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

Percentage Accurate: 76.1% → 91.0%

Time: 25.4s

Alternatives: 22

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: 76.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-298}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\left(\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\right) + \frac{\frac{\left(z \cdot t\right) \cdot \left(-1 - a\right)}{{b}^{2}}}{y}\\ \mathbf{elif}\;t\_2 \leq 10^{+303}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 (- INFINITY))
     (/ (fma y (/ z t) x) (+ 1.0 (fma y (/ b t) a)))
     (if (<= t_2 -5e-298)
       (/ (+ x (* (* y z) (/ 1.0 t))) t_1)
       (if (<= t_2 0.0)
         (+
          (+ (/ z b) (/ (/ t (/ b x)) y))
          (/ (/ (* (* z t) (- -1.0 a)) (pow b 2.0)) y))
         (if (<= t_2 1e+303)
           t_2
           (if (<= t_2 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 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(y, (z / t), x) / (1.0 + fma(y, (b / t), a));
	} else if (t_2 <= -5e-298) {
		tmp = (x + ((y * z) * (1.0 / t))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = ((z / b) + ((t / (b / x)) / y)) + ((((z * t) * (-1.0 - a)) / pow(b, 2.0)) / y);
	} else if (t_2 <= 1e+303) {
		tmp = t_2;
	} else if (t_2 <= ((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(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(fma(y, Float64(z / t), x) / Float64(1.0 + fma(y, Float64(b / t), a)));
	elseif (t_2 <= -5e-298)
		tmp = Float64(Float64(x + Float64(Float64(y * z) * Float64(1.0 / t))) / t_1);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(z / b) + Float64(Float64(t / Float64(b / x)) / y)) + Float64(Float64(Float64(Float64(z * t) * Float64(-1.0 - a)) / (b ^ 2.0)) / y));
	elseif (t_2 <= 1e+303)
		tmp = t_2;
	elseif (t_2 <= 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[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision] / N[(1.0 + N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-298], N[(N[(x + N[(N[(y * z), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(N[(z / b), $MachinePrecision] + N[(N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(z * t), $MachinePrecision] * N[(-1.0 - a), $MachinePrecision]), $MachinePrecision] / N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+303], t$95$2, If[LessEqual[t$95$2, 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 6 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 52.2%

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

      1. +-commutative 52.2%

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

      2. associate-*r/ 86.8%

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

      3. fma-define 86.8%

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

      4. +-commutative 86.8%

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

      5. associate-+l+ 86.8%

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

      6. +-commutative 86.8%

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

      7. associate-*r/ 86.7%

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

      8. fma-define 86.7%

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

   3. Simplified 86.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -5.0000000000000002e-298

   1. Initial program 99.8%

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

      1. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   if -5.0000000000000002e-298 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 62.9%

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

      1. div-inv 62.9%

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

   4. Applied egg-rr 62.9%

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

      1. clear-num 62.9%

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

      2. associate-+l+ 62.9%

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

      3. associate-*l/ 71.4%

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

      4. div-inv 71.4%

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

      5. clear-num 71.4%

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

      6. associate-/l/ 69.3%

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

      7. inv-pow 69.3%

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

   6. Applied egg-rr 69.3%

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

      1. unpow-1 69.3%

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

      2. associate-/r/ 59.1%

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

   8. Simplified 59.1%

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

   9. Taylor expanded in y around inf 65.8%

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

       1. associate-/r* 70.1%

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

       2. associate-/l* 72.3%

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

       3. associate-/r* 72.3%

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

       4. associate-*r* 72.3%

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

   11. Simplified 72.3%

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

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1e303

   1. Initial program 99.7%

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

   if 1e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 31.1%

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

   3. Taylor expanded in x around 0 62.0%

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

      1. times-frac 99.5%

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

      2. associate-+r+ 99.5%

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

      3. *-commutative 99.5%

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

      4. associate-*r/ 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+l+ 99.6%

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

      7. associate-*r/ 99.5%

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

      8. *-commutative 99.5%

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

      9. +-commutative 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-*r/ 99.6%

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

      12. fma-undefine 99.6%

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

   5. Simplified 99.6%

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

   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. Add Preprocessing

   3. Taylor expanded in y around inf 93.8%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-298}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\left(\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\right) + \frac{\frac{\left(z \cdot t\right) \cdot \left(-1 - a\right)}{{b}^{2}}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+303}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-298}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\left(\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\right) + \frac{\frac{\left(z \cdot t\right) \cdot \left(-1 - a\right)}{{b}^{2}}}{y}\\ \mathbf{elif}\;t\_2 \leq 10^{+303}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 (- INFINITY))
     (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b)))))
     (if (<= t_2 -5e-298)
       (/ (+ x (* (* y z) (/ 1.0 t))) t_1)
       (if (<= t_2 0.0)
         (+
          (+ (/ z b) (/ (/ t (/ b x)) y))
          (/ (/ (* (* z t) (- -1.0 a)) (pow b 2.0)) y))
         (if (<= t_2 1e+303)
           t_2
           (if (<= t_2 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 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else if (t_2 <= -5e-298) {
		tmp = (x + ((y * z) * (1.0 / t))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = ((z / b) + ((t / (b / x)) / y)) + ((((z * t) * (-1.0 - a)) / pow(b, 2.0)) / y);
	} else if (t_2 <= 1e+303) {
		tmp = t_2;
	} else if (t_2 <= ((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(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	elseif (t_2 <= -5e-298)
		tmp = Float64(Float64(x + Float64(Float64(y * z) * Float64(1.0 / t))) / t_1);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(z / b) + Float64(Float64(t / Float64(b / x)) / y)) + Float64(Float64(Float64(Float64(z * t) * Float64(-1.0 - a)) / (b ^ 2.0)) / y));
	elseif (t_2 <= 1e+303)
		tmp = t_2;
	elseif (t_2 <= 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[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-298], N[(N[(x + N[(N[(y * z), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(N[(z / b), $MachinePrecision] + N[(N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(z * t), $MachinePrecision] * N[(-1.0 - a), $MachinePrecision]), $MachinePrecision] / N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+303], t$95$2, If[LessEqual[t$95$2, 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 6 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 52.2%

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

      1. associate-*l/ 86.7%

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

      2. associate-+l+ 86.7%

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

      3. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

      1. associate-/r/ 86.6%

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

   6. Applied egg-rr 86.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -5.0000000000000002e-298

   1. Initial program 99.8%

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

      1. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   if -5.0000000000000002e-298 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 62.9%

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

      1. div-inv 62.9%

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

   4. Applied egg-rr 62.9%

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

      1. clear-num 62.9%

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

      2. associate-+l+ 62.9%

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

      3. associate-*l/ 71.4%

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

      4. div-inv 71.4%

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

      5. clear-num 71.4%

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

      6. associate-/l/ 69.3%

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

      7. inv-pow 69.3%

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

   6. Applied egg-rr 69.3%

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

      1. unpow-1 69.3%

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

      2. associate-/r/ 59.1%

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

   8. Simplified 59.1%

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

   9. Taylor expanded in y around inf 65.8%

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

       1. associate-/r* 70.1%

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

       2. associate-/l* 72.3%

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

       3. associate-/r* 72.3%

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

       4. associate-*r* 72.3%

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

   11. Simplified 72.3%

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

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1e303

   1. Initial program 99.7%

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

   if 1e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 31.1%

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

   3. Taylor expanded in x around 0 62.0%

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

      1. times-frac 99.5%

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

      2. associate-+r+ 99.5%

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

      3. *-commutative 99.5%

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

      4. associate-*r/ 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+l+ 99.6%

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

      7. associate-*r/ 99.5%

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

      8. *-commutative 99.5%

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

      9. +-commutative 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-*r/ 99.6%

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

      12. fma-undefine 99.6%

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

   5. Simplified 99.6%

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

   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. Add Preprocessing

   3. Taylor expanded in y around inf 93.8%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-298}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\left(\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\right) + \frac{\frac{\left(z \cdot t\right) \cdot \left(-1 - a\right)}{{b}^{2}}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+303}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.3% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 (- INFINITY))
     (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b)))))
     (if (<= t_1 1e+303)
       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)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= 1e+303) {
		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(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	elseif (t_1 <= 1e+303)
		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[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+303], 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

