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

Percentage Accurate: 74.6% → 92.2%

Time: 21.1s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, \frac{z}{b} \cdot \frac{t}{b}\right)}{y}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_3 := \frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-322}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ z b) (/ (fma -1.0 (/ t (/ b x)) (* (/ z b) (/ t b))) y)))
        (t_2 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0))))
        (t_3 (* (/ y t) (/ z (+ 1.0 (+ a (* y (/ b t))))))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-322)
       t_2
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 5e+302) t_2 (if (<= t_2 INFINITY) t_3 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) - (fma(-1.0, (t / (b / x)), ((z / b) * (t / b))) / y);
	double t_2 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_3 = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-322) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+302) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) - Float64(fma(-1.0, Float64(t / Float64(b / x)), Float64(Float64(z / b) * Float64(t / b))) / y))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_3 = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-322)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 5e+302)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] - N[(N[(-1.0 * N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] + N[(N[(z / b), $MachinePrecision] * N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-322], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 5e+302], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or 5e302 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 36.4%

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

      1. *-commutative 36.4%

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

      2. associate-*l/ 59.0%

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

      3. *-commutative 59.0%

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

      4. associate-*l/ 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in x around 0 61.5%

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

      1. times-frac 87.0%

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

      2. associate-*l/ 87.0%

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

      3. *-commutative 87.0%

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

   6. Simplified 87.0%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.97626e-322 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5e302

   1. Initial program 99.1%

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

   if -1.97626e-322 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0 or +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 30.4%

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

      1. *-commutative 30.4%

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

      2. associate-*l/ 30.7%

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

      3. *-commutative 30.7%

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

      4. associate-*l/ 54.3%

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

   3. Simplified 54.3%

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

   4. Taylor expanded in a around 0 16.0%

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

   5. Taylor expanded in y around -inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

         \[\leadsto \color{blue}{\frac{z}{b} - \frac{-1 \cdot \frac{t \cdot x}{b} - -1 \cdot \frac{t \cdot z}{{b}^{2}}}{y}} \]

      4. fma-neg 65.6%

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

      5. associate-/l* 69.0%

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

      6. mul-1-neg 69.0%

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

      7. remove-double-neg 69.0%

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

      8. *-commutative 69.0%

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

      9. unpow2 69.0%

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

      10. times-frac 78.3%

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

   7. Simplified 78.3%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-322}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, \frac{z}{b} \cdot \frac{t}{b}\right)}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, \frac{z}{b} \cdot \frac{t}{b}\right)}{y}\\ \end{array} \]

Alternative 2: 91.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_2 := \frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-199}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\frac{y}{\frac{t}{b}} + \left(a + 1\right)}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0))))
        (t_2 (* (/ y t) (/ z (+ 1.0 (+ a (* y (/ b t))))))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -1e-147)
       t_1
       (if (<= t_1 5e-199)
         (/ (+ x (* y (/ z t))) (+ (/ y (/ t b)) (+ a 1.0)))
         (if (<= t_1 5e+302) t_1 (if (<= t_1 INFINITY) t_2 (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -1e-147) {
		tmp = t_1;
	} else if (t_1 <= 5e-199) {
		tmp = (x + (y * (z / t))) / ((y / (t / b)) + (a + 1.0));
	} else if (t_1 <= 5e+302) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -1e-147) {
		tmp = t_1;
	} else if (t_1 <= 5e-199) {
		tmp = (x + (y * (z / t))) / ((y / (t / b)) + (a + 1.0));
	} else if (t_1 <= 5e+302) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	t_2 = (y / t) * (z / (1.0 + (a + (y * (b / t)))))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -1e-147:
		tmp = t_1
	elif t_1 <= 5e-199:
		tmp = (x + (y * (z / t))) / ((y / (t / b)) + (a + 1.0))
	elif t_1 <= 5e+302:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_2
	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(Float64(y * b) / t) + Float64(a + 1.0)))
	t_2 = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -1e-147)
		tmp = t_1;
	elseif (t_1 <= 5e-199)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y / Float64(t / b)) + Float64(a + 1.0)));
	elseif (t_1 <= 5e+302)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	t_2 = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -1e-147)
		tmp = t_1;
	elseif (t_1 <= 5e-199)
		tmp = (x + (y * (z / t))) / ((y / (t / b)) + (a + 1.0));
	elseif (t_1 <= 5e+302)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -1e-147], t$95$1, If[LessEqual[t$95$1, 5e-199], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+302], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or 5e302 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 36.4%

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

      1. *-commutative 36.4%

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

      2. associate-*l/ 59.0%

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

      3. *-commutative 59.0%

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

      4. associate-*l/ 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in x around 0 61.5%

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

      1. times-frac 87.0%

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

      2. associate-*l/ 87.0%

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

      3. *-commutative 87.0%

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

   6. Simplified 87.0%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -9.9999999999999997e-148 or 4.9999999999999996e-199 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5e302

   1. Initial program 99.7%

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

   if -9.9999999999999997e-148 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.9999999999999996e-199

