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

Percentage Accurate: 75.1% → 89.2%

Time: 13.7s

Alternatives: 17

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 10^{-240}:\\ \;\;\;\;\frac{t_1}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} - \frac{a}{y} \cdot \left(\frac{z}{b} \cdot \frac{t}{b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_2 (- INFINITY))
     (/ (+ z (/ t (/ y x))) b)
     (if (<= t_2 -5e-242)
       t_2
       (if (<= t_2 1e-240)
         (/ t_1 (+ (+ a 1.0) (* y (/ b t))))
         (if (<= t_2 5e+255)
           t_2
           (if (<= t_2 INFINITY)
             (* (/ y t) (/ z (+ 1.0 (fma y (/ b t) a))))
             (- (/ z b) (* (/ a y) (* (/ z b) (/ t b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (z + (t / (y / x))) / b;
	} else if (t_2 <= -5e-242) {
		tmp = t_2;
	} else if (t_2 <= 1e-240) {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= 5e+255) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / (1.0 + fma(y, (b / t), a)));
	} else {
		tmp = (z / b) - ((a / y) * ((z / b) * (t / 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(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / b);
	elseif (t_2 <= -5e-242)
		tmp = t_2;
	elseif (t_2 <= 1e-240)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_2 <= 5e+255)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + fma(y, Float64(b / t), a))));
	else
		tmp = Float64(Float64(z / b) - Float64(Float64(a / y) * Float64(Float64(z / b) * Float64(t / b))));
	end
	return 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[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$2, -5e-242], t$95$2, If[LessEqual[t$95$2, 1e-240], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+255], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] - N[(N[(a / y), $MachinePrecision] * N[(N[(z / b), $MachinePrecision] * N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 13.1%

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

      1. *-commutative 13.1%

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

      2. associate-/l* 38.9%

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

      3. associate-*l/ 37.6%

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

   3. Simplified 37.6%

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

   4. Taylor expanded in y around -inf 46.1%

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

      1. +-commutative 46.1%

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

      2. associate-*r/ 46.1%

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

      3. distribute-lft-out-- 46.1%

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

      4. associate-*r* 46.1%

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

      5. metadata-eval 46.1%

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

      6. *-lft-identity 46.1%

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

      7. associate-/l* 46.1%

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

      8. associate-/l* 55.2%

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

      9. *-commutative 55.2%

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

      10. associate-/r* 55.2%

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

      11. unpow2 55.2%

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

   6. Simplified 55.2%

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

   7. Taylor expanded in b around inf 64.8%

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

      1. associate-*l/ 73.5%

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

      2. *-commutative 73.5%

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

   9. Simplified 73.5%

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

   10. Taylor expanded in b around 0 64.8%

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

       1. +-commutative 64.8%

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

       2. associate-/l* 73.5%

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

   12. Simplified 73.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.9999999999999998e-242 or 9.9999999999999997e-241 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000002e255

   1. Initial program 99.7%

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

   if -4.9999999999999998e-242 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 9.9999999999999997e-241

   1. Initial program 64.6%

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

      1. associate-/l* 76.4%

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

   3. Simplified 76.4%

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

      1. div-inv 76.4%

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

      2. clear-num 76.4%

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

   5. Applied egg-rr 76.4%

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

   if 5.0000000000000002e255 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 16.5%

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

      1. *-commutative 16.5%

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

      2. associate-/l* 64.4%

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

      3. associate-*l/ 57.8%

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

   3. Simplified 57.8%

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

   4. Taylor expanded in x around 0 27.6%

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

      1. times-frac 87.2%

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

      2. associate-*r/ 87.2%

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

      3. fma-def 87.2%

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

   6. Simplified 87.2%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-/l* 0.6%

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

      3. associate-*l/ 13.6%

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

   3. Simplified 13.6%

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

   4. Taylor expanded in y around -inf 60.3%

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

      1. +-commutative 60.3%

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

      2. associate-*r/ 60.3%

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

      3. distribute-lft-out-- 60.3%

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

      4. associate-*r* 60.3%

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

      5. metadata-eval 60.3%

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

      6. *-lft-identity 60.3%

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

      7. associate-/l* 60.3%

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

      8. associate-/l* 67.0%

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

      9. *-commutative 67.0%

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

      10. associate-/r* 96.6%

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

      11. unpow2 96.6%

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

   6. Simplified 96.6%

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

   7. Taylor expanded in a around inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. times-frac 80.0%

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

      3. distribute-lft-neg-in 80.0%

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

      4. associate-/l* 96.6%

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

      5. unpow2 96.6%

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

      6. associate-*l/ 96.9%

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

      7. associate-/r/ 96.9%

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

      8. associate-/r/ 96.7%

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

   9. Simplified 96.7%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -5 \cdot 10^{-242}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{-240}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+255}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} - \frac{a}{y} \cdot \left(\frac{z}{b} \cdot \frac{t}{b}\right)\\ \end{array} \]

Alternative 2: 88.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 10^{-240}:\\ \;\;\;\;\frac{t_1}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+255}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t))))
        (t_3 (/ (+ z (/ t (/ y x))) b)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -5e-242)
       t_2
       (if (<= t_2 1e-240)
         (/ t_1 (+ (+ a 1.0) (* y (/ b t))))
         (if (<= t_2 5e+255) t_2 t_3))))))

