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

Percentage Accurate: 75.5% → 91.0%

Time: 20.1s

Alternatives: 19

Speedup: 0.6×

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: 75.5% 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: 91.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, \frac{z \cdot t}{\frac{{b}^{2}}{a + 1}}\right)}{y}\\ \mathbf{elif}\;t\_1 \leq 10^{+303}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 (- INFINITY))
     (* (/ y t) (/ z (+ (+ a 1.0) (* y (/ b t)))))
     (if (<= t_1 -1e-299)
       t_1
       (if (<= t_1 0.0)
         (-
          (/ z b)
          (/ (fma -1.0 (/ t (/ b x)) (/ (* z t) (/ (pow b 2.0) (+ a 1.0)))) y))
         (if (<= t_1 1e+303) 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 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / ((a + 1.0) + (y * (b / t))));
	} else if (t_1 <= -1e-299) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) - (fma(-1.0, (t / (b / x)), ((z * t) / (pow(b, 2.0) / (a + 1.0)))) / y);
	} else if (t_1 <= 1e+303) {
		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 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t)))));
	elseif (t_1 <= -1e-299)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z / b) - Float64(fma(-1.0, Float64(t / Float64(b / x)), Float64(Float64(z * t) / Float64((b ^ 2.0) / Float64(a + 1.0)))) / y));
	elseif (t_1 <= 1e+303)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return 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, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-299], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z / b), $MachinePrecision] - N[(N[(-1.0 * N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / N[(N[Power[b, 2.0], $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+303], t$95$1, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 34.2%

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

      1. *-commutative 34.2%

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

      2. associate-*l/ 53.3%

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

      3. *-commutative 53.3%

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

      4. associate-*l/ 53.3%

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

   3. Simplified 53.3%

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

   5. Taylor expanded in x around 0 57.7%

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

      1. times-frac 90.0%

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

      2. associate-+r+ 90.0%

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

      3. associate-*l/ 90.1%

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

      4. *-commutative 90.1%

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

   7. Simplified 90.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -9.99999999999999992e-300 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1e303

   1. Initial program 98.5%

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

   if -9.99999999999999992e-300 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 42.5%

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

      1. *-commutative 42.5%

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

      2. associate-*l/ 43.1%

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

      3. *-commutative 43.1%

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

      4. associate-*l/ 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in y around -inf 67.2%

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

      1. +-commutative 67.2%

         \[\leadsto \color{blue}{\frac{z}{b} + -1 \cdot \frac{-1 \cdot \frac{t \cdot x}{b} - -1 \cdot \frac{t \cdot \left(z \cdot \left(1 + a\right)\right)}{{b}^{2}}}{y}} \]

      2. mul-1-neg 67.2%

         \[\leadsto \frac{z}{b} + \color{blue}{\left(-\frac{-1 \cdot \frac{t \cdot x}{b} - -1 \cdot \frac{t \cdot \left(z \cdot \left(1 + a\right)\right)}{{b}^{2}}}{y}\right)} \]

      3. unsub-neg 67.2%

         \[\leadsto \color{blue}{\frac{z}{b} - \frac{-1 \cdot \frac{t \cdot x}{b} - -1 \cdot \frac{t \cdot \left(z \cdot \left(1 + a\right)\right)}{{b}^{2}}}{y}} \]

      4. fma-neg 67.2%

         \[\leadsto \frac{z}{b} - \frac{\color{blue}{\mathsf{fma}\left(-1, \frac{t \cdot x}{b}, --1 \cdot \frac{t \cdot \left(z \cdot \left(1 + a\right)\right)}{{b}^{2}}\right)}}{y} \]

      5. associate-/l* 74.9%

         \[\leadsto \frac{z}{b} - \frac{\mathsf{fma}\left(-1, \color{blue}{\frac{t}{\frac{b}{x}}}, --1 \cdot \frac{t \cdot \left(z \cdot \left(1 + a\right)\right)}{{b}^{2}}\right)}{y} \]

      6. mul-1-neg 74.9%

         \[\leadsto \frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, -\color{blue}{\left(-\frac{t \cdot \left(z \cdot \left(1 + a\right)\right)}{{b}^{2}}\right)}\right)}{y} \]

      7. remove-double-neg 74.9%

         \[\leadsto \frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, \color{blue}{\frac{t \cdot \left(z \cdot \left(1 + a\right)\right)}{{b}^{2}}}\right)}{y} \]

      8. associate-*r* 74.9%

         \[\leadsto \frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, \frac{\color{blue}{\left(t \cdot z\right) \cdot \left(1 + a\right)}}{{b}^{2}}\right)}{y} \]

      9. associate-/l* 75.3%

         \[\leadsto \frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, \color{blue}{\frac{t \cdot z}{\frac{{b}^{2}}{1 + a}}}\right)}{y} \]

   7. Simplified 75.3%

      \[\leadsto \color{blue}{\frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, \frac{t \cdot z}{\frac{{b}^{2}}{1 + a}}\right)}{y}} \]

   if 1e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 9.7%

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

      1. *-commutative 9.7%

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

      2. associate-*l/ 20.2%

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

      3. *-commutative 20.2%

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

      4. associate-*l/ 28.0%

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

   3. Simplified 28.0%

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

   5. Taylor expanded in t around 0 82.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-299}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, \frac{z \cdot t}{\frac{{b}^{2}}{a + 1}}\right)}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+303}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \left(a + 1\right) + y \cdot \frac{b}{t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t\_2}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-253}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t\_2}\\ \mathbf{elif}\;t\_1 \leq 10^{+303}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (+ (+ a 1.0) (* y (/ b t)))))
   (if (<= t_1 (- INFINITY))
     (* (/ y t) (/ z t_2))
     (if (<= t_1 -2e-192)
       t_1
       (if (<= t_1 2e-253)
         (/ (+ x (* y (/ z t))) t_2)
         (if (<= t_1 1e+303) 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 t_2 = (a + 1.0) + (y * (b / t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / t_2);
	} else if (t_1 <= -2e-192) {
		tmp = t_1;
	} else if (t_1 <= 2e-253) {
		tmp = (x + (y * (z / t))) / t_2;
	} else if (t_1 <= 1e+303) {
		tmp = t_1;
	} 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 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = (a + 1.0) + (y * (b / t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / t_2);
	} else if (t_1 <= -2e-192) {
		tmp = t_1;
	} else if (t_1 <= 2e-253) {
		tmp = (x + (y * (z / t))) / t_2;
	} else if (t_1 <= 1e+303) {
		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))
	t_2 = (a + 1.0) + (y * (b / t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y / t) * (z / t_2)
	elif t_1 <= -2e-192:
		tmp = t_1
	elif t_1 <= 2e-253:
		tmp = (x + (y * (z / t))) / t_2
	elif t_1 <= 1e+303:
		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)))
	t_2 = Float64(Float64(a + 1.0) + Float64(y * Float64(b / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / t_2));
	elseif (t_1 <= -2e-192)
		tmp = t_1;
	elseif (t_1 <= 2e-253)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_2);
	elseif (t_1 <= 1e+303)
		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));
	t_2 = (a + 1.0) + (y * (b / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y / t) * (z / t_2);
	elseif (t_1 <= -2e-192)
		tmp = t_1;
	elseif (t_1 <= 2e-253)
		tmp = (x + (y * (z / t))) / t_2;
	elseif (t_1 <= 1e+303)
		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]}, Block[{t$95$2 = N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-192], t$95$1, If[LessEqual[t$95$1, 2e-253], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 1e+303], t$95$1, N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 34.2%