   1. Initial program 52.2%

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

      1. associate-*l/ 86.7%

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

      2. associate-+l+ 86.7%

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

      3. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

      1. associate-/r/ 86.6%

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

   6. Applied egg-rr 86.6%

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

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

   1. Initial program 91.6%

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

   if 1e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 31.1%

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

   3. Taylor expanded in x around 0 62.0%

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

      1. times-frac 99.5%

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

      2. associate-+r+ 99.5%

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

      3. *-commutative 99.5%

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

      4. associate-*r/ 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+l+ 99.6%

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

      7. associate-*r/ 99.5%

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

      8. *-commutative 99.5%

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

      9. +-commutative 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-*r/ 99.6%

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

      12. fma-undefine 99.6%

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

   5. Simplified 99.6%

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

   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. Add Preprocessing

   3. Taylor expanded in y around inf 93.8%

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

4. Final simplification 92.1%

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

Alternative 4: 89.3% accurate, 0.2× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0))))
        (t_2 (+ a (+ 1.0 (/ y (/ t b))))))
   (if (<= t_1 (- INFINITY))
     (/ (+ x (* z (/ y t))) t_2)
     (if (<= t_1 1e+303)
       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)) / (((y * b) / t) + (a + 1.0));
	double t_2 = a + (1.0 + (y / (t / b)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x + (z * (y / t))) / t_2;
	} else if (t_1 <= 1e+303) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / t_2);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = a + (1.0 + (y / (t / b)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + (z * (y / t))) / t_2;
	} else if (t_1 <= 1e+303) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / t_2);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	t_2 = a + (1.0 + (y / (t / b)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x + (z * (y / t))) / t_2
	elif t_1 <= 1e+303:
		tmp = t_1
	elif t_1 <= math.inf:
		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(Float64(y * b) / t) + Float64(a + 1.0)))
	t_2 = Float64(a + Float64(1.0 + Float64(y / Float64(t / b))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_2);
	elseif (t_1 <= 1e+303)
		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

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	t_2 = a + (1.0 + (y / (t / b)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x + (z * (y / t))) / t_2;
	elseif (t_1 <= 1e+303)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = (y / t) * (z / t_2);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 1e+303], 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 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 52.2%

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

      1. associate-*l/ 86.7%

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

      2. associate-+l+ 86.7%

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

      3. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

      1. associate-/r/ 86.6%

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

   6. Applied egg-rr 86.6%

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

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

   1. Initial program 91.6%

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

   if 1e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 31.1%

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

   3. Taylor expanded in x around 0 31.1%

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

      1. associate-/l/ 62.0%

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

      2. *-commutative 62.0%

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

      3. times-frac 99.5%

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

      4. associate-+l+ 99.5%

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

      5. associate-/l* 99.4%

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

   5. Applied egg-rr 99.4%

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

   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. Add Preprocessing

   3. Taylor expanded in y around inf 93.8%

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

4. Final simplification 92.1%

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

Alternative 5: 60.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} \cdot \frac{z}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{b}{\frac{t}{y}}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ y t) (/ z (+ a (+ 1.0 (/ y (/ t b))))))))
   (if (<= t -1.7e-40)
     (/ x (+ (+ a 1.0) (* y (/ b t))))
     (if (<= t -1.75e-133)
       t_1
       (if (<= t -8.5e-186)
         (/ x (+ (/ (* y b) t) (+ a 1.0)))
         (if (<= t 1.65e-107)
           (/ z b)
           (if (<= t 3.1e-33)
             (/ x (+ (+ a 1.0) (/ b (/ t y))))
             (if (<= t 8e+115) t_1 (/ (+ x (/ y (/ t z))) (+ a 1.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y / t) * (z / (a + (1.0 + (y / (t / b)))));
	double tmp;
	if (t <= -1.7e-40) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if (t <= -1.75e-133) {
		tmp = t_1;
	} else if (t <= -8.5e-186) {
		tmp = x / (((y * b) / t) + (a + 1.0));
	} else if (t <= 1.65e-107) {
		tmp = z / b;
	} else if (t <= 3.1e-33) {
		tmp = x / ((a + 1.0) + (b / (t / y)));
	} else if (t <= 8e+115) {
		tmp = t_1;
	} else {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / t) * (z / (a + (1.0d0 + (y / (t / b)))))
    if (t <= (-1.7d-40)) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    else if (t <= (-1.75d-133)) then
        tmp = t_1
    else if (t <= (-8.5d-186)) then
        tmp = x / (((y * b) / t) + (a + 1.0d0))
    else if (t <= 1.65d-107) then
        tmp = z / b
    else if (t <= 3.1d-33) then
        tmp = x / ((a + 1.0d0) + (b / (t / y)))
    else if (t <= 8d+115) then
        tmp = t_1
    else
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y / t) * (z / (a + (1.0 + (y / (t / b)))));
	double tmp;
	if (t <= -1.7e-40) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if (t <= -1.75e-133) {
		tmp = t_1;
	} else if (t <= -8.5e-186) {
		tmp = x / (((y * b) / t) + (a + 1.0));
	} else if (t <= 1.65e-107) {
		tmp = z / b;
	} else if (t <= 3.1e-33) {
		tmp = x / ((a + 1.0) + (b / (t / y)));
	} else if (t <= 8e+115) {
		tmp = t_1;
	} else {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y / t) * (z / (a + (1.0 + (y / (t / b)))))
	tmp = 0
	if t <= -1.7e-40:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	elif t <= -1.75e-133:
		tmp = t_1
	elif t <= -8.5e-186:
		tmp = x / (((y * b) / t) + (a + 1.0))
	elif t <= 1.65e-107:
		tmp = z / b
	elif t <= 3.1e-33:
		tmp = x / ((a + 1.0) + (b / (t / y)))
	elif t <= 8e+115:
		tmp = t_1
	else:
		tmp = (x + (y / (t / z))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y / t) * Float64(z / Float64(a + Float64(1.0 + Float64(y / Float64(t / b))))))
	tmp = 0.0
	if (t <= -1.7e-40)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t <= -1.75e-133)
		tmp = t_1;
	elseif (t <= -8.5e-186)
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	elseif (t <= 1.65e-107)
		tmp = Float64(z / b);
	elseif (t <= 3.1e-33)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b / Float64(t / y))));
	elseif (t <= 8e+115)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y / t) * (z / (a + (1.0 + (y / (t / b)))));
	tmp = 0.0;
	if (t <= -1.7e-40)
		tmp = x / ((a + 1.0) + (y * (b / t)));
	elseif (t <= -1.75e-133)
		tmp = t_1;
	elseif (t <= -8.5e-186)
		tmp = x / (((y * b) / t) + (a + 1.0));
	elseif (t <= 1.65e-107)
		tmp = z / b;
	elseif (t <= 3.1e-33)
		tmp = x / ((a + 1.0) + (b / (t / y)));
	elseif (t <= 8e+115)
		tmp = t_1;
	else
		tmp = (x + (y / (t / z))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e-40], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.75e-133], t$95$1, If[LessEqual[t, -8.5e-186], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e-107], N[(z / b), $MachinePrecision], If[LessEqual[t, 3.1e-33], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+115], t$95$1, N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.69999999999999992e-40

   1. Initial program 83.7%

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

      1. div-inv 83.7%

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

   4. Applied egg-rr 83.7%

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

   5. Taylor expanded in x around inf 69.2%

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

      1. associate-+r+ 69.2%

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

      2. associate-/l* 73.5%

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

   7. Simplified 73.5%

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

      1. associate-/r/ 73.5%

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

   9. Applied egg-rr 73.5%

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

   if -1.69999999999999992e-40 < t < -1.75000000000000001e-133 or 3.09999999999999997e-33 < t < 8.0000000000000001e115

