-230)
     (/ t_1 (+ (+ a 1.0) (/ y (/ t b))))
     (if (<= t 1.25e-157)
       (/ (* y z) (+ (* y b) (* t a)))
       (/ t_1 (+ (+ a 1.0) (* y (/ b t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (t <= -2.9e-230) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 1.25e-157) {
		tmp = (y * z) / ((y * b) + (t * a));
	} else {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (t <= (-2.9d-230)) then
        tmp = t_1 / ((a + 1.0d0) + (y / (t / b)))
    else if (t <= 1.25d-157) then
        tmp = (y * z) / ((y * b) + (t * a))
    else
        tmp = t_1 / ((a + 1.0d0) + (y * (b / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (t <= -2.9e-230) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 1.25e-157) {
		tmp = (y * z) / ((y * b) + (t * a));
	} else {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	tmp = 0
	if t <= -2.9e-230:
		tmp = t_1 / ((a + 1.0) + (y / (t / b)))
	elif t <= 1.25e-157:
		tmp = (y * z) / ((y * b) + (t * a))
	else:
		tmp = t_1 / ((a + 1.0) + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -2.9e-230)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t <= 1.25e-157)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * a)));
	else
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (t <= -2.9e-230)
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	elseif (t <= 1.25e-157)
		tmp = (y * z) / ((y * b) + (t * a));
	else
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e-230], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-157], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.90000000000000005e-230

   1. Initial program 86.9%

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

      1. associate-/l* 86.1%

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

      2. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

      1. clear-num 87.8%

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

      2. un-div-inv 87.8%

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

   6. Applied egg-rr 87.8%

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

   if -2.90000000000000005e-230 < t < 1.25000000000000005e-157

   1. Initial program 63.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 56.2%

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

   4. Taylor expanded in x around 0 56.5%

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

   5. Taylor expanded in t around 0 79.4%

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

   if 1.25000000000000005e-157 < t

   1. Initial program 79.6%

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

      1. associate-/l* 82.2%

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

      2. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-230}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-157}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{x + z \cdot \left(y \cdot \frac{1}{t}\right)}{a + 1}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-77}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.5e-93)
   (/ (+ x (* z (* y (/ 1.0 t)))) (+ a 1.0))
   (if (<= t 3e-77)
     (/ (* y z) (+ (* y b) (* t a)))
     (if (<= t 6.7e+24)
       (/ (+ x (/ (* y z) t)) (+ a 1.0))
       (/ x (+ 1.0 (+ a (* y (/ b t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.5e-93) {
		tmp = (x + (z * (y * (1.0 / t)))) / (a + 1.0);
	} else if (t <= 3e-77) {
		tmp = (y * z) / ((y * b) + (t * a));
	} else if (t <= 6.7e+24) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = x / (1.0 + (a + (y * (b / t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9.5d-93)) then
        tmp = (x + (z * (y * (1.0d0 / t)))) / (a + 1.0d0)
    else if (t <= 3d-77) then
        tmp = (y * z) / ((y * b) + (t * a))
    else if (t <= 6.7d+24) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.5e-93) {
		tmp = (x + (z * (y * (1.0 / t)))) / (a + 1.0);
	} else if (t <= 3e-77) {
		tmp = (y * z) / ((y * b) + (t * a));
	} else if (t <= 6.7e+24) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = x / (1.0 + (a + (y * (b / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.5e-93:
		tmp = (x + (z * (y * (1.0 / t)))) / (a + 1.0)
	elif t <= 3e-77:
		tmp = (y * z) / ((y * b) + (t * a))
	elif t <= 6.7e+24:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = x / (1.0 + (a + (y * (b / t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.5e-93)
		tmp = Float64(Float64(x + Float64(z * Float64(y * Float64(1.0 / t)))) / Float64(a + 1.0));
	elseif (t <= 3e-77)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * a)));
	elseif (t <= 6.7e+24)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.5e-93)
		tmp = (x + (z * (y * (1.0 / t)))) / (a + 1.0);
	elseif (t <= 3e-77)
		tmp = (y * z) / ((y * b) + (t * a));
	elseif (t <= 6.7e+24)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	else
		tmp = x / (1.0 + (a + (y * (b / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.5e-93], N[(N[(x + N[(z * N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-77], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.7e+24], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.5000000000000001e-93