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

      1. *-commutative 34.2%

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

      2. associate-*l/ 53.3%

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

      3. *-commutative 53.3%

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

      4. associate-*l/ 53.3%

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

   3. Simplified 53.3%

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

   5. Taylor expanded in x around 0 57.7%

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

      1. times-frac 90.0%

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

      2. associate-+r+ 90.0%

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

      3. associate-*l/ 90.1%

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

      4. *-commutative 90.1%

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

   7. Simplified 90.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -2.0000000000000002e-192 or 2.0000000000000001e-253 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1e303

   1. Initial program 99.6%

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

   if -2.0000000000000002e-192 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e-253

   1. Initial program 57.5%

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

      1. *-commutative 57.5%

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

      2. associate-*l/ 60.3%

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

      3. *-commutative 60.3%

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

      4. associate-*l/ 78.9%

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

   3. Simplified 78.9%

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

   if 1e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 9.7%

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

      1. *-commutative 9.7%

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

      2. associate-*l/ 20.2%

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

      3. *-commutative 20.2%

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

      4. associate-*l/ 28.0%

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

   3. Simplified 28.0%

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

   5. Taylor expanded in t around 0 82.1%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-192}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{-253}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+303}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq -0.011:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \frac{y}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2e+166)
   (/ z b)
   (if (<= y -1.02e+15)
     (* (/ y t) (/ z (+ a 1.0)))
     (if (<= y -0.011)
       (/ z b)
       (if (<= y -6.6e-100)
         (/ x (+ 1.0 (/ (* y b) t)))
         (if (<= y -7e-150)
           (* z (/ y (* t (+ a 1.0))))
           (if (<= y 9e+92) (/ x (+ a 1.0)) (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2e+166) {
		tmp = z / b;
	} else if (y <= -1.02e+15) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= -0.011) {
		tmp = z / b;
	} else if (y <= -6.6e-100) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (y <= -7e-150) {
		tmp = z * (y / (t * (a + 1.0)));
	} else if (y <= 9e+92) {
		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 (y <= (-2d+166)) then
        tmp = z / b
    else if (y <= (-1.02d+15)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= (-0.011d0)) then
        tmp = z / b
    else if (y <= (-6.6d-100)) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (y <= (-7d-150)) then
        tmp = z * (y / (t * (a + 1.0d0)))
    else if (y <= 9d+92) 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 (y <= -2e+166) {
		tmp = z / b;
	} else if (y <= -1.02e+15) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= -0.011) {
		tmp = z / b;
	} else if (y <= -6.6e-100) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (y <= -7e-150) {
		tmp = z * (y / (t * (a + 1.0)));
	} else if (y <= 9e+92) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2e+166:
		tmp = z / b
	elif y <= -1.02e+15:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= -0.011:
		tmp = z / b
	elif y <= -6.6e-100:
		tmp = x / (1.0 + ((y * b) / t))
	elif y <= -7e-150:
		tmp = z * (y / (t * (a + 1.0)))
	elif y <= 9e+92:
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2e+166)
		tmp = Float64(z / b);
	elseif (y <= -1.02e+15)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= -0.011)
		tmp = Float64(z / b);
	elseif (y <= -6.6e-100)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (y <= -7e-150)
		tmp = Float64(z * Float64(y / Float64(t * Float64(a + 1.0))));
	elseif (y <= 9e+92)
		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 (y <= -2e+166)
		tmp = z / b;
	elseif (y <= -1.02e+15)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= -0.011)
		tmp = z / b;
	elseif (y <= -6.6e-100)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (y <= -7e-150)
		tmp = z * (y / (t * (a + 1.0)));
	elseif (y <= 9e+92)
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2e+166], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.02e+15], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.011], N[(z / b), $MachinePrecision], If[LessEqual[y, -6.6e-100], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-150], N[(z * N[(y / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+92], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.99999999999999988e166 or -1.02e15 < y < -0.010999999999999999 or 8.9999999999999998e92 < y

   1. Initial program 41.1%

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

      1. *-commutative 41.1%

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

      2. associate-*l/ 45.4%

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

      3. *-commutative 45.4%

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

      4. associate-*l/ 56.6%

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

   3. Simplified 56.6%

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

   5. Taylor expanded in t around 0 65.5%

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

   if -1.99999999999999988e166 < y < -1.02e15

   1. Initial program 67.8%

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

      1. *-commutative 67.8%

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

      2. associate-*l/ 70.0%

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

      3. *-commutative 70.0%

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

      4. associate-*l/ 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in x around 0 43.1%

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

   6. Taylor expanded in y around 0 32.5%

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

      1. times-frac 41.8%

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

   8. Simplified 41.8%

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

   if -0.010999999999999999 < y < -6.59999999999999993e-100

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

      4. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around inf 69.7%

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

      1. associate-+r+ 69.7%

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

      2. associate-*l/ 69.7%

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

      3. *-commutative 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in a around 0 51.2%

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

   if -6.59999999999999993e-100 < y < -6.9999999999999996e-150

   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. *-commutative 87.8%

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

      2. associate-*l/ 76.0%

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

      3. *-commutative 76.0%

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

      4. associate-*l/ 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in x around 0 75.3%

