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

Percentage Accurate: 75.1% → 92.7%

Time: 20.5s

Alternatives: 18

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_2 := z \cdot \frac{y}{t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \left(\frac{x}{b} - \frac{z}{{b}^{2}}\right)}{y}\\ \mathbf{elif}\;t\_1 \leq 10^{+294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0))))
        (t_2 (* z (/ y (* t (fma y (/ b t) (+ a 1.0)))))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -1e-307)
       t_1
       (if (<= t_1 0.0)
         (+ (/ z b) (/ (* t (- (/ x b) (/ z (pow b 2.0)))) y))
         (if (<= t_1 1e+294) t_1 (if (<= t_1 INFINITY) t_2 (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = z * (y / (t * fma(y, (b / t), (a + 1.0))));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -1e-307) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + ((t * ((x / b) - (z / pow(b, 2.0)))) / y);
	} else if (t_1 <= 1e+294) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_2 = Float64(z * Float64(y / Float64(t * fma(y, Float64(b / t), Float64(a + 1.0)))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -1e-307)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(Float64(x / b) - Float64(z / (b ^ 2.0)))) / y));
	elseif (t_1 <= 1e+294)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y / N[(t * N[(y * N[(b / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -1e-307], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(N[(x / b), $MachinePrecision] - N[(z / N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+294], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or 1.00000000000000007e294 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 24.2%

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

      1. associate-/l* 44.8%

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

      2. associate-/l* 44.6%

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

   3. Simplified 44.6%

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

   5. Taylor expanded in x around 0 49.9%

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

      1. associate-/l* 81.9%

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

      2. associate-+r+ 81.9%

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

      3. associate-*r/ 60.5%

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

      4. *-commutative 60.5%

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

      5. associate-/r/ 81.9%

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

      6. +-commutative 81.9%

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

      7. associate-/r/ 60.5%

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

      8. *-commutative 60.5%

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

      9. associate-*r/ 81.9%

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

      10. associate-*l/ 81.7%

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

      11. *-commutative 81.7%

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

      12. fma-define 81.7%

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

   7. Simplified 81.7%

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

      1. clear-num 81.6%

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

      2. un-div-inv 81.7%

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

      3. fma-undefine 81.7%

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

      4. +-commutative 81.7%

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

      5. +-commutative 81.7%

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

      6. associate-+l+ 81.7%

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

      7. associate-*r/ 81.9%

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

      8. *-commutative 81.9%

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

      9. +-commutative 81.9%

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

      10. *-commutative 81.9%

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

      11. associate-*r/ 81.7%

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

      12. fma-define 81.7%

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

   9. Applied egg-rr 81.7%

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

       1. associate-/r/ 84.5%

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

       2. fma-undefine 84.5%

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

       3. *-commutative 84.5%

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

       4. associate-*l/ 87.5%

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

       5. +-commutative 87.5%

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

       6. associate-*l/ 84.5%

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

       7. *-commutative 84.5%

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

       8. associate-+l+ 84.5%

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

       9. +-commutative 84.5%

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

       10. fma-define 84.5%

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

       11. +-commutative 84.5%

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

   11. Simplified 84.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -9.99999999999999909e-308 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1.00000000000000007e294

   1. Initial program 99.6%

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

   if -9.99999999999999909e-308 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 51.9%

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

      1. associate-/l* 51.7%

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

      2. associate-/l* 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in a around 0 33.8%

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

      1. associate-/l* 47.7%

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

   7. Applied egg-rr 47.7%

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

   8. Taylor expanded in y around -inf 76.5%

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

      1. +-commutative 76.5%

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

      2. mul-1-neg 76.5%

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

      3. unsub-neg 76.5%

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

      4. distribute-lft-out-- 76.5%

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

      5. mul-1-neg 76.5%

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

      6. associate-/l* 80.9%

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

      7. associate-/l* 80.9%

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

      8. distribute-lft-out-- 80.9%

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

   10. Simplified 80.9%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.7%

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

      2. associate-/l* 14.2%

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

   3. Simplified 14.2%

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

   5. Taylor expanded in y around inf 100.0%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -1 \cdot 10^{-307}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \left(\frac{x}{b} - \frac{z}{{b}^{2}}\right)}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+294}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;z \cdot \frac{y}{t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_2 := z \cdot \frac{y}{t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0))))
        (t_2 (* z (/ y (* t (fma y (/ b t) (+ a 1.0)))))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 1e+294) t_1 (if (<= t_1 INFINITY) t_2 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = z * (y / (t * fma(y, (b / t), (a + 1.0))));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 1e+294) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_2 = Float64(z * Float64(y / Float64(t * fma(y, Float64(b / t), Float64(a + 1.0)))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 1e+294)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y / N[(t * N[(y * N[(b / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 1e+294], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or 1.00000000000000007e294 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 24.2%