   1. Initial program 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-*l/ 69.3%

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

      3. *-commutative 69.3%

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

      4. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in b around 0 69.3%

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

      1. *-commutative 69.3%

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

      2. associate-/l* 80.1%

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

   6. Simplified 80.1%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 1.1%

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

      3. *-commutative 1.1%

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

      4. associate-*l/ 33.2%

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

   3. Simplified 33.2%

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

   4. Taylor expanded in t around 0 85.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -1 \cdot 10^{-147}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{-199}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\frac{y}{\frac{t}{b}} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \left(a + y \cdot \frac{b}{t}\right)\\ t_2 := \frac{y}{t} \cdot \frac{z}{t_1}\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+196}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ 1.0 (+ a (* y (/ b t))))) (t_2 (* (/ y t) (/ z t_1))))
   (if (<= z -9.8e+45)
     t_2
     (if (<= z 4.9e-88)
       (/ x t_1)
       (if (<= z 3.5e+196) (/ (+ x (/ z (/ t y))) (+ a 1.0)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + (a + (y * (b / t)));
	double t_2 = (y / t) * (z / t_1);
	double tmp;
	if (z <= -9.8e+45) {
		tmp = t_2;
	} else if (z <= 4.9e-88) {
		tmp = x / t_1;
	} else if (z <= 3.5e+196) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 + (a + (y * (b / t)))
    t_2 = (y / t) * (z / t_1)
    if (z <= (-9.8d+45)) then
        tmp = t_2
    else if (z <= 4.9d-88) then
        tmp = x / t_1
    else if (z <= 3.5d+196) then
        tmp = (x + (z / (t / y))) / (a + 1.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + (a + (y * (b / t)));
	double t_2 = (y / t) * (z / t_1);
	double tmp;
	if (z <= -9.8e+45) {
		tmp = t_2;
	} else if (z <= 4.9e-88) {
		tmp = x / t_1;
	} else if (z <= 3.5e+196) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 + (a + (y * (b / t)))
	t_2 = (y / t) * (z / t_1)
	tmp = 0
	if z <= -9.8e+45:
		tmp = t_2
	elif z <= 4.9e-88:
		tmp = x / t_1
	elif z <= 3.5e+196:
		tmp = (x + (z / (t / y))) / (a + 1.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))
	t_2 = Float64(Float64(y / t) * Float64(z / t_1))
	tmp = 0.0
	if (z <= -9.8e+45)
		tmp = t_2;
	elseif (z <= 4.9e-88)
		tmp = Float64(x / t_1);
	elseif (z <= 3.5e+196)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + 1.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 + (a + (y * (b / t)));
	t_2 = (y / t) * (z / t_1);
	tmp = 0.0;
	if (z <= -9.8e+45)
		tmp = t_2;
	elseif (z <= 4.9e-88)
		tmp = x / t_1;
	elseif (z <= 3.5e+196)
		tmp = (x + (z / (t / y))) / (a + 1.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / t), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+45], t$95$2, If[LessEqual[z, 4.9e-88], N[(x / t$95$1), $MachinePrecision], If[LessEqual[z, 3.5e+196], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.8000000000000004e45 or 3.4999999999999998e196 < z

   1. Initial program 60.2%

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

      1. *-commutative 60.2%

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

      2. associate-*l/ 60.8%

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

      3. *-commutative 60.8%

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

      4. associate-*l/ 70.2%

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

   3. Simplified 70.2%

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

   4. Taylor expanded in x around 0 48.1%

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

      1. times-frac 57.8%

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

      2. associate-*l/ 63.7%

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

      3. *-commutative 63.7%

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

   6. Simplified 63.7%

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

   if -9.8000000000000004e45 < z < 4.90000000000000028e-88

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

      2. associate-*l/ 86.5%

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

      3. *-commutative 86.5%

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

      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. Taylor expanded in x around inf 76.6%

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

      1. associate-*l/ 78.3%

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

      2. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   if 4.90000000000000028e-88 < z < 3.4999999999999998e196

   1. Initial program 79.2%

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

      1. *-commutative 79.2%

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

      2. associate-*l/ 77.6%

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

      3. *-commutative 77.6%

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

      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. Taylor expanded in b around 0 61.0%

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

      1. clear-num 61.0%

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

      2. inv-pow 61.0%

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

      3. *-commutative 61.0%

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

      4. associate-/r* 62.3%

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

   6. Applied egg-rr 62.3%

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

      1. unpow-1 62.3%

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

      2. associate-/l/ 61.0%

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

      3. associate-/r* 64.1%

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

   8. Simplified 64.1%

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

   9. Taylor expanded in t around 0 61.0%

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

       1. associate-*r/ 62.4%

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

       2. *-commutative 62.4%

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

       3. associate-/r/ 64.1%

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

   11. Simplified 64.1%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+196}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \]

