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

Percentage Accurate: 74.5% → 91.7%

Time: 21.3s

Alternatives: 21

Speedup: 0.8×

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: 74.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, \frac{z}{b} \cdot \frac{t}{b}\right)}{y}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t \cdot \frac{t_3}{z}}\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{+283}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t_3}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_3 (+ a (fma y (/ b t) 1.0))))
   (if (<= t_2 (- INFINITY))
     (/ y (* t (/ t_3 z)))
     (if (<= t_2 -1e-308)
       t_2
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 1e+283)
           t_2
           (if (<= t_2 INFINITY) (* (/ y t) (/ z 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)) / ((a + 1.0) + ((y * b) / t));
	double t_3 = a + fma(y, (b / t), 1.0);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y / (t * (t_3 / z));
	} else if (t_2 <= -1e-308) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+283) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / 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(a + 1.0) + Float64(Float64(y * b) / t)))
	t_3 = Float64(a + fma(y, Float64(b / t), 1.0))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y / Float64(t * Float64(t_3 / z)));
	elseif (t_2 <= -1e-308)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 1e+283)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / 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[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(y * N[(b / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y / N[(t * N[(t$95$3 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-308], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 1e+283], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$3), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 23.0%

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

      1. *-commutative 23.0%

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

      2. associate-*l/ 49.0%

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

      3. *-commutative 49.0%

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

      4. associate-*l/ 49.0%

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

   3. Simplified 49.0%

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

   4. Taylor expanded in x around 0 57.4%

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

      1. times-frac 56.9%

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

      2. +-commutative 56.9%

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

      3. +-commutative 56.9%

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

      4. associate-*l/ 56.9%

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

      5. *-commutative 56.9%

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

      6. +-commutative 56.9%

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

      7. associate-+r+ 56.9%

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

      8. fma-udef 56.9%

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

   6. Simplified 56.9%

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

      1. *-commutative 56.9%

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

      2. clear-num 56.9%

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

      3. frac-times 82.6%

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

      4. *-un-lft-identity 82.6%

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

   8. Applied egg-rr 82.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -9.9999999999999991e-309 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 9.99999999999999955e282

   1. Initial program 99.2%

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

   if -9.9999999999999991e-309 < (/.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 30.7%

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

      1. *-commutative 30.7%

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

      2. associate-*l/ 30.0%

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

      3. *-commutative 30.0%

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

      4. associate-*l/ 43.6%

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

   3. Simplified 43.6%

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

   4. Taylor expanded in a around 0 21.8%

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

   5. Taylor expanded in y around -inf 79.1%

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

      1. +-commutative 79.1%

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

      2. mul-1-neg 79.1%

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

      3. unsub-neg 79.1%

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

      4. fma-neg 79.1%

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

      5. associate-/l* 82.6%

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

      6. mul-1-neg 82.6%

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

      7. remove-double-neg 82.6%

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

      8. *-commutative 82.6%

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

      9. unpow2 82.6%

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

      10. times-frac 86.2%

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

   7. Simplified 86.2%

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

   if 9.99999999999999955e282 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 47.2%

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

      1. *-commutative 47.2%

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

      2. associate-*l/ 70.8%

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

      3. *-commutative 70.8%

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

      4. associate-*l/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in x around 0 58.4%

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

      1. times-frac 94.0%

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

      2. +-commutative 94.0%

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

      3. +-commutative 94.0%

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

      4. associate-*l/ 94.0%

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

      5. *-commutative 94.0%

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

      6. +-commutative 94.0%

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

      7. associate-+r+ 94.0%

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

      8. fma-udef 94.0%

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

   6. Simplified 94.0%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{t \cdot \frac{a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-308}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, \frac{z}{b} \cdot \frac{t}{b}\right)}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+283}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} - \frac{\mathsf{fma}\left(-1, \frac{t}{\frac{b}{x}}, \frac{z}{b} \cdot \frac{t}{b}\right)}{y}\\ \end{array} \]

Alternative 2: 89.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{z}{b} + \left(\frac{t}{b} \cdot \frac{x}{y} + \frac{t}{b \cdot b} \cdot \frac{z \cdot \left(-1 - a\right)}{y}\right)\\ \mathbf{elif}\;t_1 \leq 10^{+283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (/ z b)
     (if (<= t_1 -1e-308)
       t_1
       (if (<= t_1 0.0)
         (+
          (/ z b)
          (+ (* (/ t b) (/ x y)) (* (/ t (* b b)) (/ (* z (- -1.0 a)) y))))
         (if (<= t_1 1e+283)
           t_1
           (if (<= t_1 INFINITY)
             (* (/ y t) (/ z (+ a (fma y (/ b t) 1.0))))
             (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z / b;
	} else if (t_1 <= -1e-308) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + (((t / b) * (x / y)) + ((t / (b * b)) * ((z * (-1.0 - a)) / y)));
	} else if (t_1 <= 1e+283) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / (a + fma(y, (b / t), 1.0)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z / b);
	elseif (t_1 <= -1e-308)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(t / b) * Float64(x / y)) + Float64(Float64(t / Float64(b * b)) * Float64(Float64(z * Float64(-1.0 - a)) / y))));
	elseif (t_1 <= 1e+283)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + fma(y, Float64(b / t), 1.0))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z / b), $MachinePrecision], If[LessEqual[t$95$1, -1e-308], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(b * b), $MachinePrecision]), $MachinePrecision] * N[(N[(z * N[(-1.0 - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+283], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + N[(y * N[(b / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 8.2%

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

      1. *-commutative 8.2%

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

      2. associate-*l/ 17.7%

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

      3. *-commutative 17.7%

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

      4. associate-*l/ 27.0%

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

   3. Simplified 27.0%

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

   4. Taylor expanded in t around 0 84.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -9.9999999999999991e-309 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 9.99999999999999955e282

   1. Initial program 99.2%

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

   if -9.9999999999999991e-309 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 47.8%

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

      1. *-commutative 47.8%

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

      2. associate-*l/ 46.4%

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

      3. *-commutative 46.4%

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

      4. associate-*l/ 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in y around inf 72.9%

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

      1. associate--l+ 72.9%

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

      2. times-frac 78.1%

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

      3. times-frac 78.4%

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

      4. unpow2 78.4%

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

   6. Simplified 78.4%

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

   if 9.99999999999999955e282 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 47.2%

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

      1. *-commutative 47.2%

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

      2. associate-*l/ 70.8%

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

      3. *-commutative 70.8%

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

      4. associate-*l/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in x around 0 58.4%