   1. Initial program 72.0%

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

   3. Taylor expanded in x around 0 50.1%

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

      1. associate-/l/ 54.0%

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

      2. *-commutative 54.0%

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

      3. times-frac 65.9%

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

      4. associate-+l+ 65.9%

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

      5. associate-/l* 68.0%

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

   5. Applied egg-rr 68.0%

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

   if -1.75000000000000001e-133 < t < -8.4999999999999994e-186

   1. Initial program 86.4%

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

   3. Taylor expanded in x around inf 73.9%

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

   if -8.4999999999999994e-186 < t < 1.65000000000000002e-107

   1. Initial program 56.0%

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

   3. Taylor expanded in y around inf 70.5%

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

   if 1.65000000000000002e-107 < t < 3.09999999999999997e-33

   1. Initial program 89.4%

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

      1. div-inv 89.3%

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

   4. Applied egg-rr 89.3%

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

   5. Taylor expanded in x around inf 67.9%

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

      1. associate-+r+ 67.9%

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

      2. associate-/l* 68.0%

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

   7. Simplified 68.0%

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

   if 8.0000000000000001e115 < t

   1. Initial program 85.4%

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

      1. div-inv 85.3%

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

   4. Applied egg-rr 85.3%

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

      1. clear-num 85.2%

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

      2. associate-+l+ 85.2%

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

      3. associate-*l/ 87.5%

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

      4. div-inv 87.5%

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

      5. clear-num 87.5%

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

      6. associate-/l/ 94.9%

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

      7. inv-pow 94.9%

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

   6. Applied egg-rr 94.9%

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

      1. unpow-1 94.9%

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

      2. associate-/r/ 95.1%

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

   8. Simplified 95.1%

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

   9. Taylor expanded in b around 0 83.0%

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

       1. associate-/l* 87.9%

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

   11. Simplified 87.9%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-133}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{b}{\frac{t}{y}}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+115}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := a + \left(1 + \frac{y}{\frac{t}{b}}\right)\\ \mathbf{if}\;t \leq -1.24 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-135}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t\_2}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{t\_1 + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{1 + t\_1}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{\frac{z}{a + 1}}} + \frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t)) (t_2 (+ a (+ 1.0 (/ y (/ t b))))))
   (if (<= t -1.24e-39)
     (/ x (+ (+ a 1.0) (* y (/ b t))))
     (if (<= t -9e-135)
       (* (/ y t) (/ z t_2))
       (if (<= t -2.8e-186)
         (/ x (+ t_1 (+ a 1.0)))
         (if (<= t 1.1e-106)
           (/ z b)
           (if (<= t 5.5e-64)
             (/ x (+ 1.0 t_1))
             (if (<= t 5.5e-50)
               (* (/ z t) (/ y t_2))
               (+ (/ y (/ t (/ z (+ a 1.0)))) (/ x (+ a 1.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = a + (1.0 + (y / (t / b)));
	double tmp;
	if (t <= -1.24e-39) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if (t <= -9e-135) {
		tmp = (y / t) * (z / t_2);
	} else if (t <= -2.8e-186) {
		tmp = x / (t_1 + (a + 1.0));
	} else if (t <= 1.1e-106) {
		tmp = z / b;
	} else if (t <= 5.5e-64) {
		tmp = x / (1.0 + t_1);
	} else if (t <= 5.5e-50) {
		tmp = (z / t) * (y / t_2);
	} else {
		tmp = (y / (t / (z / (a + 1.0)))) + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * b) / t
    t_2 = a + (1.0d0 + (y / (t / b)))
    if (t <= (-1.24d-39)) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    else if (t <= (-9d-135)) then
        tmp = (y / t) * (z / t_2)
    else if (t <= (-2.8d-186)) then
        tmp = x / (t_1 + (a + 1.0d0))
    else if (t <= 1.1d-106) then
        tmp = z / b
    else if (t <= 5.5d-64) then
        tmp = x / (1.0d0 + t_1)
    else if (t <= 5.5d-50) then
        tmp = (z / t) * (y / t_2)
    else
        tmp = (y / (t / (z / (a + 1.0d0)))) + (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 t_1 = (y * b) / t;
	double t_2 = a + (1.0 + (y / (t / b)));
	double tmp;
	if (t <= -1.24e-39) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if (t <= -9e-135) {
		tmp = (y / t) * (z / t_2);
	} else if (t <= -2.8e-186) {
		tmp = x / (t_1 + (a + 1.0));
	} else if (t <= 1.1e-106) {
		tmp = z / b;
	} else if (t <= 5.5e-64) {
		tmp = x / (1.0 + t_1);
	} else if (t <= 5.5e-50) {
		tmp = (z / t) * (y / t_2);
	} else {
		tmp = (y / (t / (z / (a + 1.0)))) + (x / (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = a + (1.0 + (y / (t / b)))
	tmp = 0
	if t <= -1.24e-39:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	elif t <= -9e-135:
		tmp = (y / t) * (z / t_2)
	elif t <= -2.8e-186:
		tmp = x / (t_1 + (a + 1.0))
	elif t <= 1.1e-106:
		tmp = z / b
	elif t <= 5.5e-64:
		tmp = x / (1.0 + t_1)
	elif t <= 5.5e-50:
		tmp = (z / t) * (y / t_2)
	else:
		tmp = (y / (t / (z / (a + 1.0)))) + (x / (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(a + Float64(1.0 + Float64(y / Float64(t / b))))
	tmp = 0.0
	if (t <= -1.24e-39)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t <= -9e-135)
		tmp = Float64(Float64(y / t) * Float64(z / t_2));
	elseif (t <= -2.8e-186)
		tmp = Float64(x / Float64(t_1 + Float64(a + 1.0)));
	elseif (t <= 1.1e-106)
		tmp = Float64(z / b);
	elseif (t <= 5.5e-64)
		tmp = Float64(x / Float64(1.0 + t_1));
	elseif (t <= 5.5e-50)
		tmp = Float64(Float64(z / t) * Float64(y / t_2));
	else
		tmp = Float64(Float64(y / Float64(t / Float64(z / Float64(a + 1.0)))) + Float64(x / Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = a + (1.0 + (y / (t / b)));
	tmp = 0.0;
	if (t <= -1.24e-39)
		tmp = x / ((a + 1.0) + (y * (b / t)));
	elseif (t <= -9e-135)
		tmp = (y / t) * (z / t_2);
	elseif (t <= -2.8e-186)
		tmp = x / (t_1 + (a + 1.0));
	elseif (t <= 1.1e-106)
		tmp = z / b;
	elseif (t <= 5.5e-64)
		tmp = x / (1.0 + t_1);
	elseif (t <= 5.5e-50)
		tmp = (z / t) * (y / t_2);
	else
		tmp = (y / (t / (z / (a + 1.0)))) + (x / (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.24e-39], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-135], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.8e-186], N[(x / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e-106], N[(z / b), $MachinePrecision], If[LessEqual[t, 5.5e-64], N[(x / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-50], N[(N[(z / t), $MachinePrecision] * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(t / N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.24000000000000004e-39

   1. Initial program 83.7%

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

      1. div-inv 83.7%

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

   4. Applied egg-rr 83.7%

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

   5. Taylor expanded in x around inf 69.2%

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

      1. associate-+r+ 69.2%

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

      2. associate-/l* 73.5%

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

   7. Simplified 73.5%

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

      1. associate-/r/ 73.5%

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

   9. Applied egg-rr 73.5%

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

   if -1.24000000000000004e-39 < t < -8.99999999999999975e-135

   1. Initial program 64.4%

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

   3. Taylor expanded in x around 0 49.2%

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

      1. associate-/l/ 59.5%

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

      2. *-commutative 59.5%

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

      3. times-frac 64.3%

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

      4. associate-+l+ 64.3%

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

      5. associate-/l* 64.3%

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

   5. Applied egg-rr 64.3%

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

   if -8.99999999999999975e-135 < t < -2.79999999999999983e-186

   1. Initial program 86.4%

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

   3. Taylor expanded in x around inf 73.9%

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

   if -2.79999999999999983e-186 < t < 1.09999999999999997e-106

   1. Initial program 56.0%

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

   3. Taylor expanded in y around inf 70.5%

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

   if 1.09999999999999997e-106 < t < 5.4999999999999999e-64

   1. Initial program 81.3%

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

      1. div-inv 81.1%

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

   4. Applied egg-rr 81.1%

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

   5. Taylor expanded in x around inf 71.6%

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

      1. associate-+r+ 71.6%

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

      2. associate-/l* 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in a around 0 71.7%