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 / ((a + 1.0) + ((y * b) / t));
	double t_3 = (z + (t / (y / x))) / b;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -5e-242) {
		tmp = t_2;
	} else if (t_2 <= 1e-240) {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= 5e+255) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 / ((a + 1.0) + ((y * b) / t));
	double t_3 = (z + (t / (y / x))) / b;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -5e-242) {
		tmp = t_2;
	} else if (t_2 <= 1e-240) {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= 5e+255) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t))
	t_3 = (z + (t / (y / x))) / b
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -5e-242:
		tmp = t_2
	elif t_2 <= 1e-240:
		tmp = t_1 / ((a + 1.0) + (y * (b / t)))
	elif t_2 <= 5e+255:
		tmp = t_2
	else:
		tmp = t_3
	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(a + 1.0) + Float64(Float64(y * b) / t)))
	t_3 = Float64(Float64(z + Float64(t / Float64(y / x))) / b)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -5e-242)
		tmp = t_2;
	elseif (t_2 <= 1e-240)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_2 <= 5e+255)
		tmp = t_2;
	else
		tmp = t_3;
	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 / ((a + 1.0) + ((y * b) / t));
	t_3 = (z + (t / (y / x))) / b;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -5e-242)
		tmp = t_2;
	elseif (t_2 <= 1e-240)
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	elseif (t_2 <= 5e+255)
		tmp = t_2;
	else
		tmp = t_3;
	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[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -5e-242], t$95$2, If[LessEqual[t$95$2, 1e-240], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+255], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or 5.0000000000000002e255 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 7.2%

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

      1. *-commutative 7.2%

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

      2. associate-/l* 25.9%

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

      3. associate-*l/ 30.6%

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

   3. Simplified 30.6%

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

   4. Taylor expanded in y around -inf 44.4%

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

      1. +-commutative 44.4%

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

      2. associate-*r/ 44.4%

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

      3. distribute-lft-out-- 44.4%

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

      4. associate-*r* 44.4%

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

      5. metadata-eval 44.4%

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

      6. *-lft-identity 44.4%

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

      7. associate-/l* 44.4%

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

      8. associate-/l* 49.7%

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

      9. *-commutative 49.7%

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

      10. associate-/r* 65.3%

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

      11. unpow2 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in b around inf 72.9%

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

      1. associate-*l/ 74.5%

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

      2. *-commutative 74.5%

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

   9. Simplified 74.5%

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

   10. Taylor expanded in b around 0 73.0%

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

       1. +-commutative 73.0%

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

       2. associate-/l* 76.3%

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

   12. Simplified 76.3%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.9999999999999998e-242 or 9.9999999999999997e-241 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000002e255

   1. Initial program 99.7%

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

   if -4.9999999999999998e-242 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 9.9999999999999997e-241

   1. Initial program 64.6%

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

      1. associate-/l* 76.4%

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

   3. Simplified 76.4%

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

      1. div-inv 76.4%

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

      2. clear-num 76.4%

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

   5. Applied egg-rr 76.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -5 \cdot 10^{-242}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{-240}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+255}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]

Alternative 3: 81.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + b \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{-143}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t_1}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-216}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-69}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (* b (/ y t)))))
   (if (<= t -1.02e-143)
     (/ (+ x (* z (/ y t))) t_1)
     (if (<= t 1.22e-216)
       (/ (+ z (/ (* x t) y)) b)
       (if (<= t 3.6e-69)
         (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ y (/ t b))))
         (if (<= t 5.8e-27)
           (/ (+ z (/ t (/ y x))) b)
           (/ (+ x (/ y (/ t z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (b * (y / t));
	double tmp;
	if (t <= -1.02e-143) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t <= 1.22e-216) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 3.6e-69) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 5.8e-27) {
		tmp = (z + (t / (y / x))) / b;
	} else {
		tmp = (x + (y / (t / z))) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + 1.0d0) + (b * (y / t))
    if (t <= (-1.02d-143)) then
        tmp = (x + (z * (y / t))) / t_1
    else if (t <= 1.22d-216) then
        tmp = (z + ((x * t) / y)) / b
    else if (t <= 3.6d-69) then
        tmp = (x + ((y * z) / t)) / ((a + 1.0d0) + (y / (t / b)))
    else if (t <= 5.8d-27) then
        tmp = (z + (t / (y / x))) / b
    else
        tmp = (x + (y / (t / z))) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (b * (y / t));
	double tmp;
	if (t <= -1.02e-143) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t <= 1.22e-216) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 3.6e-69) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 5.8e-27) {
		tmp = (z + (t / (y / x))) / b;
	} else {
		tmp = (x + (y / (t / z))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + (b * (y / t))
	tmp = 0
	if t <= -1.02e-143:
		tmp = (x + (z * (y / t))) / t_1
	elif t <= 1.22e-216:
		tmp = (z + ((x * t) / y)) / b
	elif t <= 3.6e-69:
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (y / (t / b)))
	elif t <= 5.8e-27:
		tmp = (z + (t / (y / x))) / b
	else:
		tmp = (x + (y / (t / z))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(b * Float64(y / t)))
	tmp = 0.0
	if (t <= -1.02e-143)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	elseif (t <= 1.22e-216)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (t <= 3.6e-69)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t <= 5.8e-27)
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / b);
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + (b * (y / t));
	tmp = 0.0;
	if (t <= -1.02e-143)
		tmp = (x + (z * (y / t))) / t_1;
	elseif (t <= 1.22e-216)
		tmp = (z + ((x * t) / y)) / b;
	elseif (t <= 3.6e-69)
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (y / (t / b)));
	elseif (t <= 5.8e-27)
		tmp = (z + (t / (y / x))) / b;
	else
		tmp = (x + (y / (t / z))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.02e-143], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 1.22e-216], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, 3.6e-69], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-27], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.02e-143

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/l* 83.3%

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

      3. associate-*l/ 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around 0 80.3%