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

      1. times-frac 94.0%

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

      2. +-commutative 94.0%

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

      3. +-commutative 94.0%

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

      4. associate-*l/ 94.0%

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

      5. *-commutative 94.0%

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

      6. +-commutative 94.0%

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

      7. associate-+r+ 94.0%

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

      8. fma-udef 94.0%

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

   6. Simplified 94.0%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-308}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \left(\frac{t}{b} \cdot \frac{x}{y} + \frac{t}{b \cdot b} \cdot \frac{z \cdot \left(-1 - a\right)}{y}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+283}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3: 91.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{t \cdot \frac{t_2}{z}}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{z}{b} + \left(\frac{t}{b} \cdot \frac{x}{y} + \frac{t}{b \cdot b} \cdot \frac{z \cdot \left(-1 - a\right)}{y}\right)\\ \mathbf{elif}\;t_1 \leq 10^{+283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (+ a (fma y (/ b t) 1.0))))
   (if (<= t_1 (- INFINITY))
     (/ y (* t (/ t_2 z)))
     (if (<= t_1 -1e-308)
       t_1
       (if (<= t_1 0.0)
         (+
          (/ z b)
          (+ (* (/ t b) (/ x y)) (* (/ t (* b b)) (/ (* z (- -1.0 a)) y))))
         (if (<= t_1 1e+283)
           t_1
           (if (<= t_1 INFINITY) (* (/ y t) (/ z 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)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = a + fma(y, (b / t), 1.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y / (t * (t_2 / z));
	} else if (t_1 <= -1e-308) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + (((t / b) * (x / y)) + ((t / (b * b)) * ((z * (-1.0 - a)) / y)));
	} else if (t_1 <= 1e+283) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / 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(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(a + fma(y, Float64(b / t), 1.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y / Float64(t * Float64(t_2 / z)));
	elseif (t_1 <= -1e-308)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(t / b) * Float64(x / y)) + Float64(Float64(t / Float64(b * b)) * Float64(Float64(z * Float64(-1.0 - a)) / y))));
	elseif (t_1 <= 1e+283)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / t_2));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(y * N[(b / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y / N[(t * N[(t$95$2 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-308], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(b * b), $MachinePrecision]), $MachinePrecision] * N[(N[(z * N[(-1.0 - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+283], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$2), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 23.0%

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

      1. *-commutative 23.0%

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

      2. associate-*l/ 49.0%

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

      3. *-commutative 49.0%

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

      4. associate-*l/ 49.0%

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

   3. Simplified 49.0%

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

   4. Taylor expanded in x around 0 57.4%

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

      1. times-frac 56.9%

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

      2. +-commutative 56.9%

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

      3. +-commutative 56.9%

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

      4. associate-*l/ 56.9%

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

      5. *-commutative 56.9%

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

      6. +-commutative 56.9%

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

      7. associate-+r+ 56.9%

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

      8. fma-udef 56.9%

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

   6. Simplified 56.9%

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

      1. *-commutative 56.9%

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

      2. clear-num 56.9%

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

      3. frac-times 82.6%

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

      4. *-un-lft-identity 82.6%

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

   8. Applied egg-rr 82.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -9.9999999999999991e-309 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 9.99999999999999955e282

   1. Initial program 99.2%

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

   if -9.9999999999999991e-309 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 47.8%

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

      1. *-commutative 47.8%

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

      2. associate-*l/ 46.4%

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

      3. *-commutative 46.4%

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

      4. associate-*l/ 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in y around inf 72.9%

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

      1. associate--l+ 72.9%

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

      2. times-frac 78.1%

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

      3. times-frac 78.4%

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

      4. unpow2 78.4%

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

   6. Simplified 78.4%

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

   if 9.99999999999999955e282 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 47.2%

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

      1. *-commutative 47.2%

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

      2. associate-*l/ 70.8%

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

      3. *-commutative 70.8%

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

      4. associate-*l/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in x around 0 58.4%

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

      1. times-frac 94.0%

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

      2. +-commutative 94.0%

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

      3. +-commutative 94.0%

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

      4. associate-*l/ 94.0%

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

      5. *-commutative 94.0%

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

      6. +-commutative 94.0%

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

      7. associate-+r+ 94.0%

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

      8. fma-udef 94.0%

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

   6. Simplified 94.0%

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

   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/ 0.5%

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

      3. *-commutative 0.5%

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

      4. associate-*l/ 14.8%

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

   3. Simplified 14.8%

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

   4. Taylor expanded in t around 0 90.1%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{t \cdot \frac{a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-308}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \left(\frac{t}{b} \cdot \frac{x}{y} + \frac{t}{b \cdot b} \cdot \frac{z \cdot \left(-1 - a\right)}{y}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+283}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 4: 86.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{1}{t} \cdot \left(y \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (/ z b)
     (if (<= t_1 -1e-308)
       t_1
       (if (<= t_1 0.0)
         (/ z b)
         (if (<= t_1 INFINITY)
           (/ (+ x (/ z (/ t y))) (+ a (+ 1.0 (* (/ 1.0 t) (* y b)))))
           (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z / b;
	} else if (t_1 <= -1e-308) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = z / b;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + ((1.0 / t) * (y * b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z / b;
	} else if (t_1 <= -1e-308) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = z / b;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + ((1.0 / t) * (y * b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z / b
	elif t_1 <= -1e-308:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = z / b
	elif t_1 <= math.inf:
		tmp = (x + (z / (t / y))) / (a + (1.0 + ((1.0 / t) * (y * b))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z / b);
	elseif (t_1 <= -1e-308)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(z / b);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + Float64(1.0 + Float64(Float64(1.0 / t) * Float64(y * b)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z / b;
	elseif (t_1 <= -1e-308)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = z / b;
	elseif (t_1 <= Inf)
		tmp = (x + (z / (t / y))) / (a + (1.0 + ((1.0 / t) * (y * b))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z / b), $MachinePrecision], If[LessEqual[t$95$1, -1e-308], t$95$1, If[LessEqual[t$95$1, 0.0], N[(z / b), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(N[(1.0 / t), $MachinePrecision] * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

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 -9.9999999999999991e-309 < (/.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 29.4%