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

   if 5.4999999999999999e-64 < t < 5.49999999999999975e-50

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 85.4%

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

      1. associate-/l/ 85.4%

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

      2. times-frac 85.7%

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

      3. associate-+l+ 85.7%

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

      4. associate-/l* 85.7%

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

   5. Applied egg-rr 85.7%

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

   if 5.49999999999999975e-50 < t

   1. Initial program 82.6%

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

   3. Taylor expanded in y around 0 70.1%

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

   4. Taylor expanded in z around inf 69.7%

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

      1. associate-/l* 74.6%

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

      2. associate-/l* 79.8%

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

   6. Simplified 79.8%

      \[\leadsto \color{blue}{\frac{y}{\frac{t}{\frac{z}{1 + a}}}} + \frac{x}{1 + a} \]
3. Recombined 7 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.24 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-135}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{\frac{z}{a + 1}}} + \frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{b}{\frac{t}{y}}}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 4.15 \cdot 10^{-50}:\\ \;\;\;\;\left(t \cdot \left(x + \frac{y}{\frac{t}{z}}\right)\right) \cdot \frac{1}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.42e-185)
   (/ x (+ (+ a 1.0) (/ b (/ t y))))
   (if (<= t 1.65e-107)
     (/ z b)
     (if (<= t 9.2e-65)
       (/ x (+ 1.0 (/ (* y b) t)))
       (if (<= t 4.15e-50)
         (* (* t (+ x (/ y (/ t z)))) (/ 1.0 (* y b)))
         (/ (+ x (* z (/ y t))) (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.42e-185) {
		tmp = x / ((a + 1.0) + (b / (t / y)));
	} else if (t <= 1.65e-107) {
		tmp = z / b;
	} else if (t <= 9.2e-65) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= 4.15e-50) {
		tmp = (t * (x + (y / (t / z)))) * (1.0 / (y * b));
	} else {
		tmp = (x + (z * (y / 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 <= (-1.42d-185)) then
        tmp = x / ((a + 1.0d0) + (b / (t / y)))
    else if (t <= 1.65d-107) then
        tmp = z / b
    else if (t <= 9.2d-65) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (t <= 4.15d-50) then
        tmp = (t * (x + (y / (t / z)))) * (1.0d0 / (y * b))
    else
        tmp = (x + (z * (y / 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 <= -1.42e-185) {
		tmp = x / ((a + 1.0) + (b / (t / y)));
	} else if (t <= 1.65e-107) {
		tmp = z / b;
	} else if (t <= 9.2e-65) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= 4.15e-50) {
		tmp = (t * (x + (y / (t / z)))) * (1.0 / (y * b));
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.42e-185:
		tmp = x / ((a + 1.0) + (b / (t / y)))
	elif t <= 1.65e-107:
		tmp = z / b
	elif t <= 9.2e-65:
		tmp = x / (1.0 + ((y * b) / t))
	elif t <= 4.15e-50:
		tmp = (t * (x + (y / (t / z)))) * (1.0 / (y * b))
	else:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.42e-185)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b / Float64(t / y))));
	elseif (t <= 1.65e-107)
		tmp = Float64(z / b);
	elseif (t <= 9.2e-65)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (t <= 4.15e-50)
		tmp = Float64(Float64(t * Float64(x + Float64(y / Float64(t / z)))) * Float64(1.0 / Float64(y * b)));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / 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 <= -1.42e-185)
		tmp = x / ((a + 1.0) + (b / (t / y)));
	elseif (t <= 1.65e-107)
		tmp = z / b;
	elseif (t <= 9.2e-65)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (t <= 4.15e-50)
		tmp = (t * (x + (y / (t / z)))) * (1.0 / (y * b));
	else
		tmp = (x + (z * (y / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.42e-185], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e-107], N[(z / b), $MachinePrecision], If[LessEqual[t, 9.2e-65], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.15e-50], N[(N[(t * N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.42000000000000003e-185

   1. Initial program 80.4%

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

      1. div-inv 80.5%

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

   4. Applied egg-rr 80.5%

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

   5. Taylor expanded in x around inf 63.3%

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

      1. associate-+r+ 63.3%

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

      2. associate-/l* 66.1%

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

   7. Simplified 66.1%

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

   if -1.42000000000000003e-185 < t < 1.65000000000000002e-107

   1. Initial program 56.0%

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

   3. Taylor expanded in y around inf 70.5%

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

   if 1.65000000000000002e-107 < t < 9.1999999999999999e-65

   1. Initial program 81.3%

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

      1. div-inv 81.1%

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

   4. Applied egg-rr 81.1%

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

   5. Taylor expanded in x around inf 71.6%

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

      1. associate-+r+ 71.6%

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

      2. associate-/l* 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in a around 0 71.7%

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

   if 9.1999999999999999e-65 < t < 4.1499999999999998e-50

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 74.1%

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

      1. div-inv 74.1%

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

      2. associate-/l* 74.1%

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

      3. *-commutative 74.1%

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

   5. Applied egg-rr 74.1%

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

   if 4.1499999999999998e-50 < t

   1. Initial program 82.6%

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

      1. div-inv 82.5%

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

   4. Applied egg-rr 82.5%

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

   5. Taylor expanded in b around 0 73.8%

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

      1. associate-/l* 73.9%

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

      2. associate-/r/ 75.3%

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

   7. Simplified 75.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{b}{\frac{t}{y}}}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 4.15 \cdot 10^{-50}:\\ \;\;\;\;\left(t \cdot \left(x + \frac{y}{\frac{t}{z}}\right)\right) \cdot \frac{1}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{b}{\frac{t}{y}}}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-108}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-47}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.42e-185)
   (/ x (+ (+ a 1.0) (/ b (/ t y))))
   (if (<= t 2.3e-108)
     (/ z b)
     (if (<= t 9.5e-65)
       (/ x (+ 1.0 (/ (* y b) t)))
       (if (<= t 4.3e-47)
         (* (/ z t) (/ y (+ a (+ 1.0 (/ y (/ t b))))))
         (/ (+ x (* z (/ y t))) (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.42e-185) {
		tmp = x / ((a + 1.0) + (b / (t / y)));
	} else if (t <= 2.3e-108) {
		tmp = z / b;
	} else if (t <= 9.5e-65) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= 4.3e-47) {
		tmp = (z / t) * (y / (a + (1.0 + (y / (t / b)))));
	} else {
		tmp = (x + (z * (y / 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 <= (-1.42d-185)) then
        tmp = x / ((a + 1.0d0) + (b / (t / y)))
    else if (t <= 2.3d-108) then
        tmp = z / b
    else if (t <= 9.5d-65) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (t <= 4.3d-47) then
        tmp = (z / t) * (y / (a + (1.0d0 + (y / (t / b)))))
    else
        tmp = (x + (z * (y / 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 <= -1.42e-185) {
		tmp = x / ((a + 1.0) + (b / (t / y)));
	} else if (t <= 2.3e-108) {
		tmp = z / b;
	} else if (t <= 9.5e-65) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= 4.3e-47) {
		tmp = (z / t) * (y / (a + (1.0 + (y / (t / b)))));
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.42e-185:
		tmp = x / ((a + 1.0) + (b / (t / y)))
	elif t <= 2.3e-108:
		tmp = z / b
	elif t <= 9.5e-65:
		tmp = x / (1.0 + ((y * b) / t))
	elif t <= 4.3e-47:
		tmp = (z / t) * (y / (a + (1.0 + (y / (t / b)))))
	else:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.42e-185)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b / Float64(t / y))));
	elseif (t <= 2.3e-108)
		tmp = Float64(z / b);
	elseif (t <= 9.5e-65)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (t <= 4.3e-47)
		tmp = Float64(Float64(z / t) * Float64(y / Float64(a + Float64(1.0 + Float64(y / Float64(t / b))))));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / 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 <= -1.42e-185)
		tmp = x / ((a + 1.0) + (b / (t / y)));
	elseif (t <= 2.3e-108)
		tmp = z / b;
	elseif (t <= 9.5e-65)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (t <= 4.3e-47)
		tmp = (z / t) * (y / (a + (1.0 + (y / (t / b)))));
	else
		tmp = (x + (z * (y / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.42e-185], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-108], N[(z / b), $MachinePrecision], If[LessEqual[t, 9.5e-65], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e-47], N[(N[(z / t), $MachinePrecision] * N[(y / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.42000000000000003e-185

   1. Initial program 80.4%

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

      1. div-inv 80.5%

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

   4. Applied egg-rr 80.5%

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

   5. Taylor expanded in x around inf 63.3%

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

      1. associate-+r+ 63.3%

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

      2. associate-/l* 66.1%

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

   7. Simplified 66.1%

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

   if -1.42000000000000003e-185 < t < 2.29999999999999996e-108

   1. Initial program 56.0%

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

   3. Taylor expanded in y around inf 70.5%

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

   if 2.29999999999999996e-108 < t < 9.5000000000000004e-65

   1. Initial program 81.3%

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

      1. div-inv 81.1%

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

   4. Applied egg-rr 81.1%

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

   5. Taylor expanded in x around inf 71.6%

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

      1. associate-+r+ 71.6%

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

      2. associate-/l* 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in a around 0 71.7%