   1. Initial program 88.2%

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

      1. associate-/l* 90.7%

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

      2. associate-/l* 93.0%

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

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 81.9%

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

      1. associate-*r/ 83.2%

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

      2. *-commutative 83.2%

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

      3. div-inv 83.2%

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

      4. associate-*l* 84.3%

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

   7. Applied egg-rr 84.3%

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

   if -9.5000000000000001e-93 < t < 3.00000000000000016e-77

   1. Initial program 75.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 62.8%

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

   4. Taylor expanded in x around 0 53.5%

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

   5. Taylor expanded in t around 0 66.0%

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

   if 3.00000000000000016e-77 < t < 6.6999999999999999e24

   1. Initial program 86.0%

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

      1. associate-/l* 86.0%

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

      2. associate-/l* 86.0%

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

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 81.1%

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

   if 6.6999999999999999e24 < t

   1. Initial program 77.7%

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

      1. associate-/l* 83.3%

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

      2. associate-/l* 97.1%

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

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 71.9%

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

      1. associate-*l/ 80.3%

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

      2. *-commutative 80.3%

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

   7. Simplified 80.3%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{x + z \cdot \left(y \cdot \frac{1}{t}\right)}{a + 1}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-77}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-93}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.4e-93)
   (/ (+ x (* y (/ z t))) (+ a 1.0))
   (if (<= t 9.2e-67)
     (/ (* y z) (+ (* y b) (* t a)))
     (if (<= t 3.5e+23)
       (/ (+ x (/ (* y z) t)) (+ a 1.0))
       (/ x (+ 1.0 (+ a (* y (/ b t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.4e-93) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (t <= 9.2e-67) {
		tmp = (y * z) / ((y * b) + (t * a));
	} else if (t <= 3.5e+23) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = x / (1.0 + (a + (y * (b / t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.4d-93)) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else if (t <= 9.2d-67) then
        tmp = (y * z) / ((y * b) + (t * a))
    else if (t <= 3.5d+23) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.4e-93) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (t <= 9.2e-67) {
		tmp = (y * z) / ((y * b) + (t * a));
	} else if (t <= 3.5e+23) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = x / (1.0 + (a + (y * (b / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.4e-93:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	elif t <= 9.2e-67:
		tmp = (y * z) / ((y * b) + (t * a))
	elif t <= 3.5e+23:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = x / (1.0 + (a + (y * (b / t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.4e-93)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	elseif (t <= 9.2e-67)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * a)));
	elseif (t <= 3.5e+23)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.4e-93)
		tmp = (x + (y * (z / t))) / (a + 1.0);
	elseif (t <= 9.2e-67)
		tmp = (y * z) / ((y * b) + (t * a));
	elseif (t <= 3.5e+23)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	else
		tmp = x / (1.0 + (a + (y * (b / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.4e-93], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-67], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+23], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.39999999999999999e-93

