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

Percentage Accurate: 75.7% → 92.2%

Time: 17.5s

Alternatives: 17

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ t_3 := \mathsf{fma}\left(y, \frac{b}{t}, a\right) + 1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_1} + \frac{y}{t \cdot t\_1}\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-313}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \left(\frac{x}{b} - \frac{z \cdot \left(a + 1\right)}{{b}^{2}}\right)}{y}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+248}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{\frac{y}{t}}{t\_3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (/ (* y b) t)))
        (t_2 (/ (+ x (/ (* y z) t)) t_1))
        (t_3 (+ (fma y (/ b t) a) 1.0)))
   (if (<= t_2 (- INFINITY))
     (* z (+ (/ x (* z t_1)) (/ y (* t t_1))))
     (if (<= t_2 -5e-313)
       t_2
       (if (<= t_2 0.0)
         (+ (/ z b) (/ (* t (- (/ x b) (/ (* z (+ a 1.0)) (pow b 2.0)))) y))
         (if (<= t_2 5e+248)
           t_2
           (if (<= t_2 INFINITY)
             (* z (+ (/ x (* z t_3)) (/ (/ y t) t_3)))
             (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + ((y * b) / t);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double t_3 = fma(y, (b / t), a) + 1.0;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * ((x / (z * t_1)) + (y / (t * t_1)));
	} else if (t_2 <= -5e-313) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * ((x / b) - ((z * (a + 1.0)) / pow(b, 2.0)))) / y);
	} else if (t_2 <= 5e+248) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = z * ((x / (z * t_3)) + ((y / t) / t_3));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	t_3 = Float64(fma(y, Float64(b / t), a) + 1.0)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_1)) + Float64(y / Float64(t * t_1))));
	elseif (t_2 <= -5e-313)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(Float64(x / b) - Float64(Float64(z * Float64(a + 1.0)) / (b ^ 2.0)))) / y));
	elseif (t_2 <= 5e+248)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_3)) + Float64(Float64(y / t) / t_3)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(N[(x / N[(z * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-313], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(N[(x / b), $MachinePrecision] - N[(N[(z * N[(a + 1.0), $MachinePrecision]), $MachinePrecision] / N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+248], t$95$2, If[LessEqual[t$95$2, Infinity], N[(z * N[(N[(x / N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 40.4%

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

      1. associate-/l* 52.0%

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

      2. associate-/l* 51.8%

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

   3. Simplified 51.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5.00000000002e-313 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.9999999999999996e248

   1. Initial program 99.3%

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

   if -5.00000000002e-313 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 57.5%

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

      1. associate-/l* 57.4%

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

      2. associate-/l* 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in y around -inf 68.7%

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

      1. +-commutative 68.7%

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

      2. mul-1-neg 68.7%

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

      3. unsub-neg 68.7%

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

      4. distribute-lft-out-- 68.7%

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

      5. mul-1-neg 68.7%

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

      6. associate-/l* 73.8%

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

      7. associate-/l* 81.8%

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

      8. distribute-lft-out-- 81.8%

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

   7. Simplified 81.8%

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

   if 4.9999999999999996e248 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 56.0%

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

      1. associate-/l* 92.7%

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

      2. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-*r/ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-*r/ 99.8%

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

      4. associate-*l/ 99.8%

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

      5. *-commutative 99.8%

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

      6. fma-define 99.8%

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

      7. associate-/r* 99.8%

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

      8. associate-*r/ 69.0%

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

      9. +-commutative 69.0%

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

      10. associate-*r/ 99.8%

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

      11. associate-*l/ 99.9%

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

      12. *-commutative 99.9%

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

      13. fma-define 99.9%

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

   7. Simplified 99.9%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.2%

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

      2. associate-/l* 0.5%

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

   3. Simplified 0.5%

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

   5. Taylor expanded in y around inf 96.3%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)} + \frac{y}{t \cdot \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -5 \cdot 10^{-313}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \left(\frac{x}{b} - \frac{z \cdot \left(a + 1\right)}{{b}^{2}}\right)}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+248}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(\mathsf{fma}\left(y, \frac{b}{t}, a\right) + 1\right)} + \frac{\frac{y}{t}}{\mathsf{fma}\left(y, \frac{b}{t}, a\right) + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ t_3 := z \cdot \left(\frac{x}{z \cdot t\_1} + \frac{y}{t \cdot t\_1}\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-313}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \left(\frac{x}{b} - \frac{z \cdot \left(a + 1\right)}{{b}^{2}}\right)}{y}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+248}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (/ (* y b) t)))
        (t_2 (/ (+ x (/ (* y z) t)) t_1))
        (t_3 (* z (+ (/ x (* z t_1)) (/ y (* t t_1))))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -5e-313)
       t_2
       (if (<= t_2 0.0)
         (+ (/ z b) (/ (* t (- (/ x b) (/ (* z (+ a 1.0)) (pow b 2.0)))) y))
         (if (<= t_2 5e+248) t_2 (if (<= t_2 INFINITY) t_3 (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + ((y * b) / t);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double t_3 = z * ((x / (z * t_1)) + (y / (t * t_1)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -5e-313) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * ((x / b) - ((z * (a + 1.0)) / pow(b, 2.0)))) / y);
	} else if (t_2 <= 5e+248) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} 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 = (a + 1.0) + ((y * b) / t);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double t_3 = z * ((x / (z * t_1)) + (y / (t * t_1)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -5e-313) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * ((x / b) - ((z * (a + 1.0)) / Math.pow(b, 2.0)))) / y);
	} else if (t_2 <= 5e+248) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + ((y * b) / t)
	t_2 = (x + ((y * z) / t)) / t_1
	t_3 = z * ((x / (z * t_1)) + (y / (t * t_1)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -5e-313:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (z / b) + ((t * ((x / b) - ((z * (a + 1.0)) / math.pow(b, 2.0)))) / y)
	elif t_2 <= 5e+248:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	t_3 = Float64(z * Float64(Float64(x / Float64(z * t_1)) + Float64(y / Float64(t * t_1))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -5e-313)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(Float64(x / b) - Float64(Float64(z * Float64(a + 1.0)) / (b ^ 2.0)))) / y));
	elseif (t_2 <= 5e+248)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + ((y * b) / t);
	t_2 = (x + ((y * z) / t)) / t_1;
	t_3 = z * ((x / (z * t_1)) + (y / (t * t_1)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -5e-313)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (z / b) + ((t * ((x / b) - ((z * (a + 1.0)) / (b ^ 2.0)))) / y);
	elseif (t_2 <= 5e+248)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x / N[(z * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -5e-313], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(N[(x / b), $MachinePrecision] - N[(N[(z * N[(a + 1.0), $MachinePrecision]), $MachinePrecision] / N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+248], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, N[(z / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or 4.9999999999999996e248 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 50.1%