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

   6. Taylor expanded in y around 0 75.3%

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

      1. associate-/l* 63.8%

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

      2. associate-/r/ 75.1%

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

   8. Applied egg-rr 75.1%

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

   if -6.9999999999999996e-150 < y < 8.9999999999999998e92

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-*l/ 90.0%

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

      3. *-commutative 90.0%

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

      4. associate-*l/ 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in t around inf 61.0%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq -0.011:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \frac{y}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq -0.2:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2e+166)
   (/ z b)
   (if (<= y -1.1e+14)
     (* (/ y t) (/ z (+ a 1.0)))
     (if (<= y -0.2)
       (/ z b)
       (if (<= y -6e-102)
         (/ x (+ 1.0 (/ (* y b) t)))
         (if (<= y -6e-150)
           (/ (* y z) (* t (+ a 1.0)))
           (if (<= y 9e+92) (/ x (+ a 1.0)) (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2e+166) {
		tmp = z / b;
	} else if (y <= -1.1e+14) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= -0.2) {
		tmp = z / b;
	} else if (y <= -6e-102) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (y <= -6e-150) {
		tmp = (y * z) / (t * (a + 1.0));
	} else if (y <= 9e+92) {
		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 (y <= (-2d+166)) then
        tmp = z / b
    else if (y <= (-1.1d+14)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= (-0.2d0)) then
        tmp = z / b
    else if (y <= (-6d-102)) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (y <= (-6d-150)) then
        tmp = (y * z) / (t * (a + 1.0d0))
    else if (y <= 9d+92) 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 (y <= -2e+166) {
		tmp = z / b;
	} else if (y <= -1.1e+14) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= -0.2) {
		tmp = z / b;
	} else if (y <= -6e-102) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (y <= -6e-150) {
		tmp = (y * z) / (t * (a + 1.0));
	} else if (y <= 9e+92) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2e+166:
		tmp = z / b
	elif y <= -1.1e+14:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= -0.2:
		tmp = z / b
	elif y <= -6e-102:
		tmp = x / (1.0 + ((y * b) / t))
	elif y <= -6e-150:
		tmp = (y * z) / (t * (a + 1.0))
	elif y <= 9e+92:
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2e+166)
		tmp = Float64(z / b);
	elseif (y <= -1.1e+14)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= -0.2)
		tmp = Float64(z / b);
	elseif (y <= -6e-102)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (y <= -6e-150)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(a + 1.0)));
	elseif (y <= 9e+92)
		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 (y <= -2e+166)
		tmp = z / b;
	elseif (y <= -1.1e+14)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= -0.2)
		tmp = z / b;
	elseif (y <= -6e-102)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (y <= -6e-150)
		tmp = (y * z) / (t * (a + 1.0));
	elseif (y <= 9e+92)
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2e+166], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.1e+14], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.2], N[(z / b), $MachinePrecision], If[LessEqual[y, -6e-102], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e-150], N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+92], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.99999999999999988e166 or -1.1e14 < y < -0.20000000000000001 or 8.9999999999999998e92 < y

   1. Initial program 41.1%

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

      1. *-commutative 41.1%

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

      2. associate-*l/ 45.4%

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

      3. *-commutative 45.4%

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

      4. associate-*l/ 56.6%

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

   3. Simplified 56.6%

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

   5. Taylor expanded in t around 0 65.5%

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

   if -1.99999999999999988e166 < y < -1.1e14

   1. Initial program 67.8%

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

      1. *-commutative 67.8%

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

      2. associate-*l/ 70.0%

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

      3. *-commutative 70.0%

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

      4. associate-*l/ 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in x around 0 43.1%

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

   6. Taylor expanded in y around 0 32.5%

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

      1. times-frac 41.8%

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

   8. Simplified 41.8%

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

   if -0.20000000000000001 < y < -6e-102

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

      4. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around inf 69.7%

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

      1. associate-+r+ 69.7%

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

      2. associate-*l/ 69.7%

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

      3. *-commutative 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in a around 0 51.2%

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

   if -6e-102 < y < -6.0000000000000003e-150

   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. *-commutative 87.8%

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

      2. associate-*l/ 76.0%

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

      3. *-commutative 76.0%

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

      4. associate-*l/ 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in x around 0 75.3%

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

   6. Taylor expanded in y around 0 75.3%

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

   if -6.0000000000000003e-150 < y < 8.9999999999999998e92

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-*l/ 90.0%

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

      3. *-commutative 90.0%

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

      4. associate-*l/ 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in t around inf 61.0%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq -0.2:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+97}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq -0.0035:\\ \;\;\;\;\frac{y \cdot z}{t + y \cdot b}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2e+166)
   (/ z b)
   (if (<= y -2.8e+97)
     (* (/ y t) (/ z (+ a 1.0)))
     (if (<= y -0.0035)
       (/ (* y z) (+ t (* y b)))
       (if (<= y -7.6e-98)
         (/ x (+ 1.0 (/ (* y b) t)))
         (if (<= y -7e-150)
           (/ (* y z) (* t (+ a 1.0)))
           (if (<= y 1.3e+93) (/ x (+ a 1.0)) (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2e+166) {
		tmp = z / b;
	} else if (y <= -2.8e+97) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= -0.0035) {
		tmp = (y * z) / (t + (y * b));
	} else if (y <= -7.6e-98) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (y <= -7e-150) {
		tmp = (y * z) / (t * (a + 1.0));
	} else if (y <= 1.3e+93) {
		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 (y <= (-2d+166)) then
        tmp = z / b
    else if (y <= (-2.8d+97)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= (-0.0035d0)) then
        tmp = (y * z) / (t + (y * b))
    else if (y <= (-7.6d-98)) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (y <= (-7d-150)) then
        tmp = (y * z) / (t * (a + 1.0d0))
    else if (y <= 1.3d+93) 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 (y <= -2e+166) {
		tmp = z / b;
	} else if (y <= -2.8e+97) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= -0.0035) {
		tmp = (y * z) / (t + (y * b));
	} else if (y <= -7.6e-98) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (y <= -7e-150) {
		tmp = (y * z) / (t * (a + 1.0));
	} else if (y <= 1.3e+93) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2e+166:
		tmp = z / b
	elif y <= -2.8e+97:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= -0.0035:
		tmp = (y * z) / (t + (y * b))
	elif y <= -7.6e-98:
		tmp = x / (1.0 + ((y * b) / t))
	elif y <= -7e-150:
		tmp = (y * z) / (t * (a + 1.0))
	elif y <= 1.3e+93:
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2e+166)
		tmp = Float64(z / b);
	elseif (y <= -2.8e+97)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= -0.0035)
		tmp = Float64(Float64(y * z) / Float64(t + Float64(y * b)));
	elseif (y <= -7.6e-98)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (y <= -7e-150)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(a + 1.0)));
	elseif (y <= 1.3e+93)
		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 (y <= -2e+166)
		tmp = z / b;
	elseif (y <= -2.8e+97)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= -0.0035)
		tmp = (y * z) / (t + (y * b));
	elseif (y <= -7.6e-98)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (y <= -7e-150)
		tmp = (y * z) / (t * (a + 1.0));
	elseif (y <= 1.3e+93)
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2e+166], N[(z / b), $MachinePrecision], If[LessEqual[y, -2.8e+97], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.0035], N[(N[(y * z), $MachinePrecision] / N[(t + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.6e-98], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-150], N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+93], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.99999999999999988e166 or 1.3e93 < y