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

      1. associate-/l* 44.8%

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

      2. associate-/l* 44.6%

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

   3. Simplified 44.6%

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

   5. Taylor expanded in x around 0 49.9%

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

      1. associate-/l* 81.9%

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

      2. associate-+r+ 81.9%

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

      3. associate-*r/ 60.5%

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

      4. *-commutative 60.5%

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

      5. associate-/r/ 81.9%

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

      6. +-commutative 81.9%

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

      7. associate-/r/ 60.5%

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

      8. *-commutative 60.5%

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

      9. associate-*r/ 81.9%

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

      10. associate-*l/ 81.7%

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

      11. *-commutative 81.7%

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

      12. fma-define 81.7%

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

   7. Simplified 81.7%

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

      1. clear-num 81.6%

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

      2. un-div-inv 81.7%

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

      3. fma-undefine 81.7%

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

      4. +-commutative 81.7%

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

      5. +-commutative 81.7%

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

      6. associate-+l+ 81.7%

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

      7. associate-*r/ 81.9%

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

      8. *-commutative 81.9%

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

      9. +-commutative 81.9%

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

      10. *-commutative 81.9%

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

      11. associate-*r/ 81.7%

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

      12. fma-define 81.7%

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

   9. Applied egg-rr 81.7%

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

       1. associate-/r/ 84.5%

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

       2. fma-undefine 84.5%

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

       3. *-commutative 84.5%

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

       4. associate-*l/ 87.5%

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

       5. +-commutative 87.5%

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

       6. associate-*l/ 84.5%

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

       7. *-commutative 84.5%

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

       8. associate-+l+ 84.5%

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

       9. +-commutative 84.5%

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

       10. fma-define 84.5%

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

       11. +-commutative 84.5%

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

   11. Simplified 84.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1.00000000000000007e294

   1. Initial program 89.6%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.7%

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

      2. associate-/l* 14.2%

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

   3. Simplified 14.2%

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

   5. Taylor expanded in y around inf 100.0%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+294}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;z \cdot \frac{y}{t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_2 := y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0))))
        (t_2 (* y (/ z (+ (* y b) (* t (+ a 1.0)))))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 1e+294) t_1 (if (<= t_1 INFINITY) t_2 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = y * (z / ((y * b) + (t * (a + 1.0))));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 1e+294) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = y * (z / ((y * b) + (t * (a + 1.0))));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 1e+294) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	t_2 = y * (z / ((y * b) + (t * (a + 1.0))))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 1e+294:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_2 = Float64(y * Float64(z / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0)))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 1e+294)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	t_2 = y * (z / ((y * b) + (t * (a + 1.0))));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 1e+294)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 1e+294], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or 1.00000000000000007e294 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 24.2%

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

      1. associate-/l* 44.8%

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

      2. associate-/l* 44.6%

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

   3. Simplified 44.6%

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

   5. Taylor expanded in x around 0 49.9%

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

      1. associate-/l* 81.9%

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

      2. associate-+r+ 81.9%

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

      3. associate-*r/ 60.5%

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

      4. *-commutative 60.5%

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

      5. associate-/r/ 81.9%

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

      6. +-commutative 81.9%

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

      7. associate-/r/ 60.5%

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

      8. *-commutative 60.5%

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

      9. associate-*r/ 81.9%

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

      10. associate-*l/ 81.7%

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

      11. *-commutative 81.7%

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

      12. fma-define 81.7%

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

   7. Simplified 81.7%

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

   8. Taylor expanded in t around 0 82.0%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1.00000000000000007e294

   1. Initial program 89.6%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.7%

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

      2. associate-/l* 14.2%

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

   3. Simplified 14.2%

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

   5. Taylor expanded in y around inf 100.0%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+294}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-189}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-165}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-41}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + 1}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) a)))
   (if (<= a -7.5e+23)
     t_1
     (if (<= a -4.5e-189)
       (/ z b)
       (if (<= a 8.5e-165)
         (+ x (* z (/ y t)))
         (if (<= a 6.2e-41)
           (/ z b)
           (if (<= a 5.8e-6)
             (/ x (+ (/ (* y b) t) 1.0))
             (if (<= a 8.2e+18) (/ x (+ 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;
	double tmp;
	if (a <= -7.5e+23) {
		tmp = t_1;
	} else if (a <= -4.5e-189) {
		tmp = z / b;
	} else if (a <= 8.5e-165) {
		tmp = x + (z * (y / t));
	} else if (a <= 6.2e-41) {
		tmp = z / b;
	} else if (a <= 5.8e-6) {
		tmp = x / (((y * b) / t) + 1.0);
	} else if (a <= 8.2e+18) {
		tmp = x / (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
    if (a <= (-7.5d+23)) then
        tmp = t_1
    else if (a <= (-4.5d-189)) then
        tmp = z / b
    else if (a <= 8.5d-165) then
        tmp = x + (z * (y / t))
    else if (a <= 6.2d-41) then
        tmp = z / b
    else if (a <= 5.8d-6) then
        tmp = x / (((y * b) / t) + 1.0d0)
    else if (a <= 8.2d+18) then
        tmp = x / (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;
	double tmp;
	if (a <= -7.5e+23) {
		tmp = t_1;
	} else if (a <= -4.5e-189) {
		tmp = z / b;
	} else if (a <= 8.5e-165) {
		tmp = x + (z * (y / t));
	} else if (a <= 6.2e-41) {
		tmp = z / b;
	} else if (a <= 5.8e-6) {
		tmp = x / (((y * b) / t) + 1.0);
	} else if (a <= 8.2e+18) {
		tmp = x / (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
	tmp = 0
	if a <= -7.5e+23:
		tmp = t_1
	elif a <= -4.5e-189:
		tmp = z / b
	elif a <= 8.5e-165:
		tmp = x + (z * (y / t))
	elif a <= 6.2e-41:
		tmp = z / b
	elif a <= 5.8e-6:
		tmp = x / (((y * b) / t) + 1.0)
	elif a <= 8.2e+18:
		tmp = x / (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))) / a)
	tmp = 0.0
	if (a <= -7.5e+23)
		tmp = t_1;
	elseif (a <= -4.5e-189)
		tmp = Float64(z / b);
	elseif (a <= 8.5e-165)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (a <= 6.2e-41)
		tmp = Float64(z / b);
	elseif (a <= 5.8e-6)
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + 1.0));
	elseif (a <= 8.2e+18)
		tmp = Float64(x / 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;
	tmp = 0.0;
	if (a <= -7.5e+23)
		tmp = t_1;
	elseif (a <= -4.5e-189)
		tmp = z / b;
	elseif (a <= 8.5e-165)
		tmp = x + (z * (y / t));
	elseif (a <= 6.2e-41)
		tmp = z / b;
	elseif (a <= 5.8e-6)
		tmp = x / (((y * b) / t) + 1.0);
	elseif (a <= 8.2e+18)
		tmp = x / (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] / a), $MachinePrecision]}, If[LessEqual[a, -7.5e+23], t$95$1, If[LessEqual[a, -4.5e-189], N[(z / b), $MachinePrecision], If[LessEqual[a, 8.5e-165], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-41], N[(z / b), $MachinePrecision], If[LessEqual[a, 5.8e-6], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+18], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.49999999999999987e23 or 8.2e18 < a

   1. Initial program 75.2%

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

      1. associate-/l* 71.2%

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

      2. associate-/l* 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in a around inf 60.7%

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

   if -7.49999999999999987e23 < a < -4.4999999999999996e-189 or 8.5e-165 < a < 6.20000000000000001e-41

   1. Initial program 57.4%

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

      1. associate-/l* 55.8%

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

      2. associate-/l* 64.9%

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

   3. Simplified 64.9%

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

   5. Taylor expanded in y around inf 65.0%

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

   if -4.4999999999999996e-189 < a < 8.5e-165

   1. Initial program 74.1%

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

      1. associate-/l* 75.3%

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

      2. associate-/l* 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in y around 0 58.4%