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

      1. associate-/l* 77.2%

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

      2. associate-/l* 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5.00000000002e-313 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.9999999999999996e248

   1. Initial program 99.3%

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

   if -5.00000000002e-313 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 57.5%

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

      1. associate-/l* 57.4%

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

      2. associate-/l* 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in y around -inf 68.7%

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

      1. +-commutative 68.7%

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

      2. mul-1-neg 68.7%

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

      3. unsub-neg 68.7%

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

      4. distribute-lft-out-- 68.7%

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

      5. mul-1-neg 68.7%

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

      6. associate-/l* 73.8%

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

      7. associate-/l* 81.8%

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

      8. distribute-lft-out-- 81.8%

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

   7. Simplified 81.8%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.2%

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

      2. associate-/l* 0.5%

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

   3. Simplified 0.5%

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

   5. Taylor expanded in y around inf 96.3%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)} + \frac{y}{t \cdot \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -5 \cdot 10^{-313}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \left(\frac{x}{b} - \frac{z \cdot \left(a + 1\right)}{{b}^{2}}\right)}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+248}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)} + \frac{y}{t \cdot \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ t_3 := z \cdot \left(\frac{x}{z \cdot t\_1} + \frac{y}{t \cdot t\_1}\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-313}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+248}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (/ (* y b) t)))
        (t_2 (/ (+ x (/ (* y z) t)) t_1))
        (t_3 (* z (+ (/ x (* z t_1)) (/ y (* t t_1))))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -5e-313)
       t_2
       (if (<= t_2 0.0)
         (/ z b)
         (if (<= t_2 5e+248) t_2 (if (<= t_2 INFINITY) t_3 (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + ((y * b) / t);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double t_3 = z * ((x / (z * t_1)) + (y / (t * t_1)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -5e-313) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = z / b;
	} else if (t_2 <= 5e+248) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} 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 = (a + 1.0) + ((y * b) / t);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double t_3 = z * ((x / (z * t_1)) + (y / (t * t_1)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -5e-313) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = z / b;
	} else if (t_2 <= 5e+248) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + ((y * b) / t)
	t_2 = (x + ((y * z) / t)) / t_1
	t_3 = z * ((x / (z * t_1)) + (y / (t * t_1)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -5e-313:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = z / b
	elif t_2 <= 5e+248:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	t_3 = Float64(z * Float64(Float64(x / Float64(z * t_1)) + Float64(y / Float64(t * t_1))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -5e-313)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(z / b);
	elseif (t_2 <= 5e+248)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + ((y * b) / t);
	t_2 = (x + ((y * z) / t)) / t_1;
	t_3 = z * ((x / (z * t_1)) + (y / (t * t_1)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -5e-313)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = z / b;
	elseif (t_2 <= 5e+248)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x / N[(z * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -5e-313], t$95$2, If[LessEqual[t$95$2, 0.0], N[(z / b), $MachinePrecision], If[LessEqual[t$95$2, 5e+248], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, N[(z / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or 4.9999999999999996e248 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 50.1%

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

      1. associate-/l* 77.2%

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

      2. associate-/l* 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5.00000000002e-313 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.9999999999999996e248

   1. Initial program 99.3%

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

   if -5.00000000002e-313 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0 or +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 34.1%

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

      1. associate-/l* 34.1%

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

      2. associate-/l* 43.2%

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

   3. Simplified 43.2%

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

   5. Taylor expanded in y around inf 82.2%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)} + \frac{y}{t \cdot \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -5 \cdot 10^{-313}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+248}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)} + \frac{y}{t \cdot \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \left(a + t\_1\right) + 1\\ t_3 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + t\_1}\\ t_4 := \frac{x}{t\_2} + \frac{y \cdot z}{t \cdot t\_2}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{-246}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{-277}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+248}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ (+ a t_1) 1.0))
        (t_3 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) t_1)))
        (t_4 (+ (/ x t_2) (/ (* y z) (* t t_2)))))
   (if (<= t_3 -5e-246)
     t_4
     (if (<= t_3 4e-277)
       (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (/ y (/ t b))))
       (if (<= t_3 5e+248) t_4 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (a + t_1) + 1.0;
	double t_3 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double t_4 = (x / t_2) + ((y * z) / (t * t_2));
	double tmp;
	if (t_3 <= -5e-246) {
		tmp = t_4;
	} else if (t_3 <= 4e-277) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	} else if (t_3 <= 5e+248) {
		tmp = t_4;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (y * b) / t
    t_2 = (a + t_1) + 1.0d0
    t_3 = (x + ((y * z) / t)) / ((a + 1.0d0) + t_1)
    t_4 = (x / t_2) + ((y * z) / (t * t_2))
    if (t_3 <= (-5d-246)) then
        tmp = t_4
    else if (t_3 <= 4d-277) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y / (t / b)))
    else if (t_3 <= 5d+248) then
        tmp = t_4
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (a + t_1) + 1.0;
	double t_3 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double t_4 = (x / t_2) + ((y * z) / (t * t_2));
	double tmp;
	if (t_3 <= -5e-246) {
		tmp = t_4;
	} else if (t_3 <= 4e-277) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	} else if (t_3 <= 5e+248) {
		tmp = t_4;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (a + t_1) + 1.0
	t_3 = (x + ((y * z) / t)) / ((a + 1.0) + t_1)
	t_4 = (x / t_2) + ((y * z) / (t * t_2))
	tmp = 0
	if t_3 <= -5e-246:
		tmp = t_4
	elif t_3 <= 4e-277:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)))
	elif t_3 <= 5e+248:
		tmp = t_4
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(Float64(a + t_1) + 1.0)
	t_3 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + t_1))
	t_4 = Float64(Float64(x / t_2) + Float64(Float64(y * z) / Float64(t * t_2)))
	tmp = 0.0
	if (t_3 <= -5e-246)
		tmp = t_4;
	elseif (t_3 <= 4e-277)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t_3 <= 5e+248)
		tmp = t_4;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = (a + t_1) + 1.0;
	t_3 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	t_4 = (x / t_2) + ((y * z) / (t * t_2));
	tmp = 0.0;
	if (t_3 <= -5e-246)
		tmp = t_4;
	elseif (t_3 <= 4e-277)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	elseif (t_3 <= 5e+248)
		tmp = t_4;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + t$95$1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x / t$95$2), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e-246], t$95$4, If[LessEqual[t$95$3, 4e-277], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+248], t$95$4, N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -4.9999999999999997e-246 or 3.99999999999999988e-277 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.9999999999999996e248