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

      1. associate-*l/ 88.1%

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

      2. *-commutative 88.1%

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

   6. Simplified 88.1%

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

   if -1.02e-143 < t < 1.2200000000000001e-216

   1. Initial program 46.7%

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

      1. *-commutative 46.7%

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

      2. associate-/l* 40.0%

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

      3. associate-*l/ 35.9%

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

   3. Simplified 35.9%

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

   4. Taylor expanded in y around -inf 63.0%

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

      1. +-commutative 63.0%

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

      2. associate-*r/ 63.0%

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

      3. distribute-lft-out-- 63.0%

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

      4. associate-*r* 63.0%

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

      5. metadata-eval 63.0%

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

      6. *-lft-identity 63.0%

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

      7. associate-/l* 61.0%

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

      8. associate-/l* 61.1%

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

      9. *-commutative 61.1%

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

      10. associate-/r* 71.3%

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

      11. unpow2 71.3%

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

   6. Simplified 71.3%

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

   7. Taylor expanded in b around inf 79.8%

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

      1. associate-*l/ 75.3%

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

      2. *-commutative 75.3%

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

   9. Simplified 75.3%

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

   10. Taylor expanded in b around 0 79.9%

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

   if 1.2200000000000001e-216 < t < 3.60000000000000018e-69

   1. Initial program 77.8%

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

      1. associate-/l* 73.2%

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

   3. Simplified 73.2%

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

   if 3.60000000000000018e-69 < t < 5.80000000000000008e-27

   1. Initial program 34.2%

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

      1. *-commutative 34.2%

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

      2. associate-/l* 34.2%

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

      3. associate-*l/ 33.9%

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

   3. Simplified 33.9%

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

   4. Taylor expanded in y around -inf 67.9%

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

      1. +-commutative 67.9%

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

      2. associate-*r/ 67.9%

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

      3. distribute-lft-out-- 67.9%

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

      4. associate-*r* 67.9%

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

      5. metadata-eval 67.9%

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

      6. *-lft-identity 67.9%

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

      7. associate-/l* 67.9%

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

      8. associate-/l* 67.9%

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

      9. *-commutative 67.9%

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

      10. associate-/r* 84.5%

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

      11. unpow2 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in b around inf 100.0%

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

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in b around 0 100.0%

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

       1. +-commutative 100.0%

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

       2. associate-/l* 100.0%

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

   12. Simplified 100.0%

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

   if 5.80000000000000008e-27 < t

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/l* 88.0%

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

      3. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

      1. associate-/r/ 93.9%

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

   5. Applied egg-rr 93.9%

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

      1. associate-*l/ 88.0%

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

      2. *-commutative 88.0%

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

      3. associate-/l* 93.9%

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

   7. Applied egg-rr 93.9%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-143}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-216}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-69}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 4: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-141} \lor \neg \left(t \leq 4.2 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1e-141) (not (<= t 4.2e-27)))
   (/ (+ x (* z (/ y t))) (+ (+ a 1.0) (* b (/ y t))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e-141) || !(t <= 4.2e-27)) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z + ((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 <= (-1d-141)) .or. (.not. (t <= 4.2d-27))) then
        tmp = (x + (z * (y / t))) / ((a + 1.0d0) + (b * (y / t)))
    else
        tmp = (z + ((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 <= -1e-141) || !(t <= 4.2e-27)) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1e-141) or not (t <= 4.2e-27):
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1e-141) || !(t <= 4.2e-27))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1e-141) || ~((t <= 4.2e-27)))
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1e-141], N[Not[LessEqual[t, 4.2e-27]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1e-141 or 4.20000000000000031e-27 < t

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-/l* 85.4%

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

      3. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in z around 0 83.8%

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

      1. associate-*l/ 90.1%

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

      2. *-commutative 90.1%

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

   6. Simplified 90.1%

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

   if -1e-141 < t < 4.20000000000000031e-27

   1. Initial program 54.7%

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

      1. *-commutative 54.7%

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

      2. associate-/l* 47.9%

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

      3. associate-*l/ 45.2%

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

   3. Simplified 45.2%

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

   4. Taylor expanded in y around -inf 57.3%

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

      1. +-commutative 57.3%

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

      2. associate-*r/ 57.3%

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

      3. distribute-lft-out-- 57.3%

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

      4. associate-*r* 57.3%

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

      5. metadata-eval 57.3%

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

      6. *-lft-identity 57.3%

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

      7. associate-/l* 54.7%

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

      8. associate-/l* 54.8%

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

      9. *-commutative 54.8%

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

      10. associate-/r* 62.6%

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

      11. unpow2 62.6%

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

   6. Simplified 62.6%

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

   7. Taylor expanded in b around inf 73.2%

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

      1. associate-*l/ 69.1%

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

      2. *-commutative 69.1%

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

   9. Simplified 69.1%

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

   10. Taylor expanded in b around 0 73.2%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-141} \lor \neg \left(t \leq 4.2 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 5: 81.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + b \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{-142}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t_1}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (* b (/ y t)))))
   (if (<= t -4.7e-142)
     (/ (+ x (* z (/ y t))) t_1)
     (if (<= t 4.2e-27)
       (/ (+ z (/ (* x t) y)) b)
       (/ (+ x (* y (/ z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (b * (y / t));
	double tmp;
	if (t <= -4.7e-142) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t <= 4.2e-27) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y * (z / t))) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + 1.0d0) + (b * (y / t))
    if (t <= (-4.7d-142)) then
        tmp = (x + (z * (y / t))) / t_1
    else if (t <= 4.2d-27) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + (y * (z / t))) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (b * (y / t));
	double tmp;
	if (t <= -4.7e-142) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t <= 4.2e-27) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y * (z / t))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + (b * (y / t))
	tmp = 0
	if t <= -4.7e-142:
		tmp = (x + (z * (y / t))) / t_1
	elif t <= 4.2e-27:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + (y * (z / t))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(b * Float64(y / t)))
	tmp = 0.0
	if (t <= -4.7e-142)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	elseif (t <= 4.2e-27)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + (b * (y / t));
	tmp = 0.0;
	if (t <= -4.7e-142)
		tmp = (x + (z * (y / t))) / t_1;
	elseif (t <= 4.2e-27)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + (y * (z / t))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.7e-142], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 4.2e-27], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.6999999999999999e-142