   1. Initial program 88.2%

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

      1. associate-/l* 90.7%

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

      2. associate-/l* 93.0%

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

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 81.9%

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

      1. associate-*r/ 83.2%

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

      2. *-commutative 83.2%

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

   7. Applied egg-rr 83.2%

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

   if -1.39999999999999999e-93 < t < 9.2000000000000002e-67

   1. Initial program 75.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 62.8%

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

   4. Taylor expanded in x around 0 53.5%

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

   5. Taylor expanded in t around 0 66.0%

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

   if 9.2000000000000002e-67 < t < 3.5000000000000002e23

   1. Initial program 86.0%

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

      1. associate-/l* 86.0%

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

      2. associate-/l* 86.0%

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

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 81.1%

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

   if 3.5000000000000002e23 < t

   1. Initial program 77.7%

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

      1. associate-/l* 83.3%

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

      2. associate-/l* 97.1%

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

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 71.9%

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

      1. associate-*l/ 80.3%

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

      2. *-commutative 80.3%

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

   7. Simplified 80.3%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-93}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-75}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ a 1.0))))
   (if (<= t -7.8e-94)
     t_1
     (if (<= t 1.1e-75)
       (/ (* y z) (+ (* y b) (* t a)))
       (if (<= t 2.7e+24) t_1 (/ x (+ 1.0 (+ a (* y (/ b t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -7.8e-94) {
		tmp = t_1;
	} else if (t <= 1.1e-75) {
		tmp = (y * z) / ((y * b) + (t * a));
	} else if (t <= 2.7e+24) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 + (a + (y * (b / t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / (a + 1.0d0)
    if (t <= (-7.8d-94)) then
        tmp = t_1
    else if (t <= 1.1d-75) then
        tmp = (y * z) / ((y * b) + (t * a))
    else if (t <= 2.7d+24) then
        tmp = t_1
    else
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -7.8e-94) {
		tmp = t_1;
	} else if (t <= 1.1e-75) {
		tmp = (y * z) / ((y * b) + (t * a));
	} else if (t <= 2.7e+24) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 + (a + (y * (b / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / (a + 1.0)
	tmp = 0
	if t <= -7.8e-94:
		tmp = t_1
	elif t <= 1.1e-75:
		tmp = (y * z) / ((y * b) + (t * a))
	elif t <= 2.7e+24:
		tmp = t_1
	else:
		tmp = x / (1.0 + (a + (y * (b / t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -7.8e-94)
		tmp = t_1;
	elseif (t <= 1.1e-75)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * a)));
	elseif (t <= 2.7e+24)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -7.8e-94)
		tmp = t_1;
	elseif (t <= 1.1e-75)
		tmp = (y * z) / ((y * b) + (t * a));
	elseif (t <= 2.7e+24)
		tmp = t_1;
	else
		tmp = x / (1.0 + (a + (y * (b / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e-94], t$95$1, If[LessEqual[t, 1.1e-75], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+24], t$95$1, N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.8000000000000004e-94 or 1.10000000000000003e-75 < t < 2.7e24