   1. Initial program 96.8%

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

      1. associate-/l* 92.2%

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

      2. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around 0 97.5%

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

   if -4.9999999999999997e-246 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 3.99999999999999988e-277

   1. Initial program 67.1%

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

      1. associate-/l* 68.1%

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

      2. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

      1. clear-num 77.6%

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

      2. un-div-inv 77.6%

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

   6. Applied egg-rr 77.6%

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

   if 4.9999999999999996e248 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 18.7%

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

      1. associate-/l* 31.0%

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

      2. associate-/l* 31.3%

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

   3. Simplified 31.3%

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

   5. Taylor expanded in y around inf 85.2%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -5 \cdot 10^{-246}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1} + \frac{y \cdot z}{t \cdot \left(\left(a + \frac{y \cdot b}{t}\right) + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 4 \cdot 10^{-277}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+248}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1} + \frac{y \cdot z}{t \cdot \left(\left(a + \frac{y \cdot b}{t}\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-313} \lor \neg \left(t\_1 \leq 0\right) \land t\_1 \leq 5 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (or (<= t_1 -5e-313) (and (not (<= t_1 0.0)) (<= t_1 5e+248)))
     t_1
     (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if ((t_1 <= -5e-313) || (!(t_1 <= 0.0) && (t_1 <= 5e+248))) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
    if ((t_1 <= (-5d-313)) .or. (.not. (t_1 <= 0.0d0)) .and. (t_1 <= 5d+248)) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if ((t_1 <= -5e-313) || (!(t_1 <= 0.0) && (t_1 <= 5e+248))) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if (t_1 <= -5e-313) or (not (t_1 <= 0.0) and (t_1 <= 5e+248)):
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if ((t_1 <= -5e-313) || (!(t_1 <= 0.0) && (t_1 <= 5e+248)))
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if ((t_1 <= -5e-313) || (~((t_1 <= 0.0)) && (t_1 <= 5e+248)))
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-313], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 5e+248]]], t$95$1, N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5.00000000002e-313 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.9999999999999996e248

   1. Initial program 96.7%

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

   if -5.00000000002e-313 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0 or 4.9999999999999996e248 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 37.8%

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

      1. associate-/l* 44.0%

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

      2. associate-/l* 51.6%

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

   3. Simplified 51.6%

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

   5. Taylor expanded in y around inf 79.0%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -5 \cdot 10^{-313} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0\right) \land \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+248}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{a + 1}\\ t_2 := z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.35 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+280}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ a 1.0)))
        (t_2 (* z (/ (+ (* (/ t y) (/ x z)) 1.0) b))))
   (if (<= b -2.5e+84)
     t_2
     (if (<= b 3.7e+56)
       t_1
       (if (<= b 4.8e+97)
         t_2
         (if (<= b 4.35e+148)
           t_1
           (if (<= b 3.1e+280) t_2 (/ x (+ (+ a 1.0) (/ (* y b) t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (a + 1.0);
	double t_2 = z * ((((t / y) * (x / z)) + 1.0) / b);
	double tmp;
	if (b <= -2.5e+84) {
		tmp = t_2;
	} else if (b <= 3.7e+56) {
		tmp = t_1;
	} else if (b <= 4.8e+97) {
		tmp = t_2;
	} else if (b <= 4.35e+148) {
		tmp = t_1;
	} else if (b <= 3.1e+280) {
		tmp = t_2;
	} else {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / (a + 1.0d0)
    t_2 = z * ((((t / y) * (x / z)) + 1.0d0) / b)
    if (b <= (-2.5d+84)) then
        tmp = t_2
    else if (b <= 3.7d+56) then
        tmp = t_1
    else if (b <= 4.8d+97) then
        tmp = t_2
    else if (b <= 4.35d+148) then
        tmp = t_1
    else if (b <= 3.1d+280) then
        tmp = t_2
    else
        tmp = x / ((a + 1.0d0) + ((y * b) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (a + 1.0);
	double t_2 = z * ((((t / y) * (x / z)) + 1.0) / b);
	double tmp;
	if (b <= -2.5e+84) {
		tmp = t_2;
	} else if (b <= 3.7e+56) {
		tmp = t_1;
	} else if (b <= 4.8e+97) {
		tmp = t_2;
	} else if (b <= 4.35e+148) {
		tmp = t_1;
	} else if (b <= 3.1e+280) {
		tmp = t_2;
	} else {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (a + 1.0)
	t_2 = z * ((((t / y) * (x / z)) + 1.0) / b)
	tmp = 0
	if b <= -2.5e+84:
		tmp = t_2
	elif b <= 3.7e+56:
		tmp = t_1
	elif b <= 4.8e+97:
		tmp = t_2
	elif b <= 4.35e+148:
		tmp = t_1
	elif b <= 3.1e+280:
		tmp = t_2
	else:
		tmp = x / ((a + 1.0) + ((y * b) / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0))
	t_2 = Float64(z * Float64(Float64(Float64(Float64(t / y) * Float64(x / z)) + 1.0) / b))
	tmp = 0.0
	if (b <= -2.5e+84)
		tmp = t_2;
	elseif (b <= 3.7e+56)
		tmp = t_1;
	elseif (b <= 4.8e+97)
		tmp = t_2;
	elseif (b <= 4.35e+148)
		tmp = t_1;
	elseif (b <= 3.1e+280)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (a + 1.0);
	t_2 = z * ((((t / y) * (x / z)) + 1.0) / b);
	tmp = 0.0;
	if (b <= -2.5e+84)
		tmp = t_2;
	elseif (b <= 3.7e+56)
		tmp = t_1;
	elseif (b <= 4.8e+97)
		tmp = t_2;
	elseif (b <= 4.35e+148)
		tmp = t_1;
	elseif (b <= 3.1e+280)
		tmp = t_2;
	else
		tmp = x / ((a + 1.0) + ((y * b) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(N[(N[(t / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e+84], t$95$2, If[LessEqual[b, 3.7e+56], t$95$1, If[LessEqual[b, 4.8e+97], t$95$2, If[LessEqual[b, 4.35e+148], t$95$1, If[LessEqual[b, 3.1e+280], t$95$2, N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.5e84 or 3.69999999999999997e56 < b < 4.8e97 or 4.34999999999999996e148 < b < 3.0999999999999999e280