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

   if 9.5000000000000004e-65 < t < 4.2999999999999998e-47

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 85.4%

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

      1. associate-/l/ 85.4%

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

      2. times-frac 85.7%

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

      3. associate-+l+ 85.7%

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

      4. associate-/l* 85.7%

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

   5. Applied egg-rr 85.7%

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

   if 4.2999999999999998e-47 < t

   1. Initial program 82.6%

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

      1. div-inv 82.5%

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

   4. Applied egg-rr 82.5%

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

   5. Taylor expanded in b around 0 73.8%

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

      1. associate-/l* 73.9%

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

      2. associate-/r/ 75.3%

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

   7. Simplified 75.3%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{b}{\frac{t}{y}}}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-108}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-47}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-122}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-110}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -6.8e+34)
     t_1
     (if (<= t -1.4e-122)
       (* (/ t y) (/ x b))
       (if (<= t 4.9e-110)
         (/ z b)
         (if (<= t 4.3e-33)
           (/ x (+ 1.0 (/ (* y b) t)))
           (if (<= t 5.5e+87) (* (/ y t) (/ z (+ a 1.0))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -6.8e+34) {
		tmp = t_1;
	} else if (t <= -1.4e-122) {
		tmp = (t / y) * (x / b);
	} else if (t <= 4.9e-110) {
		tmp = z / b;
	} else if (t <= 4.3e-33) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= 5.5e+87) {
		tmp = (y / t) * (z / (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-6.8d+34)) then
        tmp = t_1
    else if (t <= (-1.4d-122)) then
        tmp = (t / y) * (x / b)
    else if (t <= 4.9d-110) then
        tmp = z / b
    else if (t <= 4.3d-33) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (t <= 5.5d+87) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -6.8e+34) {
		tmp = t_1;
	} else if (t <= -1.4e-122) {
		tmp = (t / y) * (x / b);
	} else if (t <= 4.9e-110) {
		tmp = z / b;
	} else if (t <= 4.3e-33) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= 5.5e+87) {
		tmp = (y / t) * (z / (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -6.8e+34:
		tmp = t_1
	elif t <= -1.4e-122:
		tmp = (t / y) * (x / b)
	elif t <= 4.9e-110:
		tmp = z / b
	elif t <= 4.3e-33:
		tmp = x / (1.0 + ((y * b) / t))
	elif t <= 5.5e+87:
		tmp = (y / t) * (z / (a + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -6.8e+34)
		tmp = t_1;
	elseif (t <= -1.4e-122)
		tmp = Float64(Float64(t / y) * Float64(x / b));
	elseif (t <= 4.9e-110)
		tmp = Float64(z / b);
	elseif (t <= 4.3e-33)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (t <= 5.5e+87)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -6.8e+34)
		tmp = t_1;
	elseif (t <= -1.4e-122)
		tmp = (t / y) * (x / b);
	elseif (t <= 4.9e-110)
		tmp = z / b;
	elseif (t <= 4.3e-33)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (t <= 5.5e+87)
		tmp = (y / t) * (z / (a + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+34], t$95$1, If[LessEqual[t, -1.4e-122], N[(N[(t / y), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.9e-110], N[(z / b), $MachinePrecision], If[LessEqual[t, 4.3e-33], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+87], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.7999999999999999e34 or 5.50000000000000022e87 < t

   1. Initial program 82.6%

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

   3. Taylor expanded in y around 0 69.6%

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

   if -6.7999999999999999e34 < t < -1.3999999999999999e-122

   1. Initial program 79.7%

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

      1. div-inv 79.8%

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

   4. Applied egg-rr 79.8%

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

   5. Taylor expanded in x around inf 53.7%

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

      1. associate-+r+ 53.7%

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

      2. associate-/l* 53.8%

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

   7. Simplified 53.8%

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

   8. Taylor expanded in b around inf 39.8%

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

      1. *-commutative 39.8%

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

      2. times-frac 46.3%

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

   10. Simplified 46.3%

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

   if -1.3999999999999999e-122 < t < 4.8999999999999997e-110

   1. Initial program 59.8%

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

   3. Taylor expanded in y around inf 67.1%

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

   if 4.8999999999999997e-110 < t < 4.30000000000000031e-33

   1. Initial program 89.4%

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

      1. div-inv 89.3%

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

   4. Applied egg-rr 89.3%

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

   5. Taylor expanded in x around inf 67.9%

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

      1. associate-+r+ 67.9%

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

      2. associate-/l* 68.0%

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

   7. Simplified 68.0%

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

   8. Taylor expanded in a around 0 62.7%

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

   if 4.30000000000000031e-33 < t < 5.50000000000000022e87

   1. Initial program 81.8%

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

   3. Taylor expanded in x around 0 55.9%

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

   4. Taylor expanded in y around 0 42.1%

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

      1. times-frac 58.7%

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

   6. Simplified 58.7%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-122}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-110}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{b}{\frac{t}{y}}}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-48}:\\ \;\;\;\;\frac{t \cdot \left(x + \frac{y \cdot z}{t}\right)}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.2e-185)
   (/ x (+ (+ a 1.0) (/ b (/ t y))))
   (if (<= t 8.8e-107)
     (/ z b)
     (if (<= t 1.05e-64)
       (/ x (+ 1.0 (/ (* y b) t)))
       (if (<= t 2.1e-48)
         (/ (* t (+ x (/ (* y z) t))) (* y b))
         (/ (+ x (* z (/ y t))) (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.2e-185) {
		tmp = x / ((a + 1.0) + (b / (t / y)));
	} else if (t <= 8.8e-107) {
		tmp = z / b;
	} else if (t <= 1.05e-64) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= 2.1e-48) {
		tmp = (t * (x + ((y * z) / t))) / (y * b);
	} else {
		tmp = (x + (z * (y / 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 <= (-1.2d-185)) then
        tmp = x / ((a + 1.0d0) + (b / (t / y)))
    else if (t <= 8.8d-107) then
        tmp = z / b
    else if (t <= 1.05d-64) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (t <= 2.1d-48) then
        tmp = (t * (x + ((y * z) / t))) / (y * b)
    else
        tmp = (x + (z * (y / 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 <= -1.2e-185) {
		tmp = x / ((a + 1.0) + (b / (t / y)));
	} else if (t <= 8.8e-107) {
		tmp = z / b;
	} else if (t <= 1.05e-64) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= 2.1e-48) {
		tmp = (t * (x + ((y * z) / t))) / (y * b);
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.2e-185:
		tmp = x / ((a + 1.0) + (b / (t / y)))
	elif t <= 8.8e-107:
		tmp = z / b
	elif t <= 1.05e-64:
		tmp = x / (1.0 + ((y * b) / t))
	elif t <= 2.1e-48:
		tmp = (t * (x + ((y * z) / t))) / (y * b)
	else:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.2e-185)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b / Float64(t / y))));
	elseif (t <= 8.8e-107)
		tmp = Float64(z / b);
	elseif (t <= 1.05e-64)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (t <= 2.1e-48)
		tmp = Float64(Float64(t * Float64(x + Float64(Float64(y * z) / t))) / Float64(y * b));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / 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 <= -1.2e-185)
		tmp = x / ((a + 1.0) + (b / (t / y)));
	elseif (t <= 8.8e-107)
		tmp = z / b;
	elseif (t <= 1.05e-64)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (t <= 2.1e-48)
		tmp = (t * (x + ((y * z) / t))) / (y * b);
	else
		tmp = (x + (z * (y / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.2e-185], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e-107], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.05e-64], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-48], N[(N[(t * N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.2000000000000001e-185

   1. Initial program 80.4%

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

      1. div-inv 80.5%

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

   4. Applied egg-rr 80.5%

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

   5. Taylor expanded in x around inf 63.3%

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

      1. associate-+r+ 63.3%

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

      2. associate-/l* 66.1%

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

   7. Simplified 66.1%

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

   if -1.2000000000000001e-185 < t < 8.8000000000000005e-107

   1. Initial program 56.0%

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

   3. Taylor expanded in y around inf 70.5%

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

   if 8.8000000000000005e-107 < t < 1.05000000000000006e-64

   1. Initial program 81.3%

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

      1. div-inv 81.1%

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

   4. Applied egg-rr 81.1%

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

   5. Taylor expanded in x around inf 71.6%

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

      1. associate-+r+ 71.6%

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

      2. associate-/l* 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in a around 0 71.7%

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

   if 1.05000000000000006e-64 < t < 2.09999999999999989e-48

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 74.1%

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

   if 2.09999999999999989e-48 < t

   1. Initial program 82.6%

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

      1. div-inv 82.5%

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

   4. Applied egg-rr 82.5%

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

   5. Taylor expanded in b around 0 73.8%

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

      1. associate-/l* 73.9%

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

      2. associate-/r/ 75.3%

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

   7. Simplified 75.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{b}{\frac{t}{y}}}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-48}:\\ \;\;\;\;\frac{t \cdot \left(x + \frac{y \cdot z}{t}\right)}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a} + \frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{if}\;a + 1 \leq -2 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a + 1 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq 4 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ x a) (* (/ y t) (/ z a)))))
   (if (<= (+ a 1.0) -2e+101)
     t_1
     (if (<= (+ a 1.0) -2e+16)
       (/ z b)
       (if (<= (+ a 1.0) 4e+21) (/ x (+ 1.0 (/ (* y b) t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) + ((y / t) * (z / a));
	double tmp;
	if ((a + 1.0) <= -2e+101) {
		tmp = t_1;
	} else if ((a + 1.0) <= -2e+16) {
		tmp = z / b;
	} else if ((a + 1.0) <= 4e+21) {
		tmp = x / (1.0 + ((y * b) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / a) + ((y / t) * (z / a))
    if ((a + 1.0d0) <= (-2d+101)) then
        tmp = t_1
    else if ((a + 1.0d0) <= (-2d+16)) then
        tmp = z / b
    else if ((a + 1.0d0) <= 4d+21) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) + ((y / t) * (z / a));
	double tmp;
	if ((a + 1.0) <= -2e+101) {
		tmp = t_1;
	} else if ((a + 1.0) <= -2e+16) {
		tmp = z / b;
	} else if ((a + 1.0) <= 4e+21) {
		tmp = x / (1.0 + ((y * b) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) + ((y / t) * (z / a))
	tmp = 0
	if (a + 1.0) <= -2e+101:
		tmp = t_1
	elif (a + 1.0) <= -2e+16:
		tmp = z / b
	elif (a + 1.0) <= 4e+21:
		tmp = x / (1.0 + ((y * b) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) + Float64(Float64(y / t) * Float64(z / a)))
	tmp = 0.0
	if (Float64(a + 1.0) <= -2e+101)
		tmp = t_1;
	elseif (Float64(a + 1.0) <= -2e+16)
		tmp = Float64(z / b);
	elseif (Float64(a + 1.0) <= 4e+21)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) + ((y / t) * (z / a));
	tmp = 0.0;
	if ((a + 1.0) <= -2e+101)
		tmp = t_1;
	elseif ((a + 1.0) <= -2e+16)
		tmp = z / b;
	elseif ((a + 1.0) <= 4e+21)
		tmp = x / (1.0 + ((y * b) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a + 1.0), $MachinePrecision], -2e+101], t$95$1, If[LessEqual[N[(a + 1.0), $MachinePrecision], -2e+16], N[(z / b), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 4e+21], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 a 1) < -2e101 or 4e21 < (+.f64 a 1)