   1. Initial program 39.7%

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

      1. *-commutative 39.7%

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

      2. associate-*l/ 44.1%

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

      3. *-commutative 44.1%

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

      4. associate-*l/ 55.5%

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

   3. Simplified 55.5%

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

   5. Taylor expanded in t around 0 64.7%

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

   if -1.99999999999999988e166 < y < -2.7999999999999999e97

   1. Initial program 65.9%

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

      1. *-commutative 65.9%

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

      2. associate-*l/ 69.8%

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

      3. *-commutative 69.8%

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

      4. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in x around 0 38.1%

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

   6. Taylor expanded in y around 0 32.2%

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

      1. times-frac 43.1%

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

   8. Simplified 43.1%

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

   if -2.7999999999999999e97 < y < -0.00350000000000000007

   1. Initial program 74.1%

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

      1. *-commutative 74.1%

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

      2. associate-*l/ 74.3%

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

      3. *-commutative 74.3%

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

      4. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in x around 0 56.4%

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

   6. Taylor expanded in t around 0 62.3%

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

   7. Taylor expanded in a around 0 48.5%

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

   if -0.00350000000000000007 < y < -7.6000000000000006e-98

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

      4. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around inf 69.7%

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

      1. associate-+r+ 69.7%

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

      2. associate-*l/ 69.7%

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

      3. *-commutative 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in a around 0 51.2%

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

   if -7.6000000000000006e-98 < y < -6.9999999999999996e-150

   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. *-commutative 87.8%

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

      2. associate-*l/ 76.0%

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

      3. *-commutative 76.0%

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

      4. associate-*l/ 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in x around 0 75.3%

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

   6. Taylor expanded in y around 0 75.3%

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

   if -6.9999999999999996e-150 < y < 1.3e93

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-*l/ 90.0%

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

      3. *-commutative 90.0%

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

      4. associate-*l/ 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in t around inf 61.0%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+97}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq -0.0035:\\ \;\;\;\;\frac{y \cdot z}{t + y \cdot b}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-265}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+93}:\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) \cdot \frac{1}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2e+166)
   (/ z b)
   (if (<= y 9.6e-265)
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (if (<= y 1.65e-91)
       (/ x (+ 1.0 (+ a (/ (* y b) t))))
       (if (<= y 1.05e+93)
         (* (+ x (* y (/ z t))) (/ 1.0 (+ a 1.0)))
         (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2e+166) {
		tmp = z / b;
	} else if (y <= 9.6e-265) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 1.65e-91) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 1.05e+93) {
		tmp = (x + (y * (z / t))) * (1.0 / (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 (y <= (-2d+166)) then
        tmp = z / b
    else if (y <= 9.6d-265) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (y <= 1.65d-91) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (y <= 1.05d+93) then
        tmp = (x + (y * (z / t))) * (1.0d0 / (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 (y <= -2e+166) {
		tmp = z / b;
	} else if (y <= 9.6e-265) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 1.65e-91) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 1.05e+93) {
		tmp = (x + (y * (z / t))) * (1.0 / (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2e+166:
		tmp = z / b
	elif y <= 9.6e-265:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif y <= 1.65e-91:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif y <= 1.05e+93:
		tmp = (x + (y * (z / t))) * (1.0 / (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2e+166)
		tmp = Float64(z / b);
	elseif (y <= 9.6e-265)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (y <= 1.65e-91)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (y <= 1.05e+93)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) * Float64(1.0 / 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 (y <= -2e+166)
		tmp = z / b;
	elseif (y <= 9.6e-265)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (y <= 1.65e-91)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (y <= 1.05e+93)
		tmp = (x + (y * (z / t))) * (1.0 / (a + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2e+166], N[(z / b), $MachinePrecision], If[LessEqual[y, 9.6e-265], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-91], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+93], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.99999999999999988e166 or 1.0499999999999999e93 < y

   1. Initial program 39.7%

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

      1. *-commutative 39.7%

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

      2. associate-*l/ 44.1%

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

      3. *-commutative 44.1%

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

      4. associate-*l/ 55.5%

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

   3. Simplified 55.5%

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

   5. Taylor expanded in t around 0 64.7%

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

   if -1.99999999999999988e166 < y < 9.5999999999999999e-265

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-*l/ 83.9%

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

      3. *-commutative 83.9%

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

      4. associate-*l/ 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in b around 0 72.3%

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

   if 9.5999999999999999e-265 < y < 1.65000000000000006e-91

   1. Initial program 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l/ 90.4%

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

      3. *-commutative 90.4%

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

      4. associate-*l/ 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in x around inf 87.3%

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

   if 1.65000000000000006e-91 < y < 1.0499999999999999e93

   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. *-commutative 84.4%

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

      2. associate-*l/ 89.0%

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

      3. *-commutative 89.0%

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

      4. associate-*l/ 87.0%

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

   3. Simplified 87.0%

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

      1. div-inv 86.8%

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

      2. +-commutative 86.8%

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

      3. fma-def 86.8%

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

      4. associate-*l/ 88.9%

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

      5. *-commutative 88.9%

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

      6. associate-+l+ 88.9%

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

      7. +-commutative 88.9%

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

      8. associate-/l* 88.1%

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

      9. associate-/r/ 88.8%

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

      10. fma-def 88.8%

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

   6. Applied egg-rr 88.8%

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

   7. Taylor expanded in y around 0 67.9%

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

      1. fma-udef 67.9%

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

   9. Applied egg-rr 67.9%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-265}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+93}:\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) \cdot \frac{1}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq -0.15:\\ \;\;\;\;\frac{y \cdot z}{t + y \cdot b}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2e+166)
   (/ z b)
   (if (<= y -2.7e+102)
     (* (/ y t) (/ z (+ a 1.0)))
     (if (<= y -0.15)
       (/ (* y z) (+ t (* y b)))
       (if (<= y 2.2e+91) (/ x (+ 1.0 (+ a (/ (* y b) t)))) (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2e+166) {
		tmp = z / b;
	} else if (y <= -2.7e+102) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= -0.15) {
		tmp = (y * z) / (t + (y * b));
	} else if (y <= 2.2e+91) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} 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 (y <= (-2d+166)) then
        tmp = z / b
    else if (y <= (-2.7d+102)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= (-0.15d0)) then
        tmp = (y * z) / (t + (y * b))
    else if (y <= 2.2d+91) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    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 (y <= -2e+166) {
		tmp = z / b;
	} else if (y <= -2.7e+102) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= -0.15) {
		tmp = (y * z) / (t + (y * b));
	} else if (y <= 2.2e+91) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2e+166:
		tmp = z / b
	elif y <= -2.7e+102:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= -0.15:
		tmp = (y * z) / (t + (y * b))
	elif y <= 2.2e+91:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2e+166)
		tmp = Float64(z / b);
	elseif (y <= -2.7e+102)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= -0.15)
		tmp = Float64(Float64(y * z) / Float64(t + Float64(y * b)));
	elseif (y <= 2.2e+91)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2e+166)
		tmp = z / b;
	elseif (y <= -2.7e+102)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= -0.15)
		tmp = (y * z) / (t + (y * b));
	elseif (y <= 2.2e+91)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2e+166], N[(z / b), $MachinePrecision], If[LessEqual[y, -2.7e+102], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.15], N[(N[(y * z), $MachinePrecision] / N[(t + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+91], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.99999999999999988e166 or 2.19999999999999999e91 < y