   1. Initial program 87.8%

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

      1. associate-/l* 89.7%

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

      2. associate-/l* 91.6%

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

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 81.7%

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

      1. associate-*r/ 82.7%

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

      2. *-commutative 82.7%

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

   7. Applied egg-rr 82.7%

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

   if -7.8000000000000004e-94 < t < 1.10000000000000003e-75

   1. Initial program 75.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 62.8%

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

   4. Taylor expanded in x around 0 53.5%

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

   5. Taylor expanded in t around 0 66.0%

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

   if 2.7e24 < t

   1. Initial program 77.7%

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

      1. associate-/l* 83.3%

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

      2. associate-/l* 97.1%

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

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 71.9%

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

      1. associate-*l/ 80.3%

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

      2. *-commutative 80.3%

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

   7. Simplified 80.3%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-94}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-75}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{if}\;a \leq -6800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;a \leq 3000000000000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) a)))
   (if (<= a -6800000000000.0)
     t_1
     (if (<= a 3.8e-33)
       (/ x (+ 1.0 (+ a (* y (/ b t)))))
       (if (<= a 3000000000000.0) (/ z b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / a;
	double tmp;
	if (a <= -6800000000000.0) {
		tmp = t_1;
	} else if (a <= 3.8e-33) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if (a <= 3000000000000.0) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / (t / z))) / a
    if (a <= (-6800000000000.0d0)) then
        tmp = t_1
    else if (a <= 3.8d-33) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    else if (a <= 3000000000000.0d0) then
        tmp = z / b
    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 b) {
	double t_1 = (x + (y / (t / z))) / a;
	double tmp;
	if (a <= -6800000000000.0) {
		tmp = t_1;
	} else if (a <= 3.8e-33) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if (a <= 3000000000000.0) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / a
	tmp = 0
	if a <= -6800000000000.0:
		tmp = t_1
	elif a <= 3.8e-33:
		tmp = x / (1.0 + (a + (y * (b / t))))
	elif a <= 3000000000000.0:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / a)
	tmp = 0.0
	if (a <= -6800000000000.0)
		tmp = t_1;
	elseif (a <= 3.8e-33)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	elseif (a <= 3000000000000.0)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y / (t / z))) / a;
	tmp = 0.0;
	if (a <= -6800000000000.0)
		tmp = t_1;
	elseif (a <= 3.8e-33)
		tmp = x / (1.0 + (a + (y * (b / t))));
	elseif (a <= 3000000000000.0)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -6800000000000.0], t$95$1, If[LessEqual[a, 3.8e-33], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3000000000000.0], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.8e12 or 3e12 < a

   1. Initial program 82.8%

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

      1. associate-/l* 81.4%

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

      2. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

      1. clear-num 85.8%

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

      2. un-div-inv 87.1%

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

   6. Applied egg-rr 87.1%

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

      1. clear-num 85.8%

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

      2. un-div-inv 85.8%

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

   8. Applied egg-rr 87.1%

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

   9. Taylor expanded in a around inf 75.1%

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

       1. associate-/l* 75.8%

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

   11. Simplified 75.8%

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

       1. clear-num 85.8%

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

       2. un-div-inv 87.1%

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

   13. Applied egg-rr 77.1%

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

   if -6.8e12 < a < 3.79999999999999994e-33

   1. Initial program 82.2%

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

      1. associate-/l* 80.6%

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

      2. associate-/l* 82.3%

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

   3. Simplified 82.3%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 61.9%

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

      1. associate-*l/ 62.8%

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

      2. *-commutative 62.8%

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

   7. Simplified 62.8%

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

   if 3.79999999999999994e-33 < a < 3e12

   1. Initial program 48.7%

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

      1. associate-/l* 57.0%

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

      2. associate-/l* 57.0%

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

   3. Simplified 57.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 73.5%

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

Alternative 16: 54.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{if}\;a \leq -0.87:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 2800000000000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) a)))
   (if (<= a -0.87)
     t_1
     (if (<= a 1.9e-33)
       (+ x (/ (* y z) t))
       (if (<= a 2800000000000.0) (/ z b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / a;
	double tmp;
	if (a <= -0.87) {
		tmp = t_1;
	} else if (a <= 1.9e-33) {
		tmp = x + ((y * z) / t);
	} else if (a <= 2800000000000.0) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / (t / z))) / a
    if (a <= (-0.87d0)) then
        tmp = t_1
    else if (a <= 1.9d-33) then
        tmp = x + ((y * z) / t)
    else if (a <= 2800000000000.0d0) then
        tmp = z / b
    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 b) {
	double t_1 = (x + (y / (t / z))) / a;
	double tmp;
	if (a <= -0.87) {
		tmp = t_1;
	} else if (a <= 1.9e-33) {
		tmp = x + ((y * z) / t);
	} else if (a <= 2800000000000.0) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / a
	tmp = 0
	if a <= -0.87:
		tmp = t_1
	elif a <= 1.9e-33:
		tmp = x + ((y * z) / t)
	elif a <= 2800000000000.0:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / a)
	tmp = 0.0
	if (a <= -0.87)
		tmp = t_1;
	elseif (a <= 1.9e-33)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (a <= 2800000000000.0)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y / (t / z))) / a;
	tmp = 0.0;
	if (a <= -0.87)
		tmp = t_1;
	elseif (a <= 1.9e-33)
		tmp = x + ((y * z) / t);
	elseif (a <= 2800000000000.0)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -0.87], t$95$1, If[LessEqual[a, 1.9e-33], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2800000000000.0], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.869999999999999996 or 2.8e12 < a