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

      1. *-commutative 29.4%

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

      2. associate-*l/ 33.1%

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

      3. *-commutative 33.1%

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

      4. associate-*l/ 44.5%

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

   3. Simplified 44.5%

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

   4. Taylor expanded in t around 0 77.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -9.9999999999999991e-309

   1. Initial program 99.8%

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

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 93.8%

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

      3. associate-*l/ 90.9%

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

      4. *-commutative 90.9%

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

      5. cancel-sign-sub 90.9%

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

      6. *-commutative 90.9%

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

      7. associate-*l/ 93.8%

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

      8. associate-+r- 93.8%

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

      9. associate-*l/ 90.9%

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

      10. *-commutative 90.9%

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

      11. cancel-sign-sub 90.9%

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

      12. *-commutative 90.9%

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

      13. associate-/r/ 90.0%

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

   3. Simplified 90.0%

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

      1. associate-/l* 93.8%

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

      2. div-inv 93.8%

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

   5. Applied egg-rr 93.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-308}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{1}{t} \cdot \left(y \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 5: 87.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{z}{b} + \left(\frac{t}{b} \cdot \frac{x}{y} + \frac{t}{b \cdot b} \cdot \frac{z \cdot \left(-1 - a\right)}{y}\right)\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{1}{t} \cdot \left(y \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (/ z b)
     (if (<= t_1 -1e-308)
       t_1
       (if (<= t_1 0.0)
         (+
          (/ z b)
          (+ (* (/ t b) (/ x y)) (* (/ t (* b b)) (/ (* z (- -1.0 a)) y))))
         (if (<= t_1 INFINITY)
           (/ (+ x (/ z (/ t y))) (+ a (+ 1.0 (* (/ 1.0 t) (* y b)))))
           (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z / b;
	} else if (t_1 <= -1e-308) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + (((t / b) * (x / y)) + ((t / (b * b)) * ((z * (-1.0 - a)) / y)));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + ((1.0 / t) * (y * b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z / b;
	} else if (t_1 <= -1e-308) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + (((t / b) * (x / y)) + ((t / (b * b)) * ((z * (-1.0 - a)) / y)));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + ((1.0 / t) * (y * b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z / b
	elif t_1 <= -1e-308:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (z / b) + (((t / b) * (x / y)) + ((t / (b * b)) * ((z * (-1.0 - a)) / y)))
	elif t_1 <= math.inf:
		tmp = (x + (z / (t / y))) / (a + (1.0 + ((1.0 / t) * (y * b))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z / b);
	elseif (t_1 <= -1e-308)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(t / b) * Float64(x / y)) + Float64(Float64(t / Float64(b * b)) * Float64(Float64(z * Float64(-1.0 - a)) / y))));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + Float64(1.0 + Float64(Float64(1.0 / t) * Float64(y * b)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z / b;
	elseif (t_1 <= -1e-308)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (z / b) + (((t / b) * (x / y)) + ((t / (b * b)) * ((z * (-1.0 - a)) / y)));
	elseif (t_1 <= Inf)
		tmp = (x + (z / (t / y))) / (a + (1.0 + ((1.0 / t) * (y * b))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z / b), $MachinePrecision], If[LessEqual[t$95$1, -1e-308], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(b * b), $MachinePrecision]), $MachinePrecision] * N[(N[(z * N[(-1.0 - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(N[(1.0 / t), $MachinePrecision] * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 8.2%

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

      1. *-commutative 8.2%

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

      2. associate-*l/ 17.7%

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

      3. *-commutative 17.7%

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

      4. associate-*l/ 27.0%

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

   3. Simplified 27.0%

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

   4. Taylor expanded in t around 0 84.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -9.9999999999999991e-309

   1. Initial program 99.8%

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

   if -9.9999999999999991e-309 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 47.8%

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

      1. *-commutative 47.8%

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

      2. associate-*l/ 46.4%

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

      3. *-commutative 46.4%

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

      4. associate-*l/ 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in y around inf 72.9%

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

      1. associate--l+ 72.9%

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

      2. times-frac 78.1%

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

      3. times-frac 78.4%

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

      4. unpow2 78.4%

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

   6. Simplified 78.4%

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

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 93.8%

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

      3. associate-*l/ 90.9%

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

      4. *-commutative 90.9%

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

      5. cancel-sign-sub 90.9%

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

      6. *-commutative 90.9%

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

      7. associate-*l/ 93.8%

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

      8. associate-+r- 93.8%

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

      9. associate-*l/ 90.9%

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

      10. *-commutative 90.9%

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

      11. cancel-sign-sub 90.9%

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

      12. *-commutative 90.9%

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

      13. associate-/r/ 90.0%

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

   3. Simplified 90.0%

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

      1. associate-/l* 93.8%

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

      2. div-inv 93.8%

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

   5. Applied egg-rr 93.8%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-308}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \left(\frac{t}{b} \cdot \frac{x}{y} + \frac{t}{b \cdot b} \cdot \frac{z \cdot \left(-1 - a\right)}{y}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{1}{t} \cdot \left(y \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 6: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-308} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 10^{+283}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (/ z b)
     (if (or (<= t_1 -1e-308) (and (not (<= t_1 0.0)) (<= t_1 1e+283)))
       t_1
       (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z / b;
	} else if ((t_1 <= -1e-308) || (!(t_1 <= 0.0) && (t_1 <= 1e+283))) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z / b;
	} else if ((t_1 <= -1e-308) || (!(t_1 <= 0.0) && (t_1 <= 1e+283))) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z / b
	elif (t_1 <= -1e-308) or (not (t_1 <= 0.0) and (t_1 <= 1e+283)):
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z / b);
	elseif ((t_1 <= -1e-308) || (!(t_1 <= 0.0) && (t_1 <= 1e+283)))
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z / b;
	elseif ((t_1 <= -1e-308) || (~((t_1 <= 0.0)) && (t_1 <= 1e+283)))
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z / b), $MachinePrecision], If[Or[LessEqual[t$95$1, -1e-308], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 1e+283]]], t$95$1, N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or -9.9999999999999991e-309 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0 or 9.99999999999999955e282 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 32.9%

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

      1. *-commutative 32.9%

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

      2. associate-*l/ 40.4%

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

      3. *-commutative 40.4%

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

      4. associate-*l/ 49.6%

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

   3. Simplified 49.6%

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

   4. Taylor expanded in t around 0 72.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -9.9999999999999991e-309 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 9.99999999999999955e282

