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

Percentage Accurate: 75.4% → 89.9%

Time: 13.8s

Alternatives: 14

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: 75.4% 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: 89.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{1}{\frac{b}{z} + \frac{\frac{t}{\frac{z}{a + 1}} - \frac{b}{\frac{z \cdot \frac{z}{t}}{x}}}{y}}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{-25}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{b}{z} + t \cdot \left(\frac{\frac{a - -1}{z}}{y} - \frac{b}{y} \cdot \frac{\frac{x}{z}}{z}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 (- INFINITY))
     (/
      1.0
      (+ (/ b z) (/ (- (/ t (/ z (+ a 1.0))) (/ b (/ (* z (/ z t)) x))) y)))
     (if (<= t_1 -2e-296)
       t_1
       (if (<= t_1 4e-25)
         (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
         (if (<= t_1 5e+284)
           t_1
           (/
            1.0
            (+
             (/ b z)
             (* t (- (/ (/ (- a -1.0) z) y) (* (/ b y) (/ (/ x z) z))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = 1.0 / ((b / z) + (((t / (z / (a + 1.0))) - (b / ((z * (z / t)) / x))) / y));
	} else if (t_1 <= -2e-296) {
		tmp = t_1;
	} else if (t_1 <= 4e-25) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_1 <= 5e+284) {
		tmp = t_1;
	} else {
		tmp = 1.0 / ((b / z) + (t * ((((a - -1.0) / z) / y) - ((b / y) * ((x / z) / z)))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = 1.0 / ((b / z) + (((t / (z / (a + 1.0))) - (b / ((z * (z / t)) / x))) / y));
	} else if (t_1 <= -2e-296) {
		tmp = t_1;
	} else if (t_1 <= 4e-25) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_1 <= 5e+284) {
		tmp = t_1;
	} else {
		tmp = 1.0 / ((b / z) + (t * ((((a - -1.0) / z) / y) - ((b / y) * ((x / z) / z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = 1.0 / ((b / z) + (((t / (z / (a + 1.0))) - (b / ((z * (z / t)) / x))) / y))
	elif t_1 <= -2e-296:
		tmp = t_1
	elif t_1 <= 4e-25:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	elif t_1 <= 5e+284:
		tmp = t_1
	else:
		tmp = 1.0 / ((b / z) + (t * ((((a - -1.0) / z) / y) - ((b / y) * ((x / z) / z)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(1.0 / Float64(Float64(b / z) + Float64(Float64(Float64(t / Float64(z / Float64(a + 1.0))) - Float64(b / Float64(Float64(z * Float64(z / t)) / x))) / y)));
	elseif (t_1 <= -2e-296)
		tmp = t_1;
	elseif (t_1 <= 4e-25)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_1 <= 5e+284)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(Float64(b / z) + Float64(t * Float64(Float64(Float64(Float64(a - -1.0) / z) / y) - Float64(Float64(b / y) * Float64(Float64(x / z) / z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = 1.0 / ((b / z) + (((t / (z / (a + 1.0))) - (b / ((z * (z / t)) / x))) / y));
	elseif (t_1 <= -2e-296)
		tmp = t_1;
	elseif (t_1 <= 4e-25)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	elseif (t_1 <= 5e+284)
		tmp = t_1;
	else
		tmp = 1.0 / ((b / z) + (t * ((((a - -1.0) / z) / y) - ((b / y) * ((x / z) / z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(1.0 / N[(N[(b / z), $MachinePrecision] + N[(N[(N[(t / N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[(z * N[(z / t), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-296], t$95$1, If[LessEqual[t$95$1, 4e-25], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+284], t$95$1, N[(1.0 / N[(N[(b / z), $MachinePrecision] + N[(t * N[(N[(N[(N[(a - -1.0), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision] - N[(N[(b / y), $MachinePrecision] * N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 10.4%

