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

Percentage Accurate: 74.5% → 90.0%

Time: 16.5s

Alternatives: 23

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: 74.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{t\_1 + \left(a + 1\right)}\\ t_4 := 1 + \left(a + t\_1\right)\\ t_5 := \mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_4} + \frac{y}{t \cdot t\_4}\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+188}:\\ \;\;\;\;\frac{t\_2}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{t\_5} + \frac{\frac{y}{t}}{t\_5}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 (+ t_1 (+ a 1.0))))
        (t_4 (+ 1.0 (+ a t_1)))
        (t_5 (fma y (/ b t) (+ a 1.0))))
   (if (<= t_3 (- INFINITY))
     (* z (+ (/ x (* z t_4)) (/ y (* t t_4))))
     (if (<= t_3 2e+188)
       (/ t_2 (+ (* b (/ y t)) (+ a 1.0)))
       (if (<= t_3 INFINITY)
         (* z (+ (/ (/ x z) t_5) (/ (/ y t) t_5)))
         (+ (/ z b) (* (/ t b) (/ x y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / (t_1 + (a + 1.0));
	double t_4 = 1.0 + (a + t_1);
	double t_5 = fma(y, (b / t), (a + 1.0));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = z * ((x / (z * t_4)) + (y / (t * t_4)));
	} else if (t_3 <= 2e+188) {
		tmp = t_2 / ((b * (y / t)) + (a + 1.0));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = z * (((x / z) / t_5) + ((y / t) / t_5));
	} else {
		tmp = (z / b) + ((t / b) * (x / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / Float64(t_1 + Float64(a + 1.0)))
	t_4 = Float64(1.0 + Float64(a + t_1))
	t_5 = fma(y, Float64(b / t), Float64(a + 1.0))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_4)) + Float64(y / Float64(t * t_4))));
	elseif (t_3 <= 2e+188)
		tmp = Float64(t_2 / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	elseif (t_3 <= Inf)
		tmp = Float64(z * Float64(Float64(Float64(x / z) / t_5) + Float64(Float64(y / t) / t_5)));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * N[(b / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(z * N[(N[(x / N[(z * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+188], N[(t$95$2 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(z * N[(N[(N[(x / z), $MachinePrecision] / t$95$5), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 16.4%

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

      1. associate-/l* 40.8%

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

      2. associate-/l* 40.1%

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

   3. Simplified 40.1%

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

   5. Taylor expanded in z around inf 89.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2e188

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-/l* 93.8%

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

   4. Applied egg-rr 93.8%

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

   if 2e188 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 50.1%

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

      1. associate-/l* 61.0%

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

      2. associate-/l* 61.0%

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

   3. Simplified 61.0%

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

   5. Taylor expanded in z around inf 88.9%

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

      1. associate-/r* 92.5%

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

      2. +-commutative 92.5%

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

      3. associate-*r/ 92.5%

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

      4. +-commutative 92.5%

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

      5. associate-+r+ 92.5%

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

      6. associate-*r/ 92.5%

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

      7. associate-*l/ 92.6%

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

      8. *-commutative 92.6%

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

      9. fma-undefine 92.6%

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

      10. +-commutative 92.6%

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

      11. associate-/r* 92.7%

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

      12. +-commutative 92.7%

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

      13. associate-*r/ 88.7%

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

      14. +-commutative 88.7%

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

      15. associate-+r+ 88.7%

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

   7. Simplified 92.7%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.3%

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

      2. associate-/l* 9.3%

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

   3. Simplified 9.3%

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

   5. Taylor expanded in b around inf 1.7%

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

   6. Taylor expanded in z around inf 33.8%

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

   7. Taylor expanded in z around 0 91.3%

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

      1. times-frac 91.3%

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

   9. Simplified 91.3%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+188}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)} + \frac{\frac{y}{t}}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := 1 + \left(a + t\_1\right)\\ t_3 := x + \frac{y \cdot z}{t}\\ t_4 := \frac{t\_3}{t\_1 + \left(a + 1\right)}\\ t_5 := z \cdot \left(\frac{x}{z \cdot t\_2} + \frac{y}{t \cdot t\_2}\right)\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+241}:\\ \;\;\;\;\frac{t\_3}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ 1.0 (+ a t_1)))
        (t_3 (+ x (/ (* y z) t)))
        (t_4 (/ t_3 (+ t_1 (+ a 1.0))))
        (t_5 (* z (+ (/ x (* z t_2)) (/ y (* t t_2))))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 2e+241)
       (/ t_3 (+ (* b (/ y t)) (+ a 1.0)))
       (if (<= t_4 INFINITY) t_5 (+ (/ z b) (* (/ t b) (/ x y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = 1.0 + (a + t_1);
	double t_3 = x + ((y * z) / t);
	double t_4 = t_3 / (t_1 + (a + 1.0));
	double t_5 = z * ((x / (z * t_2)) + (y / (t * t_2)));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= 2e+241) {
		tmp = t_3 / ((b * (y / t)) + (a + 1.0));
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} else {
		tmp = (z / b) + ((t / b) * (x / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = 1.0 + (a + t_1);
	double t_3 = x + ((y * z) / t);
	double t_4 = t_3 / (t_1 + (a + 1.0));
	double t_5 = z * ((x / (z * t_2)) + (y / (t * t_2)));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= 2e+241) {
		tmp = t_3 / ((b * (y / t)) + (a + 1.0));
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = (z / b) + ((t / b) * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = 1.0 + (a + t_1)
	t_3 = x + ((y * z) / t)
	t_4 = t_3 / (t_1 + (a + 1.0))
	t_5 = z * ((x / (z * t_2)) + (y / (t * t_2)))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= 2e+241:
		tmp = t_3 / ((b * (y / t)) + (a + 1.0))
	elif t_4 <= math.inf:
		tmp = t_5
	else:
		tmp = (z / b) + ((t / b) * (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(1.0 + Float64(a + t_1))
	t_3 = Float64(x + Float64(Float64(y * z) / t))
	t_4 = Float64(t_3 / Float64(t_1 + Float64(a + 1.0)))
	t_5 = Float64(z * Float64(Float64(x / Float64(z * t_2)) + Float64(y / Float64(t * t_2))))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= 2e+241)
		tmp = Float64(t_3 / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = 1.0 + (a + t_1);
	t_3 = x + ((y * z) / t);
	t_4 = t_3 / (t_1 + (a + 1.0));
	t_5 = z * ((x / (z * t_2)) + (y / (t * t_2)));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= 2e+241)
		tmp = t_3 / ((b * (y / t)) + (a + 1.0));
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = (z / b) + ((t / b) * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(z * N[(N[(x / N[(z * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, 2e+241], N[(t$95$3 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$5, N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or 2.0000000000000001e241 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 28.5%