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

   6. Taylor expanded in a around 0 55.9%

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

      1. *-commutative 55.9%

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

      2. associate-/l* 60.4%

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

   8. Applied egg-rr 60.4%

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

   if 6.20000000000000001e-41 < a < 5.8000000000000004e-6

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 94.2%

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

   6. Taylor expanded in x around inf 69.9%

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

   if 5.8000000000000004e-6 < a < 8.2e18

   1. Initial program 66.7%

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

      1. associate-/l* 66.7%

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

      2. associate-/l* 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in y around 0 52.2%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-189}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-165}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-41}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + 1}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{if}\;a \leq -4.9 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-189}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-164}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-41}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + 1}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) a)))
   (if (<= a -4.9e+23)
     t_1
     (if (<= a -5.7e-189)
       (/ z b)
       (if (<= a 1.55e-164)
         (+ x (* z (/ y t)))
         (if (<= a 2.15e-41)
           (/ z b)
           (if (<= a 3.5e-7)
             (/ x (+ (/ (* y b) t) 1.0))
             (if (<= a 8.2e+18) (/ x (+ 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 / (t / z))) / a;
	double tmp;
	if (a <= -4.9e+23) {
		tmp = t_1;
	} else if (a <= -5.7e-189) {
		tmp = z / b;
	} else if (a <= 1.55e-164) {
		tmp = x + (z * (y / t));
	} else if (a <= 2.15e-41) {
		tmp = z / b;
	} else if (a <= 3.5e-7) {
		tmp = x / (((y * b) / t) + 1.0);
	} else if (a <= 8.2e+18) {
		tmp = x / (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 / (t / z))) / a
    if (a <= (-4.9d+23)) then
        tmp = t_1
    else if (a <= (-5.7d-189)) then
        tmp = z / b
    else if (a <= 1.55d-164) then
        tmp = x + (z * (y / t))
    else if (a <= 2.15d-41) then
        tmp = z / b
    else if (a <= 3.5d-7) then
        tmp = x / (((y * b) / t) + 1.0d0)
    else if (a <= 8.2d+18) then
        tmp = x / (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 / (t / z))) / a;
	double tmp;
	if (a <= -4.9e+23) {
		tmp = t_1;
	} else if (a <= -5.7e-189) {
		tmp = z / b;
	} else if (a <= 1.55e-164) {
		tmp = x + (z * (y / t));
	} else if (a <= 2.15e-41) {
		tmp = z / b;
	} else if (a <= 3.5e-7) {
		tmp = x / (((y * b) / t) + 1.0);
	} else if (a <= 8.2e+18) {
		tmp = x / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / a
	tmp = 0
	if a <= -4.9e+23:
		tmp = t_1
	elif a <= -5.7e-189:
		tmp = z / b
	elif a <= 1.55e-164:
		tmp = x + (z * (y / t))
	elif a <= 2.15e-41:
		tmp = z / b
	elif a <= 3.5e-7:
		tmp = x / (((y * b) / t) + 1.0)
	elif a <= 8.2e+18:
		tmp = x / (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(t / z))) / a)
	tmp = 0.0
	if (a <= -4.9e+23)
		tmp = t_1;
	elseif (a <= -5.7e-189)
		tmp = Float64(z / b);
	elseif (a <= 1.55e-164)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (a <= 2.15e-41)
		tmp = Float64(z / b);
	elseif (a <= 3.5e-7)
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + 1.0));
	elseif (a <= 8.2e+18)
		tmp = Float64(x / 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 / (t / z))) / a;
	tmp = 0.0;
	if (a <= -4.9e+23)
		tmp = t_1;
	elseif (a <= -5.7e-189)
		tmp = z / b;
	elseif (a <= 1.55e-164)
		tmp = x + (z * (y / t));
	elseif (a <= 2.15e-41)
		tmp = z / b;
	elseif (a <= 3.5e-7)
		tmp = x / (((y * b) / t) + 1.0);
	elseif (a <= 8.2e+18)
		tmp = x / (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[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -4.9e+23], t$95$1, If[LessEqual[a, -5.7e-189], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.55e-164], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.15e-41], N[(z / b), $MachinePrecision], If[LessEqual[a, 3.5e-7], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+18], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.9000000000000003e23 or 8.2e18 < a

   1. Initial program 75.2%

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

      1. associate-/l* 71.2%

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

      2. associate-/l* 71.1%

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

   3. Simplified 71.1%

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

      1. clear-num 71.1%

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

      2. un-div-inv 72.3%

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

   6. Applied egg-rr 72.3%

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

   7. Taylor expanded in a around inf 61.9%

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

   if -4.9000000000000003e23 < a < -5.6999999999999999e-189 or 1.55e-164 < a < 2.1499999999999999e-41

   1. Initial program 57.4%

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

      1. associate-/l* 55.8%

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

      2. associate-/l* 64.9%

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

   3. Simplified 64.9%

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

   5. Taylor expanded in y around inf 65.0%

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

   if -5.6999999999999999e-189 < a < 1.55e-164

   1. Initial program 74.1%

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

      1. associate-/l* 75.3%

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

      2. associate-/l* 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in y around 0 58.4%