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/l* 83.3%

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

      3. associate-*l/ 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around 0 80.3%

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

      1. associate-*l/ 88.1%

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

      2. *-commutative 88.1%

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

   6. Simplified 88.1%

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

   if -4.6999999999999999e-142 < t < 4.20000000000000031e-27

   1. Initial program 54.7%

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

      1. *-commutative 54.7%

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

      2. associate-/l* 47.9%

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

      3. associate-*l/ 45.2%

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

   3. Simplified 45.2%

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

   4. Taylor expanded in y around -inf 57.3%

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

      1. +-commutative 57.3%

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

      2. associate-*r/ 57.3%

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

      3. distribute-lft-out-- 57.3%

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

      4. associate-*r* 57.3%

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

      5. metadata-eval 57.3%

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

      6. *-lft-identity 57.3%

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

      7. associate-/l* 54.7%

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

      8. associate-/l* 54.8%

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

      9. *-commutative 54.8%

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

      10. associate-/r* 62.6%

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

      11. unpow2 62.6%

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

   6. Simplified 62.6%

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

   7. Taylor expanded in b around inf 73.2%

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

      1. associate-*l/ 69.1%

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

      2. *-commutative 69.1%

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

   9. Simplified 69.1%

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

   10. Taylor expanded in b around 0 73.2%

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

   if 4.20000000000000031e-27 < t

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/l* 88.0%

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

      3. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

      1. associate-/r/ 93.9%

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

   5. Applied egg-rr 93.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-142}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 6: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + b \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-144}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t_1}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (* b (/ y t)))))
   (if (<= t -1.15e-144)
     (/ (+ x (* z (/ y t))) t_1)
     (if (<= t 5.8e-27)
       (/ (+ z (/ (* x t) y)) b)
       (/ (+ x (/ y (/ t z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (b * (y / t));
	double tmp;
	if (t <= -1.15e-144) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t <= 5.8e-27) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y / (t / z))) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + 1.0d0) + (b * (y / t))
    if (t <= (-1.15d-144)) then
        tmp = (x + (z * (y / t))) / t_1
    else if (t <= 5.8d-27) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + (y / (t / z))) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (b * (y / t));
	double tmp;
	if (t <= -1.15e-144) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t <= 5.8e-27) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y / (t / z))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + (b * (y / t))
	tmp = 0
	if t <= -1.15e-144:
		tmp = (x + (z * (y / t))) / t_1
	elif t <= 5.8e-27:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + (y / (t / z))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(b * Float64(y / t)))
	tmp = 0.0
	if (t <= -1.15e-144)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	elseif (t <= 5.8e-27)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + (b * (y / t));
	tmp = 0.0;
	if (t <= -1.15e-144)
		tmp = (x + (z * (y / t))) / t_1;
	elseif (t <= 5.8e-27)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + (y / (t / z))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e-144], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 5.8e-27], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15e-144

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/l* 83.3%

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

      3. associate-*l/ 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around 0 80.3%

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

      1. associate-*l/ 88.1%

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

      2. *-commutative 88.1%

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

   6. Simplified 88.1%

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

   if -1.15e-144 < t < 5.80000000000000008e-27

   1. Initial program 54.7%

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

      1. *-commutative 54.7%

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

      2. associate-/l* 47.9%

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

      3. associate-*l/ 45.2%

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

   3. Simplified 45.2%

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

   4. Taylor expanded in y around -inf 57.3%

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

      1. +-commutative 57.3%

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

      2. associate-*r/ 57.3%

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

      3. distribute-lft-out-- 57.3%

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

      4. associate-*r* 57.3%

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

      5. metadata-eval 57.3%

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

      6. *-lft-identity 57.3%

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

      7. associate-/l* 54.7%

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

      8. associate-/l* 54.8%

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

      9. *-commutative 54.8%

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

      10. associate-/r* 62.6%

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

      11. unpow2 62.6%

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

   6. Simplified 62.6%

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

   7. Taylor expanded in b around inf 73.2%

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

      1. associate-*l/ 69.1%

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

      2. *-commutative 69.1%

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

   9. Simplified 69.1%

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

   10. Taylor expanded in b around 0 73.2%

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

   if 5.80000000000000008e-27 < t

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/l* 88.0%

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

      3. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

      1. associate-/r/ 93.9%

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

   5. Applied egg-rr 93.9%

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

      1. associate-*l/ 88.0%

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

      2. *-commutative 88.0%

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

      3. associate-/l* 93.9%

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

   7. Applied egg-rr 93.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-144}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 7: 60.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+31}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -8.5e+94)
     t_1
     (if (<= t -8.8e-38)
       (+ (/ z b) (/ (* x (/ t b)) y))
       (if (<= t -9.8e-51)
         t_1
         (if (<= t -4.3e-67)
           (* (/ y t) (/ z (+ a 1.0)))
           (if (<= t 4.1e+31) (/ (+ z (/ (* x t) y)) b) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -8.5e+94) {
		tmp = t_1;
	} else if (t <= -8.8e-38) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} else if (t <= -9.8e-51) {
		tmp = t_1;
	} else if (t <= -4.3e-67) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 4.1e+31) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-8.5d+94)) then
        tmp = t_1
    else if (t <= (-8.8d-38)) then
        tmp = (z / b) + ((x * (t / b)) / y)
    else if (t <= (-9.8d-51)) then
        tmp = t_1
    else if (t <= (-4.3d-67)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (t <= 4.1d+31) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -8.5e+94) {
		tmp = t_1;
	} else if (t <= -8.8e-38) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} else if (t <= -9.8e-51) {
		tmp = t_1;
	} else if (t <= -4.3e-67) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 4.1e+31) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -8.5e+94:
		tmp = t_1
	elif t <= -8.8e-38:
		tmp = (z / b) + ((x * (t / b)) / y)
	elif t <= -9.8e-51:
		tmp = t_1
	elif t <= -4.3e-67:
		tmp = (y / t) * (z / (a + 1.0))
	elif t <= 4.1e+31:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -8.5e+94)
		tmp = t_1;
	elseif (t <= -8.8e-38)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / b)) / y));
	elseif (t <= -9.8e-51)
		tmp = t_1;
	elseif (t <= -4.3e-67)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (t <= 4.1e+31)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -8.5e+94)
		tmp = t_1;
	elseif (t <= -8.8e-38)
		tmp = (z / b) + ((x * (t / b)) / y);
	elseif (t <= -9.8e-51)
		tmp = t_1;
	elseif (t <= -4.3e-67)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (t <= 4.1e+31)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+94], t$95$1, If[LessEqual[t, -8.8e-38], N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.8e-51], t$95$1, If[LessEqual[t, -4.3e-67], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e+31], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.50000000000000054e94 or -8.80000000000000029e-38 < t < -9.79999999999999948e-51 or 4.1000000000000002e31 < t