   1. Initial program 40.0%

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

      1. *-commutative 40.0%

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

      2. associate-*l/ 44.2%

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

      3. *-commutative 44.2%

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

      4. associate-*l/ 55.4%

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

   3. Simplified 55.4%

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

   5. Taylor expanded in t around 0 64.3%

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

   if -1.99999999999999988e166 < y < -2.7000000000000001e102

   1. Initial program 65.9%

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

      1. *-commutative 65.9%

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

      2. associate-*l/ 69.8%

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

      3. *-commutative 69.8%

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

      4. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in x around 0 38.1%

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

   6. Taylor expanded in y around 0 32.2%

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

      1. times-frac 43.1%

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

   8. Simplified 43.1%

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

   if -2.7000000000000001e102 < y < -0.149999999999999994

   1. Initial program 74.1%

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

      1. *-commutative 74.1%

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

      2. associate-*l/ 74.3%

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

      3. *-commutative 74.3%

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

      4. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in x around 0 56.4%

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

   6. Taylor expanded in t around 0 62.3%

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

   7. Taylor expanded in a around 0 48.5%

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

   if -0.149999999999999994 < y < 2.19999999999999999e91

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in x around inf 70.2%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq -0.15:\\ \;\;\;\;\frac{y \cdot z}{t + y \cdot b}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+112}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;y \leq -0.0062:\\ \;\;\;\;\frac{y \cdot z}{t + y \cdot b}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.1e+166)
   (/ z b)
   (if (<= y -6.2e+112)
     (/ x (+ (+ a 1.0) (* y (/ b t))))
     (if (<= y -0.0062)
       (/ (* y z) (+ t (* y b)))
       (if (<= y 6.4e+89) (/ x (+ 1.0 (+ a (/ (* y b) t)))) (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.1e+166) {
		tmp = z / b;
	} else if (y <= -6.2e+112) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if (y <= -0.0062) {
		tmp = (y * z) / (t + (y * b));
	} else if (y <= 6.4e+89) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} 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 (y <= (-3.1d+166)) then
        tmp = z / b
    else if (y <= (-6.2d+112)) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    else if (y <= (-0.0062d0)) then
        tmp = (y * z) / (t + (y * b))
    else if (y <= 6.4d+89) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    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 (y <= -3.1e+166) {
		tmp = z / b;
	} else if (y <= -6.2e+112) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if (y <= -0.0062) {
		tmp = (y * z) / (t + (y * b));
	} else if (y <= 6.4e+89) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.1e+166:
		tmp = z / b
	elif y <= -6.2e+112:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	elif y <= -0.0062:
		tmp = (y * z) / (t + (y * b))
	elif y <= 6.4e+89:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.1e+166)
		tmp = Float64(z / b);
	elseif (y <= -6.2e+112)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (y <= -0.0062)
		tmp = Float64(Float64(y * z) / Float64(t + Float64(y * b)));
	elseif (y <= 6.4e+89)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.1e+166)
		tmp = z / b;
	elseif (y <= -6.2e+112)
		tmp = x / ((a + 1.0) + (y * (b / t)));
	elseif (y <= -0.0062)
		tmp = (y * z) / (t + (y * b));
	elseif (y <= 6.4e+89)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.1e+166], N[(z / b), $MachinePrecision], If[LessEqual[y, -6.2e+112], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.0062], N[(N[(y * z), $MachinePrecision] / N[(t + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+89], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.09999999999999983e166 or 6.39999999999999974e89 < y

   1. Initial program 40.0%

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

      1. *-commutative 40.0%

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

      2. associate-*l/ 44.2%

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

      3. *-commutative 44.2%

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

      4. associate-*l/ 55.4%

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

   3. Simplified 55.4%

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

   5. Taylor expanded in t around 0 64.3%

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

   if -3.09999999999999983e166 < y < -6.19999999999999965e112

   1. Initial program 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*l/ 65.8%

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

      3. *-commutative 65.8%

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

      4. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in x around inf 32.7%

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

      1. associate-+r+ 32.7%

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

      2. associate-*l/ 45.5%

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

      3. *-commutative 45.5%

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

   7. Simplified 45.5%

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

   if -6.19999999999999965e112 < y < -0.00619999999999999978

   1. Initial program 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-*l/ 77.2%

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

      3. *-commutative 77.2%

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

      4. associate-*l/ 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in x around 0 55.9%

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

   6. Taylor expanded in t around 0 61.1%

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

   7. Taylor expanded in a around 0 49.0%

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

   if -0.00619999999999999978 < y < 6.39999999999999974e89

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in x around inf 70.2%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+112}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;y \leq -0.0062:\\ \;\;\;\;\frac{y \cdot z}{t + y \cdot b}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+107}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq -0.18:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2e+166)
   (/ z b)
   (if (<= y -2.65e+107)
     (* (/ y t) (/ z (+ a 1.0)))
     (if (<= y -0.18)
       (/ (* y z) (+ (* y b) (* t a)))
       (if (<= y 5e+90) (/ x (+ 1.0 (+ a (/ (* y b) t)))) (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2e+166) {
		tmp = z / b;
	} else if (y <= -2.65e+107) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= -0.18) {
		tmp = (y * z) / ((y * b) + (t * a));
	} else if (y <= 5e+90) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} 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 (y <= (-2d+166)) then
        tmp = z / b
    else if (y <= (-2.65d+107)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= (-0.18d0)) then
        tmp = (y * z) / ((y * b) + (t * a))
    else if (y <= 5d+90) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    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 (y <= -2e+166) {
		tmp = z / b;
	} else if (y <= -2.65e+107) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= -0.18) {
		tmp = (y * z) / ((y * b) + (t * a));
	} else if (y <= 5e+90) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2e+166:
		tmp = z / b
	elif y <= -2.65e+107:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= -0.18:
		tmp = (y * z) / ((y * b) + (t * a))
	elif y <= 5e+90:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2e+166)
		tmp = Float64(z / b);
	elseif (y <= -2.65e+107)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= -0.18)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * a)));
	elseif (y <= 5e+90)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2e+166)
		tmp = z / b;
	elseif (y <= -2.65e+107)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= -0.18)
		tmp = (y * z) / ((y * b) + (t * a));
	elseif (y <= 5e+90)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2e+166], N[(z / b), $MachinePrecision], If[LessEqual[y, -2.65e+107], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.18], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+90], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.99999999999999988e166 or 5.0000000000000004e90 < y