   1. Initial program 64.5%

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

      1. associate-/l* 62.0%

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

      2. associate-/l* 58.0%

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

   3. Simplified 58.0%

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

   5. Taylor expanded in z around inf 66.3%

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

      1. associate-+r+ 66.3%

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

      2. *-commutative 66.3%

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

      3. associate-+r+ 66.3%

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

      4. *-commutative 66.3%

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

   7. Simplified 66.3%

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

   8. Taylor expanded in b around inf 64.2%

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

      1. associate-/l* 64.1%

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

      2. times-frac 66.0%

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

   10. Simplified 66.0%

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

   if -2.5e84 < b < 3.69999999999999997e56 or 4.8e97 < b < 4.34999999999999996e148

   1. Initial program 87.3%

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

      1. associate-/l* 87.3%

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

      2. associate-/l* 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in b around 0 79.3%

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

   if 3.0999999999999999e280 < b

   1. Initial program 86.1%

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

      1. associate-/l* 86.1%

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

      2. associate-/l* 72.7%

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

   3. Simplified 72.7%

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

   5. Taylor expanded in x around inf 86.1%

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

      1. associate-+r+ 86.1%

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

      2. *-commutative 86.1%

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

   7. Simplified 86.1%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+84}:\\ \;\;\;\;z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+56}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \mathbf{elif}\;b \leq 4.35 \cdot 10^{+148}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+280}:\\ \;\;\;\;z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-177}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-208}:\\ \;\;\;\;z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-227}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5e-177)
   (/ (+ x (/ y (/ t z))) (+ (+ a 1.0) (* y (/ b t))))
   (if (<= t -1.65e-208)
     (* z (/ (+ (* (/ t y) (/ x z)) 1.0) b))
     (if (<= t -5.2e-227)
       (/ x (+ (+ a 1.0) (/ (* y b) t)))
       (if (<= t 8.5e-127)
         (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
         (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (/ y (/ t b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5e-177) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= -1.65e-208) {
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b);
	} else if (t <= -5.2e-227) {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	} else if (t <= 8.5e-127) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5d-177)) then
        tmp = (x + (y / (t / z))) / ((a + 1.0d0) + (y * (b / t)))
    else if (t <= (-1.65d-208)) then
        tmp = z * ((((t / y) * (x / z)) + 1.0d0) / b)
    else if (t <= (-5.2d-227)) then
        tmp = x / ((a + 1.0d0) + ((y * b) / t))
    else if (t <= 8.5d-127) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y / (t / b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5e-177) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= -1.65e-208) {
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b);
	} else if (t <= -5.2e-227) {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	} else if (t <= 8.5e-127) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5e-177:
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)))
	elif t <= -1.65e-208:
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b)
	elif t <= -5.2e-227:
		tmp = x / ((a + 1.0) + ((y * b) / t))
	elif t <= 8.5e-127:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	else:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5e-177)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t <= -1.65e-208)
		tmp = Float64(z * Float64(Float64(Float64(Float64(t / y) * Float64(x / z)) + 1.0) / b));
	elseif (t <= -5.2e-227)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)));
	elseif (t <= 8.5e-127)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5e-177)
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	elseif (t <= -1.65e-208)
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b);
	elseif (t <= -5.2e-227)
		tmp = x / ((a + 1.0) + ((y * b) / t));
	elseif (t <= 8.5e-127)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	else
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5e-177], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.65e-208], N[(z * N[(N[(N[(N[(t / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.2e-227], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-127], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5e-177