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

   6. Taylor expanded in a around 0 55.9%

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

      1. *-commutative 55.9%

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

      2. associate-/l* 60.4%

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

   8. Applied egg-rr 60.4%

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

   if 2.1499999999999999e-41 < a < 3.49999999999999984e-7

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 94.2%

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

   6. Taylor expanded in x around inf 69.9%

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

   if 3.49999999999999984e-7 < a < 8.2e18

   1. Initial program 66.7%

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

      1. associate-/l* 66.7%

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

      2. associate-/l* 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in y around 0 52.2%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{+23}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-189}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-164}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-41}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + 1}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{if}\;a \leq -1.14 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-188}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-165}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + 1}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) a)))
   (if (<= a -1.14e+26)
     t_1
     (if (<= a -5.4e-188)
       (/ z b)
       (if (<= a 9e-165)
         (+ x (* z (/ y t)))
         (if (<= a 7.5e-42)
           (/ z b)
           (if (<= a 2.9e-7)
             (/ x (+ (/ (* y b) t) 1.0))
             (if (<= a 8.2e+18) (/ x (+ 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;
	double tmp;
	if (a <= -1.14e+26) {
		tmp = t_1;
	} else if (a <= -5.4e-188) {
		tmp = z / b;
	} else if (a <= 9e-165) {
		tmp = x + (z * (y / t));
	} else if (a <= 7.5e-42) {
		tmp = z / b;
	} else if (a <= 2.9e-7) {
		tmp = x / (((y * b) / t) + 1.0);
	} else if (a <= 8.2e+18) {
		tmp = x / (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
    if (a <= (-1.14d+26)) then
        tmp = t_1
    else if (a <= (-5.4d-188)) then
        tmp = z / b
    else if (a <= 9d-165) then
        tmp = x + (z * (y / t))
    else if (a <= 7.5d-42) then
        tmp = z / b
    else if (a <= 2.9d-7) then
        tmp = x / (((y * b) / t) + 1.0d0)
    else if (a <= 8.2d+18) then
        tmp = x / (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;
	double tmp;
	if (a <= -1.14e+26) {
		tmp = t_1;
	} else if (a <= -5.4e-188) {
		tmp = z / b;
	} else if (a <= 9e-165) {
		tmp = x + (z * (y / t));
	} else if (a <= 7.5e-42) {
		tmp = z / b;
	} else if (a <= 2.9e-7) {
		tmp = x / (((y * b) / t) + 1.0);
	} else if (a <= 8.2e+18) {
		tmp = x / (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
	tmp = 0
	if a <= -1.14e+26:
		tmp = t_1
	elif a <= -5.4e-188:
		tmp = z / b
	elif a <= 9e-165:
		tmp = x + (z * (y / t))
	elif a <= 7.5e-42:
		tmp = z / b
	elif a <= 2.9e-7:
		tmp = x / (((y * b) / t) + 1.0)
	elif a <= 8.2e+18:
		tmp = x / (a + 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 <= -1.14e+26)
		tmp = t_1;
	elseif (a <= -5.4e-188)
		tmp = Float64(z / b);
	elseif (a <= 9e-165)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (a <= 7.5e-42)
		tmp = Float64(z / b);
	elseif (a <= 2.9e-7)
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + 1.0));
	elseif (a <= 8.2e+18)
		tmp = Float64(x / 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;
	tmp = 0.0;
	if (a <= -1.14e+26)
		tmp = t_1;
	elseif (a <= -5.4e-188)
		tmp = z / b;
	elseif (a <= 9e-165)
		tmp = x + (z * (y / t));
	elseif (a <= 7.5e-42)
		tmp = z / b;
	elseif (a <= 2.9e-7)
		tmp = x / (((y * b) / t) + 1.0);
	elseif (a <= 8.2e+18)
		tmp = x / (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[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -1.14e+26], t$95$1, If[LessEqual[a, -5.4e-188], N[(z / b), $MachinePrecision], If[LessEqual[a, 9e-165], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-42], N[(z / b), $MachinePrecision], If[LessEqual[a, 2.9e-7], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+18], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.1399999999999999e26 or 8.2e18 < a

   1. Initial program 75.2%

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

      1. associate-/l* 71.2%

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

      2. associate-/l* 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in a around inf 64.8%

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

   if -1.1399999999999999e26 < a < -5.4000000000000002e-188 or 8.99999999999999985e-165 < a < 7.49999999999999972e-42

   1. Initial program 57.4%

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

      1. associate-/l* 55.8%

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

      2. associate-/l* 64.9%

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

   3. Simplified 64.9%

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

   5. Taylor expanded in y around inf 65.0%

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

   if -5.4000000000000002e-188 < a < 8.99999999999999985e-165

   1. Initial program 74.1%

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

      1. associate-/l* 75.3%

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

      2. associate-/l* 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in y around 0 58.4%

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

   6. Taylor expanded in a around 0 55.9%

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

      1. *-commutative 55.9%

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

      2. associate-/l* 60.4%

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

   8. Applied egg-rr 60.4%

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

   if 7.49999999999999972e-42 < a < 2.8999999999999998e-7

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 94.2%

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

   6. Taylor expanded in x around inf 69.9%

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

   if 2.8999999999999998e-7 < a < 8.2e18

   1. Initial program 66.7%

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

      1. associate-/l* 66.7%

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

      2. associate-/l* 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in y around 0 52.2%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.14 \cdot 10^{+26}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-188}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-165}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + 1}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + 1}\\ t_2 := \frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 0.25:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) 1.0)))
        (t_2 (/ (+ x (* z (/ y t))) (+ a 1.0))))
   (if (<= a -6e+20)
     t_2
     (if (<= a 1.55e-164)
       t_1
       (if (<= a 7.2e-42) (/ z b) (if (<= a 0.25) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((y * (b / t)) + 1.0);
	double t_2 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (a <= -6e+20) {
		tmp = t_2;
	} else if (a <= 1.55e-164) {
		tmp = t_1;
	} else if (a <= 7.2e-42) {
		tmp = z / b;
	} else if (a <= 0.25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / ((y * (b / t)) + 1.0d0)
    t_2 = (x + (z * (y / t))) / (a + 1.0d0)
    if (a <= (-6d+20)) then
        tmp = t_2
    else if (a <= 1.55d-164) then
        tmp = t_1
    else if (a <= 7.2d-42) then
        tmp = z / b
    else if (a <= 0.25d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((y * (b / t)) + 1.0);
	double t_2 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (a <= -6e+20) {
		tmp = t_2;
	} else if (a <= 1.55e-164) {
		tmp = t_1;
	} else if (a <= 7.2e-42) {
		tmp = z / b;
	} else if (a <= 0.25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / ((y * (b / t)) + 1.0)
	t_2 = (x + (z * (y / t))) / (a + 1.0)
	tmp = 0
	if a <= -6e+20:
		tmp = t_2
	elif a <= 1.55e-164:
		tmp = t_1
	elif a <= 7.2e-42:
		tmp = z / b
	elif a <= 0.25:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y * Float64(b / t)) + 1.0))
	t_2 = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (a <= -6e+20)
		tmp = t_2;
	elseif (a <= 1.55e-164)
		tmp = t_1;
	elseif (a <= 7.2e-42)
		tmp = Float64(z / b);
	elseif (a <= 0.25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / ((y * (b / t)) + 1.0);
	t_2 = (x + (z * (y / t))) / (a + 1.0);
	tmp = 0.0;
	if (a <= -6e+20)
		tmp = t_2;
	elseif (a <= 1.55e-164)
		tmp = t_1;
	elseif (a <= 7.2e-42)
		tmp = z / b;
	elseif (a <= 0.25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+20], t$95$2, If[LessEqual[a, 1.55e-164], t$95$1, If[LessEqual[a, 7.2e-42], N[(z / b), $MachinePrecision], If[LessEqual[a, 0.25], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6e20 or 0.25 < a