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

      1. associate-/l* 49.2%

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

      2. associate-/l* 48.9%

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

   3. Simplified 48.9%

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

   5. Taylor expanded in z around inf 90.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e241

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-/l* 94.0%

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

   4. Applied egg-rr 94.0%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.3%

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

      2. associate-/l* 9.3%

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

   3. Simplified 9.3%

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

   5. Taylor expanded in b around inf 1.7%

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

   6. Taylor expanded in z around inf 33.8%

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

   7. Taylor expanded in z around 0 91.3%

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

      1. times-frac 91.3%

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

   9. Simplified 91.3%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+241}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{t\_1 + \left(a + 1\right)}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{y}{t \cdot \left(1 + \left(a + t\_1\right)\right)} + \frac{\frac{x}{a}}{z}\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+281}:\\ \;\;\;\;\frac{t\_2}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 (+ t_1 (+ a 1.0)))))
   (if (<= t_3 (- INFINITY))
     (* z (+ (/ y (* t (+ 1.0 (+ a t_1)))) (/ (/ x a) z)))
     (if (<= t_3 2e+281)
       (/ t_2 (+ (* b (/ y t)) (+ a 1.0)))
       (+ (/ z b) (/ (* x t) (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / (t_1 + (a + 1.0));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = z * ((y / (t * (1.0 + (a + t_1)))) + ((x / a) / z));
	} else if (t_3 <= 2e+281) {
		tmp = t_2 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / (t_1 + (a + 1.0));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((y / (t * (1.0 + (a + t_1)))) + ((x / a) / z));
	} else if (t_3 <= 2e+281) {
		tmp = t_2 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = x + ((y * z) / t)
	t_3 = t_2 / (t_1 + (a + 1.0))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = z * ((y / (t * (1.0 + (a + t_1)))) + ((x / a) / z))
	elif t_3 <= 2e+281:
		tmp = t_2 / ((b * (y / t)) + (a + 1.0))
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / Float64(t_1 + Float64(a + 1.0)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(y / Float64(t * Float64(1.0 + Float64(a + t_1)))) + Float64(Float64(x / a) / z)));
	elseif (t_3 <= 2e+281)
		tmp = Float64(t_2 / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = x + ((y * z) / t);
	t_3 = t_2 / (t_1 + (a + 1.0));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = z * ((y / (t * (1.0 + (a + t_1)))) + ((x / a) / z));
	elseif (t_3 <= 2e+281)
		tmp = t_2 / ((b * (y / t)) + (a + 1.0));
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(z * N[(N[(y / N[(t * N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+281], N[(t$95$2 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 16.4%

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

      1. associate-/l* 40.8%

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

      2. associate-/l* 40.1%

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

   3. Simplified 40.1%

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

   5. Taylor expanded in z around inf 89.2%

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

   6. Taylor expanded in a around inf 79.0%

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

      1. associate-/r* 79.0%

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

   8. Simplified 79.0%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e281

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-/l* 94.1%

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

   4. Applied egg-rr 94.1%

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

   if 2.0000000000000001e281 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 13.5%

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

      1. associate-/l* 23.2%

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

      2. associate-/l* 28.0%

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

   3. Simplified 28.0%

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

   5. Taylor expanded in b around inf 14.4%

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

   6. Taylor expanded in t around 0 76.3%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{\frac{x}{a}}{z}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+281}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+281}:\\ \;\;\;\;\frac{t\_1}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ t_1 (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_2 (- INFINITY))
     (* (/ y t) (/ z (+ 1.0 (+ a (* y (/ b t))))))
     (if (<= t_2 2e+281)
       (/ t_1 (+ (* b (/ y t)) (+ a 1.0)))
       (+ (/ z b) (/ (* x t) (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	} else if (t_2 <= 2e+281) {
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = (z / b) + ((x * t) / (y * 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);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	} else if (t_2 <= 2e+281) {
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))))
	elif t_2 <= 2e+281:
		tmp = t_1 / ((b * (y / t)) + (a + 1.0))
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))));
	elseif (t_2 <= 2e+281)
		tmp = Float64(t_1 / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	elseif (t_2 <= 2e+281)
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+281], N[(t$95$1 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 16.4%

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

      1. associate-/l* 40.8%

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

      2. associate-/l* 40.1%

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

   3. Simplified 40.1%

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

   5. Taylor expanded in x around 0 65.2%

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

      1. times-frac 85.0%

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

      2. associate-*l/ 69.8%

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

      3. *-commutative 69.8%

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

   7. Simplified 69.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e281

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-/l* 94.1%

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

   4. Applied egg-rr 94.1%

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

   if 2.0000000000000001e281 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 13.5%

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

      1. associate-/l* 23.2%

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

      2. associate-/l* 28.0%

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

   3. Simplified 28.0%

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

   5. Taylor expanded in b around inf 14.4%

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

   6. Taylor expanded in t around 0 76.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+281}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-217}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-166}:\\ \;\;\;\;\frac{x}{1 + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+32}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* z (/ y t))) a)))
   (if (<= a -1.35e+23)
     t_1
     (if (<= a -7.8e-66)
       (/ z b)
       (if (<= a -3.3e-283)
         (/ x (+ 1.0 (* y (/ b t))))
         (if (<= a 2.25e-217)
           (/ z b)
           (if (<= a 3.4e-166)
             (/ x (+ 1.0 (/ y (/ t b))))
             (if (<= a 3.8e+32) (/ z b) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -1.35e+23) {
		tmp = t_1;
	} else if (a <= -7.8e-66) {
		tmp = z / b;
	} else if (a <= -3.3e-283) {
		tmp = x / (1.0 + (y * (b / t)));
	} else if (a <= 2.25e-217) {
		tmp = z / b;
	} else if (a <= 3.4e-166) {
		tmp = x / (1.0 + (y / (t / b)));
	} else if (a <= 3.8e+32) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z * (y / t))) / a
    if (a <= (-1.35d+23)) then
        tmp = t_1
    else if (a <= (-7.8d-66)) then
        tmp = z / b
    else if (a <= (-3.3d-283)) then
        tmp = x / (1.0d0 + (y * (b / t)))
    else if (a <= 2.25d-217) then
        tmp = z / b
    else if (a <= 3.4d-166) then
        tmp = x / (1.0d0 + (y / (t / b)))
    else if (a <= 3.8d+32) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -1.35e+23) {
		tmp = t_1;
	} else if (a <= -7.8e-66) {
		tmp = z / b;
	} else if (a <= -3.3e-283) {
		tmp = x / (1.0 + (y * (b / t)));
	} else if (a <= 2.25e-217) {
		tmp = z / b;
	} else if (a <= 3.4e-166) {
		tmp = x / (1.0 + (y / (t / b)));
	} else if (a <= 3.8e+32) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (y / t))) / a
	tmp = 0
	if a <= -1.35e+23:
		tmp = t_1
	elif a <= -7.8e-66:
		tmp = z / b
	elif a <= -3.3e-283:
		tmp = x / (1.0 + (y * (b / t)))
	elif a <= 2.25e-217:
		tmp = z / b
	elif a <= 3.4e-166:
		tmp = x / (1.0 + (y / (t / b)))
	elif a <= 3.8e+32:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(y / t))) / a)
	tmp = 0.0
	if (a <= -1.35e+23)
		tmp = t_1;
	elseif (a <= -7.8e-66)
		tmp = Float64(z / b);
	elseif (a <= -3.3e-283)
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(b / t))));
	elseif (a <= 2.25e-217)
		tmp = Float64(z / b);
	elseif (a <= 3.4e-166)
		tmp = Float64(x / Float64(1.0 + Float64(y / Float64(t / b))));
	elseif (a <= 3.8e+32)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (y / t))) / a;
	tmp = 0.0;
	if (a <= -1.35e+23)
		tmp = t_1;
	elseif (a <= -7.8e-66)
		tmp = z / b;
	elseif (a <= -3.3e-283)
		tmp = x / (1.0 + (y * (b / t)));
	elseif (a <= 2.25e-217)
		tmp = z / b;
	elseif (a <= 3.4e-166)
		tmp = x / (1.0 + (y / (t / b)));
	elseif (a <= 3.8e+32)
		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[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -1.35e+23], t$95$1, If[LessEqual[a, -7.8e-66], N[(z / b), $MachinePrecision], If[LessEqual[a, -3.3e-283], N[(x / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e-217], N[(z / b), $MachinePrecision], If[LessEqual[a, 3.4e-166], N[(x / N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+32], N[(z / b), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.3499999999999999e23 or 3.8000000000000003e32 < a

   1. Initial program 74.1%

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

      1. *-commutative 74.1%

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

      2. associate-/l* 74.9%

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

   4. Applied egg-rr 74.9%

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

   5. Taylor expanded in a around inf 67.4%

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

   if -1.3499999999999999e23 < a < -7.79999999999999965e-66 or -3.30000000000000019e-283 < a < 2.2499999999999999e-217 or 3.3999999999999997e-166 < a < 3.8000000000000003e32