   1. Initial program 82.3%

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

      1. associate-/l* 83.7%

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

      2. associate-/l* 85.6%

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

   3. Simplified 85.6%

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

      1. clear-num 85.6%

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

      2. un-div-inv 86.6%

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

   6. Applied egg-rr 86.6%

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

   if -5e-177 < t < -1.65000000000000003e-208

   1. Initial program 51.5%

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

      1. associate-/l* 51.5%

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

      2. associate-/l* 39.3%

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

   3. Simplified 39.3%

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

   5. Taylor expanded in z around inf 52.7%

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

      1. associate-+r+ 52.7%

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

      2. *-commutative 52.7%

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

      3. associate-+r+ 52.7%

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

      4. *-commutative 52.7%

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

   7. Simplified 52.7%

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

   8. Taylor expanded in b around inf 75.3%

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

      1. associate-/l* 75.1%

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

      2. times-frac 99.8%

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

   10. Simplified 99.8%

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

   if -1.65000000000000003e-208 < t < -5.20000000000000023e-227

   1. Initial program 87.7%

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

      1. associate-/l* 75.8%

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

      2. associate-/l* 52.3%

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

   3. Simplified 52.3%

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

   5. Taylor expanded in x around inf 75.8%

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

      1. associate-+r+ 75.8%

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

      2. *-commutative 75.8%

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

   7. Simplified 75.8%

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

   if -5.20000000000000023e-227 < t < 8.5e-127

   1. Initial program 66.8%

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

      1. associate-/l* 57.4%

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

      2. associate-/l* 46.0%

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

   3. Simplified 46.0%

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

   5. Taylor expanded in x around 0 53.9%

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

   6. Taylor expanded in t around 0 73.0%

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

   if 8.5e-127 < t

   1. Initial program 84.2%

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

      1. associate-/l* 86.6%

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

      2. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

      1. clear-num 87.8%

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

      2. un-div-inv 88.2%

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

   6. Applied egg-rr 88.2%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-177}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-208}:\\ \;\;\;\;z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-227}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -3.05 \cdot 10^{-176}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-207}:\\ \;\;\;\;z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-228}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-126}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= t -3.05e-176)
     (/ t_1 (+ (+ a 1.0) (* y (/ b t))))
     (if (<= t -1.08e-207)
       (* z (/ (+ (* (/ t y) (/ x z)) 1.0) b))
       (if (<= t -4.7e-228)
         (/ x (+ (+ a 1.0) (/ (* y b) t)))
         (if (<= t 3.9e-126)
           (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
           (/ t_1 (+ (+ a 1.0) (/ y (/ t b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (t <= -3.05e-176) {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	} else if (t <= -1.08e-207) {
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b);
	} else if (t <= -4.7e-228) {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	} else if (t <= 3.9e-126) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (t <= (-3.05d-176)) then
        tmp = t_1 / ((a + 1.0d0) + (y * (b / t)))
    else if (t <= (-1.08d-207)) then
        tmp = z * ((((t / y) * (x / z)) + 1.0d0) / b)
    else if (t <= (-4.7d-228)) then
        tmp = x / ((a + 1.0d0) + ((y * b) / t))
    else if (t <= 3.9d-126) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else
        tmp = t_1 / ((a + 1.0d0) + (y / (t / b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (t <= -3.05e-176) {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	} else if (t <= -1.08e-207) {
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b);
	} else if (t <= -4.7e-228) {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	} else if (t <= 3.9e-126) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	tmp = 0
	if t <= -3.05e-176:
		tmp = t_1 / ((a + 1.0) + (y * (b / t)))
	elif t <= -1.08e-207:
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b)
	elif t <= -4.7e-228:
		tmp = x / ((a + 1.0) + ((y * b) / t))
	elif t <= 3.9e-126:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	else:
		tmp = t_1 / ((a + 1.0) + (y / (t / b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -3.05e-176)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t <= -1.08e-207)
		tmp = Float64(z * Float64(Float64(Float64(Float64(t / y) * Float64(x / z)) + 1.0) / b));
	elseif (t <= -4.7e-228)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)));
	elseif (t <= 3.9e-126)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	else
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (t <= -3.05e-176)
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	elseif (t <= -1.08e-207)
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b);
	elseif (t <= -4.7e-228)
		tmp = x / ((a + 1.0) + ((y * b) / t));
	elseif (t <= 3.9e-126)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	else
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.05e-176], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.08e-207], N[(z * N[(N[(N[(N[(t / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.7e-228], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-126], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.0500000000000001e-176

   1. Initial program 82.3%

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

      1. associate-/l* 83.7%

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

      2. associate-/l* 85.6%

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

   3. Simplified 85.6%

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

   if -3.0500000000000001e-176 < t < -1.08e-207

   1. Initial program 51.5%

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

      1. associate-/l* 51.5%

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

      2. associate-/l* 39.3%

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

   3. Simplified 39.3%

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

   5. Taylor expanded in z around inf 52.7%

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

      1. associate-+r+ 52.7%

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

      2. *-commutative 52.7%

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

      3. associate-+r+ 52.7%

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

      4. *-commutative 52.7%

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

   7. Simplified 52.7%

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

   8. Taylor expanded in b around inf 75.3%

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

      1. associate-/l* 75.1%

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

      2. times-frac 99.8%

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

   10. Simplified 99.8%

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

   if -1.08e-207 < t < -4.7000000000000002e-228

   1. Initial program 87.7%

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

      1. associate-/l* 75.8%

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

      2. associate-/l* 52.3%

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

   3. Simplified 52.3%

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

   5. Taylor expanded in x around inf 75.8%

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

      1. associate-+r+ 75.8%

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

      2. *-commutative 75.8%

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

   7. Simplified 75.8%

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

   if -4.7000000000000002e-228 < t < 3.8999999999999998e-126

   1. Initial program 66.8%

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

      1. associate-/l* 57.4%

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

      2. associate-/l* 46.0%

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

   3. Simplified 46.0%

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

   5. Taylor expanded in x around 0 53.9%

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

   6. Taylor expanded in t around 0 73.0%

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

   if 3.8999999999999998e-126 < t

   1. Initial program 84.2%

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

      1. associate-/l* 86.6%

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

      2. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

      1. clear-num 87.8%

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

      2. un-div-inv 88.2%

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

   6. Applied egg-rr 88.2%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{-176}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-207}:\\ \;\;\;\;z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-228}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-126}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-207}:\\ \;\;\;\;z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-227}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-126}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -3.4e-179)
     t_1
     (if (<= t -8.6e-207)
       (* z (/ (+ (* (/ t y) (/ x z)) 1.0) b))
       (if (<= t -5.2e-227)
         (/ x (+ (+ a 1.0) (/ (* y b) t)))
         (if (<= t 1.7e-126) (/ (* y z) (+ (* y b) (* t (+ a 1.0)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -3.4e-179) {
		tmp = t_1;
	} else if (t <= -8.6e-207) {
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b);
	} else if (t <= -5.2e-227) {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	} else if (t <= 1.7e-126) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    if (t <= (-3.4d-179)) then
        tmp = t_1
    else if (t <= (-8.6d-207)) then
        tmp = z * ((((t / y) * (x / z)) + 1.0d0) / b)
    else if (t <= (-5.2d-227)) then
        tmp = x / ((a + 1.0d0) + ((y * b) / t))
    else if (t <= 1.7d-126) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -3.4e-179) {
		tmp = t_1;
	} else if (t <= -8.6e-207) {
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b);
	} else if (t <= -5.2e-227) {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	} else if (t <= 1.7e-126) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	tmp = 0
	if t <= -3.4e-179:
		tmp = t_1
	elif t <= -8.6e-207:
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b)
	elif t <= -5.2e-227:
		tmp = x / ((a + 1.0) + ((y * b) / t))
	elif t <= 1.7e-126:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -3.4e-179)
		tmp = t_1;
	elseif (t <= -8.6e-207)
		tmp = Float64(z * Float64(Float64(Float64(Float64(t / y) * Float64(x / z)) + 1.0) / b));
	elseif (t <= -5.2e-227)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)));
	elseif (t <= 1.7e-126)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -3.4e-179)
		tmp = t_1;
	elseif (t <= -8.6e-207)
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b);
	elseif (t <= -5.2e-227)
		tmp = x / ((a + 1.0) + ((y * b) / t));
	elseif (t <= 1.7e-126)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e-179], t$95$1, If[LessEqual[t, -8.6e-207], N[(z * N[(N[(N[(N[(t / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.2e-227], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-126], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.3999999999999997e-179 or 1.7e-126 < t