   1. Initial program 77.5%

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

   3. Taylor expanded in a around inf 66.4%

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

   4. Taylor expanded in x around 0 61.9%

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

      1. *-commutative 61.9%

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

      2. times-frac 73.0%

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

   6. Simplified 73.0%

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

   if -2e101 < (+.f64 a 1) < -2e16

   1. Initial program 48.1%

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

   3. Taylor expanded in y around inf 71.7%

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

   if -2e16 < (+.f64 a 1) < 4e21

   1. Initial program 76.1%

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

      1. div-inv 76.1%

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

   4. Applied egg-rr 76.1%

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

   5. Taylor expanded in x around inf 56.7%

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

      1. associate-+r+ 56.7%

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

      2. associate-/l* 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in a around 0 56.7%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -2 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{a} + \frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{elif}\;a + 1 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq 4 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} + \frac{y}{t} \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a} + \frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{if}\;a + 1 \leq -2 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a + 1 \leq -1 \cdot 10^{+39}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq 10^{+106}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{b}{\frac{t}{y}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ x a) (* (/ y t) (/ z a)))))
   (if (<= (+ a 1.0) -2e+101)
     t_1
     (if (<= (+ a 1.0) -1e+39)
       (/ z b)
       (if (<= (+ a 1.0) 1e+106) (/ x (+ (+ a 1.0) (/ b (/ t y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) + ((y / t) * (z / a));
	double tmp;
	if ((a + 1.0) <= -2e+101) {
		tmp = t_1;
	} else if ((a + 1.0) <= -1e+39) {
		tmp = z / b;
	} else if ((a + 1.0) <= 1e+106) {
		tmp = x / ((a + 1.0) + (b / (t / y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / a) + ((y / t) * (z / a))
    if ((a + 1.0d0) <= (-2d+101)) then
        tmp = t_1
    else if ((a + 1.0d0) <= (-1d+39)) then
        tmp = z / b
    else if ((a + 1.0d0) <= 1d+106) then
        tmp = x / ((a + 1.0d0) + (b / (t / y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) + ((y / t) * (z / a));
	double tmp;
	if ((a + 1.0) <= -2e+101) {
		tmp = t_1;
	} else if ((a + 1.0) <= -1e+39) {
		tmp = z / b;
	} else if ((a + 1.0) <= 1e+106) {
		tmp = x / ((a + 1.0) + (b / (t / y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) + ((y / t) * (z / a))
	tmp = 0
	if (a + 1.0) <= -2e+101:
		tmp = t_1
	elif (a + 1.0) <= -1e+39:
		tmp = z / b
	elif (a + 1.0) <= 1e+106:
		tmp = x / ((a + 1.0) + (b / (t / y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) + Float64(Float64(y / t) * Float64(z / a)))
	tmp = 0.0
	if (Float64(a + 1.0) <= -2e+101)
		tmp = t_1;
	elseif (Float64(a + 1.0) <= -1e+39)
		tmp = Float64(z / b);
	elseif (Float64(a + 1.0) <= 1e+106)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b / Float64(t / y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) + ((y / t) * (z / a));
	tmp = 0.0;
	if ((a + 1.0) <= -2e+101)
		tmp = t_1;
	elseif ((a + 1.0) <= -1e+39)
		tmp = z / b;
	elseif ((a + 1.0) <= 1e+106)
		tmp = x / ((a + 1.0) + (b / (t / y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a + 1.0), $MachinePrecision], -2e+101], t$95$1, If[LessEqual[N[(a + 1.0), $MachinePrecision], -1e+39], N[(z / b), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 1e+106], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 a 1) < -2e101 or 1.00000000000000009e106 < (+.f64 a 1)

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf 68.3%

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

   4. Taylor expanded in x around 0 63.0%

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

      1. *-commutative 63.0%

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

      2. times-frac 76.3%

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

   6. Simplified 76.3%

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

   if -2e101 < (+.f64 a 1) < -9.9999999999999994e38

   1. Initial program 41.3%

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

   3. Taylor expanded in y around inf 80.8%

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

   if -9.9999999999999994e38 < (+.f64 a 1) < 1.00000000000000009e106

   1. Initial program 77.3%

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

      1. div-inv 77.3%

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

   4. Applied egg-rr 77.3%

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

   5. Taylor expanded in x around inf 59.2%

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

      1. associate-+r+ 59.2%

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

      2. associate-/l* 62.1%

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

   7. Simplified 62.1%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -2 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{a} + \frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{elif}\;a + 1 \leq -1 \cdot 10^{+39}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq 10^{+106}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{b}{\frac{t}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} + \frac{y}{t} \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{a} + \frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -5.4e-123)
     t_1
     (if (<= t 1.1e-106)
       (/ z b)
       (if (<= t 5e-40)
         (/ x (+ 1.0 (/ (* y b) t)))
         (if (<= t 2.05e+45) (+ (/ x a) (* (/ y t) (/ z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -5.4e-123) {
		tmp = t_1;
	} else if (t <= 1.1e-106) {
		tmp = z / b;
	} else if (t <= 5e-40) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= 2.05e+45) {
		tmp = (x / a) + ((y / t) * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((a + 1.0d0) + (y * (b / t)))
    if (t <= (-5.4d-123)) then
        tmp = t_1
    else if (t <= 1.1d-106) then
        tmp = z / b
    else if (t <= 5d-40) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (t <= 2.05d+45) then
        tmp = (x / a) + ((y / t) * (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -5.4e-123) {
		tmp = t_1;
	} else if (t <= 1.1e-106) {
		tmp = z / b;
	} else if (t <= 5e-40) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= 2.05e+45) {
		tmp = (x / a) + ((y / t) * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a + 1.0) + (y * (b / t)))
	tmp = 0
	if t <= -5.4e-123:
		tmp = t_1
	elif t <= 1.1e-106:
		tmp = z / b
	elif t <= 5e-40:
		tmp = x / (1.0 + ((y * b) / t))
	elif t <= 2.05e+45:
		tmp = (x / a) + ((y / t) * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -5.4e-123)
		tmp = t_1;
	elseif (t <= 1.1e-106)
		tmp = Float64(z / b);
	elseif (t <= 5e-40)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (t <= 2.05e+45)
		tmp = Float64(Float64(x / a) + Float64(Float64(y / t) * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / ((a + 1.0) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -5.4e-123)
		tmp = t_1;
	elseif (t <= 1.1e-106)
		tmp = z / b;
	elseif (t <= 5e-40)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (t <= 2.05e+45)
		tmp = (x / a) + ((y / t) * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e-123], t$95$1, If[LessEqual[t, 1.1e-106], N[(z / b), $MachinePrecision], If[LessEqual[t, 5e-40], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e+45], N[(N[(x / a), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.4000000000000002e-123 or 2.05000000000000006e45 < t