   1. Initial program 75.2%

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

      1. associate-/l* 71.4%

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

      2. associate-/l* 71.2%

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

   3. Simplified 71.2%

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

      1. clear-num 71.2%

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

      2. un-div-inv 72.4%

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

   6. Applied egg-rr 72.4%

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

   7. Taylor expanded in y around 0 62.4%

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

      1. associate-/r/ 66.7%

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

   9. Applied egg-rr 66.7%

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

   if -6e20 < a < 1.55e-164 or 7.2000000000000004e-42 < a < 0.25

   1. Initial program 71.8%

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

      1. associate-/l* 71.5%

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

      2. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in a around 0 70.9%

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

      1. associate-*l/ 75.1%

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

      2. *-commutative 75.1%

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

   7. Simplified 75.1%

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

   if 1.55e-164 < a < 7.2000000000000004e-42

   1. Initial program 45.3%

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

      1. associate-/l* 45.7%

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

      2. associate-/l* 59.1%

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

   3. Simplified 59.1%

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

   5. Taylor expanded in y around inf 81.3%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+20}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-164}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + 1}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 0.25:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+180}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{\left(a + b \cdot \frac{y}{t}\right) + 1}\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+37} \lor \neg \left(b \leq 1.35 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.4e+180)
   (/ z b)
   (if (<= b -3.3e+61)
     (/ x (+ (+ a (* b (/ y t))) 1.0))
     (if (or (<= b -1.15e+37) (not (<= b 1.35e+34)))
       (/ z b)
       (/ (+ x (* y (/ z t))) (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.4e+180) {
		tmp = z / b;
	} else if (b <= -3.3e+61) {
		tmp = x / ((a + (b * (y / t))) + 1.0);
	} else if ((b <= -1.15e+37) || !(b <= 1.35e+34)) {
		tmp = z / b;
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.4d+180)) then
        tmp = z / b
    else if (b <= (-3.3d+61)) then
        tmp = x / ((a + (b * (y / t))) + 1.0d0)
    else if ((b <= (-1.15d+37)) .or. (.not. (b <= 1.35d+34))) then
        tmp = z / b
    else
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.4e+180) {
		tmp = z / b;
	} else if (b <= -3.3e+61) {
		tmp = x / ((a + (b * (y / t))) + 1.0);
	} else if ((b <= -1.15e+37) || !(b <= 1.35e+34)) {
		tmp = z / b;
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.4e+180:
		tmp = z / b
	elif b <= -3.3e+61:
		tmp = x / ((a + (b * (y / t))) + 1.0)
	elif (b <= -1.15e+37) or not (b <= 1.35e+34):
		tmp = z / b
	else:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.4e+180)
		tmp = Float64(z / b);
	elseif (b <= -3.3e+61)
		tmp = Float64(x / Float64(Float64(a + Float64(b * Float64(y / t))) + 1.0));
	elseif ((b <= -1.15e+37) || !(b <= 1.35e+34))
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.4e+180)
		tmp = z / b;
	elseif (b <= -3.3e+61)
		tmp = x / ((a + (b * (y / t))) + 1.0);
	elseif ((b <= -1.15e+37) || ~((b <= 1.35e+34)))
		tmp = z / b;
	else
		tmp = (x + (y * (z / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.4e+180], N[(z / b), $MachinePrecision], If[LessEqual[b, -3.3e+61], N[(x / N[(N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -1.15e+37], N[Not[LessEqual[b, 1.35e+34]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.40000000000000006e180 or -3.2999999999999998e61 < b < -1.15000000000000001e37 or 1.35e34 < b

   1. Initial program 56.1%

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

      1. associate-/l* 53.2%

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

      2. associate-/l* 58.9%

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

   3. Simplified 58.9%

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

   5. Taylor expanded in y around inf 63.2%

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

   if -1.40000000000000006e180 < b < -3.2999999999999998e61

   1. Initial program 70.0%

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

      1. associate-*r/ 70.1%

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

      2. *-commutative 70.1%

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

      3. div-inv 70.1%

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

      4. associate-*l* 69.9%

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

   4. Applied egg-rr 69.9%

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

      1. *-commutative 69.9%

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

      2. associate-*l/ 69.9%

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

      3. *-un-lft-identity 69.9%

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

      4. associate-/r/ 70.1%

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

      5. clear-num 70.0%

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

   6. Applied egg-rr 70.0%

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

   7. Taylor expanded in x around inf 55.0%

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

      1. associate-/l* 60.0%

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

   9. Simplified 60.0%

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

   if -1.15000000000000001e37 < b < 1.35e34

   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* 80.2%

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

      2. associate-/l* 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in y around 0 73.2%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+180}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{\left(a + b \cdot \frac{y}{t}\right) + 1}\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+37} \lor \neg \left(b \leq 1.35 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+179}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{\left(a + b \cdot \frac{y}{t}\right) + 1}\\ \mathbf{elif}\;b \leq -1.46 \cdot 10^{+47} \lor \neg \left(b \leq 1.45 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.7e+179)
   (/ z b)
   (if (<= b -6.5e+61)
     (/ x (+ (+ a (* b (/ y t))) 1.0))
     (if (or (<= b -1.46e+47) (not (<= b 1.45e+34)))
       (/ z b)
       (/ (+ x (* z (/ y t))) (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e+179) {
		tmp = z / b;
	} else if (b <= -6.5e+61) {
		tmp = x / ((a + (b * (y / t))) + 1.0);
	} else if ((b <= -1.46e+47) || !(b <= 1.45e+34)) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.7d+179)) then
        tmp = z / b
    else if (b <= (-6.5d+61)) then
        tmp = x / ((a + (b * (y / t))) + 1.0d0)
    else if ((b <= (-1.46d+47)) .or. (.not. (b <= 1.45d+34))) then
        tmp = z / b
    else
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e+179) {
		tmp = z / b;
	} else if (b <= -6.5e+61) {
		tmp = x / ((a + (b * (y / t))) + 1.0);
	} else if ((b <= -1.46e+47) || !(b <= 1.45e+34)) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.7e+179:
		tmp = z / b
	elif b <= -6.5e+61:
		tmp = x / ((a + (b * (y / t))) + 1.0)
	elif (b <= -1.46e+47) or not (b <= 1.45e+34):
		tmp = z / b
	else:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.7e+179)
		tmp = Float64(z / b);
	elseif (b <= -6.5e+61)
		tmp = Float64(x / Float64(Float64(a + Float64(b * Float64(y / t))) + 1.0));
	elseif ((b <= -1.46e+47) || !(b <= 1.45e+34))
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.7e+179)
		tmp = z / b;
	elseif (b <= -6.5e+61)
		tmp = x / ((a + (b * (y / t))) + 1.0);
	elseif ((b <= -1.46e+47) || ~((b <= 1.45e+34)))
		tmp = z / b;
	else
		tmp = (x + (z * (y / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.7e+179], N[(z / b), $MachinePrecision], If[LessEqual[b, -6.5e+61], N[(x / N[(N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -1.46e+47], N[Not[LessEqual[b, 1.45e+34]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.6999999999999999e179 or -6.4999999999999996e61 < b < -1.46000000000000006e47 or 1.4500000000000001e34 < b