Alternative 4: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;t \leq -3.05 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-88}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \frac{y}{t + t \cdot a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (+ a (* y (/ b t)))))))
   (if (<= t -3.05e-49)
     t_1
     (if (<= t -1.15e-88)
       (/ z b)
       (if (<= t -3.5e-123)
         (* z (/ y (+ t (* t a))))
         (if (<= t 3.2e-93) (/ z b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -3.05e-49) {
		tmp = t_1;
	} else if (t <= -1.15e-88) {
		tmp = z / b;
	} else if (t <= -3.5e-123) {
		tmp = z * (y / (t + (t * a)));
	} else if (t <= 3.2e-93) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 + (a + (y * (b / t))))
    if (t <= (-3.05d-49)) then
        tmp = t_1
    else if (t <= (-1.15d-88)) then
        tmp = z / b
    else if (t <= (-3.5d-123)) then
        tmp = z * (y / (t + (t * a)))
    else if (t <= 3.2d-93) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -3.05e-49) {
		tmp = t_1;
	} else if (t <= -1.15e-88) {
		tmp = z / b;
	} else if (t <= -3.5e-123) {
		tmp = z * (y / (t + (t * a)));
	} else if (t <= 3.2e-93) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a + (y * (b / t))))
	tmp = 0
	if t <= -3.05e-49:
		tmp = t_1
	elif t <= -1.15e-88:
		tmp = z / b
	elif t <= -3.5e-123:
		tmp = z * (y / (t + (t * a)))
	elif t <= 3.2e-93:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))))
	tmp = 0.0
	if (t <= -3.05e-49)
		tmp = t_1;
	elseif (t <= -1.15e-88)
		tmp = Float64(z / b);
	elseif (t <= -3.5e-123)
		tmp = Float64(z * Float64(y / Float64(t + Float64(t * a))));
	elseif (t <= 3.2e-93)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (a + (y * (b / t))));
	tmp = 0.0;
	if (t <= -3.05e-49)
		tmp = t_1;
	elseif (t <= -1.15e-88)
		tmp = z / b;
	elseif (t <= -3.5e-123)
		tmp = z * (y / (t + (t * a)));
	elseif (t <= 3.2e-93)
		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[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.05e-49], t$95$1, If[LessEqual[t, -1.15e-88], N[(z / b), $MachinePrecision], If[LessEqual[t, -3.5e-123], N[(z * N[(y / N[(t + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-93], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.04999999999999982e-49 or 3.1999999999999999e-93 < t

   1. Initial program 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-*l/ 84.2%

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

      3. *-commutative 84.2%

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

      4. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in x around inf 68.4%

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

      1. associate-*l/ 71.4%

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

      2. *-commutative 71.4%

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

   6. Simplified 71.4%

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

   if -3.04999999999999982e-49 < t < -1.14999999999999993e-88 or -3.4999999999999999e-123 < t < 3.1999999999999999e-93

   1. Initial program 66.7%

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

      1. *-commutative 66.7%

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

      2. associate-*l/ 59.8%

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

      3. *-commutative 59.8%

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

      4. associate-*l/ 51.8%

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

   3. Simplified 51.8%

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

   4. Taylor expanded in t around 0 56.8%

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

   if -1.14999999999999993e-88 < t < -3.4999999999999999e-123

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

      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/ 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in b around 0 67.5%

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

   5. Taylor expanded in x around 0 59.4%

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

      1. associate-/l* 59.4%

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

   7. Simplified 59.4%

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

      1. associate-/r/ 59.6%

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

      2. distribute-rgt-in 59.6%

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

      3. *-un-lft-identity 59.6%

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

   9. Applied egg-rr 59.6%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-88}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \frac{y}{t + t \cdot a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \]

Alternative 5: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-88}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-117}:\\ \;\;\;\;z \cdot \frac{y}{t + t \cdot a}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.9e-49)
   (/ x (+ 1.0 (+ a (* y (/ b t)))))
   (if (<= t -3.8e-88)
     (/ z b)
     (if (<= t -1.3e-117)
       (* z (/ y (+ t (* t a))))
       (if (<= t 9.2e-91) (/ z b) (/ x (+ 1.0 (+ a (/ y (/ t b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.9e-49) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if (t <= -3.8e-88) {
		tmp = z / b;
	} else if (t <= -1.3e-117) {
		tmp = z * (y / (t + (t * a)));
	} else if (t <= 9.2e-91) {
		tmp = z / b;
	} else {
		tmp = x / (1.0 + (a + (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 (t <= (-2.9d-49)) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    else if (t <= (-3.8d-88)) then
        tmp = z / b
    else if (t <= (-1.3d-117)) then
        tmp = z * (y / (t + (t * a)))
    else if (t <= 9.2d-91) then
        tmp = z / b
    else
        tmp = x / (1.0d0 + (a + (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 (t <= -2.9e-49) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if (t <= -3.8e-88) {
		tmp = z / b;
	} else if (t <= -1.3e-117) {
		tmp = z * (y / (t + (t * a)));
	} else if (t <= 9.2e-91) {
		tmp = z / b;
	} else {
		tmp = x / (1.0 + (a + (y / (t / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.9e-49:
		tmp = x / (1.0 + (a + (y * (b / t))))
	elif t <= -3.8e-88:
		tmp = z / b
	elif t <= -1.3e-117:
		tmp = z * (y / (t + (t * a)))
	elif t <= 9.2e-91:
		tmp = z / b
	else:
		tmp = x / (1.0 + (a + (y / (t / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.9e-49)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	elseif (t <= -3.8e-88)
		tmp = Float64(z / b);
	elseif (t <= -1.3e-117)
		tmp = Float64(z * Float64(y / Float64(t + Float64(t * a))));
	elseif (t <= 9.2e-91)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y / Float64(t / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.9e-49)
		tmp = x / (1.0 + (a + (y * (b / t))));
	elseif (t <= -3.8e-88)
		tmp = z / b;
	elseif (t <= -1.3e-117)
		tmp = z * (y / (t + (t * a)));
	elseif (t <= 9.2e-91)
		tmp = z / b;
	else
		tmp = x / (1.0 + (a + (y / (t / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.9e-49], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-88], N[(z / b), $MachinePrecision], If[LessEqual[t, -1.3e-117], N[(z * N[(y / N[(t + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-91], N[(z / b), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9e-49