   1. Initial program 70.7%

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

      1. associate-/l* 66.0%

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

      2. associate-/l* 63.6%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in y around inf 64.1%

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

   if -7.79999999999999965e-66 < a < -3.30000000000000019e-283

   1. Initial program 72.6%

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

      1. associate-/l* 74.7%

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

      2. associate-/l* 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in x around inf 56.0%

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

      1. associate-*l/ 60.0%

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

      2. *-commutative 60.0%

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

   7. Simplified 60.0%

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

   8. Taylor expanded in a around 0 56.0%

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

      1. associate-*l/ 60.0%

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

      2. *-commutative 60.0%

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

   10. Simplified 60.0%

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

   if 2.2499999999999999e-217 < a < 3.3999999999999997e-166

   1. Initial program 91.3%

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

      1. associate-/l* 91.1%

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

      2. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 67.5%

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

      1. associate-*l/ 67.5%

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

      2. *-commutative 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in a around 0 67.5%

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

      1. associate-*l/ 67.5%

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

      2. *-commutative 67.5%

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

   10. Simplified 67.5%

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

       1. clear-num 91.3%

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

       2. un-div-inv 91.4%

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

   12. Applied egg-rr 67.8%

       \[\leadsto \frac{x}{1 + \color{blue}{\frac{y}{\frac{t}{b}}}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 52.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-284}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-217}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.24 \cdot 10^{-166}:\\ \;\;\;\;\frac{x}{1 + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) a)))
   (if (<= a -1.1e+23)
     t_1
     (if (<= a -5.8e-66)
       (/ z b)
       (if (<= a -4.4e-284)
         (/ x (+ 1.0 (* y (/ b t))))
         (if (<= a 1.35e-217)
           (/ z b)
           (if (<= a 1.24e-166)
             (/ x (+ 1.0 (/ y (/ t b))))
             (if (<= a 8.2e+32) (/ z b) 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 <= -1.1e+23) {
		tmp = t_1;
	} else if (a <= -5.8e-66) {
		tmp = z / b;
	} else if (a <= -4.4e-284) {
		tmp = x / (1.0 + (y * (b / t)));
	} else if (a <= 1.35e-217) {
		tmp = z / b;
	} else if (a <= 1.24e-166) {
		tmp = x / (1.0 + (y / (t / b)));
	} else if (a <= 8.2e+32) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / a
    if (a <= (-1.1d+23)) then
        tmp = t_1
    else if (a <= (-5.8d-66)) then
        tmp = z / b
    else if (a <= (-4.4d-284)) then
        tmp = x / (1.0d0 + (y * (b / t)))
    else if (a <= 1.35d-217) then
        tmp = z / b
    else if (a <= 1.24d-166) then
        tmp = x / (1.0d0 + (y / (t / b)))
    else if (a <= 8.2d+32) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -1.1e+23) {
		tmp = t_1;
	} else if (a <= -5.8e-66) {
		tmp = z / b;
	} else if (a <= -4.4e-284) {
		tmp = x / (1.0 + (y * (b / t)));
	} else if (a <= 1.35e-217) {
		tmp = z / b;
	} else if (a <= 1.24e-166) {
		tmp = x / (1.0 + (y / (t / b)));
	} else if (a <= 8.2e+32) {
		tmp = z / b;
	} 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 <= -1.1e+23:
		tmp = t_1
	elif a <= -5.8e-66:
		tmp = z / b
	elif a <= -4.4e-284:
		tmp = x / (1.0 + (y * (b / t)))
	elif a <= 1.35e-217:
		tmp = z / b
	elif a <= 1.24e-166:
		tmp = x / (1.0 + (y / (t / b)))
	elif a <= 8.2e+32:
		tmp = z / b
	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 <= -1.1e+23)
		tmp = t_1;
	elseif (a <= -5.8e-66)
		tmp = Float64(z / b);
	elseif (a <= -4.4e-284)
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(b / t))));
	elseif (a <= 1.35e-217)
		tmp = Float64(z / b);
	elseif (a <= 1.24e-166)
		tmp = Float64(x / Float64(1.0 + Float64(y / Float64(t / b))));
	elseif (a <= 8.2e+32)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / a;
	tmp = 0.0;
	if (a <= -1.1e+23)
		tmp = t_1;
	elseif (a <= -5.8e-66)
		tmp = z / b;
	elseif (a <= -4.4e-284)
		tmp = x / (1.0 + (y * (b / t)));
	elseif (a <= 1.35e-217)
		tmp = z / b;
	elseif (a <= 1.24e-166)
		tmp = x / (1.0 + (y / (t / b)));
	elseif (a <= 8.2e+32)
		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[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -1.1e+23], t$95$1, If[LessEqual[a, -5.8e-66], N[(z / b), $MachinePrecision], If[LessEqual[a, -4.4e-284], N[(x / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-217], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.24e-166], N[(x / N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+32], N[(z / b), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.10000000000000004e23 or 8.19999999999999961e32 < a

   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* 71.6%

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

      2. associate-/l* 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in a around inf 64.7%

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

   if -1.10000000000000004e23 < a < -5.80000000000000023e-66 or -4.4000000000000001e-284 < a < 1.35000000000000008e-217 or 1.24e-166 < a < 8.19999999999999961e32

   1. Initial program 70.7%

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

      1. associate-/l* 66.0%

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

      2. associate-/l* 63.6%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in y around inf 64.1%

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

   if -5.80000000000000023e-66 < a < -4.4000000000000001e-284

   1. Initial program 72.6%

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

      1. associate-/l* 74.7%

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

      2. associate-/l* 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in x around inf 56.0%

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

      1. associate-*l/ 60.0%

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

      2. *-commutative 60.0%

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

   7. Simplified 60.0%

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

   8. Taylor expanded in a around 0 56.0%

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

      1. associate-*l/ 60.0%

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

      2. *-commutative 60.0%

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

   10. Simplified 60.0%

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

   if 1.35000000000000008e-217 < a < 1.24e-166

   1. Initial program 91.3%

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

      1. associate-/l* 91.1%

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

      2. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 67.5%

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

      1. associate-*l/ 67.5%

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

      2. *-commutative 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in a around 0 67.5%

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

      1. associate-*l/ 67.5%

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

      2. *-commutative 67.5%

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

   10. Simplified 67.5%

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

       1. clear-num 91.3%

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

       2. un-div-inv 91.4%

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

   12. Applied egg-rr 67.8%

       \[\leadsto \frac{x}{1 + \color{blue}{\frac{y}{\frac{t}{b}}}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 67.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.95 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-80}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-67} \lor \neg \left(t \leq 10^{-10}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.95e-75)
   (/ x (+ 1.0 (+ a (* y (/ b t)))))
   (if (<= t 4.9e-80)
     (+ (/ z b) (/ (* x t) (* y b)))
     (if (or (<= t 1.26e-67) (not (<= t 1e-10)))
       (/ (+ x (* y (/ z t))) (+ a 1.0))
       (+ (/ z b) (* (/ t b) (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.95e-75) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if (t <= 4.9e-80) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if ((t <= 1.26e-67) || !(t <= 1e-10)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = (z / b) + ((t / b) * (x / y));
	}
	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 <= (-3.95d-75)) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    else if (t <= 4.9d-80) then
        tmp = (z / b) + ((x * t) / (y * b))
    else if ((t <= 1.26d-67) .or. (.not. (t <= 1d-10))) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else
        tmp = (z / b) + ((t / b) * (x / y))
    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 <= -3.95e-75) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if (t <= 4.9e-80) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if ((t <= 1.26e-67) || !(t <= 1e-10)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = (z / b) + ((t / b) * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.95e-75:
		tmp = x / (1.0 + (a + (y * (b / t))))
	elif t <= 4.9e-80:
		tmp = (z / b) + ((x * t) / (y * b))
	elif (t <= 1.26e-67) or not (t <= 1e-10):
		tmp = (x + (y * (z / t))) / (a + 1.0)
	else:
		tmp = (z / b) + ((t / b) * (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.95e-75)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	elseif (t <= 4.9e-80)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	elseif ((t <= 1.26e-67) || !(t <= 1e-10))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.95e-75)
		tmp = x / (1.0 + (a + (y * (b / t))));
	elseif (t <= 4.9e-80)
		tmp = (z / b) + ((x * t) / (y * b));
	elseif ((t <= 1.26e-67) || ~((t <= 1e-10)))
		tmp = (x + (y * (z / t))) / (a + 1.0);
	else
		tmp = (z / b) + ((t / b) * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.95e-75], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.9e-80], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.26e-67], N[Not[LessEqual[t, 1e-10]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.95e-75