   1. Initial program 83.1%

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

      1. associate-/l* 84.9%

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

      2. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   if -3.3999999999999997e-179 < t < -8.6000000000000005e-207

   1. Initial program 51.5%

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

      1. associate-/l* 51.5%

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

      2. associate-/l* 39.3%

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

   3. Simplified 39.3%

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

   5. Taylor expanded in z around inf 52.7%

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

      1. associate-+r+ 52.7%

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

      2. *-commutative 52.7%

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

      3. associate-+r+ 52.7%

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

      4. *-commutative 52.7%

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

   7. Simplified 52.7%

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

   8. Taylor expanded in b around inf 75.3%

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

      1. associate-/l* 75.1%

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

      2. times-frac 99.8%

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

   10. Simplified 99.8%

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

   if -8.6000000000000005e-207 < t < -5.20000000000000023e-227

   1. Initial program 87.7%

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

      1. associate-/l* 75.8%

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

      2. associate-/l* 52.3%

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

   3. Simplified 52.3%

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

   5. Taylor expanded in x around inf 75.8%

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

      1. associate-+r+ 75.8%

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

      2. *-commutative 75.8%

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

   7. Simplified 75.8%

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

   if -5.20000000000000023e-227 < t < 1.7e-126

   1. Initial program 66.8%

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

      1. associate-/l* 57.4%

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

      2. associate-/l* 46.0%

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

   3. Simplified 46.0%

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

   5. Taylor expanded in x around 0 53.9%

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

   6. Taylor expanded in t around 0 73.0%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-179}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-207}:\\ \;\;\;\;z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-227}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-126}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{b \cdot \left(\frac{y}{t} + \frac{a + 1}{b}\right)}\\ \mathbf{if}\;b \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+56}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* b (+ (/ y t) (/ (+ a 1.0) b))))))
   (if (<= b -1e+78)
     t_1
     (if (<= b 2.4e+56)
       (/ (+ x (/ (* y z) t)) (+ a 1.0))
       (if (<= b 4e+97) (* z (/ (+ (* (/ t y) (/ x z)) 1.0) b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (b * ((y / t) + ((a + 1.0) / b)));
	double tmp;
	if (b <= -1e+78) {
		tmp = t_1;
	} else if (b <= 2.4e+56) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (b <= 4e+97) {
		tmp = z * ((((t / y) * (x / z)) + 1.0) / 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 / (b * ((y / t) + ((a + 1.0d0) / b)))
    if (b <= (-1d+78)) then
        tmp = t_1
    else if (b <= 2.4d+56) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (b <= 4d+97) then
        tmp = z * ((((t / y) * (x / z)) + 1.0d0) / 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 / (b * ((y / t) + ((a + 1.0) / b)));
	double tmp;
	if (b <= -1e+78) {
		tmp = t_1;
	} else if (b <= 2.4e+56) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (b <= 4e+97) {
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (b * ((y / t) + ((a + 1.0) / b)))
	tmp = 0
	if b <= -1e+78:
		tmp = t_1
	elif b <= 2.4e+56:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif b <= 4e+97:
		tmp = z * ((((t / y) * (x / z)) + 1.0) / b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(b * Float64(Float64(y / t) + Float64(Float64(a + 1.0) / b))))
	tmp = 0.0
	if (b <= -1e+78)
		tmp = t_1;
	elseif (b <= 2.4e+56)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (b <= 4e+97)
		tmp = Float64(z * Float64(Float64(Float64(Float64(t / y) * Float64(x / z)) + 1.0) / b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (b * ((y / t) + ((a + 1.0) / b)));
	tmp = 0.0;
	if (b <= -1e+78)
		tmp = t_1;
	elseif (b <= 2.4e+56)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (b <= 4e+97)
		tmp = z * ((((t / y) * (x / z)) + 1.0) / 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[(b * N[(N[(y / t), $MachinePrecision] + N[(N[(a + 1.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+78], t$95$1, If[LessEqual[b, 2.4e+56], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+97], N[(z * N[(N[(N[(N[(t / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.00000000000000001e78 or 4.0000000000000003e97 < b