   1. Initial program 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-*l/ 78.6%

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

      3. *-commutative 78.6%

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

      4. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in x around inf 56.1%

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

      1. associate-*l/ 60.1%

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

      2. *-commutative 60.1%

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

   6. Simplified 60.1%

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

   if -2.9e-49 < t < -3.80000000000000011e-88 or -1.29999999999999992e-117 < t < 9.19999999999999982e-91

   1. Initial program 66.7%

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

      1. *-commutative 66.7%

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

      2. associate-*l/ 59.8%

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

      3. *-commutative 59.8%

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

      4. associate-*l/ 51.8%

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

   3. Simplified 51.8%

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

   4. Taylor expanded in t around 0 56.8%

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

   if -3.80000000000000011e-88 < t < -1.29999999999999992e-117

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

      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/ 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in b around 0 67.5%

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

   5. Taylor expanded in x around 0 59.4%

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

      1. associate-/l* 59.4%

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

   7. Simplified 59.4%

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

      1. associate-/r/ 59.6%

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

      2. distribute-rgt-in 59.6%

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

      3. *-un-lft-identity 59.6%

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

   9. Applied egg-rr 59.6%

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

   if 9.19999999999999982e-91 < t

   1. Initial program 86.3%

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

      1. *-commutative 86.3%

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

      2. associate-*l/ 88.7%

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

      3. *-commutative 88.7%

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

      4. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in x around inf 78.2%

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

      1. associate-*l/ 80.4%

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

      2. *-commutative 80.4%

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

   6. Simplified 80.4%

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

      1. clear-num 80.4%

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

      2. div-inv 80.4%

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

   8. Applied egg-rr 80.4%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-88}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-117}:\\ \;\;\;\;z \cdot \frac{y}{t + t \cdot a}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \]

Alternative 6: 68.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{-11}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{elif}\;a \leq 650000:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.75e-11)
   (/ (+ x (/ z (/ t y))) (+ a 1.0))
   (if (<= a 650000.0)
     (/ (+ x (* y (/ z t))) (+ 1.0 (/ (* y b) t)))
     (/ (+ x (/ y (/ t z))) (+ a 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.75e-11) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else if (a <= 650000.0) {
		tmp = (x + (y * (z / t))) / (1.0 + ((y * b) / t));
	} else {
		tmp = (x + (y / (t / z))) / (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 (a <= (-2.75d-11)) then
        tmp = (x + (z / (t / y))) / (a + 1.0d0)
    else if (a <= 650000.0d0) then
        tmp = (x + (y * (z / t))) / (1.0d0 + ((y * b) / t))
    else
        tmp = (x + (y / (t / z))) / (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 (a <= -2.75e-11) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else if (a <= 650000.0) {
		tmp = (x + (y * (z / t))) / (1.0 + ((y * b) / t));
	} else {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.75e-11:
		tmp = (x + (z / (t / y))) / (a + 1.0)
	elif a <= 650000.0:
		tmp = (x + (y * (z / t))) / (1.0 + ((y * b) / t))
	else:
		tmp = (x + (y / (t / z))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.75e-11)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + 1.0));
	elseif (a <= 650000.0)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(1.0 + Float64(Float64(y * b) / t)));
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.75e-11)
		tmp = (x + (z / (t / y))) / (a + 1.0);
	elseif (a <= 650000.0)
		tmp = (x + (y * (z / t))) / (1.0 + ((y * b) / t));
	else
		tmp = (x + (y / (t / z))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.75e-11], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 650000.0], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.74999999999999987e-11

   1. Initial program 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-*l/ 78.6%

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

      3. *-commutative 78.6%

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

      4. associate-*l/ 78.7%

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

   3. Simplified 78.7%

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

   4. Taylor expanded in b around 0 66.2%

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

      1. clear-num 66.1%

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

      2. inv-pow 66.1%

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

      3. *-commutative 66.1%

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

      4. associate-/r* 68.0%

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

   6. Applied egg-rr 68.0%

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

      1. unpow-1 68.0%

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

      2. associate-/l/ 66.1%

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

      3. associate-/r* 70.3%

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

   8. Simplified 70.3%

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

   9. Taylor expanded in t around 0 66.2%

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

       1. associate-*r/ 68.0%

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

       2. *-commutative 68.0%

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

       3. associate-/r/ 70.3%

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

   11. Simplified 70.3%

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

   if -2.74999999999999987e-11 < a < 6.5e5

   1. Initial program 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-*l/ 77.0%

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

      3. *-commutative 77.0%

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

      4. associate-*l/ 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in a around 0 76.9%