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

      1. *-commutative 10.4%

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

      2. associate-*l/ 33.1%

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

      3. *-commutative 33.1%

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

      4. associate-*l/ 33.1%

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

   3. Simplified 33.1%

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

      1. clear-num 33.0%

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

      2. associate-*l/ 33.1%

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

      3. *-commutative 33.1%

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

      4. associate-*l/ 10.4%

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

      5. *-commutative 10.4%

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

      6. inv-pow 10.4%

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

      7. +-commutative 10.4%

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

      8. *-commutative 10.4%

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

      9. associate-*l/ 10.4%

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

      10. *-commutative 10.4%

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

      11. fma-def 10.4%

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

      12. +-commutative 10.4%

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

      13. *-commutative 10.4%

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

      14. associate-*l/ 33.0%

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

      15. fma-def 33.0%

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

   5. Applied egg-rr 33.0%

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

      1. unpow-1 33.0%

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

      2. +-commutative 33.0%

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

   7. Simplified 33.0%

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

   8. Taylor expanded in y around inf 64.8%

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

      1. associate--l+ 64.8%

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

      2. times-frac 87.9%

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

      3. times-frac 87.9%

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

      4. *-commutative 87.9%

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

      5. unpow2 87.9%

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

   10. Simplified 87.9%

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

   11. Taylor expanded in y around 0 82.4%

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

       1. associate-/l* 88.1%

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

       2. unpow2 88.1%

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

       3. associate-/l* 88.1%

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

       4. associate-/r* 88.2%

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

       5. associate-*l/ 88.2%

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

   13. Simplified 88.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -2e-296 or 4.00000000000000015e-25 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.9999999999999999e284

   1. Initial program 99.8%

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

   if -2e-296 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.00000000000000015e-25

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 76.6%

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

      3. *-commutative 76.6%

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

      4. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   if 4.9999999999999999e284 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 5.1%

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

      1. *-commutative 5.1%

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

      2. associate-*l/ 11.8%

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

      3. *-commutative 11.8%

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

      4. associate-*l/ 18.5%

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

   3. Simplified 18.5%

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

      1. clear-num 18.4%

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

      2. associate-*l/ 11.8%

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

      3. *-commutative 11.8%

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

      4. associate-*l/ 5.1%

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

      5. *-commutative 5.1%

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

      6. inv-pow 5.1%

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

      7. +-commutative 5.1%

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

      8. *-commutative 5.1%

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

      9. associate-*l/ 5.5%

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

      10. *-commutative 5.5%

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

      11. fma-def 5.5%

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

      12. +-commutative 5.5%

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

      13. *-commutative 5.5%

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

      14. associate-*l/ 18.4%

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

      15. fma-def 18.4%

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

   5. Applied egg-rr 18.4%

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

      1. unpow-1 18.4%

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

      2. +-commutative 18.4%

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

   7. Simplified 18.4%

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

   8. Taylor expanded in y around inf 76.6%

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

      1. associate--l+ 76.6%

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

      2. times-frac 76.6%

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

      3. times-frac 79.9%

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

      4. *-commutative 79.9%

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

      5. unpow2 79.9%

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

   10. Simplified 79.9%

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

   11. Taylor expanded in t around -inf 76.7%

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

       1. mul-1-neg 76.7%

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

       2. distribute-rgt-neg-in 76.7%

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

       3. sub-neg 76.7%

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

       4. associate-*r/ 76.7%

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

       5. neg-mul-1 76.7%

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

       6. *-commutative 76.7%

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

       7. associate-/r* 79.9%

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

       8. distribute-neg-in 79.9%

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

       9. metadata-eval 79.9%

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

       10. unsub-neg 79.9%

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

       11. mul-1-neg 79.9%

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

       12. remove-double-neg 79.9%

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

       13. unpow2 79.9%

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

       14. times-frac 93.2%

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

       15. associate-/r* 93.2%

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

   13. Simplified 93.2%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{1}{\frac{b}{z} + \frac{\frac{t}{\frac{z}{a + 1}} - \frac{b}{\frac{z \cdot \frac{z}{t}}{x}}}{y}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-296}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 4 \cdot 10^{-25}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+284}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{b}{z} + t \cdot \left(\frac{\frac{a - -1}{z}}{y} - \frac{b}{y} \cdot \frac{\frac{x}{z}}{z}\right)}\\ \end{array} \]