   1. Initial program 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-/l* 87.5%

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

      3. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around inf 70.1%

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

   if -8.50000000000000054e94 < t < -8.80000000000000029e-38

   1. Initial program 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-/l* 84.2%

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

      3. associate-*l/ 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in y around -inf 37.2%

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

      1. +-commutative 37.2%

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

      2. associate-*r/ 37.2%

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

      3. distribute-lft-out-- 37.2%

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

      4. associate-*r* 37.2%

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

      5. metadata-eval 37.2%

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

      6. *-lft-identity 37.2%

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

      7. associate-/l* 41.0%

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

      8. associate-/l* 41.0%

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

      9. *-commutative 41.0%

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

      10. associate-/r* 44.8%

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

      11. unpow2 44.8%

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

   6. Simplified 44.8%

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

   7. Taylor expanded in b around inf 41.9%

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

      1. associate-*l/ 45.7%

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

      2. *-commutative 45.7%

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

   9. Simplified 45.7%

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

   if -9.79999999999999948e-51 < t < -4.30000000000000027e-67

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-/l* 99.1%

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

      3. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 61.0%

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

   5. Taylor expanded in y around 0 61.7%

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

      1. times-frac 62.1%

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

   7. Simplified 62.1%

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

   if -4.30000000000000027e-67 < t < 4.1000000000000002e31

   1. Initial program 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-/l* 54.9%

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

      3. associate-*l/ 52.9%

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

   3. Simplified 52.9%

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

   4. Taylor expanded in y around -inf 56.7%

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

      1. +-commutative 56.7%

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

      2. associate-*r/ 56.7%

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

      3. distribute-lft-out-- 56.7%

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

      4. associate-*r* 56.7%

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

      5. metadata-eval 56.7%

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

      6. *-lft-identity 56.7%

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

      7. associate-/l* 54.2%

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

      8. associate-/l* 54.3%

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

      9. *-commutative 54.3%

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

      10. associate-/r* 60.1%

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

      11. unpow2 60.1%

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

   6. Simplified 60.1%

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

   7. Taylor expanded in b around inf 68.6%

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

      1. associate-*l/ 65.3%

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

      2. *-commutative 65.3%

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

   9. Simplified 65.3%

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

   10. Taylor expanded in b around 0 69.0%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+31}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 8: 66.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -80000000 \lor \neg \left(t \leq 3.2 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -80000000.0) (not (<= t 3.2e-26)))
   (/ x (+ 1.0 (+ a (* b (/ y t)))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -80000000.0) || !(t <= 3.2e-26)) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else {
		tmp = (z + ((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 <= (-80000000.0d0)) .or. (.not. (t <= 3.2d-26))) then
        tmp = x / (1.0d0 + (a + (b * (y / t))))
    else
        tmp = (z + ((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 <= -80000000.0) || !(t <= 3.2e-26)) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -80000000.0) or not (t <= 3.2e-26):
		tmp = x / (1.0 + (a + (b * (y / t))))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -80000000.0) || !(t <= 3.2e-26))
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -80000000.0) || ~((t <= 3.2e-26)))
		tmp = x / (1.0 + (a + (b * (y / t))));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -80000000.0], N[Not[LessEqual[t, 3.2e-26]], $MachinePrecision]], N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8e7 or 3.2000000000000001e-26 < t

   1. Initial program 81.4%

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

      1. *-commutative 81.4%

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

      2. associate-/l* 86.6%

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

      3. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around inf 68.5%

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

      1. associate-*l/ 69.8%

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

   6. Applied egg-rr 69.8%

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

   if -8e7 < t < 3.2000000000000001e-26

   1. Initial program 62.5%

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

      1. *-commutative 62.5%

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

      2. associate-/l* 56.6%

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

      3. associate-*l/ 54.6%

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

   3. Simplified 54.6%

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

   4. Taylor expanded in y around -inf 52.2%

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

      1. +-commutative 52.2%

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

      2. associate-*r/ 52.2%

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

      3. distribute-lft-out-- 52.2%

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

      4. associate-*r* 52.2%

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

      5. metadata-eval 52.2%

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

      6. *-lft-identity 52.2%

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

      7. associate-/l* 50.4%

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

      8. associate-/l* 50.4%

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

      9. *-commutative 50.4%

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

      10. associate-/r* 56.1%

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

      11. unpow2 56.1%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in b around inf 63.9%