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

   if 6.5e5 < a

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

      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/ 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. Taylor expanded in b around 0 61.7%

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

      1. associate-*l/ 59.0%

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

      2. *-commutative 59.0%

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

      3. associate-/l* 61.7%

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

   6. Applied egg-rr 61.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{-11}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{elif}\;a \leq 650000:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \end{array} \]

Alternative 7: 76.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{t}{b}}\\ \mathbf{if}\;y \leq -4 \cdot 10^{-77}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t_1 + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + t_1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ y (/ t b))))
   (if (<= y -4e-77)
     (/ (+ x (* y (/ z t))) (+ t_1 (+ a 1.0)))
     (/ (+ x (/ z (/ t y))) (+ a (+ 1.0 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / (t / b);
	double tmp;
	if (y <= -4e-77) {
		tmp = (x + (y * (z / t))) / (t_1 + (a + 1.0));
	} else {
		tmp = (x + (z / (t / y))) / (a + (1.0 + t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (t / b)
    if (y <= (-4d-77)) then
        tmp = (x + (y * (z / t))) / (t_1 + (a + 1.0d0))
    else
        tmp = (x + (z / (t / y))) / (a + (1.0d0 + t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / (t / b);
	double tmp;
	if (y <= -4e-77) {
		tmp = (x + (y * (z / t))) / (t_1 + (a + 1.0));
	} else {
		tmp = (x + (z / (t / y))) / (a + (1.0 + t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y / (t / b)
	tmp = 0
	if y <= -4e-77:
		tmp = (x + (y * (z / t))) / (t_1 + (a + 1.0))
	else:
		tmp = (x + (z / (t / y))) / (a + (1.0 + t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y / Float64(t / b))
	tmp = 0.0
	if (y <= -4e-77)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(t_1 + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + Float64(1.0 + t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y / (t / b);
	tmp = 0.0;
	if (y <= -4e-77)
		tmp = (x + (y * (z / t))) / (t_1 + (a + 1.0));
	else
		tmp = (x + (z / (t / y))) / (a + (1.0 + t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e-77], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9999999999999997e-77

   1. Initial program 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-*l/ 64.9%

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

      3. *-commutative 64.9%

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

      4. associate-*l/ 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in b around 0 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-/l* 74.5%

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

   6. Simplified 74.5%

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

   if -3.9999999999999997e-77 < y

   1. Initial program 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-/l* 83.5%

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

      3. associate-*l/ 86.5%

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

      4. *-commutative 86.5%

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

      5. cancel-sign-sub 86.5%

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

      6. *-commutative 86.5%

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

      7. associate-*l/ 83.5%

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

      8. associate-+r- 83.5%

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

      9. associate-*l/ 86.5%

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

      10. *-commutative 86.5%

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

      11. cancel-sign-sub 86.5%

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

      12. *-commutative 86.5%

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

      13. associate-/r/ 83.4%

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

   3. Simplified 83.4%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-77}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\frac{y}{\frac{t}{b}} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \]

Alternative 8: 54.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + y \cdot \frac{b}{t}}\\ t_2 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a \leq -2100000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-155}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 9000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (* y (/ b t))))) (t_2 (/ (+ x (* y (/ z t))) a)))
   (if (<= a -2100000000000.0)
     t_2
     (if (<= a 4.4e-191)
       t_1
       (if (<= a 2.7e-155) (/ z b) (if (<= a 9000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (y * (b / t)));
	double t_2 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -2100000000000.0) {
		tmp = t_2;
	} else if (a <= 4.4e-191) {
		tmp = t_1;
	} else if (a <= 2.7e-155) {
		tmp = z / b;
	} else if (a <= 9000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (1.0d0 + (y * (b / t)))
    t_2 = (x + (y * (z / t))) / a
    if (a <= (-2100000000000.0d0)) then
        tmp = t_2
    else if (a <= 4.4d-191) then
        tmp = t_1
    else if (a <= 2.7d-155) then
        tmp = z / b
    else if (a <= 9000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (y * (b / t)));
	double t_2 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -2100000000000.0) {
		tmp = t_2;
	} else if (a <= 4.4e-191) {
		tmp = t_1;
	} else if (a <= 2.7e-155) {
		tmp = z / b;
	} else if (a <= 9000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (y * (b / t)))
	t_2 = (x + (y * (z / t))) / a
	tmp = 0
	if a <= -2100000000000.0:
		tmp = t_2
	elif a <= 4.4e-191:
		tmp = t_1
	elif a <= 2.7e-155:
		tmp = z / b
	elif a <= 9000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(y * Float64(b / t))))
	t_2 = Float64(Float64(x + Float64(y * Float64(z / t))) / a)
	tmp = 0.0
	if (a <= -2100000000000.0)
		tmp = t_2;
	elseif (a <= 4.4e-191)
		tmp = t_1;
	elseif (a <= 2.7e-155)
		tmp = Float64(z / b);
	elseif (a <= 9000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (y * (b / t)));
	t_2 = (x + (y * (z / t))) / a;
	tmp = 0.0;
	if (a <= -2100000000000.0)
		tmp = t_2;
	elseif (a <= 4.4e-191)
		tmp = t_1;
	elseif (a <= 2.7e-155)
		tmp = z / b;
	elseif (a <= 9000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -2100000000000.0], t$95$2, If[LessEqual[a, 4.4e-191], t$95$1, If[LessEqual[a, 2.7e-155], N[(z / b), $MachinePrecision], If[LessEqual[a, 9000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1e12 or 9e3 < a