   1. Initial program 99.2%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-308} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0\right) \land \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+283}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 7: 56.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{if}\;a + 1 \leq -500000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a + 1 \leq 1.05:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a + 1 \leq 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a + 1 \leq 5 \cdot 10^{+94}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) a)))
   (if (<= (+ a 1.0) -500000000.0)
     t_1
     (if (<= (+ a 1.0) 1.05)
       (/ x (+ 1.0 (* b (/ y t))))
       (if (<= (+ a 1.0) 1e+72)
         t_1
         (if (<= (+ a 1.0) 5e+94) (/ z b) (/ (+ x (/ z (/ t y))) a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / a;
	double tmp;
	if ((a + 1.0) <= -500000000.0) {
		tmp = t_1;
	} else if ((a + 1.0) <= 1.05) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if ((a + 1.0) <= 1e+72) {
		tmp = t_1;
	} else if ((a + 1.0) <= 5e+94) {
		tmp = z / b;
	} else {
		tmp = (x + (z / (t / y))) / 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 + (y / (t / z))) / a
    if ((a + 1.0d0) <= (-500000000.0d0)) then
        tmp = t_1
    else if ((a + 1.0d0) <= 1.05d0) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else if ((a + 1.0d0) <= 1d+72) then
        tmp = t_1
    else if ((a + 1.0d0) <= 5d+94) then
        tmp = z / b
    else
        tmp = (x + (z / (t / y))) / 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 + (y / (t / z))) / a;
	double tmp;
	if ((a + 1.0) <= -500000000.0) {
		tmp = t_1;
	} else if ((a + 1.0) <= 1.05) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if ((a + 1.0) <= 1e+72) {
		tmp = t_1;
	} else if ((a + 1.0) <= 5e+94) {
		tmp = z / b;
	} else {
		tmp = (x + (z / (t / y))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / a
	tmp = 0
	if (a + 1.0) <= -500000000.0:
		tmp = t_1
	elif (a + 1.0) <= 1.05:
		tmp = x / (1.0 + (b * (y / t)))
	elif (a + 1.0) <= 1e+72:
		tmp = t_1
	elif (a + 1.0) <= 5e+94:
		tmp = z / b
	else:
		tmp = (x + (z / (t / y))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / a)
	tmp = 0.0
	if (Float64(a + 1.0) <= -500000000.0)
		tmp = t_1;
	elseif (Float64(a + 1.0) <= 1.05)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	elseif (Float64(a + 1.0) <= 1e+72)
		tmp = t_1;
	elseif (Float64(a + 1.0) <= 5e+94)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y / (t / z))) / a;
	tmp = 0.0;
	if ((a + 1.0) <= -500000000.0)
		tmp = t_1;
	elseif ((a + 1.0) <= 1.05)
		tmp = x / (1.0 + (b * (y / t)));
	elseif ((a + 1.0) <= 1e+72)
		tmp = t_1;
	elseif ((a + 1.0) <= 5e+94)
		tmp = z / b;
	else
		tmp = (x + (z / (t / y))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[N[(a + 1.0), $MachinePrecision], -500000000.0], t$95$1, If[LessEqual[N[(a + 1.0), $MachinePrecision], 1.05], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 1e+72], t$95$1, If[LessEqual[N[(a + 1.0), $MachinePrecision], 5e+94], N[(z / b), $MachinePrecision], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 a 1) < -5e8 or 1.05000000000000004 < (+.f64 a 1) < 9.99999999999999944e71

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-*l/ 84.8%

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

      3. *-commutative 84.8%

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

      4. associate-*l/ 83.6%

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

   3. Simplified 83.6%

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

      1. associate-*l/ 83.6%

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

      2. *-commutative 83.6%

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

      3. associate-/l* 84.9%

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

   5. Applied egg-rr 84.9%

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

   6. Taylor expanded in a around inf 66.3%

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

   if -5e8 < (+.f64 a 1) < 1.05000000000000004

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 74.1%

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

      3. *-commutative 74.1%

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

      4. associate-*l/ 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in x around inf 57.8%

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

      1. div-inv 57.7%

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

      2. *-commutative 57.7%

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

      3. *-commutative 57.7%

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

   6. Applied egg-rr 57.7%

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

   7. Taylor expanded in a around 0 56.3%

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

      1. *-rgt-identity 56.3%

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

      2. associate-*r* 56.3%

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

      3. *-commutative 56.3%

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

      4. associate-*r/ 56.3%

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

      5. *-commutative 56.3%

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

      6. associate-*l* 57.1%

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

      7. associate-*r/ 57.1%

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

      8. *-rgt-identity 57.1%

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

   9. Simplified 57.1%

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

   if 9.99999999999999944e71 < (+.f64 a 1) < 5.0000000000000001e94

   1. Initial program 43.3%

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

      1. *-commutative 43.3%

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

      2. associate-*l/ 43.3%

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

      3. *-commutative 43.3%

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

      4. associate-*l/ 5.0%

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

   3. Simplified 5.0%

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

   4. Taylor expanded in t around 0 61.3%

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

   if 5.0000000000000001e94 < (+.f64 a 1)

   1. Initial program 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-/l* 75.7%

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

      3. associate-*l/ 83.7%

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

      4. *-commutative 83.7%

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

      5. cancel-sign-sub 83.7%

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

      6. *-commutative 83.7%

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

      7. associate-*l/ 75.7%

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

      8. associate-+r- 75.7%

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

      9. associate-*l/ 83.7%

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

      10. *-commutative 83.7%

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

      11. cancel-sign-sub 83.7%

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

      12. *-commutative 83.7%

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

      13. associate-/r/ 81.7%

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

   3. Simplified 81.7%

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

      1. associate-/l* 75.7%

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

      2. div-inv 75.7%

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

   5. Applied egg-rr 75.7%

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

   6. Taylor expanded in a around inf 77.8%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -500000000:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{elif}\;a + 1 \leq 1.05:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a + 1 \leq 10^{+72}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{elif}\;a + 1 \leq 5 \cdot 10^{+94}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a}\\ \end{array} \]

Alternative 8: 80.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-179} \lor \neg \left(t \leq 6.8 \cdot 10^{-126}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5e-179) (not (<= t 6.8e-126)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (/ (* y z) (+ (* y b) (* t (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5e-179) || !(t <= 6.8e-126)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (y * z) / ((y * b) + (t * (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 ((t <= (-5d-179)) .or. (.not. (t <= 6.8d-126))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (y * z) / ((y * b) + (t * (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 ((t <= -5e-179) || !(t <= 6.8e-126)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5e-179) or not (t <= 6.8e-126):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5e-179) || !(t <= 6.8e-126))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5e-179) || ~((t <= 6.8e-126)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5e-179], N[Not[LessEqual[t, 6.8e-126]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.9999999999999998e-179 or 6.8e-126 < t