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

      1. associate-*l/ 60.7%

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

      2. *-commutative 60.7%

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

   9. Simplified 60.7%

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

   10. Taylor expanded in b around 0 65.2%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -80000000 \lor \neg \left(t \leq 3.2 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 9: 69.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-54} \lor \neg \left(t \leq 2.8 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.5e-54) (not (<= t 2.8e+32)))
   (/ (+ x (* y (/ z t))) (+ a 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.5e-54) || !(t <= 2.8e+32)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = (z + ((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 <= (-3.5d-54)) .or. (.not. (t <= 2.8d+32))) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else
        tmp = (z + ((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 <= -3.5e-54) || !(t <= 2.8e+32)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.5e-54) or not (t <= 2.8e+32):
		tmp = (x + (y * (z / t))) / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.5e-54) || !(t <= 2.8e+32))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.5e-54) || ~((t <= 2.8e+32)))
		tmp = (x + (y * (z / t))) / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.5e-54], N[Not[LessEqual[t, 2.8e+32]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.49999999999999982e-54 or 2.8e32 < t

   1. Initial program 81.8%

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

      1. *-commutative 81.8%

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

      2. associate-/l* 87.0%

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

      3. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

      1. associate-/r/ 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in y around 0 82.4%

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

   if -3.49999999999999982e-54 < t < 2.8e32

   1. Initial program 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-/l* 56.6%

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

      3. associate-*l/ 54.7%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in y around -inf 55.5%

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

      1. +-commutative 55.5%

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

      2. associate-*r/ 55.5%

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

      3. distribute-lft-out-- 55.5%

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

      4. associate-*r* 55.5%

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

      5. metadata-eval 55.5%

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

      6. *-lft-identity 55.5%

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

      7. associate-/l* 53.2%

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

      8. associate-/l* 53.2%

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

      9. *-commutative 53.2%

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

      10. associate-/r* 58.8%

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

      11. unpow2 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in b around inf 67.1%

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

      1. associate-*l/ 63.9%

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

      2. *-commutative 63.9%

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

   9. Simplified 63.9%

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

   10. Taylor expanded in b around 0 68.3%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-54} \lor \neg \left(t \leq 2.8 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 10: 69.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-53} \lor \neg \left(t \leq 6.2 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.05e-53) (not (<= t 6.2e+31)))
   (/ (+ x (/ y (/ t z))) (+ a 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.05e-53) || !(t <= 6.2e+31)) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else {
		tmp = (z + ((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 <= (-1.05d-53)) .or. (.not. (t <= 6.2d+31))) then
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    else
        tmp = (z + ((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 <= -1.05e-53) || !(t <= 6.2e+31)) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.05e-53) or not (t <= 6.2e+31):
		tmp = (x + (y / (t / z))) / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.05e-53) || !(t <= 6.2e+31))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.05e-53) || ~((t <= 6.2e+31)))
		tmp = (x + (y / (t / z))) / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.05e-53], N[Not[LessEqual[t, 6.2e+31]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.04999999999999989e-53 or 6.2000000000000004e31 < t

   1. Initial program 81.8%

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

      1. *-commutative 81.8%

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

      2. associate-/l* 87.0%

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

      3. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

      1. associate-/r/ 94.0%

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

   5. Applied egg-rr 94.0%

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

      1. associate-*l/ 85.0%

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

      2. *-commutative 85.0%

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

      3. associate-/l* 94.0%

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

   7. Applied egg-rr 94.0%

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

   8. Taylor expanded in y around 0 82.5%

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

   if -1.04999999999999989e-53 < t < 6.2000000000000004e31

   1. Initial program 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-/l* 56.6%

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

      3. associate-*l/ 54.7%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in y around -inf 55.5%

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

      1. +-commutative 55.5%

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

      2. associate-*r/ 55.5%

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

      3. distribute-lft-out-- 55.5%

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

      4. associate-*r* 55.5%

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

      5. metadata-eval 55.5%

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

      6. *-lft-identity 55.5%

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

      7. associate-/l* 53.2%

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

      8. associate-/l* 53.2%

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

      9. *-commutative 53.2%

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

      10. associate-/r* 58.8%

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

      11. unpow2 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in b around inf 67.1%

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

      1. associate-*l/ 63.9%

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

      2. *-commutative 63.9%

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

   9. Simplified 63.9%

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

   10. Taylor expanded in b around 0 68.3%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-53} \lor \neg \left(t \leq 6.2 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 11: 65.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-143}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3e-143)
   (/ x (+ 1.0 (+ a (/ y (/ t b)))))
   (if (<= t 5.8e-27)
     (/ (+ z (/ (* x t) y)) b)
     (/ x (+ 1.0 (+ a (* b (/ y t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3e-143) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else if (t <= 5.8e-27) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (1.0 + (a + (b * (y / t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3d-143)) then
        tmp = x / (1.0d0 + (a + (y / (t / b))))
    else if (t <= 5.8d-27) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = x / (1.0d0 + (a + (b * (y / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3e-143) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else if (t <= 5.8e-27) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (1.0 + (a + (b * (y / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3e-143:
		tmp = x / (1.0 + (a + (y / (t / b))))
	elif t <= 5.8e-27:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x / (1.0 + (a + (b * (y / t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3e-143)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y / Float64(t / b)))));
	elseif (t <= 5.8e-27)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3e-143)
		tmp = x / (1.0 + (a + (y / (t / b))));
	elseif (t <= 5.8e-27)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x / (1.0 + (a + (b * (y / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3e-143], N[(x / N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-27], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.99999999999999985e-143