   1. Initial program 40.0%

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

      1. *-commutative 40.0%

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

      2. associate-*l/ 44.2%

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

      3. *-commutative 44.2%

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

      4. associate-*l/ 55.4%

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

   3. Simplified 55.4%

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

   5. Taylor expanded in t around 0 64.3%

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

   if -1.99999999999999988e166 < y < -2.65e107

   1. Initial program 65.9%

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

      1. *-commutative 65.9%

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

      2. associate-*l/ 69.8%

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

      3. *-commutative 69.8%

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

      4. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in x around 0 38.1%

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

   6. Taylor expanded in y around 0 32.2%

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

      1. times-frac 43.1%

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

   8. Simplified 43.1%

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

   if -2.65e107 < y < -0.17999999999999999

   1. Initial program 74.1%

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

      1. *-commutative 74.1%

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

      2. associate-*l/ 74.3%

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

      3. *-commutative 74.3%

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

      4. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in x around 0 56.4%

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

   6. Taylor expanded in t around 0 62.3%

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

   7. Taylor expanded in a around inf 55.5%

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

   if -0.17999999999999999 < y < 5.0000000000000004e90

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in x around inf 70.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+107}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq -0.18:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot a}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ a 1.0))))
   (if (<= y -4.1e+166)
     (/ z b)
     (if (<= y 1.52e-266)
       t_1
       (if (<= y 6.2e+75)
         (/ x (+ 1.0 (+ a (/ (* y b) t))))
         (if (<= y 1e+94) 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);
	double tmp;
	if (y <= -4.1e+166) {
		tmp = z / b;
	} else if (y <= 1.52e-266) {
		tmp = t_1;
	} else if (y <= 6.2e+75) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 1e+94) {
		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)
    if (y <= (-4.1d+166)) then
        tmp = z / b
    else if (y <= 1.52d-266) then
        tmp = t_1
    else if (y <= 6.2d+75) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (y <= 1d+94) 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);
	double tmp;
	if (y <= -4.1e+166) {
		tmp = z / b;
	} else if (y <= 1.52e-266) {
		tmp = t_1;
	} else if (y <= 6.2e+75) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 1e+94) {
		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)
	tmp = 0
	if y <= -4.1e+166:
		tmp = z / b
	elif y <= 1.52e-266:
		tmp = t_1
	elif y <= 6.2e+75:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif y <= 1e+94:
		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(a + 1.0))
	tmp = 0.0
	if (y <= -4.1e+166)
		tmp = Float64(z / b);
	elseif (y <= 1.52e-266)
		tmp = t_1;
	elseif (y <= 6.2e+75)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (y <= 1e+94)
		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);
	tmp = 0.0;
	if (y <= -4.1e+166)
		tmp = z / b;
	elseif (y <= 1.52e-266)
		tmp = t_1;
	elseif (y <= 6.2e+75)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (y <= 1e+94)
		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[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+166], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.52e-266], t$95$1, If[LessEqual[y, 6.2e+75], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+94], t$95$1, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1000000000000003e166 or 1e94 < y

   1. Initial program 39.7%

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

      1. *-commutative 39.7%

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

      2. associate-*l/ 44.1%

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

      3. *-commutative 44.1%

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

      4. associate-*l/ 55.5%

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

   3. Simplified 55.5%

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

   5. Taylor expanded in t around 0 64.7%

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

   if -4.1000000000000003e166 < y < 1.52000000000000001e-266 or 6.2000000000000002e75 < y < 1e94

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-*l/ 84.0%

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

      3. *-commutative 84.0%

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

      4. associate-*l/ 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in b around 0 73.2%

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

   if 1.52000000000000001e-266 < y < 6.2000000000000002e75

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

      2. associate-*l/ 90.0%

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

      3. *-commutative 90.0%

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

      4. associate-*l/ 84.3%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in x around inf 73.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-266}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 10^{+94}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+231} \lor \neg \left(y \leq 1.1 \cdot 10^{+109}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.75e+231) (not (<= y 1.1e+109)))
   (/ z b)
   (/ (+ 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) {
	double tmp;
	if ((y <= -1.75e+231) || !(y <= 1.1e+109)) {
		tmp = z / b;
	} else {
		tmp = (x + (y * (z / t))) / ((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) :: tmp
    if ((y <= (-1.75d+231)) .or. (.not. (y <= 1.1d+109))) then
        tmp = z / b
    else
        tmp = (x + (y * (z / t))) / ((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 tmp;
	if ((y <= -1.75e+231) || !(y <= 1.1e+109)) {
		tmp = z / b;
	} else {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.75e+231) or not (y <= 1.1e+109):
		tmp = z / b
	else:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.75e+231) || !(y <= 1.1e+109))
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / 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)
	tmp = 0.0;
	if ((y <= -1.75e+231) || ~((y <= 1.1e+109)))
		tmp = z / b;
	else
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.75e+231], N[Not[LessEqual[y, 1.1e+109]], $MachinePrecision]], N[(z / b), $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]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7499999999999999e231 or 1.1e109 < y

   1. Initial program 37.0%

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

      1. *-commutative 37.0%

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

      2. associate-*l/ 39.5%

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

      3. *-commutative 39.5%

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

      4. associate-*l/ 48.5%

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

   3. Simplified 48.5%

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

   5. Taylor expanded in t around 0 67.8%

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

   if -1.7499999999999999e231 < y < 1.1e109

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

      2. associate-*l/ 83.7%

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

      3. *-commutative 83.7%

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

      4. associate-*l/ 84.6%

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

   3. Simplified 84.6%

      \[\leadsto \color{blue}{\frac{x + \frac{z}{t} \cdot y}{\left(a + 1\right) + \frac{b}{t} \cdot y}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+231} \lor \neg \left(y \leq 1.1 \cdot 10^{+109}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+230} \lor \neg \left(y \leq 1.1 \cdot 10^{+109}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.1e+230) (not (<= y 1.1e+109)))
   (/ z b)
   (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (/ y (/ t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.1e+230) || !(y <= 1.1e+109)) {
		tmp = z / b;
	} else {
		tmp = (x + (y / (t / z))) / (a + (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 ((y <= (-3.1d+230)) .or. (.not. (y <= 1.1d+109))) then
        tmp = z / b
    else
        tmp = (x + (y / (t / z))) / (a + (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 ((y <= -3.1e+230) || !(y <= 1.1e+109)) {
		tmp = z / b;
	} else {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.1e+230) or not (y <= 1.1e+109):
		tmp = z / b
	else:
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.1e+230) || !(y <= 1.1e+109))
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 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 ((y <= -3.1e+230) || ~((y <= 1.1e+109)))
		tmp = z / b;
	else
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.1e+230], N[Not[LessEqual[y, 1.1e+109]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.09999999999999981e230 or 1.1e109 < y