   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/ 86.3%

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

      3. *-commutative 86.3%

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

      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%

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

   if -4.9999999999999998e-179 < t < 6.8e-126

   1. Initial program 59.6%

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

      1. *-commutative 59.6%

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

      2. associate-*l/ 51.4%

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

      3. *-commutative 51.4%

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

      4. associate-*l/ 43.2%

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

   3. Simplified 43.2%

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

   4. Taylor expanded in x around 0 45.5%

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

   5. Taylor expanded in t around 0 62.1%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-179} \lor \neg \left(t \leq 6.8 \cdot 10^{-126}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \end{array} \]

Alternative 9: 80.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + y \cdot \frac{b}{t}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{-181}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t_1}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (* y (/ b t)))))
   (if (<= t -4.2e-181)
     (/ (+ x (/ y (/ t z))) t_1)
     (if (<= t 8.5e-127)
       (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
       (/ (+ x (* y (/ z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (y * (b / t));
	double tmp;
	if (t <= -4.2e-181) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= 8.5e-127) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y * (z / t))) / 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 = (a + 1.0d0) + (y * (b / t))
    if (t <= (-4.2d-181)) then
        tmp = (x + (y / (t / z))) / t_1
    else if (t <= 8.5d-127) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else
        tmp = (x + (y * (z / t))) / 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 = (a + 1.0) + (y * (b / t));
	double tmp;
	if (t <= -4.2e-181) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= 8.5e-127) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y * (z / t))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + (y * (b / t))
	tmp = 0
	if t <= -4.2e-181:
		tmp = (x + (y / (t / z))) / t_1
	elif t <= 8.5e-127:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	else:
		tmp = (x + (y * (z / t))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(y * Float64(b / t)))
	tmp = 0.0
	if (t <= -4.2e-181)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	elseif (t <= 8.5e-127)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + (y * (b / t));
	tmp = 0.0;
	if (t <= -4.2e-181)
		tmp = (x + (y / (t / z))) / t_1;
	elseif (t <= 8.5e-127)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	else
		tmp = (x + (y * (z / t))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e-181], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 8.5e-127], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.20000000000000006e-181

   1. Initial program 86.2%

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

      1. *-commutative 86.2%

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

      2. associate-*l/ 87.2%

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

      3. *-commutative 87.2%

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

      4. associate-*l/ 86.2%

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

   3. Simplified 86.2%

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

      1. associate-*l/ 85.2%

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

      2. *-commutative 85.2%

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

      3. associate-/l* 87.2%

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

   5. Applied egg-rr 87.2%

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

   if -4.20000000000000006e-181 < t < 8.5e-127

   1. Initial program 59.6%

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

      1. *-commutative 59.6%

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

      2. associate-*l/ 51.4%

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

      3. *-commutative 51.4%

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

      4. associate-*l/ 43.2%

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

   3. Simplified 43.2%

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

   4. Taylor expanded in x around 0 45.5%

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

   5. Taylor expanded in t around 0 62.1%

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

   if 8.5e-127 < t

   1. Initial program 82.5%

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

      1. *-commutative 82.5%

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

      2. associate-*l/ 85.3%

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

      3. *-commutative 85.3%

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

      4. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-181}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]

Alternative 10: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-130}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.8e-235)
   (/ (+ x (/ z (/ t y))) (+ a (+ 1.0 (/ y (/ t b)))))
   (if (<= t 2.9e-130)
     (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
     (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.8e-235) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	} else if (t <= 2.9e-130) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.8d-235)) then
        tmp = (x + (z / (t / y))) / (a + (1.0d0 + (y / (t / b))))
    else if (t <= 2.9d-130) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.8e-235) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	} else if (t <= 2.9e-130) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.8e-235:
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))))
	elif t <= 2.9e-130:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	else:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.8e-235)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	elseif (t <= 2.9e-130)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.8e-235)
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	elseif (t <= 2.9e-130)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	else
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.8e-235], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-130], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.79999999999999995e-235

   1. Initial program 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-/l* 84.4%

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

      3. associate-*l/ 84.1%

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

      4. *-commutative 84.1%

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

      5. cancel-sign-sub 84.1%

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

      6. *-commutative 84.1%

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

      7. associate-*l/ 84.4%

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

      8. associate-+r- 84.4%

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

      9. associate-*l/ 84.1%

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

      10. *-commutative 84.1%

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

      11. cancel-sign-sub 84.1%

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

      12. *-commutative 84.1%

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

      13. associate-/r/ 84.1%

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

   3. Simplified 84.1%

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

   if -2.79999999999999995e-235 < t < 2.9e-130

   1. Initial program 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-*l/ 49.8%

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

      3. *-commutative 49.8%

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

      4. associate-*l/ 41.3%

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

   3. Simplified 41.3%

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

   4. Taylor expanded in x around 0 45.8%

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

   5. Taylor expanded in t around 0 63.0%

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

   if 2.9e-130 < t

   1. Initial program 82.5%

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

      1. *-commutative 82.5%

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

      2. associate-*l/ 85.3%

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

      3. *-commutative 85.3%

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

      4. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-130}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]

Alternative 11: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (+ a (/ (* y b) t))))))
   (if (<= y -1.45e+21)
     (/ z b)
     (if (<= y 9e-187)
       t_1
       (if (<= y 6.4e-156)
         (* (/ y t) (/ z (+ a 1.0)))
         (if (<= y 7e+105) t_1 (/ z b)))))))

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 (y <= -1.45e+21) {
		tmp = z / b;
	} else if (y <= 9e-187) {
		tmp = t_1;
	} else if (y <= 6.4e-156) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 7e+105) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 + (a + ((y * b) / t)))
    if (y <= (-1.45d+21)) then
        tmp = z / b
    else if (y <= 9d-187) then
        tmp = t_1
    else if (y <= 6.4d-156) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= 7d+105) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + ((y * b) / t)));
	double tmp;
	if (y <= -1.45e+21) {
		tmp = z / b;
	} else if (y <= 9e-187) {
		tmp = t_1;
	} else if (y <= 6.4e-156) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 7e+105) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a + ((y * b) / t)))
	tmp = 0
	if y <= -1.45e+21:
		tmp = z / b
	elif y <= 9e-187:
		tmp = t_1
	elif y <= 6.4e-156:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= 7e+105:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))))
	tmp = 0.0
	if (y <= -1.45e+21)
		tmp = Float64(z / b);
	elseif (y <= 9e-187)
		tmp = t_1;
	elseif (y <= 6.4e-156)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= 7e+105)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (a + ((y * b) / t)));
	tmp = 0.0;
	if (y <= -1.45e+21)
		tmp = z / b;
	elseif (y <= 9e-187)
		tmp = t_1;
	elseif (y <= 6.4e-156)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= 7e+105)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+21], N[(z / b), $MachinePrecision], If[LessEqual[y, 9e-187], t$95$1, If[LessEqual[y, 6.4e-156], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+105], t$95$1, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e21 or 6.99999999999999982e105 < y