   1. Initial program 73.6%

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

      1. *-commutative 73.6%

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

      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/ 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in a around inf 66.0%

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

   if -2.1e12 < a < 4.39999999999999996e-191 or 2.69999999999999981e-155 < a < 9e3

   1. Initial program 79.5%

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

      1. *-commutative 79.5%

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

      2. associate-*l/ 77.4%

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

      3. *-commutative 77.4%

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

      4. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in x around inf 58.0%

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

      1. associate-*l/ 59.6%

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

      2. *-commutative 59.6%

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

   6. Simplified 59.6%

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

   7. Taylor expanded in a around 0 56.4%

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

      1. *-commutative 56.4%

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

      2. associate-*r/ 58.0%

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

   9. Simplified 58.0%

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

   if 4.39999999999999996e-191 < a < 2.69999999999999981e-155

   1. Initial program 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-*l/ 63.6%

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

      3. *-commutative 63.6%

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

      4. associate-*l/ 51.8%

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

   3. Simplified 51.8%

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

   4. Taylor expanded in t around 0 89.8%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2100000000000:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-155}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 9000:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]

Alternative 9: 63.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+157}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{y}}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.8e+131)
   (/ z b)
   (if (<= b 7.5e+157) (/ (+ x (/ 1.0 (/ (/ t y) z))) (+ a 1.0)) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.8e+131) {
		tmp = z / b;
	} else if (b <= 7.5e+157) {
		tmp = (x + (1.0 / ((t / y) / z))) / (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 (b <= (-2.8d+131)) then
        tmp = z / b
    else if (b <= 7.5d+157) then
        tmp = (x + (1.0d0 / ((t / y) / z))) / (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 (b <= -2.8e+131) {
		tmp = z / b;
	} else if (b <= 7.5e+157) {
		tmp = (x + (1.0 / ((t / y) / z))) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.8e+131:
		tmp = z / b
	elif b <= 7.5e+157:
		tmp = (x + (1.0 / ((t / y) / z))) / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.8e+131)
		tmp = Float64(z / b);
	elseif (b <= 7.5e+157)
		tmp = Float64(Float64(x + Float64(1.0 / Float64(Float64(t / y) / z))) / 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 (b <= -2.8e+131)
		tmp = z / b;
	elseif (b <= 7.5e+157)
		tmp = (x + (1.0 / ((t / y) / z))) / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.8e+131], N[(z / b), $MachinePrecision], If[LessEqual[b, 7.5e+157], N[(N[(x + N[(1.0 / N[(N[(t / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.8000000000000001e131 or 7.5e157 < b

   1. Initial program 54.2%

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

      1. *-commutative 54.2%

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

      2. associate-*l/ 51.8%

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

      3. *-commutative 51.8%

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

      4. associate-*l/ 64.4%

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

   3. Simplified 64.4%

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

   4. Taylor expanded in t around 0 56.1%

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

   if -2.8000000000000001e131 < b < 7.5e157

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-*l/ 85.1%

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

      3. *-commutative 85.1%

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

      4. associate-*l/ 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in b around 0 69.5%

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

      1. clear-num 69.5%

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

      2. inv-pow 69.5%

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

      3. *-commutative 69.5%

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

      4. associate-/r* 70.0%

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

   6. Applied egg-rr 70.0%

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

      1. unpow-1 70.0%

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

      2. associate-/l/ 69.5%

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

      3. associate-/r* 72.2%

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

   8. Simplified 72.2%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+157}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{y}}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 10: 74.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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))) / ((y * (b / t)) + (a + 1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.5%

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

   1. *-commutative 76.5%

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

   2. associate-*l/ 76.3%

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

   3. *-commutative 76.3%

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

   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. Final simplification 78.9%

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

Alternative 11: 74.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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))) / ((y / (t / b)) + (a + 1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.5%

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

   1. *-commutative 76.5%

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

   2. associate-*l/ 76.3%

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

   3. *-commutative 76.3%

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

   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. Taylor expanded in b around 0 76.3%

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

   1. *-commutative 76.3%

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

   2. associate-/l* 79.1%

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

6. Simplified 79.1%

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

7. Final simplification 79.1%

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

Alternative 12: 63.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+131} \lor \neg \left(b \leq 10^{+158}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.6e+131) (not (<= b 1e+158)))
   (/ z b)
   (/ (+ x (/ z (/ t y))) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.6e+131) || !(b <= 1e+158)) {
		tmp = z / b;
	} else {
		tmp = (x + (z / (t / y))) / (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 ((b <= (-5.6d+131)) .or. (.not. (b <= 1d+158))) then
        tmp = z / b
    else
        tmp = (x + (z / (t / y))) / (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 ((b <= -5.6e+131) || !(b <= 1e+158)) {
		tmp = z / b;
	} else {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.6e+131) or not (b <= 1e+158):
		tmp = z / b
	else:
		tmp = (x + (z / (t / y))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.6e+131) || !(b <= 1e+158))
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.6e+131) || ~((b <= 1e+158)))
		tmp = z / b;
	else
		tmp = (x + (z / (t / y))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.6e+131], N[Not[LessEqual[b, 1e+158]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.6000000000000001e131 or 9.99999999999999953e157 < b