   1. Initial program 69.0%

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

      1. associate-/l* 65.8%

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

      2. associate-/l* 60.2%

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

   3. Simplified 60.2%

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

   5. Taylor expanded in x around inf 56.4%

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

   6. Taylor expanded in b around -inf 64.6%

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

      1. associate-*r* 64.6%

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

      2. neg-mul-1 64.6%

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

      3. mul-1-neg 64.6%

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

      4. unsub-neg 64.6%

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

      5. associate-*r/ 64.6%

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

      6. mul-1-neg 64.6%

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

   8. Simplified 64.6%

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

   if -1.00000000000000001e78 < b < 2.40000000000000013e56

   1. Initial program 88.9%

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

      1. associate-/l* 88.9%

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

      2. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in b around 0 80.8%

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

   if 2.40000000000000013e56 < b < 4.0000000000000003e97

   1. Initial program 40.9%

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

      1. associate-/l* 50.2%

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

      2. associate-/l* 51.2%

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

   3. Simplified 51.2%

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

   5. Taylor expanded in z around inf 51.2%

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

      1. associate-+r+ 51.2%

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

      2. *-commutative 51.2%

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

      3. associate-+r+ 51.2%

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

      4. *-commutative 51.2%

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

   7. Simplified 51.2%

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

   8. Taylor expanded in b around inf 76.5%

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

      1. associate-/l* 76.2%

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

      2. times-frac 76.7%

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

   10. Simplified 76.7%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{b \cdot \left(\frac{y}{t} + \frac{a + 1}{b}\right)}\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+56}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \frac{\frac{t}{y} \cdot \frac{x}{z} + 1}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(\frac{y}{t} + \frac{a + 1}{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+56}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= b -2.5e+78)
     t_1
     (if (<= b 3.7e+56)
       (/ (+ x (/ (* y z) t)) (+ a 1.0))
       (if (<= b 9.5e+97) (/ 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) + ((y * b) / t));
	double tmp;
	if (b <= -2.5e+78) {
		tmp = t_1;
	} else if (b <= 3.7e+56) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (b <= 9.5e+97) {
		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) + ((y * b) / t))
    if (b <= (-2.5d+78)) then
        tmp = t_1
    else if (b <= 3.7d+56) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (b <= 9.5d+97) 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) + ((y * b) / t));
	double tmp;
	if (b <= -2.5e+78) {
		tmp = t_1;
	} else if (b <= 3.7e+56) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (b <= 9.5e+97) {
		tmp = z / b;
	} 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 b <= -2.5e+78:
		tmp = t_1
	elif b <= 3.7e+56:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif b <= 9.5e+97:
		tmp = z / b
	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(Float64(y * b) / t)))
	tmp = 0.0
	if (b <= -2.5e+78)
		tmp = t_1;
	elseif (b <= 3.7e+56)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (b <= 9.5e+97)
		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) + ((y * b) / t));
	tmp = 0.0;
	if (b <= -2.5e+78)
		tmp = t_1;
	elseif (b <= 3.7e+56)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (b <= 9.5e+97)
		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[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e+78], t$95$1, If[LessEqual[b, 3.7e+56], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+97], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.49999999999999992e78 or 9.49999999999999975e97 < b

   1. Initial program 69.0%

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

      1. associate-/l* 65.8%

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

      2. associate-/l* 60.2%

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

   3. Simplified 60.2%

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

   5. Taylor expanded in x around inf 61.2%

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

      1. associate-+r+ 61.2%

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

      2. *-commutative 61.2%

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

   7. Simplified 61.2%

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

   if -2.49999999999999992e78 < b < 3.69999999999999997e56

   1. Initial program 88.9%

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

      1. associate-/l* 88.9%

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

      2. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in b around 0 80.8%

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

   if 3.69999999999999997e56 < b < 9.49999999999999975e97

   1. Initial program 40.9%

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

      1. associate-/l* 50.2%

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

      2. associate-/l* 51.2%

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

   3. Simplified 51.2%

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

   5. Taylor expanded in y around inf 73.2%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+56}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;b \leq -9 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+55}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+97}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= b -9e+77)
     t_1
     (if (<= b 8.4e+55)
       (/ (+ x (* y (/ z t))) (+ a 1.0))
       (if (<= b 4.3e+97) (/ 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) + ((y * b) / t));
	double tmp;
	if (b <= -9e+77) {
		tmp = t_1;
	} else if (b <= 8.4e+55) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (b <= 4.3e+97) {
		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) + ((y * b) / t))
    if (b <= (-9d+77)) then
        tmp = t_1
    else if (b <= 8.4d+55) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else if (b <= 4.3d+97) 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) + ((y * b) / t));
	double tmp;
	if (b <= -9e+77) {
		tmp = t_1;
	} else if (b <= 8.4e+55) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (b <= 4.3e+97) {
		tmp = z / b;
	} 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 b <= -9e+77:
		tmp = t_1
	elif b <= 8.4e+55:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	elif b <= 4.3e+97:
		tmp = z / b
	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(Float64(y * b) / t)))
	tmp = 0.0
	if (b <= -9e+77)
		tmp = t_1;
	elseif (b <= 8.4e+55)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	elseif (b <= 4.3e+97)
		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) + ((y * b) / t));
	tmp = 0.0;
	if (b <= -9e+77)
		tmp = t_1;
	elseif (b <= 8.4e+55)
		tmp = (x + (y * (z / t))) / (a + 1.0);
	elseif (b <= 4.3e+97)
		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[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e+77], t$95$1, If[LessEqual[b, 8.4e+55], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e+97], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.00000000000000049e77 or 4.2999999999999998e97 < b