Alternative 2: 90.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_2 := \frac{1}{\frac{b}{z} + \frac{\frac{t}{\frac{z}{a + 1}} - \frac{b}{\frac{z \cdot \frac{z}{t}}{x}}}{y}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{-25}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0))))
        (t_2
         (/
          1.0
          (+
           (/ b z)
           (/ (- (/ t (/ z (+ a 1.0))) (/ b (/ (* z (/ z t)) x))) y)))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -2e-296)
       t_1
       (if (<= t_1 4e-25)
         (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
         (if (<= t_1 5e+284) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = 1.0 / ((b / z) + (((t / (z / (a + 1.0))) - (b / ((z * (z / t)) / x))) / y));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -2e-296) {
		tmp = t_1;
	} else if (t_1 <= 4e-25) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_1 <= 5e+284) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = 1.0 / ((b / z) + (((t / (z / (a + 1.0))) - (b / ((z * (z / t)) / x))) / y));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -2e-296) {
		tmp = t_1;
	} else if (t_1 <= 4e-25) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_1 <= 5e+284) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	t_2 = 1.0 / ((b / z) + (((t / (z / (a + 1.0))) - (b / ((z * (z / t)) / x))) / y))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -2e-296:
		tmp = t_1
	elif t_1 <= 4e-25:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	elif t_1 <= 5e+284:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_2 = Float64(1.0 / Float64(Float64(b / z) + Float64(Float64(Float64(t / Float64(z / Float64(a + 1.0))) - Float64(b / Float64(Float64(z * Float64(z / t)) / x))) / y)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -2e-296)
		tmp = t_1;
	elseif (t_1 <= 4e-25)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_1 <= 5e+284)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	t_2 = 1.0 / ((b / z) + (((t / (z / (a + 1.0))) - (b / ((z * (z / t)) / x))) / y));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -2e-296)
		tmp = t_1;
	elseif (t_1 <= 4e-25)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	elseif (t_1 <= 5e+284)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 / N[(N[(b / z), $MachinePrecision] + N[(N[(N[(t / N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[(z * N[(z / t), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -2e-296], t$95$1, If[LessEqual[t$95$1, 4e-25], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+284], t$95$1, t$95$2]]]]]]

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 4.9999999999999999e284 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 7.0%

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

      1. *-commutative 7.0%

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

      2. associate-*l/ 19.5%

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

      3. *-commutative 19.5%

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

      4. associate-*l/ 23.8%

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

   3. Simplified 23.8%

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

      1. clear-num 23.7%

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

      2. associate-*l/ 19.5%

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

      3. *-commutative 19.5%

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

      4. associate-*l/ 7.0%

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

      5. *-commutative 7.0%

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

      6. inv-pow 7.0%

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

      7. +-commutative 7.0%

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

      8. *-commutative 7.0%

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

      9. associate-*l/ 7.3%

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

      10. *-commutative 7.3%

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

      11. fma-def 7.3%

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

      12. +-commutative 7.3%

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

      13. *-commutative 7.3%

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

      14. associate-*l/ 23.7%

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

      15. fma-def 23.7%

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

   5. Applied egg-rr 23.7%

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

      1. unpow-1 23.7%

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

      2. +-commutative 23.7%

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

   7. Simplified 23.7%

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

   8. Taylor expanded in y around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. times-frac 80.7%

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

      3. times-frac 82.8%

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

      4. *-commutative 82.8%

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

      5. unpow2 82.8%

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

   10. Simplified 82.8%

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

   11. Taylor expanded in y around 0 82.9%

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

       1. associate-/l* 82.8%

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

       2. unpow2 82.8%

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

       3. associate-/l* 85.0%

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

       4. associate-/r* 91.4%

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

       5. associate-*l/ 91.4%

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

   13. Simplified 91.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -2e-296 or 4.00000000000000015e-25 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.9999999999999999e284

   1. Initial program 99.8%

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

   if -2e-296 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.00000000000000015e-25

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 76.6%

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

      3. *-commutative 76.6%

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

      4. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{1}{\frac{b}{z} + \frac{\frac{t}{\frac{z}{a + 1}} - \frac{b}{\frac{z \cdot \frac{z}{t}}{x}}}{y}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-296}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 4 \cdot 10^{-25}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+284}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{b}{z} + \frac{\frac{t}{\frac{z}{a + 1}} - \frac{b}{\frac{z \cdot \frac{z}{t}}{x}}}{y}}\\ \end{array} \]