   1. Initial program 82.9%

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

      1. associate-/l* 87.4%

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

      2. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf 71.9%

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

      1. associate-*l/ 78.1%

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

      2. *-commutative 78.1%

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

   7. Simplified 78.1%

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

   if -3.95e-75 < t < 4.8999999999999999e-80

   1. Initial program 63.3%

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

      1. associate-/l* 50.6%

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

      2. associate-/l* 45.0%

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

   3. Simplified 45.0%

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

   5. Taylor expanded in b around inf 48.8%

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

   6. Taylor expanded in t around 0 72.7%

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

   if 4.8999999999999999e-80 < t < 1.26e-67 or 1.00000000000000004e-10 < t

   1. Initial program 80.4%

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

      1. associate-/l* 86.6%

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

      2. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in y around 0 71.0%

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

   if 1.26e-67 < t < 1.00000000000000004e-10

   1. Initial program 68.0%

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

      1. associate-/l* 67.8%

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

      2. associate-/l* 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in b around inf 58.2%

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

   6. Taylor expanded in z around inf 58.0%

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

   7. Taylor expanded in z around 0 83.7%

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

      1. times-frac 83.7%

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

   9. Simplified 83.7%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.95 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-80}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-67} \lor \neg \left(t \leq 10^{-10}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-23}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+106} \lor \neg \left(t \leq 5 \cdot 10^{+170}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.9e-72)
   (/ x (+ 1.0 (+ a (* y (/ b t)))))
   (if (<= t 2.55e-23)
     (+ (/ z b) (/ (* x t) (* y b)))
     (if (or (<= t 7.8e+106) (not (<= t 5e+170)))
       (/ x (+ 1.0 (+ a (/ y (/ t b)))))
       (/ (+ x (* y (/ z t))) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.9e-72) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if (t <= 2.55e-23) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if ((t <= 7.8e+106) || !(t <= 5e+170)) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else {
		tmp = (x + (y * (z / t))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.9d-72)) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    else if (t <= 2.55d-23) then
        tmp = (z / b) + ((x * t) / (y * b))
    else if ((t <= 7.8d+106) .or. (.not. (t <= 5d+170))) then
        tmp = x / (1.0d0 + (a + (y / (t / b))))
    else
        tmp = (x + (y * (z / t))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.9e-72) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if (t <= 2.55e-23) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if ((t <= 7.8e+106) || !(t <= 5e+170)) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else {
		tmp = (x + (y * (z / t))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.9e-72:
		tmp = x / (1.0 + (a + (y * (b / t))))
	elif t <= 2.55e-23:
		tmp = (z / b) + ((x * t) / (y * b))
	elif (t <= 7.8e+106) or not (t <= 5e+170):
		tmp = x / (1.0 + (a + (y / (t / b))))
	else:
		tmp = (x + (y * (z / t))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.9e-72)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	elseif (t <= 2.55e-23)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	elseif ((t <= 7.8e+106) || !(t <= 5e+170))
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y / Float64(t / b)))));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.9e-72)
		tmp = x / (1.0 + (a + (y * (b / t))));
	elseif (t <= 2.55e-23)
		tmp = (z / b) + ((x * t) / (y * b));
	elseif ((t <= 7.8e+106) || ~((t <= 5e+170)))
		tmp = x / (1.0 + (a + (y / (t / b))));
	else
		tmp = (x + (y * (z / t))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.9e-72], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e-23], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 7.8e+106], N[Not[LessEqual[t, 5e+170]], $MachinePrecision]], N[(x / N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.89999999999999998e-72

   1. Initial program 82.9%

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

      1. associate-/l* 87.4%

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

      2. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf 71.9%

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

      1. associate-*l/ 78.1%

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

      2. *-commutative 78.1%

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

   7. Simplified 78.1%

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

   if -2.89999999999999998e-72 < t < 2.55000000000000005e-23

   1. Initial program 64.1%

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

      1. associate-/l* 52.8%

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

      2. associate-/l* 47.7%

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

   3. Simplified 47.7%

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

   5. Taylor expanded in b around inf 46.4%

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

   6. Taylor expanded in t around 0 69.9%

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

   if 2.55000000000000005e-23 < t < 7.79999999999999937e106 or 4.99999999999999977e170 < t

   1. Initial program 78.9%

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

      1. associate-/l* 85.6%

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

      2. associate-/l* 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around inf 58.7%

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

      1. associate-*l/ 62.1%

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

      2. *-commutative 62.1%

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

   7. Simplified 62.1%

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

      1. clear-num 89.1%

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

      2. un-div-inv 89.1%

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

   9. Applied egg-rr 62.1%

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

   if 7.79999999999999937e106 < t < 4.99999999999999977e170

   1. Initial program 86.8%

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

      1. associate-/l* 93.0%

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

      2. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in a around inf 80.2%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-23}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+106} \lor \neg \left(t \leq 5 \cdot 10^{+170}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+106} \lor \neg \left(t \leq 5.2 \cdot 10^{+170}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (+ a (* y (/ b t)))))))
   (if (<= t -2.8e-76)
     t_1
     (if (<= t 4.3e-26)
       (+ (/ z b) (/ (* x t) (* y b)))
       (if (or (<= t 7.8e+106) (not (<= t 5.2e+170)))
         t_1
         (/ (+ x (* y (/ z t))) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -2.8e-76) {
		tmp = t_1;
	} else if (t <= 4.3e-26) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if ((t <= 7.8e+106) || !(t <= 5.2e+170)) {
		tmp = t_1;
	} else {
		tmp = (x + (y * (z / t))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 + (a + (y * (b / t))))
    if (t <= (-2.8d-76)) then
        tmp = t_1
    else if (t <= 4.3d-26) then
        tmp = (z / b) + ((x * t) / (y * b))
    else if ((t <= 7.8d+106) .or. (.not. (t <= 5.2d+170))) then
        tmp = t_1
    else
        tmp = (x + (y * (z / t))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -2.8e-76) {
		tmp = t_1;
	} else if (t <= 4.3e-26) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if ((t <= 7.8e+106) || !(t <= 5.2e+170)) {
		tmp = t_1;
	} else {
		tmp = (x + (y * (z / t))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a + (y * (b / t))))
	tmp = 0
	if t <= -2.8e-76:
		tmp = t_1
	elif t <= 4.3e-26:
		tmp = (z / b) + ((x * t) / (y * b))
	elif (t <= 7.8e+106) or not (t <= 5.2e+170):
		tmp = t_1
	else:
		tmp = (x + (y * (z / t))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))))
	tmp = 0.0
	if (t <= -2.8e-76)
		tmp = t_1;
	elseif (t <= 4.3e-26)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	elseif ((t <= 7.8e+106) || !(t <= 5.2e+170))
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (a + (y * (b / t))));
	tmp = 0.0;
	if (t <= -2.8e-76)
		tmp = t_1;
	elseif (t <= 4.3e-26)
		tmp = (z / b) + ((x * t) / (y * b));
	elseif ((t <= 7.8e+106) || ~((t <= 5.2e+170)))
		tmp = t_1;
	else
		tmp = (x + (y * (z / t))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e-76], t$95$1, If[LessEqual[t, 4.3e-26], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 7.8e+106], N[Not[LessEqual[t, 5.2e+170]], $MachinePrecision]], t$95$1, N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8000000000000001e-76 or 4.29999999999999988e-26 < t < 7.79999999999999937e106 or 5.1999999999999996e170 < t