   1. Initial program 83.2%

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

      1. associate-/l* 81.8%

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

      2. associate-/l* 86.1%

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

   3. Simplified 86.1%

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

      1. clear-num 86.1%

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

      2. un-div-inv 87.3%

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

   6. Applied egg-rr 87.3%

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

      1. clear-num 86.1%

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

      2. un-div-inv 86.1%

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

   8. Applied egg-rr 87.3%

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

   9. Taylor expanded in a around inf 74.5%

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

       1. associate-/l* 75.2%

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

   11. Simplified 75.2%

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

       1. clear-num 86.1%

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

       2. un-div-inv 87.3%

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

   13. Applied egg-rr 76.4%

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

   if -0.869999999999999996 < a < 1.89999999999999997e-33

   1. Initial program 82.4%

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

      1. associate-/l* 80.7%

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

      2. associate-/l* 81.6%

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

   3. Simplified 81.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 56.3%

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

   6. Taylor expanded in a around 0 56.1%

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

   if 1.89999999999999997e-33 < a < 2.8e12

   1. Initial program 45.4%

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

      1. associate-/l* 53.1%

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

      2. associate-/l* 60.6%

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

   3. Simplified 60.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 68.2%

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

Alternative 17: 54.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+14}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) a)))
   (if (<= a -1.0)
     t_1
     (if (<= a 6.5e-36) (+ x (/ (* y z) t)) (if (<= a 1.3e+14) (/ z b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -1.0) {
		tmp = t_1;
	} else if (a <= 6.5e-36) {
		tmp = x + ((y * z) / t);
	} else if (a <= 1.3e+14) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / a
    if (a <= (-1.0d0)) then
        tmp = t_1
    else if (a <= 6.5d-36) then
        tmp = x + ((y * z) / t)
    else if (a <= 1.3d+14) then
        tmp = z / b
    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 b) {
	double t_1 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -1.0) {
		tmp = t_1;
	} else if (a <= 6.5e-36) {
		tmp = x + ((y * z) / t);
	} else if (a <= 1.3e+14) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / a
	tmp = 0
	if a <= -1.0:
		tmp = t_1
	elif a <= 6.5e-36:
		tmp = x + ((y * z) / t)
	elif a <= 1.3e+14:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / a)
	tmp = 0.0
	if (a <= -1.0)
		tmp = t_1;
	elseif (a <= 6.5e-36)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (a <= 1.3e+14)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / a;
	tmp = 0.0;
	if (a <= -1.0)
		tmp = t_1;
	elseif (a <= 6.5e-36)
		tmp = x + ((y * z) / t);
	elseif (a <= 1.3e+14)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -1.0], t$95$1, If[LessEqual[a, 6.5e-36], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+14], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1 or 1.3e14 < a