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/l* 83.3%

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

      3. associate-*l/ 88.1%

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

   3. Simplified 88.1%

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

      1. associate-/r/ 87.1%

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

   5. Applied egg-rr 87.1%

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

      1. associate-*l/ 80.3%

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

      2. *-commutative 80.3%

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

      3. associate-/l* 87.4%

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

   7. Applied egg-rr 87.4%

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

   8. Taylor expanded in x around inf 62.5%

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

      1. associate-/l* 62.2%

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

   10. Simplified 62.2%

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

   if -2.99999999999999985e-143 < t < 5.80000000000000008e-27

   1. Initial program 54.7%

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

      1. *-commutative 54.7%

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

      2. associate-/l* 47.9%

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

      3. associate-*l/ 45.2%

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

   3. Simplified 45.2%

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

   4. Taylor expanded in y around -inf 57.3%

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

      1. +-commutative 57.3%

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

      2. associate-*r/ 57.3%

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

      3. distribute-lft-out-- 57.3%

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

      4. associate-*r* 57.3%

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

      5. metadata-eval 57.3%

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

      6. *-lft-identity 57.3%

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

      7. associate-/l* 54.7%

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

      8. associate-/l* 54.8%

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

      9. *-commutative 54.8%

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

      10. associate-/r* 62.6%

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

      11. unpow2 62.6%

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

   6. Simplified 62.6%

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

   7. Taylor expanded in b around inf 73.2%

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

      1. associate-*l/ 69.1%

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

      2. *-commutative 69.1%

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

   9. Simplified 69.1%

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

   10. Taylor expanded in b around 0 73.2%

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

   if 5.80000000000000008e-27 < t

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/l* 88.0%

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

      3. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around inf 68.1%

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

      1. associate-*l/ 70.5%

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

   6. Applied egg-rr 70.5%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-143}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \end{array} \]

Alternative 12: 64.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.22e-141)
   (/ x (+ 1.0 (+ a (/ (* y b) t))))
   (if (<= t 9.5e-27)
     (/ (+ z (/ (* x t) y)) b)
     (/ x (+ 1.0 (+ a (* b (/ y t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.22e-141) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (t <= 9.5e-27) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (1.0 + (a + (b * (y / t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.22d-141)) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (t <= 9.5d-27) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = x / (1.0d0 + (a + (b * (y / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.22e-141) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (t <= 9.5e-27) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (1.0 + (a + (b * (y / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.22e-141:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif t <= 9.5e-27:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x / (1.0 + (a + (b * (y / t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.22e-141)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (t <= 9.5e-27)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.22e-141)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (t <= 9.5e-27)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x / (1.0 + (a + (b * (y / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.22e-141], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-27], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.22e-141

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/l* 83.3%

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

      3. associate-*l/ 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in x around inf 62.5%

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

   if -1.22e-141 < t < 9.50000000000000037e-27

   1. Initial program 54.7%

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

      1. *-commutative 54.7%

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

      2. associate-/l* 47.9%

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

      3. associate-*l/ 45.2%

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

   3. Simplified 45.2%

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

   4. Taylor expanded in y around -inf 57.3%

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

      1. +-commutative 57.3%

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

      2. associate-*r/ 57.3%

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

      3. distribute-lft-out-- 57.3%

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

      4. associate-*r* 57.3%

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

      5. metadata-eval 57.3%

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

      6. *-lft-identity 57.3%

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

      7. associate-/l* 54.7%

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

      8. associate-/l* 54.8%

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

      9. *-commutative 54.8%

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

      10. associate-/r* 62.6%

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

      11. unpow2 62.6%

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

   6. Simplified 62.6%

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

   7. Taylor expanded in b around inf 73.2%

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

      1. associate-*l/ 69.1%

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

      2. *-commutative 69.1%

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

   9. Simplified 69.1%

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

   10. Taylor expanded in b around 0 73.2%

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

   if 9.50000000000000037e-27 < t

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/l* 88.0%

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

      3. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around inf 68.1%

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

      1. associate-*l/ 70.5%

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

   6. Applied egg-rr 70.5%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \end{array} \]

Alternative 13: 54.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+54} \lor \neg \left(t \leq -3.5 \cdot 10^{-37} \lor \neg \left(t \leq -1.22 \cdot 10^{-141}\right) \land t \leq 1.25 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.5e+54)
         (not
          (or (<= t -3.5e-37) (and (not (<= t -1.22e-141)) (<= t 1.25e-11)))))
   (/ x (+ a 1.0))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.5e+54) || !((t <= -3.5e-37) || (!(t <= -1.22e-141) && (t <= 1.25e-11)))) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.5d+54)) .or. (.not. (t <= (-3.5d-37)) .or. (.not. (t <= (-1.22d-141))) .and. (t <= 1.25d-11))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.5e+54) || !((t <= -3.5e-37) || (!(t <= -1.22e-141) && (t <= 1.25e-11)))) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.5e+54) or not ((t <= -3.5e-37) or (not (t <= -1.22e-141) and (t <= 1.25e-11))):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.5e+54) || !((t <= -3.5e-37) || (!(t <= -1.22e-141) && (t <= 1.25e-11))))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.5e+54) || ~(((t <= -3.5e-37) || (~((t <= -1.22e-141)) && (t <= 1.25e-11)))))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.5e+54], N[Not[Or[LessEqual[t, -3.5e-37], And[N[Not[LessEqual[t, -1.22e-141]], $MachinePrecision], LessEqual[t, 1.25e-11]]]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4999999999999999e54 or -3.5000000000000001e-37 < t < -1.22e-141 or 1.25000000000000005e-11 < t

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-/l* 85.9%

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

      3. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 61.6%

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

   if -1.4999999999999999e54 < t < -3.5000000000000001e-37 or -1.22e-141 < t < 1.25000000000000005e-11