   1. Initial program 56.1%

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

      1. associate-/l* 53.2%

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

      2. associate-/l* 58.9%

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

   3. Simplified 58.9%

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

   5. Taylor expanded in y around inf 63.2%

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

   if -3.6999999999999999e179 < b < -6.4999999999999996e61

   1. Initial program 70.0%

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

      1. associate-*r/ 70.1%

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

      2. *-commutative 70.1%

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

      3. div-inv 70.1%

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

      4. associate-*l* 69.9%

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

   4. Applied egg-rr 69.9%

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

      1. *-commutative 69.9%

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

      2. associate-*l/ 69.9%

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

      3. *-un-lft-identity 69.9%

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

      4. associate-/r/ 70.1%

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

      5. clear-num 70.0%

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

   6. Applied egg-rr 70.0%

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

   7. Taylor expanded in x around inf 55.0%

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

      1. associate-/l* 60.0%

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

   9. Simplified 60.0%

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

   if -1.46000000000000006e47 < b < 1.4500000000000001e34

   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* 80.2%

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

      2. associate-/l* 80.9%

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

   3. Simplified 80.9%

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

      1. clear-num 80.9%

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

      2. un-div-inv 81.9%

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

   6. Applied egg-rr 81.9%

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

   7. Taylor expanded in y around 0 74.2%

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

      1. associate-/r/ 78.1%

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

   9. Applied egg-rr 78.1%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+179}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{\left(a + b \cdot \frac{y}{t}\right) + 1}\\ \mathbf{elif}\;b \leq -1.46 \cdot 10^{+47} \lor \neg \left(b \leq 1.45 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+179}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{\left(a + b \cdot \frac{y}{t}\right) + 1}\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+34}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9e+179)
   (/ z b)
   (if (<= b -5.6e+82)
     (/ x (+ (+ a (* b (/ y t))) 1.0))
     (if (<= b -5.5e+41)
       (* y (/ z (+ (* y b) (* t (+ a 1.0)))))
       (if (<= b 1.05e+34) (/ (+ x (* z (/ y t))) (+ a 1.0)) (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9e+179) {
		tmp = z / b;
	} else if (b <= -5.6e+82) {
		tmp = x / ((a + (b * (y / t))) + 1.0);
	} else if (b <= -5.5e+41) {
		tmp = y * (z / ((y * b) + (t * (a + 1.0))));
	} else if (b <= 1.05e+34) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9d+179)) then
        tmp = z / b
    else if (b <= (-5.6d+82)) then
        tmp = x / ((a + (b * (y / t))) + 1.0d0)
    else if (b <= (-5.5d+41)) then
        tmp = y * (z / ((y * b) + (t * (a + 1.0d0))))
    else if (b <= 1.05d+34) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9e+179) {
		tmp = z / b;
	} else if (b <= -5.6e+82) {
		tmp = x / ((a + (b * (y / t))) + 1.0);
	} else if (b <= -5.5e+41) {
		tmp = y * (z / ((y * b) + (t * (a + 1.0))));
	} else if (b <= 1.05e+34) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9e+179:
		tmp = z / b
	elif b <= -5.6e+82:
		tmp = x / ((a + (b * (y / t))) + 1.0)
	elif b <= -5.5e+41:
		tmp = y * (z / ((y * b) + (t * (a + 1.0))))
	elif b <= 1.05e+34:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9e+179)
		tmp = Float64(z / b);
	elseif (b <= -5.6e+82)
		tmp = Float64(x / Float64(Float64(a + Float64(b * Float64(y / t))) + 1.0));
	elseif (b <= -5.5e+41)
		tmp = Float64(y * Float64(z / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0)))));
	elseif (b <= 1.05e+34)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9e+179)
		tmp = z / b;
	elseif (b <= -5.6e+82)
		tmp = x / ((a + (b * (y / t))) + 1.0);
	elseif (b <= -5.5e+41)
		tmp = y * (z / ((y * b) + (t * (a + 1.0))));
	elseif (b <= 1.05e+34)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9e+179], N[(z / b), $MachinePrecision], If[LessEqual[b, -5.6e+82], N[(x / N[(N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.5e+41], N[(y * N[(z / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e+34], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.0000000000000005e179 or 1.05000000000000009e34 < b