   1. Initial program 83.2%

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

      1. associate-/l* 81.8%

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

      2. associate-/l* 86.1%

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

   3. Simplified 86.1%

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

      1. clear-num 86.1%

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

      2. un-div-inv 87.3%

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

   6. Applied egg-rr 87.3%

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

      1. clear-num 86.1%

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

      2. un-div-inv 86.1%

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

   8. Applied egg-rr 87.3%

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

   9. Taylor expanded in a around inf 74.5%

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

       1. associate-/l* 75.2%

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

   11. Simplified 75.2%

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

   if -1 < a < 6.50000000000000012e-36

   1. Initial program 82.4%

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

      1. associate-/l* 80.7%

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

      2. associate-/l* 81.6%

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

   3. Simplified 81.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 56.3%

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

   6. Taylor expanded in a around 0 56.1%

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

   if 6.50000000000000012e-36 < a < 1.3e14

   1. Initial program 45.4%

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

      1. associate-/l* 53.1%

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

      2. associate-/l* 60.6%

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

   3. Simplified 60.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 68.2%

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

Alternative 18: 55.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1650000:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -8.2e-90)
     t_1
     (if (<= t 1.2e-44)
       (/ z b)
       (if (<= t 1650000.0) (/ (* y z) (* t (+ a 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -8.2e-90) {
		tmp = t_1;
	} else if (t <= 1.2e-44) {
		tmp = z / b;
	} else if (t <= 1650000.0) {
		tmp = (y * z) / (t * (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-8.2d-90)) then
        tmp = t_1
    else if (t <= 1.2d-44) then
        tmp = z / b
    else if (t <= 1650000.0d0) then
        tmp = (y * z) / (t * (a + 1.0d0))
    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 b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -8.2e-90) {
		tmp = t_1;
	} else if (t <= 1.2e-44) {
		tmp = z / b;
	} else if (t <= 1650000.0) {
		tmp = (y * z) / (t * (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -8.2e-90:
		tmp = t_1
	elif t <= 1.2e-44:
		tmp = z / b
	elif t <= 1650000.0:
		tmp = (y * z) / (t * (a + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -8.2e-90)
		tmp = t_1;
	elseif (t <= 1.2e-44)
		tmp = Float64(z / b);
	elseif (t <= 1650000.0)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(a + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -8.2e-90)
		tmp = t_1;
	elseif (t <= 1.2e-44)
		tmp = z / b;
	elseif (t <= 1650000.0)
		tmp = (y * z) / (t * (a + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e-90], t$95$1, If[LessEqual[t, 1.2e-44], N[(z / b), $MachinePrecision], If[LessEqual[t, 1650000.0], N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.2000000000000007e-90 or 1.65e6 < t

   1. Initial program 83.7%

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

      1. associate-/l* 87.5%

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

      2. associate-/l* 94.9%

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

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.9%

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

   if -8.2000000000000007e-90 < t < 1.20000000000000004e-44

   1. Initial program 75.3%

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

      1. associate-/l* 66.1%

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

      2. associate-/l* 62.0%

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

   3. Simplified 62.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 51.5%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if 1.20000000000000004e-44 < t < 1.65e6

   1. Initial program 99.4%

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

      1. associate-/l* 99.4%

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

      2. associate-/l* 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 99.4%

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

   6. Taylor expanded in x around 0 85.8%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1650000:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 55.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 205000:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -5e-91)
     t_1
     (if (<= t 1.2e-44)
       (/ z b)
       (if (<= t 205000.0) (* y (/ (/ z t) (+ a 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -5e-91) {
		tmp = t_1;
	} else if (t <= 1.2e-44) {
		tmp = z / b;
	} else if (t <= 205000.0) {
		tmp = y * ((z / t) / (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-5d-91)) then
        tmp = t_1
    else if (t <= 1.2d-44) then
        tmp = z / b
    else if (t <= 205000.0d0) then
        tmp = y * ((z / t) / (a + 1.0d0))
    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 b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -5e-91) {
		tmp = t_1;
	} else if (t <= 1.2e-44) {
		tmp = z / b;
	} else if (t <= 205000.0) {
		tmp = y * ((z / t) / (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -5e-91:
		tmp = t_1
	elif t <= 1.2e-44:
		tmp = z / b
	elif t <= 205000.0:
		tmp = y * ((z / t) / (a + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -5e-91)
		tmp = t_1;
	elseif (t <= 1.2e-44)
		tmp = Float64(z / b);
	elseif (t <= 205000.0)
		tmp = Float64(y * Float64(Float64(z / t) / Float64(a + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -5e-91)
		tmp = t_1;
	elseif (t <= 1.2e-44)
		tmp = z / b;
	elseif (t <= 205000.0)
		tmp = y * ((z / t) / (a + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-91], t$95$1, If[LessEqual[t, 1.2e-44], N[(z / b), $MachinePrecision], If[LessEqual[t, 205000.0], N[(y * N[(N[(z / t), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.99999999999999997e-91 or 205000 < t