   1. Initial program 45.1%

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

      1. *-commutative 45.1%

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

      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/ 60.2%

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

   3. Simplified 60.2%

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

   4. Taylor expanded in t around 0 62.2%

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

   if -1.45e21 < y < 8.9999999999999996e-187 or 6.39999999999999964e-156 < y < 6.99999999999999982e105

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

      2. associate-*l/ 89.2%

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

      3. *-commutative 89.2%

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

      4. associate-*l/ 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in x around inf 69.5%

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

   if 8.9999999999999996e-187 < y < 6.39999999999999964e-156

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l/ 42.5%

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

      3. *-commutative 42.5%

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

      4. associate-*l/ 42.5%

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

   3. Simplified 42.5%

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

   4. Taylor expanded in x around 0 95.8%

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

      1. times-frac 95.8%

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

      2. +-commutative 95.8%

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

      3. +-commutative 95.8%

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

      4. associate-*l/ 95.8%

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

      5. *-commutative 95.8%

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

      6. +-commutative 95.8%

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

      7. associate-+r+ 95.8%

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

      8. fma-udef 95.8%

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

   6. Simplified 95.8%

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

   7. Taylor expanded in y around 0 95.8%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-187}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 12: 55.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -500000000 \lor \neg \left(a + 1 \leq 1.05\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ a 1.0) -500000000.0) (not (<= (+ a 1.0) 1.05)))
   (/ (+ x (* y (/ z t))) a)
   (/ x (+ 1.0 (* b (/ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -500000000.0) || !((a + 1.0) <= 1.05)) {
		tmp = (x + (y * (z / t))) / a;
	} else {
		tmp = x / (1.0 + (b * (y / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((a + 1.0d0) <= (-500000000.0d0)) .or. (.not. ((a + 1.0d0) <= 1.05d0))) then
        tmp = (x + (y * (z / t))) / a
    else
        tmp = x / (1.0d0 + (b * (y / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -500000000.0) || !((a + 1.0) <= 1.05)) {
		tmp = (x + (y * (z / t))) / a;
	} else {
		tmp = x / (1.0 + (b * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a + 1.0) <= -500000000.0) or not ((a + 1.0) <= 1.05):
		tmp = (x + (y * (z / t))) / a
	else:
		tmp = x / (1.0 + (b * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a + 1.0) <= -500000000.0) || !(Float64(a + 1.0) <= 1.05))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	else
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a + 1.0) <= -500000000.0) || ~(((a + 1.0) <= 1.05)))
		tmp = (x + (y * (z / t))) / a;
	else
		tmp = x / (1.0 + (b * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -500000000.0], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 1.05]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a 1) < -5e8 or 1.05000000000000004 < (+.f64 a 1)

   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/ 79.2%

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

      3. *-commutative 79.2%

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

      4. associate-*l/ 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in a around inf 65.8%

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

   if -5e8 < (+.f64 a 1) < 1.05000000000000004

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 74.1%

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

      3. *-commutative 74.1%

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

      4. associate-*l/ 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in x around inf 57.8%

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

      1. div-inv 57.7%

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

      2. *-commutative 57.7%

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

      3. *-commutative 57.7%

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

   6. Applied egg-rr 57.7%

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

   7. Taylor expanded in a around 0 56.3%

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

      1. *-rgt-identity 56.3%

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

      2. associate-*r* 56.3%

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

      3. *-commutative 56.3%

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

      4. associate-*r/ 56.3%

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

      5. *-commutative 56.3%

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

      6. associate-*l* 57.1%

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

      7. associate-*r/ 57.1%

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

      8. *-rgt-identity 57.1%

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

   9. Simplified 57.1%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -500000000 \lor \neg \left(a + 1 \leq 1.05\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 13: 55.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -500000000 \lor \neg \left(a + 1 \leq 1.05\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ a 1.0) -500000000.0) (not (<= (+ a 1.0) 1.05)))
   (/ (+ x (/ y (/ t z))) a)
   (/ x (+ 1.0 (* b (/ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -500000000.0) || !((a + 1.0) <= 1.05)) {
		tmp = (x + (y / (t / z))) / a;
	} else {
		tmp = x / (1.0 + (b * (y / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((a + 1.0d0) <= (-500000000.0d0)) .or. (.not. ((a + 1.0d0) <= 1.05d0))) then
        tmp = (x + (y / (t / z))) / a
    else
        tmp = x / (1.0d0 + (b * (y / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -500000000.0) || !((a + 1.0) <= 1.05)) {
		tmp = (x + (y / (t / z))) / a;
	} else {
		tmp = x / (1.0 + (b * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a + 1.0) <= -500000000.0) or not ((a + 1.0) <= 1.05):
		tmp = (x + (y / (t / z))) / a
	else:
		tmp = x / (1.0 + (b * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a + 1.0) <= -500000000.0) || !(Float64(a + 1.0) <= 1.05))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / a);
	else
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a + 1.0) <= -500000000.0) || ~(((a + 1.0) <= 1.05)))
		tmp = (x + (y / (t / z))) / a;
	else
		tmp = x / (1.0 + (b * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -500000000.0], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 1.05]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a 1) < -5e8 or 1.05000000000000004 < (+.f64 a 1)

   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/ 79.2%

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

      3. *-commutative 79.2%

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

      4. associate-*l/ 79.2%

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

   3. Simplified 79.2%

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

      1. associate-*l/ 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-/l* 80.1%

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

   5. Applied egg-rr 80.1%

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

   6. Taylor expanded in a around inf 66.6%

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

   if -5e8 < (+.f64 a 1) < 1.05000000000000004

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 74.1%

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

      3. *-commutative 74.1%

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

      4. associate-*l/ 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in x around inf 57.8%