   1. Initial program 54.2%

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

      1. *-commutative 54.2%

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

      2. associate-*l/ 51.8%

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

      3. *-commutative 51.8%

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

      4. associate-*l/ 64.4%

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

   3. Simplified 64.4%

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

   4. Taylor expanded in t around 0 56.1%

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

   if -5.6000000000000001e131 < b < 9.99999999999999953e157

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-*l/ 85.1%

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

      3. *-commutative 85.1%

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

      4. associate-*l/ 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in b around 0 69.5%

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

      1. clear-num 69.5%

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

      2. inv-pow 69.5%

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

      3. *-commutative 69.5%

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

      4. associate-/r* 70.0%

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

   6. Applied egg-rr 70.0%

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

      1. unpow-1 70.0%

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

      2. associate-/l/ 69.5%

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

      3. associate-/r* 72.2%

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

   8. Simplified 72.2%

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

   9. Taylor expanded in t around 0 69.5%

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

       1. associate-*r/ 70.0%

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

       2. *-commutative 70.0%

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

       3. associate-/r/ 72.2%

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

   11. Simplified 72.2%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+131} \lor \neg \left(b \leq 10^{+158}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \end{array} \]

Alternative 13: 61.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+131}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+157}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.1e+131)
   (/ z b)
   (if (<= b 3.5e+157) (/ (+ x (* y (/ z t))) (+ a 1.0)) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.1e+131) {
		tmp = z / b;
	} else if (b <= 3.5e+157) {
		tmp = (x + (y * (z / t))) / (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 (b <= (-3.1d+131)) then
        tmp = z / b
    else if (b <= 3.5d+157) then
        tmp = (x + (y * (z / t))) / (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 (b <= -3.1e+131) {
		tmp = z / b;
	} else if (b <= 3.5e+157) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.1e+131:
		tmp = z / b
	elif b <= 3.5e+157:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.1e+131)
		tmp = Float64(z / b);
	elseif (b <= 3.5e+157)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / 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 (b <= -3.1e+131)
		tmp = z / b;
	elseif (b <= 3.5e+157)
		tmp = (x + (y * (z / t))) / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.1e+131], N[(z / b), $MachinePrecision], If[LessEqual[b, 3.5e+157], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.10000000000000016e131 or 3.50000000000000002e157 < b

   1. Initial program 54.2%

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

      1. *-commutative 54.2%

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

      2. associate-*l/ 51.8%

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

      3. *-commutative 51.8%

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

      4. associate-*l/ 64.4%

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

   3. Simplified 64.4%

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

   4. Taylor expanded in t around 0 56.1%

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

   if -3.10000000000000016e131 < b < 3.50000000000000002e157

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-*l/ 85.1%

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

      3. *-commutative 85.1%

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

      4. associate-*l/ 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in b around 0 70.0%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+131}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+157}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 14: 40.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot a\\ \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-155}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+127}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* x a))))
   (if (<= a -1.0)
     (/ x a)
     (if (<= a 1.5e-191)
       t_1
       (if (<= a 2.05e-155)
         (/ z b)
         (if (<= a 7.8e-26) t_1 (if (<= a 1.4e+127) (/ z b) (/ x a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (x * a);
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= 1.5e-191) {
		tmp = t_1;
	} else if (a <= 2.05e-155) {
		tmp = z / b;
	} else if (a <= 7.8e-26) {
		tmp = t_1;
	} else if (a <= 1.4e+127) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x - (x * a)
    if (a <= (-1.0d0)) then
        tmp = x / a
    else if (a <= 1.5d-191) then
        tmp = t_1
    else if (a <= 2.05d-155) then
        tmp = z / b
    else if (a <= 7.8d-26) then
        tmp = t_1
    else if (a <= 1.4d+127) 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 t_1 = x - (x * a);
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= 1.5e-191) {
		tmp = t_1;
	} else if (a <= 2.05e-155) {
		tmp = z / b;
	} else if (a <= 7.8e-26) {
		tmp = t_1;
	} else if (a <= 1.4e+127) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (x * a)
	tmp = 0
	if a <= -1.0:
		tmp = x / a
	elif a <= 1.5e-191:
		tmp = t_1
	elif a <= 2.05e-155:
		tmp = z / b
	elif a <= 7.8e-26:
		tmp = t_1
	elif a <= 1.4e+127:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(x * a))
	tmp = 0.0
	if (a <= -1.0)
		tmp = Float64(x / a);
	elseif (a <= 1.5e-191)
		tmp = t_1;
	elseif (a <= 2.05e-155)
		tmp = Float64(z / b);
	elseif (a <= 7.8e-26)
		tmp = t_1;
	elseif (a <= 1.4e+127)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (x * a);
	tmp = 0.0;
	if (a <= -1.0)
		tmp = x / a;
	elseif (a <= 1.5e-191)
		tmp = t_1;
	elseif (a <= 2.05e-155)
		tmp = z / b;
	elseif (a <= 7.8e-26)
		tmp = t_1;
	elseif (a <= 1.4e+127)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(x * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.0], N[(x / a), $MachinePrecision], If[LessEqual[a, 1.5e-191], t$95$1, If[LessEqual[a, 2.05e-155], N[(z / b), $MachinePrecision], If[LessEqual[a, 7.8e-26], t$95$1, If[LessEqual[a, 1.4e+127], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1 or 1.4000000000000001e127 < a