   1. Initial program 57.8%

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

      1. associate-/l* 54.8%

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

      2. associate-/l* 60.6%

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

   3. Simplified 60.6%

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

   5. Taylor expanded in y around inf 62.0%

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

   if -9.0000000000000005e179 < b < -5.6000000000000001e82

   1. Initial program 78.5%

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

      1. associate-*r/ 78.6%

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

      2. *-commutative 78.6%

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

      3. div-inv 78.6%

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

      4. associate-*l* 78.3%

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

   4. Applied egg-rr 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-*l/ 78.3%

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

      3. *-un-lft-identity 78.3%

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

      4. associate-/r/ 78.6%

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

      5. clear-num 78.5%

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

   6. Applied egg-rr 78.5%

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

   7. Taylor expanded in x around inf 63.8%

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

      1. associate-/l* 71.1%

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

   9. Simplified 71.1%

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

   if -5.6000000000000001e82 < b < -5.5000000000000003e41

   1. Initial program 35.9%

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

      1. associate-/l* 35.9%

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

      2. associate-/l* 36.0%

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

   3. Simplified 36.0%

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

   5. Taylor expanded in x around 0 46.0%

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

      1. associate-/l* 56.5%

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

      2. associate-+r+ 56.5%

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

      3. associate-*r/ 56.5%

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

      4. *-commutative 56.5%

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

      5. associate-/r/ 56.6%

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

      6. +-commutative 56.6%

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

      7. associate-/r/ 56.5%

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

      8. *-commutative 56.5%

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

      9. associate-*r/ 56.5%

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

      10. associate-*l/ 56.7%

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

      11. *-commutative 56.7%

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

      12. fma-define 56.7%

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

   7. Simplified 56.7%

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

   8. Taylor expanded in t around 0 67.6%

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

   if -5.5000000000000003e41 < b < 1.05000000000000009e34

   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* 80.2%

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

      2. associate-/l* 80.9%

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

   3. Simplified 80.9%

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

      1. clear-num 80.9%

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

      2. un-div-inv 81.9%

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

   6. Applied egg-rr 81.9%

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

   7. Taylor expanded in y around 0 74.2%

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

      1. associate-/r/ 78.1%

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

   9. Applied egg-rr 78.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+179}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{\left(a + b \cdot \frac{y}{t}\right) + 1}\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+34}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-174} \lor \neg \left(t \leq 5.5 \cdot 10^{-212}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.6e-174) (not (<= t 5.5e-212)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.6e-174) || !(t <= 5.5e-212)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.6d-174)) .or. (.not. (t <= 5.5d-212))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.6e-174) || !(t <= 5.5e-212)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.6e-174) or not (t <= 5.5e-212):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.6e-174) || !(t <= 5.5e-212))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.6e-174) || ~((t <= 5.5e-212)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.6e-174], N[Not[LessEqual[t, 5.5e-212]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6000000000000002e-174 or 5.49999999999999995e-212 < t

   1. Initial program 80.0%

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

      1. associate-/l* 80.0%

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

      2. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   if -2.6000000000000002e-174 < t < 5.49999999999999995e-212

   1. Initial program 42.0%

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

      1. associate-/l* 33.7%

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

      2. associate-/l* 30.2%

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

   3. Simplified 30.2%

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

   5. Taylor expanded in y around inf 72.1%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-174} \lor \neg \left(t \leq 5.5 \cdot 10^{-212}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-174}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.6e-174)
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (if (<= t 5.8e-212)
     (/ z b)
     (/ (+ x (* z (/ y t))) (+ (/ (* y b) t) (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.6e-174) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 5.8e-212) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.6d-174)) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else if (t <= 5.8d-212) then
        tmp = z / b
    else
        tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.6e-174) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 5.8e-212) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.6e-174:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	elif t <= 5.8e-212:
		tmp = z / b
	else:
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.6e-174)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t <= 5.8e-212)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.6e-174)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	elseif (t <= 5.8e-212)
		tmp = z / b;
	else
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.6e-174], 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, 5.8e-212], N[(z / b), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6000000000000002e-174

   1. Initial program 74.8%

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

      1. associate-/l* 77.6%

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

      2. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

   if -2.6000000000000002e-174 < t < 5.7999999999999999e-212

   1. Initial program 42.0%

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

      1. associate-/l* 33.7%

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

      2. associate-/l* 30.2%

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

   3. Simplified 30.2%

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

   5. Taylor expanded in y around inf 72.1%

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

   if 5.7999999999999999e-212 < t

   1. Initial program 85.2%

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

      1. *-commutative 25.9%

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

      2. associate-/l* 25.9%

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

   4. Applied egg-rr 85.3%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-174}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 78.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-174}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.6e-174)
   (/ (+ x (/ y (/ t z))) (+ (+ a 1.0) (* y (/ b t))))
   (if (<= t 5.5e-212)
     (/ z b)
     (/ (+ x (* z (/ y t))) (+ (/ (* y b) t) (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.6e-174) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 5.5e-212) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.6d-174)) then
        tmp = (x + (y / (t / z))) / ((a + 1.0d0) + (y * (b / t)))
    else if (t <= 5.5d-212) then
        tmp = z / b
    else
        tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.6e-174) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 5.5e-212) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.6e-174:
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)))
	elif t <= 5.5e-212:
		tmp = z / b
	else:
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.6e-174)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t <= 5.5e-212)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.6e-174)
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	elseif (t <= 5.5e-212)
		tmp = z / b;
	else
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.6e-174], 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, 5.5e-212], N[(z / b), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6000000000000002e-174

   1. Initial program 74.8%

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

      1. associate-/l* 77.6%

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

      2. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

      1. clear-num 86.2%

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

      2. un-div-inv 86.7%

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

   6. Applied egg-rr 86.7%

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

   if -2.6000000000000002e-174 < t < 5.49999999999999995e-212

   1. Initial program 42.0%

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

      1. associate-/l* 33.7%

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

      2. associate-/l* 30.2%

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

   3. Simplified 30.2%

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

   5. Taylor expanded in y around inf 72.1%

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

   if 5.49999999999999995e-212 < t

   1. Initial program 85.2%

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

      1. *-commutative 25.9%

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

      2. associate-/l* 25.9%

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

   4. Applied egg-rr 85.3%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-174}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + 1}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-100} \lor \neg \left(t \leq 4.3 \cdot 10^{-41}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -3.7e+68)
     t_1
     (if (<= t -1.55e-49)
       (/ x (+ (/ (* y b) t) 1.0))
       (if (or (<= t -9.5e-100) (not (<= t 4.3e-41))) t_1 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -3.7e+68) {
		tmp = t_1;
	} else if (t <= -1.55e-49) {
		tmp = x / (((y * b) / t) + 1.0);
	} else if ((t <= -9.5e-100) || !(t <= 4.3e-41)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-3.7d+68)) then
        tmp = t_1
    else if (t <= (-1.55d-49)) then
        tmp = x / (((y * b) / t) + 1.0d0)
    else if ((t <= (-9.5d-100)) .or. (.not. (t <= 4.3d-41))) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -3.7e+68) {
		tmp = t_1;
	} else if (t <= -1.55e-49) {
		tmp = x / (((y * b) / t) + 1.0);
	} else if ((t <= -9.5e-100) || !(t <= 4.3e-41)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -3.7e+68:
		tmp = t_1
	elif t <= -1.55e-49:
		tmp = x / (((y * b) / t) + 1.0)
	elif (t <= -9.5e-100) or not (t <= 4.3e-41):
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -3.7e+68)
		tmp = t_1;
	elseif (t <= -1.55e-49)
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + 1.0));
	elseif ((t <= -9.5e-100) || !(t <= 4.3e-41))
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -3.7e+68)
		tmp = t_1;
	elseif (t <= -1.55e-49)
		tmp = x / (((y * b) / t) + 1.0);
	elseif ((t <= -9.5e-100) || ~((t <= 4.3e-41)))
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+68], t$95$1, If[LessEqual[t, -1.55e-49], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -9.5e-100], N[Not[LessEqual[t, 4.3e-41]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.69999999999999998e68 or -1.55e-49 < t < -9.4999999999999992e-100 or 4.2999999999999999e-41 < t