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

      1. div-inv 57.7%

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

      2. *-commutative 57.7%

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

      3. *-commutative 57.7%

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

   6. Applied egg-rr 57.7%

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

   7. Taylor expanded in a around 0 56.3%

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

      1. *-rgt-identity 56.3%

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

      2. associate-*r* 56.3%

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

      3. *-commutative 56.3%

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

      4. associate-*r/ 56.3%

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

      5. *-commutative 56.3%

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

      6. associate-*l* 57.1%

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

      7. associate-*r/ 57.1%

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

      8. *-rgt-identity 57.1%

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

   9. Simplified 57.1%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -500000000 \lor \neg \left(a + 1 \leq 1.05\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 14: 55.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+20}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= y -1.1e+20)
     (/ z b)
     (if (<= y 9e-187)
       t_1
       (if (<= y 4e-148)
         (* (/ y t) (/ z (+ a 1.0)))
         (if (<= y 9e+71) t_1 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (y <= -1.1e+20) {
		tmp = z / b;
	} else if (y <= 9e-187) {
		tmp = t_1;
	} else if (y <= 4e-148) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 9e+71) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (y <= (-1.1d+20)) then
        tmp = z / b
    else if (y <= 9d-187) then
        tmp = t_1
    else if (y <= 4d-148) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= 9d+71) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (y <= -1.1e+20) {
		tmp = z / b;
	} else if (y <= 9e-187) {
		tmp = t_1;
	} else if (y <= 4e-148) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 9e+71) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if y <= -1.1e+20:
		tmp = z / b
	elif y <= 9e-187:
		tmp = t_1
	elif y <= 4e-148:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= 9e+71:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (y <= -1.1e+20)
		tmp = Float64(z / b);
	elseif (y <= 9e-187)
		tmp = t_1;
	elseif (y <= 4e-148)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= 9e+71)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (y <= -1.1e+20)
		tmp = z / b;
	elseif (y <= 9e-187)
		tmp = t_1;
	elseif (y <= 4e-148)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= 9e+71)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+20], N[(z / b), $MachinePrecision], If[LessEqual[y, 9e-187], t$95$1, If[LessEqual[y, 4e-148], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+71], t$95$1, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e20 or 9.00000000000000087e71 < y

   1. Initial program 48.7%

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

      1. *-commutative 48.7%

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

      2. associate-*l/ 55.5%

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

      3. *-commutative 55.5%

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

      4. associate-*l/ 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in t around 0 59.1%

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

   if -1.1e20 < y < 8.9999999999999996e-187 or 3.99999999999999974e-148 < y < 9.00000000000000087e71

   1. Initial program 93.7%

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

      1. *-commutative 93.7%

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

      2. associate-*l/ 90.0%

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

      3. *-commutative 90.0%

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

      4. associate-*l/ 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in t around inf 60.9%

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

   if 8.9999999999999996e-187 < y < 3.99999999999999974e-148

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-*l/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*l/ 45.0%

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

   3. Simplified 45.0%

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

   4. Taylor expanded in x around 0 82.8%

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

      1. times-frac 83.1%

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

      2. +-commutative 83.1%

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

      3. +-commutative 83.1%

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

      4. associate-*l/ 83.1%

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

      5. *-commutative 83.1%

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

      6. +-commutative 83.1%

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

      7. associate-+r+ 83.1%

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

      8. fma-udef 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in y around 0 83.0%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+20}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-187}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 15: 61.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-33} \lor \neg \left(z \leq 1.15 \cdot 10^{-112}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.5e-33) (not (<= z 1.15e-112)))
   (/ (+ x (* y (/ z t))) (+ a 1.0))
   (/ x (+ 1.0 (+ a (/ (* y b) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.5e-33) || !(z <= 1.15e-112)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-5.5d-33)) .or. (.not. (z <= 1.15d-112))) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.5e-33) || !(z <= 1.15e-112)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.5e-33) or not (z <= 1.15e-112):
		tmp = (x + (y * (z / t))) / (a + 1.0)
	else:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.5e-33) || !(z <= 1.15e-112))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.5e-33) || ~((z <= 1.15e-112)))
		tmp = (x + (y * (z / t))) / (a + 1.0);
	else
		tmp = x / (1.0 + (a + ((y * b) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.5e-33], N[Not[LessEqual[z, 1.15e-112]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5e-33 or 1.14999999999999995e-112 < z

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

      2. associate-*l/ 68.6%

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

      3. *-commutative 68.6%

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

      4. associate-*l/ 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in b around 0 61.0%

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

   if -5.5e-33 < z < 1.14999999999999995e-112

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*l/ 88.6%

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

      3. *-commutative 88.6%

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

      4. associate-*l/ 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in x around inf 82.4%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-33} \lor \neg \left(z \leq 1.15 \cdot 10^{-112}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]

Alternative 16: 61.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-32} \lor \neg \left(z \leq 8.8 \cdot 10^{-99}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.2e-32) (not (<= z 8.8e-99)))
   (/ (+ x (/ y (/ t z))) (+ a 1.0))
   (/ x (+ 1.0 (+ a (/ (* y b) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.2e-32) || !(z <= 8.8e-99)) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.2d-32)) .or. (.not. (z <= 8.8d-99))) then
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    else
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.2e-32) || !(z <= 8.8e-99)) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.2e-32) or not (z <= 8.8e-99):
		tmp = (x + (y / (t / z))) / (a + 1.0)
	else:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.2e-32) || !(z <= 8.8e-99))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.2e-32) || ~((z <= 8.8e-99)))
		tmp = (x + (y / (t / z))) / (a + 1.0);
	else
		tmp = x / (1.0 + (a + ((y * b) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.2e-32], N[Not[LessEqual[z, 8.8e-99]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2000000000000001e-32 or 8.80000000000000018e-99 < z

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

      2. associate-*l/ 68.6%

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

      3. *-commutative 68.6%

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

      4. associate-*l/ 71.8%

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

   3. Simplified 71.8%

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

      1. associate-*l/ 71.2%

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

      2. *-commutative 71.2%

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

      3. associate-/l* 73.4%

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

   5. Applied egg-rr 73.4%

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

   6. Taylor expanded in b around 0 61.7%

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

   if -1.2000000000000001e-32 < z < 8.80000000000000018e-99

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*l/ 88.6%

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

      3. *-commutative 88.6%

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

      4. associate-*l/ 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in x around inf 82.4%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-32} \lor \neg \left(z \leq 8.8 \cdot 10^{-99}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]