   1. Initial program 77.3%

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

      1. *-commutative 77.3%

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

      2. associate-*l/ 81.4%

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

      3. *-commutative 81.4%

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

      4. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in x around inf 59.9%

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

      1. associate-*l/ 58.0%

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

      2. *-commutative 58.0%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in a around inf 55.1%

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

   if -1 < a < 1.5e-191 or 2.0499999999999999e-155 < a < 7.79999999999999973e-26

   1. Initial program 79.9%

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

      1. *-commutative 79.9%

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

      2. associate-*l/ 77.6%

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

      3. *-commutative 77.6%

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

      4. associate-*l/ 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in t around inf 49.2%

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

   5. Taylor expanded in a around 0 48.3%

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

      1. mul-1-neg 48.3%

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

      2. unsub-neg 48.3%

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

   7. Simplified 48.3%

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

   if 1.5e-191 < a < 2.0499999999999999e-155 or 7.79999999999999973e-26 < a < 1.4000000000000001e127

   1. Initial program 65.7%

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

      1. *-commutative 65.7%

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

      2. associate-*l/ 61.6%

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

      3. *-commutative 61.6%

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

      4. associate-*l/ 66.0%

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

   3. Simplified 66.0%

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

   4. Taylor expanded in t around 0 52.4%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-191}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-155}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-26}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+127}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 15: 54.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-31}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.35e-31) (/ z b) (if (<= y 2.8e+142) (/ 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 <= -1.35e-31) {
		tmp = z / b;
	} else if (y <= 2.8e+142) {
		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 <= (-1.35d-31)) then
        tmp = z / b
    else if (y <= 2.8d+142) 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 <= -1.35e-31) {
		tmp = z / b;
	} else if (y <= 2.8e+142) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.35e-31:
		tmp = z / b
	elif y <= 2.8e+142:
		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 <= -1.35e-31)
		tmp = Float64(z / b);
	elseif (y <= 2.8e+142)
		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 <= -1.35e-31)
		tmp = z / b;
	elseif (y <= 2.8e+142)
		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, -1.35e-31], N[(z / b), $MachinePrecision], If[LessEqual[y, 2.8e+142], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35000000000000007e-31 or 2.8e142 < y

   1. Initial program 55.0%

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

      1. *-commutative 55.0%

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

      2. associate-*l/ 60.1%

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

      3. *-commutative 60.1%

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

      4. associate-*l/ 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in t around 0 52.2%

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

   if -1.35000000000000007e-31 < y < 2.8e142

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

      2. associate-*l/ 86.5%

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

      3. *-commutative 86.5%

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

      4. associate-*l/ 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in t around inf 62.0%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-31}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 16: 42.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+127}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8.2e+54) (/ x a) (if (<= a 1.9e+127) (/ z b) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8.2e+54) {
		tmp = x / a;
	} else if (a <= 1.9e+127) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-8.2d+54)) then
        tmp = x / a
    else if (a <= 1.9d+127) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8.2e+54) {
		tmp = x / a;
	} else if (a <= 1.9e+127) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -8.2e+54:
		tmp = x / a
	elif a <= 1.9e+127:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -8.2e+54)
		tmp = Float64(x / a);
	elseif (a <= 1.9e+127)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -8.2e+54)
		tmp = x / a;
	elseif (a <= 1.9e+127)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -8.2e+54], N[(x / a), $MachinePrecision], If[LessEqual[a, 1.9e+127], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.19999999999999935e54 or 1.8999999999999999e127 < a

   1. Initial program 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-*l/ 82.6%

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

      3. *-commutative 82.6%

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

      4. associate-*l/ 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in x around inf 61.9%

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

      1. associate-*l/ 59.8%

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

      2. *-commutative 59.8%

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

   6. Simplified 59.8%

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

   7. Taylor expanded in a around inf 58.6%

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

   if -8.19999999999999935e54 < a < 1.8999999999999999e127

   1. Initial program 75.6%

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

      1. *-commutative 75.6%

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

      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/ 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in t around 0 39.1%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+127}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 17: 25.1% 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 76.5%

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

   1. *-commutative 76.5%

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

   2. associate-*l/ 76.3%

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

   3. *-commutative 76.3%

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

   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. Taylor expanded in x around inf 54.3%

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

   1. associate-*l/ 55.4%

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

   2. *-commutative 55.4%

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

6. Simplified 55.4%

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

7. Taylor expanded in a around inf 26.6%

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

8. Final simplification 26.6%

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

Developer target: 79.4% accurate, 0.7× 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 2023280 
(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))))