   1. Initial program 81.2%

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

      1. associate-/l* 86.6%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf 66.0%

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

      1. associate-*l/ 71.0%

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

      2. *-commutative 71.0%

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

   7. Simplified 71.0%

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

   if -2.8000000000000001e-76 < t < 4.29999999999999988e-26

   1. Initial program 64.1%

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

      1. associate-/l* 52.8%

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

      2. associate-/l* 47.7%

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

   3. Simplified 47.7%

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

   5. Taylor expanded in b around inf 46.4%

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

   6. Taylor expanded in t around 0 69.9%

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

   if 7.79999999999999937e106 < t < 5.1999999999999996e170

   1. Initial program 86.8%

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

      1. associate-/l* 93.0%

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

      2. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in a around inf 80.2%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+106} \lor \neg \left(t \leq 5.2 \cdot 10^{+170}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ t_2 := \frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* x t) (* y b)))) (t_2 (/ (+ x (* z (/ y t))) a)))
   (if (<= a -4.4e+79)
     t_2
     (if (<= a -1.15e-90)
       t_1
       (if (<= a -2.05e-215)
         (/ x (+ 1.0 (* y (/ b t))))
         (if (<= a 9e+31) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * t) / (y * b));
	double t_2 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -4.4e+79) {
		tmp = t_2;
	} else if (a <= -1.15e-90) {
		tmp = t_1;
	} else if (a <= -2.05e-215) {
		tmp = x / (1.0 + (y * (b / t)));
	} else if (a <= 9e+31) {
		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 = (z / b) + ((x * t) / (y * b))
    t_2 = (x + (z * (y / t))) / a
    if (a <= (-4.4d+79)) then
        tmp = t_2
    else if (a <= (-1.15d-90)) then
        tmp = t_1
    else if (a <= (-2.05d-215)) then
        tmp = x / (1.0d0 + (y * (b / t)))
    else if (a <= 9d+31) 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 = (z / b) + ((x * t) / (y * b));
	double t_2 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -4.4e+79) {
		tmp = t_2;
	} else if (a <= -1.15e-90) {
		tmp = t_1;
	} else if (a <= -2.05e-215) {
		tmp = x / (1.0 + (y * (b / t)));
	} else if (a <= 9e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((x * t) / (y * b))
	t_2 = (x + (z * (y / t))) / a
	tmp = 0
	if a <= -4.4e+79:
		tmp = t_2
	elif a <= -1.15e-90:
		tmp = t_1
	elif a <= -2.05e-215:
		tmp = x / (1.0 + (y * (b / t)))
	elif a <= 9e+31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)))
	t_2 = Float64(Float64(x + Float64(z * Float64(y / t))) / a)
	tmp = 0.0
	if (a <= -4.4e+79)
		tmp = t_2;
	elseif (a <= -1.15e-90)
		tmp = t_1;
	elseif (a <= -2.05e-215)
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(b / t))));
	elseif (a <= 9e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((x * t) / (y * b));
	t_2 = (x + (z * (y / t))) / a;
	tmp = 0.0;
	if (a <= -4.4e+79)
		tmp = t_2;
	elseif (a <= -1.15e-90)
		tmp = t_1;
	elseif (a <= -2.05e-215)
		tmp = x / (1.0 + (y * (b / t)));
	elseif (a <= 9e+31)
		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[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -4.4e+79], t$95$2, If[LessEqual[a, -1.15e-90], t$95$1, If[LessEqual[a, -2.05e-215], N[(x / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+31], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.3999999999999998e79 or 8.9999999999999992e31 < a

   1. Initial program 74.7%

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

      1. *-commutative 74.7%

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

      2. associate-/l* 75.6%

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

   4. Applied egg-rr 75.6%

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

   5. Taylor expanded in a around inf 70.1%

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

   if -4.3999999999999998e79 < a < -1.1499999999999999e-90 or -2.04999999999999992e-215 < a < 8.9999999999999992e31

   1. Initial program 71.0%

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

      1. associate-/l* 68.6%

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

      2. associate-/l* 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in b around inf 45.7%

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

   6. Taylor expanded in t around 0 66.7%

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

   if -1.1499999999999999e-90 < a < -2.04999999999999992e-215

   1. Initial program 81.5%

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

      1. associate-/l* 81.7%

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

      2. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in x around inf 63.1%

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

      1. associate-*l/ 66.8%

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

      2. *-commutative 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in a around 0 63.1%

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

      1. associate-*l/ 66.8%

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

      2. *-commutative 66.8%

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

   10. Simplified 66.8%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+79}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-90}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+31}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ t_2 := \frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{if}\;a \leq -1 \cdot 10^{+83}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (* (/ t b) (/ x y)))) (t_2 (/ (+ x (* z (/ y t))) a)))
   (if (<= a -1e+83)
     t_2
     (if (<= a -2.9e-96)
       t_1
       (if (<= a -2.65e-215)
         (/ x (+ 1.0 (* y (/ b t))))
         (if (<= a 1.95e+31) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / b) * (x / y));
	double t_2 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -1e+83) {
		tmp = t_2;
	} else if (a <= -2.9e-96) {
		tmp = t_1;
	} else if (a <= -2.65e-215) {
		tmp = x / (1.0 + (y * (b / t)));
	} else if (a <= 1.95e+31) {
		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 = (z / b) + ((t / b) * (x / y))
    t_2 = (x + (z * (y / t))) / a
    if (a <= (-1d+83)) then
        tmp = t_2
    else if (a <= (-2.9d-96)) then
        tmp = t_1
    else if (a <= (-2.65d-215)) then
        tmp = x / (1.0d0 + (y * (b / t)))
    else if (a <= 1.95d+31) 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 = (z / b) + ((t / b) * (x / y));
	double t_2 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -1e+83) {
		tmp = t_2;
	} else if (a <= -2.9e-96) {
		tmp = t_1;
	} else if (a <= -2.65e-215) {
		tmp = x / (1.0 + (y * (b / t)));
	} else if (a <= 1.95e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t / b) * (x / y))
	t_2 = (x + (z * (y / t))) / a
	tmp = 0
	if a <= -1e+83:
		tmp = t_2
	elif a <= -2.9e-96:
		tmp = t_1
	elif a <= -2.65e-215:
		tmp = x / (1.0 + (y * (b / t)))
	elif a <= 1.95e+31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)))
	t_2 = Float64(Float64(x + Float64(z * Float64(y / t))) / a)
	tmp = 0.0
	if (a <= -1e+83)
		tmp = t_2;
	elseif (a <= -2.9e-96)
		tmp = t_1;
	elseif (a <= -2.65e-215)
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(b / t))));
	elseif (a <= 1.95e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((t / b) * (x / y));
	t_2 = (x + (z * (y / t))) / a;
	tmp = 0.0;
	if (a <= -1e+83)
		tmp = t_2;
	elseif (a <= -2.9e-96)
		tmp = t_1;
	elseif (a <= -2.65e-215)
		tmp = x / (1.0 + (y * (b / t)));
	elseif (a <= 1.95e+31)
		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[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -1e+83], t$95$2, If[LessEqual[a, -2.9e-96], t$95$1, If[LessEqual[a, -2.65e-215], N[(x / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e+31], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.00000000000000003e83 or 1.95e31 < a