Alternative 17: 62.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.4e-34)
   (/ (+ x (/ y (/ t z))) (+ a 1.0))
   (if (<= z 1.15e-102)
     (/ x (+ 1.0 (+ a (/ (* y b) t))))
     (/ (+ 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 (z <= -3.4e-34) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (z <= 1.15e-102) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} 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 (z <= (-3.4d-34)) then
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    else if (z <= 1.15d-102) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    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 (z <= -3.4e-34) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (z <= 1.15e-102) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.4e-34:
		tmp = (x + (y / (t / z))) / (a + 1.0)
	elif z <= 1.15e-102:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = (x + (z / (t / y))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.4e-34)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	elseif (z <= 1.15e-102)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	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 (z <= -3.4e-34)
		tmp = (x + (y / (t / z))) / (a + 1.0);
	elseif (z <= 1.15e-102)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = (x + (z / (t / y))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.4e-34], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-102], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4000000000000001e-34

   1. Initial program 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-*l/ 69.6%

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

      3. *-commutative 69.6%

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

      4. associate-*l/ 75.4%

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

   3. Simplified 75.4%

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

      1. associate-*l/ 69.7%

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

      2. *-commutative 69.7%

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

      3. associate-/l* 76.4%

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

   5. Applied egg-rr 76.4%

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

   6. Taylor expanded in b around 0 63.7%

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

   if -3.4000000000000001e-34 < z < 1.14999999999999993e-102

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*l/ 88.6%

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

      3. *-commutative 88.6%

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

      4. associate-*l/ 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in x around inf 82.4%

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

   if 1.14999999999999993e-102 < z

   1. Initial program 72.4%

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

      1. *-commutative 72.4%

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

      2. associate-/l* 75.8%

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

      3. associate-*l/ 73.2%

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

      4. *-commutative 73.2%

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

      5. cancel-sign-sub 73.2%

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

      6. *-commutative 73.2%

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

      7. associate-*l/ 75.8%

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

      8. associate-+r- 75.8%

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

      9. associate-*l/ 73.2%

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

      10. *-commutative 73.2%

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

      11. cancel-sign-sub 73.2%

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

      12. *-commutative 73.2%

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

      13. associate-/r/ 75.8%

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

   3. Simplified 75.8%

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

      1. associate-/l* 75.8%

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

      2. div-inv 75.8%

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

   5. Applied egg-rr 75.8%

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

   6. Taylor expanded in y around 0 64.7%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \end{array} \]

Alternative 18: 56.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+20} \lor \neg \left(y \leq 8.5 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9e+20) (not (<= y 8.5e+71))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e+20) || !(y <= 8.5e+71)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9d+20)) .or. (.not. (y <= 8.5d+71))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e+20) || !(y <= 8.5e+71)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9e+20) or not (y <= 8.5e+71):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9e+20) || !(y <= 8.5e+71))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9e+20) || ~((y <= 8.5e+71)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9e+20], N[Not[LessEqual[y, 8.5e+71]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9e20 or 8.4999999999999996e71 < y

   1. Initial program 48.7%

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

      1. *-commutative 48.7%

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

      2. associate-*l/ 55.5%

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

      3. *-commutative 55.5%

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

      4. associate-*l/ 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in t around 0 59.1%

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

   if -9e20 < y < 8.4999999999999996e71

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      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/ 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 58.6%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+20} \lor \neg \left(y \leq 8.5 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 19: 40.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 0.057:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.0) (/ x a) (if (<= a 0.057) x (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= 0.057) {
		tmp = x;
	} 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 <= (-1.0d0)) then
        tmp = x / a
    else if (a <= 0.057d0) then
        tmp = x
    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 <= -1.0) {
		tmp = x / a;
	} else if (a <= 0.057) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.0:
		tmp = x / a
	elif a <= 0.057:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.0)
		tmp = Float64(x / a);
	elseif (a <= 0.057)
		tmp = x;
	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 <= -1.0)
		tmp = x / a;
	elseif (a <= 0.057)
		tmp = x;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.0], N[(x / a), $MachinePrecision], If[LessEqual[a, 0.057], x, N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 0.0570000000000000021 < a

   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/ 79.2%

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

      3. *-commutative 79.2%

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

      4. associate-*l/ 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in x around inf 54.3%

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

   5. Taylor expanded in a around inf 47.0%

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

   if -1 < a < 0.0570000000000000021

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 74.1%

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

      3. *-commutative 74.1%

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

      4. associate-*l/ 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in a around 0 72.3%

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

   5. Taylor expanded in t around inf 39.9%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 0.057:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 20: 42.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -32500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+65}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -32500000000000.0) x (if (<= t 1.7e+65) (/ z b) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -32500000000000.0) {
		tmp = x;
	} else if (t <= 1.7e+65) {
		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 (t <= (-32500000000000.0d0)) then
        tmp = x
    else if (t <= 1.7d+65) 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 (t <= -32500000000000.0) {
		tmp = x;
	} else if (t <= 1.7e+65) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -32500000000000.0:
		tmp = x
	elif t <= 1.7e+65:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -32500000000000.0)
		tmp = x;
	elseif (t <= 1.7e+65)
		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 (t <= -32500000000000.0)
		tmp = x;
	elseif (t <= 1.7e+65)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -32500000000000.0], x, If[LessEqual[t, 1.7e+65], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.25e13

   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/ 96.5%

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

      3. *-commutative 96.5%

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

      4. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in a around 0 55.3%

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

   5. Taylor expanded in t around inf 34.4%

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

   if -3.25e13 < t < 1.7e65

   1. Initial program 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-*l/ 63.9%

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

      3. *-commutative 63.9%

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

      4. associate-*l/ 58.5%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in t around 0 49.3%

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

   if 1.7e65 < t

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

      2. associate-*l/ 88.6%

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

      3. *-commutative 88.6%

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

      4. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around inf 69.2%

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

   5. Taylor expanded in a around inf 40.4%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -32500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+65}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 21: 19.5% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.7%

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

   1. *-commutative 77.7%

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

   2. associate-*l/ 76.7%

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

   3. *-commutative 76.7%

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

   4. associate-*l/ 76.0%

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

3. Simplified 76.0%

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

4. Taylor expanded in a around 0 45.4%

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

5. Taylor expanded in t around inf 21.4%

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

6. Final simplification 21.4%

   \[\leadsto x \]

Developer target: 79.9% 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 2023275 
(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))))