   1. Initial program 82.4%

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

      1. div-inv 82.4%

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

   4. Applied egg-rr 82.4%

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

   5. Taylor expanded in x around inf 66.8%

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

      1. associate-+r+ 66.8%

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

      2. associate-/l* 70.3%

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

   7. Simplified 70.3%

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

      1. associate-/r/ 70.4%

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

   9. Applied egg-rr 70.4%

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

   if -5.4000000000000002e-123 < t < 1.09999999999999997e-106

   1. Initial program 59.8%

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

   3. Taylor expanded in y around inf 67.1%

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

   if 1.09999999999999997e-106 < t < 4.99999999999999965e-40

   1. Initial program 88.8%

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

      1. div-inv 88.7%

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

   4. Applied egg-rr 88.7%

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

   5. Taylor expanded in x around inf 66.0%

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

      1. associate-+r+ 66.0%

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

      2. associate-/l* 66.1%

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

   7. Simplified 66.1%

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

   8. Taylor expanded in a around 0 66.1%

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

   if 4.99999999999999965e-40 < t < 2.05000000000000006e45

   1. Initial program 78.9%

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

   3. Taylor expanded in a around inf 54.3%

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

   4. Taylor expanded in x around 0 54.0%

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

      1. *-commutative 54.0%

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

      2. times-frac 72.8%

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

   6. Simplified 72.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{a} + \frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{b}{\frac{t}{y}}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{1}{\frac{b}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.15e-185)
   (/ x (+ (+ a 1.0) (/ b (/ t y))))
   (if (<= t 4.4e-107)
     (/ z b)
     (if (<= t 2.3e-64)
       (/ x (+ 1.0 (/ (* y b) t)))
       (if (<= t 8.5e-49)
         (/ 1.0 (/ b z))
         (/ (+ x (* z (/ y t))) (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.15e-185) {
		tmp = x / ((a + 1.0) + (b / (t / y)));
	} else if (t <= 4.4e-107) {
		tmp = z / b;
	} else if (t <= 2.3e-64) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= 8.5e-49) {
		tmp = 1.0 / (b / z);
	} else {
		tmp = (x + (z * (y / 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 <= (-1.15d-185)) then
        tmp = x / ((a + 1.0d0) + (b / (t / y)))
    else if (t <= 4.4d-107) then
        tmp = z / b
    else if (t <= 2.3d-64) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (t <= 8.5d-49) then
        tmp = 1.0d0 / (b / z)
    else
        tmp = (x + (z * (y / 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 <= -1.15e-185) {
		tmp = x / ((a + 1.0) + (b / (t / y)));
	} else if (t <= 4.4e-107) {
		tmp = z / b;
	} else if (t <= 2.3e-64) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= 8.5e-49) {
		tmp = 1.0 / (b / z);
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.15e-185:
		tmp = x / ((a + 1.0) + (b / (t / y)))
	elif t <= 4.4e-107:
		tmp = z / b
	elif t <= 2.3e-64:
		tmp = x / (1.0 + ((y * b) / t))
	elif t <= 8.5e-49:
		tmp = 1.0 / (b / z)
	else:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.15e-185)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b / Float64(t / y))));
	elseif (t <= 4.4e-107)
		tmp = Float64(z / b);
	elseif (t <= 2.3e-64)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (t <= 8.5e-49)
		tmp = Float64(1.0 / Float64(b / z));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / 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 <= -1.15e-185)
		tmp = x / ((a + 1.0) + (b / (t / y)));
	elseif (t <= 4.4e-107)
		tmp = z / b;
	elseif (t <= 2.3e-64)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (t <= 8.5e-49)
		tmp = 1.0 / (b / z);
	else
		tmp = (x + (z * (y / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.15e-185], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-107], N[(z / b), $MachinePrecision], If[LessEqual[t, 2.3e-64], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-49], N[(1.0 / N[(b / z), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.15e-185

   1. Initial program 80.4%

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

      1. div-inv 80.5%

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

   4. Applied egg-rr 80.5%

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

   5. Taylor expanded in x around inf 63.3%

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

      1. associate-+r+ 63.3%

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

      2. associate-/l* 66.1%

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

   7. Simplified 66.1%

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

   if -1.15e-185 < t < 4.40000000000000025e-107

   1. Initial program 56.0%

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

   3. Taylor expanded in y around inf 70.5%

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

   if 4.40000000000000025e-107 < t < 2.3000000000000001e-64

   1. Initial program 81.3%

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

      1. div-inv 81.1%

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

   4. Applied egg-rr 81.1%

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

   5. Taylor expanded in x around inf 71.6%

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

      1. associate-+r+ 71.6%

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

      2. associate-/l* 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in a around 0 71.7%

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

   if 2.3000000000000001e-64 < t < 8.50000000000000069e-49

   1. Initial program 99.7%

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

      1. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. clear-num 99.4%

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

      2. associate-+l+ 99.4%

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

      3. associate-*l/ 80.2%

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

      4. div-inv 80.5%

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

      5. clear-num 80.5%

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

      6. associate-/l/ 80.5%

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

      7. inv-pow 80.5%

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

   6. Applied egg-rr 80.5%

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

      1. unpow-1 80.5%

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

      2. associate-/r/ 80.0%

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

   8. Simplified 80.0%

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

   9. Taylor expanded in y around inf 74.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{b}{z}}} \]

   if 8.50000000000000069e-49 < t

   1. Initial program 82.6%

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

      1. div-inv 82.5%

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

   4. Applied egg-rr 82.5%

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

   5. Taylor expanded in b around 0 73.8%

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

      1. associate-/l* 73.9%

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

      2. associate-/r/ 75.3%

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

   7. Simplified 75.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{b}{\frac{t}{y}}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{1}{\frac{b}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{if}\;a + 1 \leq -2 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a + 1 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq 4 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* z (/ y t))) a)))
   (if (<= (+ a 1.0) -2e+101)
     t_1
     (if (<= (+ a 1.0) -2e+16)
       (/ z b)
       (if (<= (+ a 1.0) 4e+21) (/ x (+ 1.0 (/ (* y b) t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / a;
	double tmp;
	if ((a + 1.0) <= -2e+101) {
		tmp = t_1;
	} else if ((a + 1.0) <= -2e+16) {
		tmp = z / b;
	} else if ((a + 1.0) <= 4e+21) {
		tmp = x / (1.0 + ((y * b) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z * (y / t))) / a
    if ((a + 1.0d0) <= (-2d+101)) then
        tmp = t_1
    else if ((a + 1.0d0) <= (-2d+16)) then
        tmp = z / b
    else if ((a + 1.0d0) <= 4d+21) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / a;
	double tmp;
	if ((a + 1.0) <= -2e+101) {
		tmp = t_1;
	} else if ((a + 1.0) <= -2e+16) {
		tmp = z / b;
	} else if ((a + 1.0) <= 4e+21) {
		tmp = x / (1.0 + ((y * b) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (y / t))) / a
	tmp = 0
	if (a + 1.0) <= -2e+101:
		tmp = t_1
	elif (a + 1.0) <= -2e+16:
		tmp = z / b
	elif (a + 1.0) <= 4e+21:
		tmp = x / (1.0 + ((y * b) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(y / t))) / a)
	tmp = 0.0
	if (Float64(a + 1.0) <= -2e+101)
		tmp = t_1;
	elseif (Float64(a + 1.0) <= -2e+16)
		tmp = Float64(z / b);
	elseif (Float64(a + 1.0) <= 4e+21)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (y / t))) / a;
	tmp = 0.0;
	if ((a + 1.0) <= -2e+101)
		tmp = t_1;
	elseif ((a + 1.0) <= -2e+16)
		tmp = z / b;
	elseif ((a + 1.0) <= 4e+21)
		tmp = x / (1.0 + ((y * b) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[N[(a + 1.0), $MachinePrecision], -2e+101], t$95$1, If[LessEqual[N[(a + 1.0), $MachinePrecision], -2e+16], N[(z / b), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 4e+21], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 a 1) < -2e101 or 4e21 < (+.f64 a 1)

   1. Initial program 77.5%

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

      1. div-inv 77.5%

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

   4. Applied egg-rr 77.5%

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

   5. Taylor expanded in a around inf 66.4%

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

      1. associate-/l* 64.6%

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

      2. associate-/r/ 68.2%

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

   7. Simplified 68.2%

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

   if -2e101 < (+.f64 a 1) < -2e16

   1. Initial program 48.1%

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

   3. Taylor expanded in y around inf 71.7%

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

   if -2e16 < (+.f64 a 1) < 4e21

   1. Initial program 76.1%

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

      1. div-inv 76.1%

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

   4. Applied egg-rr 76.1%

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

   5. Taylor expanded in x around inf 56.7%

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

      1. associate-+r+ 56.7%

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

      2. associate-/l* 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in a around 0 56.7%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -2 \cdot 10^{+101}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{elif}\;a + 1 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq 4 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -2 \cdot 10^{+101}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a + 1 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq 4 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ a 1.0) -2e+101)
   (/ (+ x (/ (* y z) t)) a)
   (if (<= (+ a 1.0) -2e+16)
     (/ z b)
     (if (<= (+ a 1.0) 4e+21)
       (/ x (+ 1.0 (/ (* y b) t)))
       (/ (+ x (* z (/ y t))) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a + 1.0) <= -2e+101) {
		tmp = (x + ((y * z) / t)) / a;
	} else if ((a + 1.0) <= -2e+16) {
		tmp = z / b;
	} else if ((a + 1.0) <= 4e+21) {
		tmp = x / (1.0 + ((y * b) / t));
	} else {
		tmp = (x + (z * (y / t))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a + 1.0d0) <= (-2d+101)) then
        tmp = (x + ((y * z) / t)) / a
    else if ((a + 1.0d0) <= (-2d+16)) then
        tmp = z / b
    else if ((a + 1.0d0) <= 4d+21) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else
        tmp = (x + (z * (y / t))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a + 1.0) <= -2e+101) {
		tmp = (x + ((y * z) / t)) / a;
	} else if ((a + 1.0) <= -2e+16) {
		tmp = z / b;
	} else if ((a + 1.0) <= 4e+21) {
		tmp = x / (1.0 + ((y * b) / t));
	} else {
		tmp = (x + (z * (y / t))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a + 1.0) <= -2e+101:
		tmp = (x + ((y * z) / t)) / a
	elif (a + 1.0) <= -2e+16:
		tmp = z / b
	elif (a + 1.0) <= 4e+21:
		tmp = x / (1.0 + ((y * b) / t))
	else:
		tmp = (x + (z * (y / t))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a + 1.0) <= -2e+101)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	elseif (Float64(a + 1.0) <= -2e+16)
		tmp = Float64(z / b);
	elseif (Float64(a + 1.0) <= 4e+21)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a + 1.0) <= -2e+101)
		tmp = (x + ((y * z) / t)) / a;
	elseif ((a + 1.0) <= -2e+16)
		tmp = z / b;
	elseif ((a + 1.0) <= 4e+21)
		tmp = x / (1.0 + ((y * b) / t));
	else
		tmp = (x + (z * (y / t))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a + 1.0), $MachinePrecision], -2e+101], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], -2e+16], N[(z / b), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 4e+21], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 a 1) < -2e101