   1. Initial program 83.7%

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

      1. associate-/l* 87.5%

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

      2. associate-/l* 94.9%

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

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.9%

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

   if -4.99999999999999997e-91 < t < 1.20000000000000004e-44

   1. Initial program 75.3%

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

      1. associate-/l* 66.1%

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

      2. associate-/l* 62.0%

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

   3. Simplified 62.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 51.5%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if 1.20000000000000004e-44 < t < 205000

   1. Initial program 99.4%

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

      1. associate-/l* 99.4%

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

      2. associate-/l* 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 99.4%

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

   6. Taylor expanded in x around 0 85.8%

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

      1. associate-/l* 85.6%

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

      2. associate-/r* 85.5%

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

   8. Simplified 85.5%

      \[\leadsto \color{blue}{y \cdot \frac{\frac{z}{t}}{1 + a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 205000:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 61.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-90} \lor \neg \left(t \leq 1.25 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.8e-90) (not (<= t 1.25e-10)))
   (/ x (+ 1.0 (+ a (* y (/ b t)))))
   (/ (* y z) (+ (* y b) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.8e-90) || !(t <= 1.25e-10)) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = (y * z) / ((y * b) + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5.8d-90)) .or. (.not. (t <= 1.25d-10))) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    else
        tmp = (y * z) / ((y * b) + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.8e-90) || !(t <= 1.25e-10)) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = (y * z) / ((y * b) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.8e-90) or not (t <= 1.25e-10):
		tmp = x / (1.0 + (a + (y * (b / t))))
	else:
		tmp = (y * z) / ((y * b) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.8e-90) || !(t <= 1.25e-10))
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	else
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.8e-90) || ~((t <= 1.25e-10)))
		tmp = x / (1.0 + (a + (y * (b / t))));
	else
		tmp = (y * z) / ((y * b) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.8e-90], N[Not[LessEqual[t, 1.25e-10]], $MachinePrecision]], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.79999999999999967e-90 or 1.25000000000000008e-10 < t

   1. Initial program 84.0%

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

      1. associate-/l* 87.7%

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

      2. associate-/l* 95.0%

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

   3. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.6%

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

      1. associate-*l/ 74.8%

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

      2. *-commutative 74.8%

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

   7. Simplified 74.8%

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

   if -5.79999999999999967e-90 < t < 1.25000000000000008e-10

   1. Initial program 76.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 63.0%

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

   4. Taylor expanded in x around 0 54.1%

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

   5. Taylor expanded in t around 0 64.6%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-90} \lor \neg \left(t \leq 1.25 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 55.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-90} \lor \neg \left(t \leq 1.2 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.15e-90) (not (<= t 1.2e-44))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.15e-90) || !(t <= 1.2e-44)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.15d-90)) .or. (.not. (t <= 1.2d-44))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.15e-90) || !(t <= 1.2e-44)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.15e-90) or not (t <= 1.2e-44):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.15e-90) || !(t <= 1.2e-44))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.15e-90) || ~((t <= 1.2e-44)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.15e-90], N[Not[LessEqual[t, 1.2e-44]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1499999999999999e-90 or 1.20000000000000004e-44 < t

   1. Initial program 84.4%

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

      1. associate-/l* 88.1%

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

      2. associate-/l* 95.1%

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

   3. Simplified 95.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 63.1%

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

   if -1.1499999999999999e-90 < t < 1.20000000000000004e-44

   1. Initial program 75.3%

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

      1. associate-/l* 66.1%

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

      2. associate-/l* 62.0%

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

   3. Simplified 62.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 51.5%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-90} \lor \neg \left(t \leq 1.2 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 43.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6000000 \lor \neg \left(a \leq 2 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6000000.0) (not (<= a 2e+14))) (/ x a) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6000000.0) || !(a <= 2e+14)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-6000000.0d0)) .or. (.not. (a <= 2d+14))) then
        tmp = x / a
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6000000.0) || !(a <= 2e+14)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -6000000.0) or not (a <= 2e+14):
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -6000000.0) || !(a <= 2e+14))
		tmp = Float64(x / a);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -6000000.0) || ~((a <= 2e+14)))
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -6000000.0], N[Not[LessEqual[a, 2e+14]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6e6 or 2e14 < a