   1. Initial program 74.7%

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

      1. *-commutative 74.7%

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

      2. associate-/l* 75.6%

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

   4. Applied egg-rr 75.6%

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

   5. Taylor expanded in a around inf 70.1%

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

   if -1.00000000000000003e83 < a < -2.89999999999999994e-96 or -2.6499999999999998e-215 < a < 1.95e31

   1. Initial program 71.0%

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

      1. associate-/l* 68.6%

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

      2. associate-/l* 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in b around inf 45.7%

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

   6. Taylor expanded in z around inf 54.0%

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

   7. Taylor expanded in z around 0 66.7%

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

      1. times-frac 65.1%

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

   9. Simplified 65.1%

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

   if -2.89999999999999994e-96 < a < -2.6499999999999998e-215

   1. Initial program 81.5%

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

      1. associate-/l* 81.7%

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

      2. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in x around inf 63.1%

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

      1. associate-*l/ 66.8%

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

      2. *-commutative 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in a around 0 63.1%

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

      1. associate-*l/ 66.8%

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

      2. *-commutative 66.8%

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

   10. Simplified 66.8%

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

Alternative 12: 54.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+68}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{1 + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.2e-48)
   (/ z b)
   (if (<= y 2e-12)
     (/ x (+ a 1.0))
     (if (<= y 1.1e+68)
       (/ (* y (/ z t)) (+ a 1.0))
       (if (<= y 2.7e+105) (/ x (+ 1.0 (/ y (/ t b)))) (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.2e-48) {
		tmp = z / b;
	} else if (y <= 2e-12) {
		tmp = x / (a + 1.0);
	} else if (y <= 1.1e+68) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else if (y <= 2.7e+105) {
		tmp = x / (1.0 + (y / (t / b)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.2d-48)) then
        tmp = z / b
    else if (y <= 2d-12) then
        tmp = x / (a + 1.0d0)
    else if (y <= 1.1d+68) then
        tmp = (y * (z / t)) / (a + 1.0d0)
    else if (y <= 2.7d+105) then
        tmp = x / (1.0d0 + (y / (t / b)))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.2e-48) {
		tmp = z / b;
	} else if (y <= 2e-12) {
		tmp = x / (a + 1.0);
	} else if (y <= 1.1e+68) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else if (y <= 2.7e+105) {
		tmp = x / (1.0 + (y / (t / b)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.2e-48:
		tmp = z / b
	elif y <= 2e-12:
		tmp = x / (a + 1.0)
	elif y <= 1.1e+68:
		tmp = (y * (z / t)) / (a + 1.0)
	elif y <= 2.7e+105:
		tmp = x / (1.0 + (y / (t / b)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.2e-48)
		tmp = Float64(z / b);
	elseif (y <= 2e-12)
		tmp = Float64(x / Float64(a + 1.0));
	elseif (y <= 1.1e+68)
		tmp = Float64(Float64(y * Float64(z / t)) / Float64(a + 1.0));
	elseif (y <= 2.7e+105)
		tmp = Float64(x / Float64(1.0 + Float64(y / Float64(t / b))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.2e-48)
		tmp = z / b;
	elseif (y <= 2e-12)
		tmp = x / (a + 1.0);
	elseif (y <= 1.1e+68)
		tmp = (y * (z / t)) / (a + 1.0);
	elseif (y <= 2.7e+105)
		tmp = x / (1.0 + (y / (t / b)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.2e-48], N[(z / b), $MachinePrecision], If[LessEqual[y, 2e-12], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+68], N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+105], N[(x / N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.19999999999999975e-48 or 2.70000000000000016e105 < y

   1. Initial program 53.9%

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

      1. associate-/l* 60.6%

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

      2. associate-/l* 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in y around inf 60.7%

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

   if -5.19999999999999975e-48 < y < 1.99999999999999996e-12

   1. Initial program 92.7%

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

      1. associate-/l* 81.4%

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

      2. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in y around 0 61.3%

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

   if 1.99999999999999996e-12 < y < 1.09999999999999994e68

   1. Initial program 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-/l* 69.4%

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

   4. Applied egg-rr 69.4%

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

   5. Taylor expanded in y around 0 57.4%

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

   6. Taylor expanded in x around 0 45.5%

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

      1. associate-/l* 45.5%

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

   8. Simplified 45.5%

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

   if 1.09999999999999994e68 < y < 2.70000000000000016e105

   1. Initial program 58.3%

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

      1. associate-/l* 59.1%

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

      2. associate-/l* 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in x around inf 59.1%

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

      1. associate-*l/ 86.1%

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

      2. *-commutative 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in a around 0 45.2%

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

      1. associate-*l/ 72.1%

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

      2. *-commutative 72.1%

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

   10. Simplified 72.1%

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

       1. clear-num 86.1%

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

       2. un-div-inv 86.3%

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

   12. Applied egg-rr 72.3%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+68}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{1 + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+79} \lor \neg \left(y \leq 1.32 \cdot 10^{+101}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.4e+79) (not (<= y 1.32e+101)))
   (+ (/ z b) (* (/ t b) (/ x y)))
   (/ (+ 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 ((y <= -7.4e+79) || !(y <= 1.32e+101)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} 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 ((y <= (-7.4d+79)) .or. (.not. (y <= 1.32d+101))) then
        tmp = (z / b) + ((t / b) * (x / y))
    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 ((y <= -7.4e+79) || !(y <= 1.32e+101)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} 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 (y <= -7.4e+79) or not (y <= 1.32e+101):
		tmp = (z / b) + ((t / b) * (x / y))
	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 ((y <= -7.4e+79) || !(y <= 1.32e+101))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	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 ((y <= -7.4e+79) || ~((y <= 1.32e+101)))
		tmp = (z / b) + ((t / b) * (x / y));
	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[Or[LessEqual[y, -7.4e+79], N[Not[LessEqual[y, 1.32e+101]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $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 2 regimes

2. if y < -7.40000000000000019e79 or 1.32e101 < y

   1. Initial program 41.4%

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

      1. associate-/l* 48.1%

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

      2. associate-/l* 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in b around inf 34.3%

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

   6. Taylor expanded in z around inf 43.7%

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

   7. Taylor expanded in z around 0 69.4%

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

      1. times-frac 77.2%

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

   9. Simplified 77.2%

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

   if -7.40000000000000019e79 < y < 1.32e101

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

      2. associate-/l* 90.3%

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

   4. Applied egg-rr 90.3%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+79} \lor \neg \left(y \leq 1.32 \cdot 10^{+101}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-77} \lor \neg \left(t \leq 1.3 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.85e-77) (not (<= t 1.3e-94)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (/ y (/ t b))))
   (+ (/ z b) (/ (* x t) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.85e-77) || !(t <= 1.3e-94)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	} else {
		tmp = (z / b) + ((x * t) / (y * 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 <= (-1.85d-77)) .or. (.not. (t <= 1.3d-94))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y / (t / b)))
    else
        tmp = (z / b) + ((x * t) / (y * 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 <= -1.85e-77) || !(t <= 1.3e-94)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.85e-77) or not (t <= 1.3e-94):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)))
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.85e-77) || !(t <= 1.3e-94))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.85e-77) || ~((t <= 1.3e-94)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.85e-77], N[Not[LessEqual[t, 1.3e-94]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.84999999999999998e-77 or 1.29999999999999997e-94 < t