   1. Initial program 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-/l* 55.1%

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

      3. associate-*l/ 53.9%

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

   3. Simplified 53.9%

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

   4. Taylor expanded in t around 0 60.3%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+54} \lor \neg \left(t \leq -3.5 \cdot 10^{-37} \lor \neg \left(t \leq -1.22 \cdot 10^{-141}\right) \land t \leq 1.25 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 14: 59.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+94} \lor \neg \left(t \leq 2.9 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.8e+94) (not (<= t 2.9e+32)))
   (/ x (+ a 1.0))
   (/ (+ z (/ t (/ y x))) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.8e+94) || !(t <= 2.9e+32)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + (t / (y / x))) / 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 <= (-6.8d+94)) .or. (.not. (t <= 2.9d+32))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = (z + (t / (y / x))) / 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 <= -6.8e+94) || !(t <= 2.9e+32)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + (t / (y / x))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.8e+94) or not (t <= 2.9e+32):
		tmp = x / (a + 1.0)
	else:
		tmp = (z + (t / (y / x))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.8e+94) || !(t <= 2.9e+32))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -6.8e+94) || ~((t <= 2.9e+32)))
		tmp = x / (a + 1.0);
	else
		tmp = (z + (t / (y / x))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.8e+94], N[Not[LessEqual[t, 2.9e+32]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.8000000000000004e94 or 2.90000000000000003e32 < t

   1. Initial program 81.4%

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

      1. *-commutative 81.4%

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

      2. associate-/l* 87.2%

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

      3. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in t around inf 69.4%

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

   if -6.8000000000000004e94 < t < 2.90000000000000003e32

   1. Initial program 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-/l* 62.9%

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

      3. associate-*l/ 62.0%

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

   3. Simplified 62.0%

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

   4. Taylor expanded in y around -inf 50.6%

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

      1. +-commutative 50.6%

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

      2. associate-*r/ 50.6%

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

      3. distribute-lft-out-- 50.6%

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

      4. associate-*r* 50.6%

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

      5. metadata-eval 50.6%

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

      6. *-lft-identity 50.6%

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

      7. associate-/l* 49.4%

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

      8. associate-/l* 49.4%

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

      9. *-commutative 49.4%

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

      10. associate-/r* 54.5%

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

      11. unpow2 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in b around inf 60.5%

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

      1. associate-*l/ 58.7%

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

      2. *-commutative 58.7%

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

   9. Simplified 58.7%

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

   10. Taylor expanded in b around 0 61.8%

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

       1. +-commutative 61.8%

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

       2. associate-/l* 59.6%

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

   12. Simplified 59.6%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+94} \lor \neg \left(t \leq 2.9 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]

Alternative 15: 60.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+94} \lor \neg \left(t \leq 5.8 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.1e+94) (not (<= t 5.8e+31)))
   (/ x (+ a 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.1e+94) || !(t <= 5.8e+31)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + ((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 <= (-6.1d+94)) .or. (.not. (t <= 5.8d+31))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = (z + ((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 <= -6.1e+94) || !(t <= 5.8e+31)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.1e+94) or not (t <= 5.8e+31):
		tmp = x / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.1e+94) || !(t <= 5.8e+31))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -6.1e+94) || ~((t <= 5.8e+31)))
		tmp = x / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.1e+94], N[Not[LessEqual[t, 5.8e+31]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.10000000000000035e94 or 5.8000000000000001e31 < t

   1. Initial program 81.4%

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

      1. *-commutative 81.4%

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

      2. associate-/l* 87.2%

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

      3. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in t around inf 69.4%

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

   if -6.10000000000000035e94 < t < 5.8000000000000001e31

   1. Initial program 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-/l* 62.9%

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

      3. associate-*l/ 62.0%

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

   3. Simplified 62.0%

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

   4. Taylor expanded in y around -inf 50.6%

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

      1. +-commutative 50.6%

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

      2. associate-*r/ 50.6%

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

      3. distribute-lft-out-- 50.6%

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

      4. associate-*r* 50.6%

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

      5. metadata-eval 50.6%

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

      6. *-lft-identity 50.6%

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

      7. associate-/l* 49.4%

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

      8. associate-/l* 49.4%

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

      9. *-commutative 49.4%

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

      10. associate-/r* 54.5%

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

      11. unpow2 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in b around inf 60.5%

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

      1. associate-*l/ 58.7%

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

      2. *-commutative 58.7%

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

   9. Simplified 58.7%

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

   10. Taylor expanded in b around 0 61.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+94} \lor \neg \left(t \leq 5.8 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 16: 42.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-46}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.6e-46) (/ z b) (if (<= y 9.5e-17) (/ x a) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.6e-46) {
		tmp = z / b;
	} else if (y <= 9.5e-17) {
		tmp = x / a;
	} 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 <= (-7.6d-46)) then
        tmp = z / b
    else if (y <= 9.5d-17) then
        tmp = x / a
    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 <= -7.6e-46) {
		tmp = z / b;
	} else if (y <= 9.5e-17) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.6e-46:
		tmp = z / b
	elif y <= 9.5e-17:
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.6e-46)
		tmp = Float64(z / b);
	elseif (y <= 9.5e-17)
		tmp = Float64(x / a);
	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 <= -7.6e-46)
		tmp = z / b;
	elseif (y <= 9.5e-17)
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.6e-46], N[(z / b), $MachinePrecision], If[LessEqual[y, 9.5e-17], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5999999999999993e-46 or 9.50000000000000029e-17 < y

   1. Initial program 55.5%

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

      1. *-commutative 55.5%

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

      2. associate-/l* 58.5%

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

      3. associate-*l/ 63.0%

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

   3. Simplified 63.0%

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

   4. Taylor expanded in t around 0 47.2%

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

   if -7.5999999999999993e-46 < y < 9.50000000000000029e-17

   1. Initial program 98.0%

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

      1. *-commutative 98.0%

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

      2. associate-/l* 95.5%

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

      3. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in x around inf 76.3%

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

   5. Taylor expanded in a around inf 39.7%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-46}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 17: 24.8% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.6%

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

   1. *-commutative 73.6%

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

   2. associate-/l* 74.3%

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

   3. associate-*l/ 76.8%

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

3. Simplified 76.8%

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

4. Taylor expanded in x around inf 54.0%

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

5. Taylor expanded in a around inf 27.1%

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

6. Final simplification 27.1%

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

Developer target: 78.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

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

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