   1. Initial program 83.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 82.5%

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

   4. Taylor expanded in y around 0 52.9%

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

   if -6e6 < a < 2e14

   1. Initial program 78.7%

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

      1. associate-/l* 78.0%

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

      2. associate-/l* 79.6%

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

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 34.1%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6000000 \lor \neg \left(a \leq 2 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 43.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5900000:\\ \;\;\;\;\frac{1}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq 3000000000000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5900000.0)
   (/ 1.0 (/ a x))
   (if (<= a 3000000000000.0) (/ z b) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5900000.0) {
		tmp = 1.0 / (a / x);
	} else if (a <= 3000000000000.0) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (a <= (-5900000.0d0)) then
        tmp = 1.0d0 / (a / x)
    else if (a <= 3000000000000.0d0) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5900000.0) {
		tmp = 1.0 / (a / x);
	} else if (a <= 3000000000000.0) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5900000.0:
		tmp = 1.0 / (a / x)
	elif a <= 3000000000000.0:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5900000.0)
		tmp = Float64(1.0 / Float64(a / x));
	elseif (a <= 3000000000000.0)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5900000.0)
		tmp = 1.0 / (a / x);
	elseif (a <= 3000000000000.0)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5900000.0], N[(1.0 / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3000000000000.0], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.9e6

   1. Initial program 78.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 77.7%

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

   4. Taylor expanded in y around 0 50.6%

      \[\leadsto \color{blue}{\frac{x}{a}} \]
   5. Step-by-step derivation

      1. clear-num 50.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}}} \]

      2. inv-pow 50.8%

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

   6. Applied egg-rr 50.8%

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

      1. unpow-1 50.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}}} \]

   8. Simplified 50.8%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}}} \]

   if -5.9e6 < a < 3e12

   1. Initial program 78.7%

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

      1. associate-/l* 78.0%

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

      2. associate-/l* 79.6%

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

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 34.1%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if 3e12 < a

   1. Initial program 88.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 88.5%

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

   4. Taylor expanded in y around 0 55.8%

      \[\leadsto \color{blue}{\frac{x}{a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 24: 25.4% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / a), $MachinePrecision]

Derivation

1. Initial program 81.1%

   \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
2. Add Preprocessing

3. Taylor expanded in a around inf 57.4%

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

4. Taylor expanded in y around 0 29.5%

   \[\leadsto \color{blue}{\frac{x}{a}} \]
5. Add Preprocessing

Developer Target 1: 79.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))
   (if (< t -1.3659085366310088e-271)
     t_1
     (if (< t 3.036967103737246e-130) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 * ((x + ((y / t) * z)) * (1.0d0 / ((a + 1.0d0) + ((y / t) * b))))
    if (t < (-1.3659085366310088d-271)) then
        tmp = t_1
    else if (t < 3.036967103737246d-130) then
        tmp = z / b
    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 b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))))
	tmp = 0
	if t < -1.3659085366310088e-271:
		tmp = t_1
	elif t < 3.036967103737246e-130:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 * Float64(Float64(x + Float64(Float64(y / t) * z)) * Float64(1.0 / Float64(Float64(a + 1.0) + Float64(Float64(y / t) * b)))))
	tmp = 0.0
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	tmp = 0.0;
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 * N[(N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.3659085366310088e-271], t$95$1, If[Less[t, 3.036967103737246e-130], N[(z / b), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024156 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1707385670788761/12500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))) (if (< t 1518483551868623/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ z b) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))