   1. Initial program 81.2%

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

      1. associate-/l* 86.1%

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

      2. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

      1. clear-num 91.6%

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

      2. un-div-inv 91.7%

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

   6. Applied egg-rr 91.7%

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

   if -1.84999999999999998e-77 < t < 1.29999999999999997e-94

   1. Initial program 62.2%

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

      1. associate-/l* 49.2%

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

      2. associate-/l* 43.4%

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

   3. Simplified 43.4%

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

   5. Taylor expanded in b around inf 48.3%

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

   6. Taylor expanded in t around 0 72.9%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-77} \lor \neg \left(t \leq 1.3 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-80} \lor \neg \left(t \leq 1.26 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.5e-80) (not (<= t 1.26e-89)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (+ (/ z b) (/ (* x t) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.5e-80) || !(t <= 1.26e-89)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z / b) + ((x * t) / (y * 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 <= (-6.5d-80)) .or. (.not. (t <= 1.26d-89))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (z / b) + ((x * t) / (y * 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 <= -6.5e-80) || !(t <= 1.26e-89)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.5e-80) or not (t <= 1.26e-89):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.5e-80) || !(t <= 1.26e-89))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -6.5e-80) || ~((t <= 1.26e-89)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.5e-80], N[Not[LessEqual[t, 1.26e-89]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.49999999999999984e-80 or 1.25999999999999995e-89 < t

   1. Initial program 81.2%

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

      1. associate-/l* 86.1%

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

      2. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

   if -6.49999999999999984e-80 < t < 1.25999999999999995e-89

   1. Initial program 62.2%

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

      1. associate-/l* 49.2%

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

      2. associate-/l* 43.4%

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

   3. Simplified 43.4%

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

   5. Taylor expanded in b around inf 48.3%

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

   6. Taylor expanded in t around 0 72.9%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-80} \lor \neg \left(t \leq 1.26 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+103}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (* (/ t b) (/ x y)))))
   (if (<= y -5.8e+76)
     t_1
     (if (<= y -5.5e-47)
       (/ (* y z) (* t (+ 1.0 (+ a (/ (* y b) t)))))
       (if (<= y 1.15e+103) (/ (+ x (* z (/ y t))) (+ a 1.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / b) * (x / y));
	double tmp;
	if (y <= -5.8e+76) {
		tmp = t_1;
	} else if (y <= -5.5e-47) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (y <= 1.15e+103) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((t / b) * (x / y))
    if (y <= (-5.8d+76)) then
        tmp = t_1
    else if (y <= (-5.5d-47)) then
        tmp = (y * z) / (t * (1.0d0 + (a + ((y * b) / t))))
    else if (y <= 1.15d+103) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / b) * (x / y));
	double tmp;
	if (y <= -5.8e+76) {
		tmp = t_1;
	} else if (y <= -5.5e-47) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (y <= 1.15e+103) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t / b) * (x / y))
	tmp = 0
	if y <= -5.8e+76:
		tmp = t_1
	elif y <= -5.5e-47:
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))))
	elif y <= 1.15e+103:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)))
	tmp = 0.0
	if (y <= -5.8e+76)
		tmp = t_1;
	elseif (y <= -5.5e-47)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))));
	elseif (y <= 1.15e+103)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((t / b) * (x / y));
	tmp = 0.0;
	if (y <= -5.8e+76)
		tmp = t_1;
	elseif (y <= -5.5e-47)
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	elseif (y <= 1.15e+103)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+76], t$95$1, If[LessEqual[y, -5.5e-47], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+103], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8000000000000003e76 or 1.15000000000000004e103 < y

   1. Initial program 41.1%

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

      1. associate-/l* 49.2%

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

      2. associate-/l* 58.4%

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

   3. Simplified 58.4%

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

   5. Taylor expanded in b around inf 35.1%

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

   6. Taylor expanded in z around inf 44.7%

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

   7. Taylor expanded in z around 0 71.1%

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

      1. times-frac 77.9%

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

   9. Simplified 77.9%

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

   if -5.8000000000000003e76 < y < -5.5000000000000002e-47

   1. Initial program 85.1%

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

      1. associate-/l* 88.2%

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

      2. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in x around 0 69.8%

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

   if -5.5000000000000002e-47 < y < 1.15000000000000004e103

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-/l* 90.2%

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

   4. Applied egg-rr 90.2%

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

   5. Taylor expanded in y around 0 70.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+76}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+103}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-45}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+104}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (* (/ t b) (/ x y)))))
   (if (<= y -2.1e+78)
     t_1
     (if (<= y -6e-45)
       (* (/ y t) (/ z (+ 1.0 (+ a (* y (/ b t))))))
       (if (<= y 1.2e+104) (/ (+ x (* z (/ y t))) (+ a 1.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / b) * (x / y));
	double tmp;
	if (y <= -2.1e+78) {
		tmp = t_1;
	} else if (y <= -6e-45) {
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	} else if (y <= 1.2e+104) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((t / b) * (x / y))
    if (y <= (-2.1d+78)) then
        tmp = t_1
    else if (y <= (-6d-45)) then
        tmp = (y / t) * (z / (1.0d0 + (a + (y * (b / t)))))
    else if (y <= 1.2d+104) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / b) * (x / y));
	double tmp;
	if (y <= -2.1e+78) {
		tmp = t_1;
	} else if (y <= -6e-45) {
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	} else if (y <= 1.2e+104) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t / b) * (x / y))
	tmp = 0
	if y <= -2.1e+78:
		tmp = t_1
	elif y <= -6e-45:
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))))
	elif y <= 1.2e+104:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)))
	tmp = 0.0
	if (y <= -2.1e+78)
		tmp = t_1;
	elseif (y <= -6e-45)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))));
	elseif (y <= 1.2e+104)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((t / b) * (x / y));
	tmp = 0.0;
	if (y <= -2.1e+78)
		tmp = t_1;
	elseif (y <= -6e-45)
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	elseif (y <= 1.2e+104)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+78], t$95$1, If[LessEqual[y, -6e-45], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+104], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1000000000000001e78 or 1.2e104 < y

   1. Initial program 41.1%

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

      1. associate-/l* 49.2%

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

      2. associate-/l* 58.4%

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

   3. Simplified 58.4%

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

   5. Taylor expanded in b around inf 35.1%

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

   6. Taylor expanded in z around inf 44.7%

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

   7. Taylor expanded in z around 0 71.1%

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

      1. times-frac 77.9%

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

   9. Simplified 77.9%

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

   if -2.1000000000000001e78 < y < -6.00000000000000022e-45

   1. Initial program 85.1%

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

      1. associate-/l* 88.2%

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

      2. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in x around 0 69.8%

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

      1. times-frac 69.7%

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

      2. associate-*l/ 69.7%

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

      3. *-commutative 69.7%

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

   7. Simplified 69.7%

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

   if -6.00000000000000022e-45 < y < 1.2e104

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-/l* 90.2%

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

   4. Applied egg-rr 90.2%

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

   5. Taylor expanded in y around 0 70.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-45}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+104}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 41.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-94}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -3.65 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+50}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.9e+119)
   (/ x a)
   (if (<= a -2.7e-94)
     (/ z b)
     (if (<= a -3.65e-215) x (if (<= a 9.5e+50) (/ z b) (/ x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.9e+119) {
		tmp = x / a;
	} else if (a <= -2.7e-94) {
		tmp = z / b;
	} else if (a <= -3.65e-215) {
		tmp = x;
	} else if (a <= 9.5e+50) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-4.9d+119)) then
        tmp = x / a
    else if (a <= (-2.7d-94)) then
        tmp = z / b
    else if (a <= (-3.65d-215)) then
        tmp = x
    else if (a <= 9.5d+50) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.9e+119) {
		tmp = x / a;
	} else if (a <= -2.7e-94) {
		tmp = z / b;
	} else if (a <= -3.65e-215) {
		tmp = x;
	} else if (a <= 9.5e+50) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.9e+119:
		tmp = x / a
	elif a <= -2.7e-94:
		tmp = z / b
	elif a <= -3.65e-215:
		tmp = x
	elif a <= 9.5e+50:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.9e+119)
		tmp = Float64(x / a);
	elseif (a <= -2.7e-94)
		tmp = Float64(z / b);
	elseif (a <= -3.65e-215)
		tmp = x;
	elseif (a <= 9.5e+50)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.9e+119)
		tmp = x / a;
	elseif (a <= -2.7e-94)
		tmp = z / b;
	elseif (a <= -3.65e-215)
		tmp = x;
	elseif (a <= 9.5e+50)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.9e+119], N[(x / a), $MachinePrecision], If[LessEqual[a, -2.7e-94], N[(z / b), $MachinePrecision], If[LessEqual[a, -3.65e-215], x, If[LessEqual[a, 9.5e+50], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.89999999999999996e119 or 9.4999999999999993e50 < a