   1. Initial program 69.0%

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

      1. associate-/l* 65.8%

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

      2. associate-/l* 60.2%

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

   3. Simplified 60.2%

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

   5. Taylor expanded in x around inf 61.2%

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

      1. associate-+r+ 61.2%

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

      2. *-commutative 61.2%

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

   7. Simplified 61.2%

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

   if -9.00000000000000049e77 < b < 8.4000000000000002e55

   1. Initial program 88.9%

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

      1. associate-/l* 88.9%

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

      2. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in b around 0 80.8%

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

      1. associate-*r/ 80.2%

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

      2. *-commutative 80.2%

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

   7. Applied egg-rr 80.2%

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

   if 8.4000000000000002e55 < b < 4.2999999999999998e97

   1. Initial program 40.9%

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

      1. associate-/l* 50.2%

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

      2. associate-/l* 51.2%

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

   3. Simplified 51.2%

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

   5. Taylor expanded in y around inf 73.2%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+55}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+97}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-27}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 530000:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) a)))
   (if (<= a -1.02e+62)
     t_1
     (if (<= a -1.1e-27)
       (/ z b)
       (if (<= a 530000.0) (/ x (+ (/ (* y b) t) 1.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / a;
	double tmp;
	if (a <= -1.02e+62) {
		tmp = t_1;
	} else if (a <= -1.1e-27) {
		tmp = z / b;
	} else if (a <= 530000.0) {
		tmp = x / (((y * b) / t) + 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 + ((y * z) / t)) / a
    if (a <= (-1.02d+62)) then
        tmp = t_1
    else if (a <= (-1.1d-27)) then
        tmp = z / b
    else if (a <= 530000.0d0) then
        tmp = x / (((y * b) / t) + 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 + ((y * z) / t)) / a;
	double tmp;
	if (a <= -1.02e+62) {
		tmp = t_1;
	} else if (a <= -1.1e-27) {
		tmp = z / b;
	} else if (a <= 530000.0) {
		tmp = x / (((y * b) / t) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / a
	tmp = 0
	if a <= -1.02e+62:
		tmp = t_1
	elif a <= -1.1e-27:
		tmp = z / b
	elif a <= 530000.0:
		tmp = x / (((y * b) / t) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / a)
	tmp = 0.0
	if (a <= -1.02e+62)
		tmp = t_1;
	elseif (a <= -1.1e-27)
		tmp = Float64(z / b);
	elseif (a <= 530000.0)
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / a;
	tmp = 0.0;
	if (a <= -1.02e+62)
		tmp = t_1;
	elseif (a <= -1.1e-27)
		tmp = z / b;
	elseif (a <= 530000.0)
		tmp = x / (((y * b) / t) + 1.0);
	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[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -1.02e+62], t$95$1, If[LessEqual[a, -1.1e-27], N[(z / b), $MachinePrecision], If[LessEqual[a, 530000.0], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.02000000000000002e62 or 5.3e5 < a

   1. Initial program 76.4%

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

      1. associate-/l* 74.0%

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

      2. associate-/l* 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in a around inf 66.7%

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

   if -1.02000000000000002e62 < a < -1.09999999999999993e-27

   1. Initial program 78.6%

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

      1. associate-/l* 74.5%

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

      2. associate-/l* 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in y around inf 50.3%

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

   if -1.09999999999999993e-27 < a < 5.3e5

   1. Initial program 81.7%

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

      1. associate-/l* 82.9%

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

      2. associate-/l* 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in x around inf 58.1%

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

   6. Taylor expanded in a around 0 61.9%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+62}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-27}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 530000:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9200000000 \lor \neg \left(y \leq 1.2 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9200000000.0) (not (<= y 1.2e+130)))
   (/ z b)
   (/ x (+ (+ a 1.0) (/ (* y b) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9200000000.0) || !(y <= 1.2e+130)) {
		tmp = z / b;
	} else {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9200000000.0d0)) .or. (.not. (y <= 1.2d+130))) then
        tmp = z / b
    else
        tmp = x / ((a + 1.0d0) + ((y * b) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9200000000.0) || !(y <= 1.2e+130)) {
		tmp = z / b;
	} else {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9200000000.0) or not (y <= 1.2e+130):
		tmp = z / b
	else:
		tmp = x / ((a + 1.0) + ((y * b) / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9200000000.0) || !(y <= 1.2e+130))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9200000000.0) || ~((y <= 1.2e+130)))
		tmp = z / b;
	else
		tmp = x / ((a + 1.0) + ((y * b) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9200000000.0], N[Not[LessEqual[y, 1.2e+130]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.2e9 or 1.20000000000000012e130 < y

   1. Initial program 49.9%

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

      1. associate-/l* 54.2%

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

      2. associate-/l* 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in y around inf 63.4%

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

   if -9.2e9 < y < 1.20000000000000012e130

   1. Initial program 94.8%

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

      1. associate-/l* 91.1%

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

      2. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in x around inf 69.3%

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

      1. associate-+r+ 69.3%

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

      2. *-commutative 69.3%

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

   7. Simplified 69.3%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9200000000 \lor \neg \left(y \leq 1.2 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-73} \lor \neg \left(t \leq 5.8 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.4e-73) (not (<= t 5.8e-89))) (/ 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 <= -4.4e-73) || !(t <= 5.8e-89)) {
		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 <= (-4.4d-73)) .or. (.not. (t <= 5.8d-89))) 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 <= -4.4e-73) || !(t <= 5.8e-89)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.4e-73) or not (t <= 5.8e-89):
		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 <= -4.4e-73) || !(t <= 5.8e-89))
		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 <= -4.4e-73) || ~((t <= 5.8e-89)))
		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, -4.4e-73], N[Not[LessEqual[t, 5.8e-89]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4e-73 or 5.79999999999999984e-89 < t

   1. Initial program 86.0%

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

      1. associate-/l* 89.3%

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

      2. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in y around 0 61.2%

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

   if -4.4e-73 < t < 5.79999999999999984e-89

   1. Initial program 69.5%

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

      1. associate-/l* 63.0%

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

      2. associate-/l* 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in y around inf 55.4%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-73} \lor \neg \left(t \leq 5.8 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -300000 \lor \neg \left(y \leq 9 \cdot 10^{-93}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -300000.0) (not (<= y 9e-93))) (/ z b) (/ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -300000.0) || !(y <= 9e-93)) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-300000.0d0)) .or. (.not. (y <= 9d-93))) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -300000.0) || !(y <= 9e-93)) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -300000.0) or not (y <= 9e-93):
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -300000.0) || !(y <= 9e-93))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -300000.0) || ~((y <= 9e-93)))
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -300000.0], N[Not[LessEqual[y, 9e-93]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e5 or 9.0000000000000004e-93 < y

   1. Initial program 63.5%

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

      1. associate-/l* 67.0%

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

      2. associate-/l* 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in y around inf 51.4%

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

   if -3e5 < y < 9.0000000000000004e-93

   1. Initial program 96.9%

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

      1. associate-/l* 90.8%

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

      2. associate-/l* 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in x around inf 64.2%

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

   6. Taylor expanded in a around inf 31.0%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -300000 \lor \neg \left(y \leq 9 \cdot 10^{-93}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.5% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.0%

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

   1. associate-/l* 78.1%

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

   2. associate-/l* 75.9%

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

3. Simplified 75.9%

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

5. Taylor expanded in x around inf 55.2%

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

6. Taylor expanded in a around inf 24.3%

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

Developer target: 79.2% 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 2024101 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (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))))