   1. Initial program 37.0%

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

      1. *-commutative 37.0%

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

      2. associate-*l/ 39.5%

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

      3. *-commutative 39.5%

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

      4. associate-*l/ 48.5%

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

   3. Simplified 48.5%

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

   5. Taylor expanded in t around 0 67.8%

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

   if -3.09999999999999981e230 < y < 1.1e109

   1. Initial program 84.1%

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

      1. associate-/l* 84.2%

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

      2. associate-+l+ 84.2%

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

      3. associate-/l* 85.8%

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

   3. Simplified 85.8%

      \[\leadsto \color{blue}{\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+230} \lor \neg \left(y \leq 1.1 \cdot 10^{+109}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-8} \lor \neg \left(a \leq 1.1 \cdot 10^{-10}\right):\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) \cdot \frac{1}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{1 + \frac{y \cdot b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.1e-8) (not (<= a 1.1e-10)))
   (* (+ x (* y (/ z t))) (/ 1.0 (+ 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 <= -1.1e-8) || !(a <= 1.1e-10)) {
		tmp = (x + (y * (z / t))) * (1.0 / (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 <= (-1.1d-8)) .or. (.not. (a <= 1.1d-10))) then
        tmp = (x + (y * (z / t))) * (1.0d0 / (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 <= -1.1e-8) || !(a <= 1.1e-10)) {
		tmp = (x + (y * (z / t))) * (1.0 / (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 <= -1.1e-8) or not (a <= 1.1e-10):
		tmp = (x + (y * (z / t))) * (1.0 / (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 ((a <= -1.1e-8) || !(a <= 1.1e-10))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) * Float64(1.0 / Float64(a + 1.0)));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(1.0 + Float64(Float64(y * b) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.1e-8) || ~((a <= 1.1e-10)))
		tmp = (x + (y * (z / t))) * (1.0 / (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[a, -1.1e-8], N[Not[LessEqual[a, 1.1e-10]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0999999999999999e-8 or 1.09999999999999995e-10 < a

   1. Initial program 72.0%

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

      1. *-commutative 72.0%

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

      2. associate-*l/ 73.2%

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

      3. *-commutative 73.2%

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

      4. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

      1. div-inv 78.2%

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

      2. +-commutative 78.2%

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

      3. fma-def 78.2%

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

      4. associate-*l/ 73.0%

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

      5. *-commutative 73.0%

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

      6. associate-+l+ 73.0%

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

      7. +-commutative 73.0%

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

      8. associate-/l* 78.1%

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

      9. associate-/r/ 75.8%

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

      10. fma-def 75.8%

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

   6. Applied egg-rr 75.8%

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

   7. Taylor expanded in y around 0 64.9%

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

      1. fma-udef 64.9%

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

   9. Applied egg-rr 64.9%

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

   if -1.0999999999999999e-8 < a < 1.09999999999999995e-10

   1. Initial program 72.6%

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

      1. *-commutative 72.6%

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

      2. associate-*l/ 72.1%

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

      3. *-commutative 72.1%

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

      4. associate-*l/ 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in a around 0 72.6%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-8} \lor \neg \left(a \leq 1.1 \cdot 10^{-10}\right):\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) \cdot \frac{1}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{1 + \frac{y \cdot b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -1 \cdot 10^{+19} \lor \neg \left(a + 1 \leq 1.00002\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ a 1.0) -1e+19) (not (<= (+ a 1.0) 1.00002)))
   (/ (+ x (/ y (/ t z))) a)
   (/ x (+ 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) <= -1e+19) || !((a + 1.0) <= 1.00002)) {
		tmp = (x + (y / (t / z))) / a;
	} else {
		tmp = x / (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) <= (-1d+19)) .or. (.not. ((a + 1.0d0) <= 1.00002d0))) then
        tmp = (x + (y / (t / z))) / a
    else
        tmp = x / (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) <= -1e+19) || !((a + 1.0) <= 1.00002)) {
		tmp = (x + (y / (t / z))) / a;
	} else {
		tmp = x / (1.0 + ((y * b) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a + 1.0) <= -1e+19) or not ((a + 1.0) <= 1.00002):
		tmp = (x + (y / (t / z))) / a
	else:
		tmp = x / (1.0 + ((y * b) / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a + 1.0) <= -1e+19) || !(Float64(a + 1.0) <= 1.00002))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / a);
	else
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a + 1.0) <= -1e+19) || ~(((a + 1.0) <= 1.00002)))
		tmp = (x + (y / (t / z))) / a;
	else
		tmp = x / (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], -1e+19], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 1.00002]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a 1) < -1e19 or 1.00001999999999991 < (+.f64 a 1)

   1. Initial program 72.6%

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

      1. *-commutative 72.6%

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

      2. associate-*l/ 73.0%

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

      3. *-commutative 73.0%

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

      4. associate-*l/ 78.5%

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

   3. Simplified 78.5%

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

      1. div-inv 78.3%

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

      2. +-commutative 78.3%

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

      3. fma-def 78.3%

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

      4. associate-*l/ 72.9%

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

      5. *-commutative 72.9%

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

      6. associate-+l+ 72.9%

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

      7. +-commutative 72.9%

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

      8. associate-/l* 78.3%

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

      9. associate-/r/ 75.8%

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

      10. fma-def 75.8%

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

   6. Applied egg-rr 75.8%

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

   7. Taylor expanded in y around 0 65.0%

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

   8. Taylor expanded in a around inf 64.0%

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

      1. associate-/l* 64.6%

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

   10. Simplified 64.6%

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

   if -1e19 < (+.f64 a 1) < 1.00001999999999991

   1. Initial program 72.1%

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

      1. *-commutative 72.1%

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

      2. associate-*l/ 72.3%

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

      3. *-commutative 72.3%

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

      4. associate-*l/ 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in x around inf 54.8%

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

      1. associate-+r+ 54.8%

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

      2. associate-*l/ 52.7%

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

      3. *-commutative 52.7%

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

   7. Simplified 52.7%

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

   8. Taylor expanded in a around 0 53.9%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -1 \cdot 10^{+19} \lor \neg \left(a + 1 \leq 1.00002\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -1 \cdot 10^{+19}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{elif}\;a + 1 \leq 2000000000000:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ a 1.0) -1e+19)
   (/ (+ x (/ y (/ t z))) a)
   (if (<= (+ a 1.0) 2000000000000.0)
     (/ x (+ 1.0 (/ (* y b) t)))
     (/ (+ x (/ (* y z) t)) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a + 1.0) <= -1e+19) {
		tmp = (x + (y / (t / z))) / a;
	} else if ((a + 1.0) <= 2000000000000.0) {
		tmp = x / (1.0 + ((y * b) / t));
	} else {
		tmp = (x + ((y * z) / 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 ((a + 1.0d0) <= (-1d+19)) then
        tmp = (x + (y / (t / z))) / a
    else if ((a + 1.0d0) <= 2000000000000.0d0) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else
        tmp = (x + ((y * z) / t)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a + 1.0) <= -1e+19) {
		tmp = (x + (y / (t / z))) / a;
	} else if ((a + 1.0) <= 2000000000000.0) {
		tmp = x / (1.0 + ((y * b) / t));
	} else {
		tmp = (x + ((y * z) / t)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a + 1.0) <= -1e+19:
		tmp = (x + (y / (t / z))) / a
	elif (a + 1.0) <= 2000000000000.0:
		tmp = x / (1.0 + ((y * b) / t))
	else:
		tmp = (x + ((y * z) / t)) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a + 1.0) <= -1e+19)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / a);
	elseif (Float64(a + 1.0) <= 2000000000000.0)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a + 1.0) <= -1e+19)
		tmp = (x + (y / (t / z))) / a;
	elseif ((a + 1.0) <= 2000000000000.0)
		tmp = x / (1.0 + ((y * b) / t));
	else
		tmp = (x + ((y * z) / t)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a + 1.0), $MachinePrecision], -1e+19], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 2000000000000.0], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 a 1) < -1e19