   1. Initial program 81.9%

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

   3. Taylor expanded in a around inf 76.5%

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

   if -2e101 < (+.f64 a 1) < -2e16

   1. Initial program 48.1%

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

   3. Taylor expanded in y around inf 71.7%

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

   if -2e16 < (+.f64 a 1) < 4e21

   1. Initial program 76.1%

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

      1. div-inv 76.1%

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

   4. Applied egg-rr 76.1%

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

   5. Taylor expanded in x around inf 56.7%

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

      1. associate-+r+ 56.7%

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

      2. associate-/l* 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in a around 0 56.7%

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

   if 4e21 < (+.f64 a 1)

   1. Initial program 74.6%

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

      1. div-inv 74.6%

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

   4. Applied egg-rr 74.6%

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

   5. Taylor expanded in a around inf 59.7%

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

      1. associate-/l* 58.3%

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

      2. associate-/r/ 64.2%

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

   7. Simplified 64.2%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -2 \cdot 10^{+101}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a + 1 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq 4 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.12 \cdot 10^{+49}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.12e+49)
   (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (* b (/ y t)))))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.12e+49) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (b * (y / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.12d+49) then
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (b * (y / t))))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.12e+49) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (b * (y / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.12e+49:
		tmp = (x + (z * (y / t))) / (a + (1.0 + (b * (y / t))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.12e+49)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(b * Float64(y / t)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.12e+49)
		tmp = (x + (z * (y / t))) / (a + (1.0 + (b * (y / t))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.12e+49], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.12000000000000005e49

   1. Initial program 82.8%

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

      1. associate-*l/ 84.3%

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

      2. associate-+l+ 84.3%

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

      3. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   if 1.12000000000000005e49 < y

   1. Initial program 52.4%

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

   3. Taylor expanded in y around inf 62.6%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.12 \cdot 10^{+49}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 53.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -6.4 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-123}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-50}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -6.4e+34)
     t_1
     (if (<= t -8.8e-123) (* (/ t y) (/ x b)) (if (<= t 7e-50) (/ z b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -6.4e+34) {
		tmp = t_1;
	} else if (t <= -8.8e-123) {
		tmp = (t / y) * (x / b);
	} else if (t <= 7e-50) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-6.4d+34)) then
        tmp = t_1
    else if (t <= (-8.8d-123)) then
        tmp = (t / y) * (x / b)
    else if (t <= 7d-50) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -6.4e+34) {
		tmp = t_1;
	} else if (t <= -8.8e-123) {
		tmp = (t / y) * (x / b);
	} else if (t <= 7e-50) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -6.4e+34:
		tmp = t_1
	elif t <= -8.8e-123:
		tmp = (t / y) * (x / b)
	elif t <= 7e-50:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -6.4e+34)
		tmp = t_1;
	elseif (t <= -8.8e-123)
		tmp = Float64(Float64(t / y) * Float64(x / b));
	elseif (t <= 7e-50)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -6.4e+34)
		tmp = t_1;
	elseif (t <= -8.8e-123)
		tmp = (t / y) * (x / b);
	elseif (t <= 7e-50)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.4e+34], t$95$1, If[LessEqual[t, -8.8e-123], N[(N[(t / y), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-50], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.3999999999999997e34 or 6.99999999999999993e-50 < t

   1. Initial program 82.8%

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

   3. Taylor expanded in y around 0 62.8%

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

   if -6.3999999999999997e34 < t < -8.80000000000000025e-123

   1. Initial program 79.7%

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

      1. div-inv 79.8%

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

   4. Applied egg-rr 79.8%

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

   5. Taylor expanded in x around inf 53.7%

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

      1. associate-+r+ 53.7%

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

      2. associate-/l* 53.8%

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

   7. Simplified 53.8%

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

   8. Taylor expanded in b around inf 39.8%

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

      1. *-commutative 39.8%

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

      2. times-frac 46.3%

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

   10. Simplified 46.3%

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

   if -8.80000000000000025e-123 < t < 6.99999999999999993e-50

   1. Initial program 63.9%

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

   3. Taylor expanded in y around inf 64.0%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-123}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-50}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 42.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+166}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.2e+36)
   (/ x a)
   (if (<= t 1.5e-47) (/ z b) (if (<= t 1.3e+166) (/ x a) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.2e+36) {
		tmp = x / a;
	} else if (t <= 1.5e-47) {
		tmp = z / b;
	} else if (t <= 1.3e+166) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.2d+36)) then
        tmp = x / a
    else if (t <= 1.5d-47) then
        tmp = z / b
    else if (t <= 1.3d+166) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.2e+36) {
		tmp = x / a;
	} else if (t <= 1.5e-47) {
		tmp = z / b;
	} else if (t <= 1.3e+166) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.2e+36:
		tmp = x / a
	elif t <= 1.5e-47:
		tmp = z / b
	elif t <= 1.3e+166:
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.2e+36)
		tmp = Float64(x / a);
	elseif (t <= 1.5e-47)
		tmp = Float64(z / b);
	elseif (t <= 1.3e+166)
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.2e+36)
		tmp = x / a;
	elseif (t <= 1.5e-47)
		tmp = z / b;
	elseif (t <= 1.3e+166)
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.2e+36], N[(x / a), $MachinePrecision], If[LessEqual[t, 1.5e-47], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.3e+166], N[(x / a), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.19999999999999996e36 or 1.50000000000000008e-47 < t < 1.3e166

   1. Initial program 82.8%

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

   3. Taylor expanded in y around 0 57.5%

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

   4. Taylor expanded in a around inf 42.8%

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

   if -1.19999999999999996e36 < t < 1.50000000000000008e-47

   1. Initial program 67.3%

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

   3. Taylor expanded in y around inf 55.8%

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

   if 1.3e166 < t

   1. Initial program 83.1%

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

   3. Taylor expanded in y around 0 80.4%

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

   4. Taylor expanded in a around 0 56.9%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+166}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 55.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+34} \lor \neg \left(t \leq 1.18 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9e+34) (not (<= t 1.18e-45))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9e+34) || !(t <= 1.18e-45)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-9d+34)) .or. (.not. (t <= 1.18d-45))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9e+34) || !(t <= 1.18e-45)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9e+34) or not (t <= 1.18e-45):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9e+34) || !(t <= 1.18e-45))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -9e+34) || ~((t <= 1.18e-45)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9e+34], N[Not[LessEqual[t, 1.18e-45]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.0000000000000001e34 or 1.18e-45 < t

   1. Initial program 82.8%

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

   3. Taylor expanded in y around 0 62.8%

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

   if -9.0000000000000001e34 < t < 1.18e-45

   1. Initial program 67.3%

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

   3. Taylor expanded in y around inf 55.8%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+34} \lor \neg \left(t \leq 1.18 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 41.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-14} \lor \neg \left(a \leq 2.9 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -7.5e-14) (not (<= a 2.9e-13))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7.5e-14) || !(a <= 2.9e-13)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	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 <= (-7.5d-14)) .or. (.not. (a <= 2.9d-13))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7.5e-14) || !(a <= 2.9e-13)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -7.5e-14) or not (a <= 2.9e-13):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -7.5e-14) || !(a <= 2.9e-13))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -7.5e-14) || ~((a <= 2.9e-13)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -7.5e-14], N[Not[LessEqual[a, 2.9e-13]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -7.4999999999999996e-14 or 2.8999999999999998e-13 < a

   1. Initial program 73.4%

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

   3. Taylor expanded in y around 0 42.8%

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

   4. Taylor expanded in a around inf 42.9%

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

   if -7.4999999999999996e-14 < a < 2.8999999999999998e-13

   1. Initial program 76.4%

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

   3. Taylor expanded in y around 0 34.0%

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

   4. Taylor expanded in a around 0 34.0%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-14} \lor \neg \left(a \leq 2.9 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 19.8% 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 74.8%

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

3. Taylor expanded in y around 0 38.6%

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

4. Taylor expanded in a around 0 18.5%

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

5. Final simplification 18.5%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 80.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024034 
(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))))