   1. Initial program 83.8%

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

      1. associate-/l* 88.6%

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

      2. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in y around 0 60.0%

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

   if -3.69999999999999998e68 < t < -1.55e-49

   1. Initial program 60.9%

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

      1. associate-/l* 65.8%

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

      2. associate-/l* 75.2%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in a around 0 53.7%

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

   6. Taylor expanded in x around inf 46.1%

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

   if -9.4999999999999992e-100 < t < 4.2999999999999999e-41

   1. Initial program 60.1%

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

      1. associate-/l* 50.2%

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

      2. associate-/l* 47.6%

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

   3. Simplified 47.6%

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

   5. Taylor expanded in y around inf 57.0%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + 1}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-100} \lor \neg \left(t \leq 4.3 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-174} \lor \neg \left(t \leq 7 \cdot 10^{-159}\right):\\ \;\;\;\;\frac{x}{\left(a + b \cdot \frac{y}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.7e-174) (not (<= t 7e-159)))
   (/ x (+ (+ a (* b (/ y t))) 1.0))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.7e-174) || !(t <= 7e-159)) {
		tmp = x / ((a + (b * (y / t))) + 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 <= (-2.7d-174)) .or. (.not. (t <= 7d-159))) then
        tmp = x / ((a + (b * (y / t))) + 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 <= -2.7e-174) || !(t <= 7e-159)) {
		tmp = x / ((a + (b * (y / t))) + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.7e-174) or not (t <= 7e-159):
		tmp = x / ((a + (b * (y / t))) + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.7e-174) || !(t <= 7e-159))
		tmp = Float64(x / Float64(Float64(a + Float64(b * Float64(y / t))) + 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 <= -2.7e-174) || ~((t <= 7e-159)))
		tmp = x / ((a + (b * (y / t))) + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.7e-174], N[Not[LessEqual[t, 7e-159]], $MachinePrecision]], N[(x / N[(N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.69999999999999988e-174 or 7.00000000000000005e-159 < t

   1. Initial program 79.5%

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

      1. associate-*r/ 80.4%

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

      2. *-commutative 80.4%

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

      3. div-inv 80.4%

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

      4. associate-*l* 81.6%

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

   4. Applied egg-rr 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-*l/ 81.6%

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

      3. *-un-lft-identity 81.6%

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

      4. associate-/r/ 81.2%

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

      5. clear-num 81.2%

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

   6. Applied egg-rr 81.2%

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

   7. Taylor expanded in x around inf 57.8%

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

      1. associate-/l* 60.3%

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

   9. Simplified 60.3%

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

   if -2.69999999999999988e-174 < t < 7.00000000000000005e-159

   1. Initial program 49.0%

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

      1. associate-/l* 39.2%

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

      2. associate-/l* 36.2%

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

   3. Simplified 36.2%

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

   5. Taylor expanded in y around inf 71.3%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-174} \lor \neg \left(t \leq 7 \cdot 10^{-159}\right):\\ \;\;\;\;\frac{x}{\left(a + b \cdot \frac{y}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-100} \lor \neg \left(t \leq 4.7 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8.2e-100) (not (<= t 4.7e-41))) (/ 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 <= -8.2e-100) || !(t <= 4.7e-41)) {
		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 <= (-8.2d-100)) .or. (.not. (t <= 4.7d-41))) 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 <= -8.2e-100) || !(t <= 4.7e-41)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -8.2e-100) or not (t <= 4.7e-41):
		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 <= -8.2e-100) || !(t <= 4.7e-41))
		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 <= -8.2e-100) || ~((t <= 4.7e-41)))
		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, -8.2e-100], N[Not[LessEqual[t, 4.7e-41]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.1999999999999998e-100 or 4.7000000000000003e-41 < t

   1. Initial program 80.7%

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

      1. associate-/l* 85.4%

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

      2. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in y around 0 54.9%

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

   if -8.1999999999999998e-100 < t < 4.7000000000000003e-41

   1. Initial program 60.1%

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

      1. associate-/l* 50.2%

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

      2. associate-/l* 47.6%

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

   3. Simplified 47.6%

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

   5. Taylor expanded in y around inf 57.0%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-100} \lor \neg \left(t \leq 4.7 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 40.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-27} \lor \neg \left(y \leq 5.5 \cdot 10^{-182}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9e-27) (not (<= y 5.5e-182))) (/ z b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e-27) || !(y <= 5.5e-182)) {
		tmp = z / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9d-27)) .or. (.not. (y <= 5.5d-182))) then
        tmp = z / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e-27) || !(y <= 5.5e-182)) {
		tmp = z / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9e-27) or not (y <= 5.5e-182):
		tmp = z / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9e-27) || !(y <= 5.5e-182))
		tmp = Float64(z / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9e-27) || ~((y <= 5.5e-182)))
		tmp = z / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9e-27], N[Not[LessEqual[y, 5.5e-182]], $MachinePrecision]], N[(z / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9.0000000000000003e-27 or 5.49999999999999993e-182 < y

   1. Initial program 59.6%

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

      1. associate-/l* 62.8%

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

      2. associate-/l* 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in y around inf 47.0%

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

   if -9.0000000000000003e-27 < y < 5.49999999999999993e-182

   1. Initial program 97.3%

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

      1. associate-/l* 83.9%

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

      2. associate-/l* 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in a around 0 50.1%

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

   6. Taylor expanded in y around 0 32.2%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-27} \lor \neg \left(y \leq 5.5 \cdot 10^{-182}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 20.1% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.3%

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

   1. associate-/l* 69.3%

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

   2. associate-/l* 72.2%

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

3. Simplified 72.2%

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

5. Taylor expanded in a around 0 42.1%

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

6. Taylor expanded in y around 0 18.5%

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

7. Final simplification 18.5%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 78.7% 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 2024040 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

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

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