   1. Initial program 73.2%

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

      1. *-commutative 73.2%

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

      2. associate-*l/ 73.3%

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

      3. *-commutative 73.3%

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

      4. associate-*l/ 81.7%

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

   3. Simplified 81.7%

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

      1. div-inv 81.4%

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

      2. +-commutative 81.4%

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

      3. fma-def 81.4%

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

      4. associate-*l/ 73.1%

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

      5. *-commutative 73.1%

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

      6. associate-+l+ 73.1%

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

      7. +-commutative 73.1%

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

      8. associate-/l* 81.4%

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

      9. associate-/r/ 75.6%

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

      10. fma-def 75.6%

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

   6. Applied egg-rr 75.6%

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

   7. Taylor expanded in y around 0 66.1%

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

   8. Taylor expanded in a around inf 64.8%

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

      1. associate-/l* 66.3%

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

   10. Simplified 66.3%

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

   if -1e19 < (+.f64 a 1) < 2e12

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

      2. associate-*l/ 71.5%

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

      3. *-commutative 71.5%

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

      4. associate-*l/ 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in x around inf 53.7%

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

      1. associate-+r+ 53.7%

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

      2. associate-*l/ 52.3%

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

      3. *-commutative 52.3%

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

   7. Simplified 52.3%

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

   8. Taylor expanded in a around 0 52.8%

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

   if 2e12 < (+.f64 a 1)

   1. Initial program 76.0%

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

      1. *-commutative 76.0%

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

      2. associate-*l/ 75.0%

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

      3. *-commutative 75.0%

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

      4. associate-*l/ 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in a around inf 66.5%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -1 \cdot 10^{+19}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{elif}\;a + 1 \leq 2000000000000:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-150}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.05e+166)
   (/ z b)
   (if (<= y -2e-150)
     (* (/ y t) (/ z (+ a 1.0)))
     (if (<= y 9e+92) (/ x (+ a 1.0)) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.05e+166) {
		tmp = z / b;
	} else if (y <= -2e-150) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 9e+92) {
		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 (y <= (-2.05d+166)) then
        tmp = z / b
    else if (y <= (-2d-150)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= 9d+92) 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 (y <= -2.05e+166) {
		tmp = z / b;
	} else if (y <= -2e-150) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 9e+92) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.05e+166:
		tmp = z / b
	elif y <= -2e-150:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= 9e+92:
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.05e+166)
		tmp = Float64(z / b);
	elseif (y <= -2e-150)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= 9e+92)
		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 (y <= -2.05e+166)
		tmp = z / b;
	elseif (y <= -2e-150)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= 9e+92)
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.05e+166], N[(z / b), $MachinePrecision], If[LessEqual[y, -2e-150], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+92], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0500000000000001e166 or 8.9999999999999998e92 < y

   1. Initial program 39.7%

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

      1. *-commutative 39.7%

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

      2. associate-*l/ 44.1%

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

      3. *-commutative 44.1%

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

      4. associate-*l/ 55.5%

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

   3. Simplified 55.5%

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

   5. Taylor expanded in t around 0 64.7%

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

   if -2.0500000000000001e166 < y < -2.00000000000000001e-150

   1. Initial program 80.9%

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

      1. *-commutative 80.9%

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

      2. associate-*l/ 78.8%

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

      3. *-commutative 78.8%

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

      4. associate-*l/ 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in x around 0 48.7%

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

   6. Taylor expanded in y around 0 37.8%

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

      1. times-frac 41.1%

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

   8. Simplified 41.1%

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

   if -2.00000000000000001e-150 < y < 8.9999999999999998e92

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-*l/ 90.0%

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

      3. *-commutative 90.0%

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

      4. associate-*l/ 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in t around inf 61.0%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+166}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-150}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 54.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-62} \lor \neg \left(y \leq 9 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.7e-62) (not (<= y 9e+92))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e-62) || !(y <= 9e+92)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	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 ((y <= (-2.7d-62)) .or. (.not. (y <= 9d+92))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    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 ((y <= -2.7e-62) || !(y <= 9e+92)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.7e-62) or not (y <= 9e+92):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.7e-62) || !(y <= 9e+92))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.7e-62) || ~((y <= 9e+92)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.7e-62], N[Not[LessEqual[y, 9e+92]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.70000000000000019e-62 or 8.9999999999999998e92 < y

   1. Initial program 51.8%

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

      1. *-commutative 51.8%

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

      2. associate-*l/ 54.6%

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

      3. *-commutative 54.6%

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

      4. associate-*l/ 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in t around 0 53.0%

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

   if -2.70000000000000019e-62 < y < 8.9999999999999998e92

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*l/ 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in t around inf 58.4%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-62} \lor \neg \left(y \leq 9 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 41.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-65} \lor \neg \left(y \leq 1.12 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.2e-65) (not (<= y 1.12e+83))) (/ z b) (/ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e-65) || !(y <= 1.12e+83)) {
		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 ((y <= (-3.2d-65)) .or. (.not. (y <= 1.12d+83))) 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 ((y <= -3.2e-65) || !(y <= 1.12e+83)) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.2e-65) or not (y <= 1.12e+83):
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.2e-65) || !(y <= 1.12e+83))
		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 ((y <= -3.2e-65) || ~((y <= 1.12e+83)))
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.2e-65], N[Not[LessEqual[y, 1.12e+83]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1999999999999999e-65 or 1.12e83 < y

   1. Initial program 52.6%

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

      1. *-commutative 52.6%

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

      2. associate-*l/ 55.2%

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

      3. *-commutative 55.2%

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

      4. associate-*l/ 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in t around 0 52.2%

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

   if -3.1999999999999999e-65 < y < 1.12e83

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-*l/ 90.1%

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

      3. *-commutative 90.1%

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

      4. associate-*l/ 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in x around inf 71.4%

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

      1. associate-+r+ 71.4%

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

      2. associate-*l/ 66.9%

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

      3. *-commutative 66.9%

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

   7. Simplified 66.9%

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

   8. Taylor expanded in a around inf 32.1%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-65} \lor \neg \left(y \leq 1.12 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.3% 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 72.3%

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

   1. *-commutative 72.3%

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

   2. associate-*l/ 72.6%

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

   3. *-commutative 72.6%

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

   4. associate-*l/ 75.6%

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

3. Simplified 75.6%

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

5. Taylor expanded in x around inf 49.2%

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

   1. associate-+r+ 49.2%

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

   2. associate-*l/ 49.9%

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

   3. *-commutative 49.9%

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

7. Simplified 49.9%

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

8. Taylor expanded in a around inf 21.5%

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

9. Final simplification 21.5%

   \[\leadsto \frac{x}{a} \]
10. Add Preprocessing

Developer target: 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 2024026 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

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