   1. Initial program 73.0%

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

      1. associate-/l* 70.9%

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

      2. associate-/l* 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in x around inf 53.7%

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

      1. associate-*l/ 55.1%

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

      2. *-commutative 55.1%

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

   7. Simplified 55.1%

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

   8. Taylor expanded in a around inf 52.3%

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

   if -4.89999999999999996e119 < a < -2.7000000000000001e-94 or -3.65000000000000025e-215 < a < 9.4999999999999993e50

   1. Initial program 72.4%

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

      1. associate-/l* 69.5%

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

      2. associate-/l* 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in y around inf 54.0%

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

   if -2.7000000000000001e-94 < a < -3.65000000000000025e-215

   1. Initial program 81.5%

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

      1. associate-/l* 81.7%

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

      2. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in x around inf 63.1%

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

      1. associate-*l/ 66.8%

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

      2. *-commutative 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in a around 0 63.1%

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

      1. associate-*l/ 66.8%

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

      2. *-commutative 66.8%

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

   10. Simplified 66.8%

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

   11. Taylor expanded in y around 0 46.8%

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

Alternative 19: 69.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-28} \lor \neg \left(y \leq 4.8 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.4e-28) (not (<= y 4.8e+102)))
   (+ (/ z b) (* (/ t b) (/ x y)))
   (/ (+ 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 ((y <= -5.4e-28) || !(y <= 4.8e+102)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} 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 ((y <= (-5.4d-28)) .or. (.not. (y <= 4.8d+102))) then
        tmp = (z / b) + ((t / b) * (x / y))
    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 ((y <= -5.4e-28) || !(y <= 4.8e+102)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.4e-28) or not (y <= 4.8e+102):
		tmp = (z / b) + ((t / b) * (x / y))
	else:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.4e-28) || !(y <= 4.8e+102))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	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 ((y <= -5.4e-28) || ~((y <= 4.8e+102)))
		tmp = (z / b) + ((t / b) * (x / y));
	else
		tmp = (x + (z * (y / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.4e-28], N[Not[LessEqual[y, 4.8e+102]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.3999999999999998e-28 or 4.79999999999999989e102 < y

   1. Initial program 51.7%

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

      1. associate-/l* 58.8%

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

      2. associate-/l* 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in b around inf 38.7%

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

   6. Taylor expanded in z around inf 46.9%

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

   7. Taylor expanded in z around 0 67.7%

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

      1. times-frac 72.9%

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

   9. Simplified 72.9%

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

   if -5.3999999999999998e-28 < y < 4.79999999999999989e102

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-/l* 90.0%

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

   4. Applied egg-rr 90.0%

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

   5. Taylor expanded in y around 0 70.2%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-28} \lor \neg \left(y \leq 4.8 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 64.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-50} \lor \neg \left(y \leq 6.5 \cdot 10^{+98}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.25e-50) (not (<= y 6.5e+98)))
   (+ (/ z b) (* (/ t b) (/ x y)))
   (/ x (+ 1.0 (+ a (/ (* y b) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e-50) || !(y <= 6.5e+98)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.25d-50)) .or. (.not. (y <= 6.5d+98))) then
        tmp = (z / b) + ((t / b) * (x / y))
    else
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e-50) || !(y <= 6.5e+98)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.25e-50) or not (y <= 6.5e+98):
		tmp = (z / b) + ((t / b) * (x / y))
	else:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.25e-50) || !(y <= 6.5e+98))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.25e-50) || ~((y <= 6.5e+98)))
		tmp = (z / b) + ((t / b) * (x / y));
	else
		tmp = x / (1.0 + (a + ((y * b) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.25e-50], N[Not[LessEqual[y, 6.5e+98]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999992e-50 or 6.4999999999999999e98 < y

   1. Initial program 53.4%

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

      1. associate-/l* 59.1%

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

      2. associate-/l* 66.5%

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

   3. Simplified 66.5%

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

   5. Taylor expanded in b around inf 37.9%

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

   6. Taylor expanded in z around inf 45.6%

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

   7. Taylor expanded in z around 0 65.0%

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

      1. times-frac 70.6%

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

   9. Simplified 70.6%

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

   if -1.24999999999999992e-50 < y < 6.4999999999999999e98

   1. Initial program 90.2%

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

      1. associate-/l* 81.3%

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

      2. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in x around inf 67.0%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-50} \lor \neg \left(y \leq 6.5 \cdot 10^{+98}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 55.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-45} \lor \neg \left(y \leq 1.06 \cdot 10^{+103}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.15e-45) (not (<= y 1.06e+103))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e-45) || !(y <= 1.06e+103)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.15d-45)) .or. (.not. (y <= 1.06d+103))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e-45) || !(y <= 1.06e+103)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.15e-45) or not (y <= 1.06e+103):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.15e-45) || !(y <= 1.06e+103))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.15e-45) || ~((y <= 1.06e+103)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.15e-45], N[Not[LessEqual[y, 1.06e+103]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.14999999999999996e-45 or 1.0599999999999999e103 < y

   1. Initial program 53.5%

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

      1. associate-/l* 60.1%

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

      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 inf 60.2%

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

   if -1.14999999999999996e-45 < y < 1.0599999999999999e103

   1. Initial program 89.7%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   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* 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in y around 0 55.8%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-45} \lor \neg \left(y \leq 1.06 \cdot 10^{+103}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 40.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-38} \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.95e-38) (not (<= a 1.0))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.95e-38) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.95d-38)) .or. (.not. (a <= 1.0d0))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.95e-38) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.95e-38) or not (a <= 1.0):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.95e-38) || !(a <= 1.0))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.95e-38) || ~((a <= 1.0)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.95e-38], N[Not[LessEqual[a, 1.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.95e-38 or 1 < a

   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* 71.8%

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

      2. associate-/l* 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in x around inf 49.9%

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

      1. associate-*l/ 50.2%

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

      2. *-commutative 50.2%

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

   7. Simplified 50.2%

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

   8. Taylor expanded in a around inf 44.7%

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

   if -1.95e-38 < a < 1

   1. Initial program 72.9%

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

      1. associate-/l* 70.6%

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

      2. associate-/l* 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in x around inf 49.3%

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

      1. associate-*l/ 50.7%

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

      2. *-commutative 50.7%

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

   7. Simplified 50.7%

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

   8. Taylor expanded in a around 0 49.3%

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

      1. associate-*l/ 50.7%

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

      2. *-commutative 50.7%

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

   10. Simplified 50.7%

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

   11. Taylor expanded in y around 0 29.7%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-38} \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 20.2% 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 73.5%

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

   1. associate-/l* 71.3%

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

   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 x around inf 49.6%

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

   1. associate-*l/ 50.4%

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

   2. *-commutative 50.4%

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

7. Simplified 50.4%

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

8. Taylor expanded in a around 0 29.9%

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

   1. associate-*l/ 31.5%

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

   2. *-commutative 31.5%

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

10. Simplified 31.5%

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

11. Taylor expanded in y around 0 16.9%

    \[\leadsto \color{blue}{x} \]
12. Add Preprocessing

Developer target: 79.4% 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 2024085 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

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

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