Alternative 3: 88.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{-25}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 (- INFINITY))
     (/ (+ z (/ t (/ y x))) b)
     (if (<= t_1 -2e-296)
       t_1
       (if (<= t_1 4e-25)
         (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
         (if (<= t_1 5e+284) t_1 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (z + (t / (y / x))) / b;
	} else if (t_1 <= -2e-296) {
		tmp = t_1;
	} else if (t_1 <= 4e-25) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_1 <= 5e+284) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (z + (t / (y / x))) / b;
	} else if (t_1 <= -2e-296) {
		tmp = t_1;
	} else if (t_1 <= 4e-25) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_1 <= 5e+284) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (z + (t / (y / x))) / b
	elif t_1 <= -2e-296:
		tmp = t_1
	elif t_1 <= 4e-25:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	elif t_1 <= 5e+284:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / b);
	elseif (t_1 <= -2e-296)
		tmp = t_1;
	elseif (t_1 <= 4e-25)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_1 <= 5e+284)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (z + (t / (y / x))) / b;
	elseif (t_1 <= -2e-296)
		tmp = t_1;
	elseif (t_1 <= 4e-25)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	elseif (t_1 <= 5e+284)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, -2e-296], t$95$1, If[LessEqual[t$95$1, 4e-25], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+284], t$95$1, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 10.4%

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

      1. *-commutative 10.4%

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

      2. associate-*l/ 33.1%

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

      3. *-commutative 33.1%

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

      4. associate-*l/ 33.1%

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

   3. Simplified 33.1%

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

   4. Taylor expanded in y around inf 24.4%

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

      1. times-frac 24.1%

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

      2. associate-/l* 30.2%

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

      3. *-commutative 30.2%

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

      4. unpow2 30.2%

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

   6. Simplified 30.2%

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

   7. Taylor expanded in b around inf 71.4%

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

      1. associate-/l* 71.4%

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

   9. Simplified 71.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -2e-296 or 4.00000000000000015e-25 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.9999999999999999e284

   1. Initial program 99.8%

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

   if -2e-296 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.00000000000000015e-25

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 76.6%

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

      3. *-commutative 76.6%

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

      4. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   if 4.9999999999999999e284 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 5.1%

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

      1. *-commutative 5.1%

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

      2. associate-*l/ 11.8%

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

      3. *-commutative 11.8%

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

      4. associate-*l/ 18.5%

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

   3. Simplified 18.5%

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

   4. Taylor expanded in t around 0 81.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-296}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 4 \cdot 10^{-25}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+284}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 4: 67.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-122}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+40}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ a 1.0))))
   (if (<= t -3.6e-85)
     t_1
     (if (<= t 1.9e-122)
       (/ (+ z (/ t (/ y x))) b)
       (if (<= t 4.6e-23)
         (/ (+ x (* (* y z) (/ 1.0 t))) (+ a 1.0))
         (if (<= t 8.4e+40)
           (* (/ y t) (/ z (+ 1.0 (+ a (* y (/ b t))))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -3.6e-85) {
		tmp = t_1;
	} else if (t <= 1.9e-122) {
		tmp = (z + (t / (y / x))) / b;
	} else if (t <= 4.6e-23) {
		tmp = (x + ((y * z) * (1.0 / t))) / (a + 1.0);
	} else if (t <= 8.4e+40) {
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / (a + 1.0d0)
    if (t <= (-3.6d-85)) then
        tmp = t_1
    else if (t <= 1.9d-122) then
        tmp = (z + (t / (y / x))) / b
    else if (t <= 4.6d-23) then
        tmp = (x + ((y * z) * (1.0d0 / t))) / (a + 1.0d0)
    else if (t <= 8.4d+40) then
        tmp = (y / t) * (z / (1.0d0 + (a + (y * (b / t)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -3.6e-85) {
		tmp = t_1;
	} else if (t <= 1.9e-122) {
		tmp = (z + (t / (y / x))) / b;
	} else if (t <= 4.6e-23) {
		tmp = (x + ((y * z) * (1.0 / t))) / (a + 1.0);
	} else if (t <= 8.4e+40) {
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / (a + 1.0)
	tmp = 0
	if t <= -3.6e-85:
		tmp = t_1
	elif t <= 1.9e-122:
		tmp = (z + (t / (y / x))) / b
	elif t <= 4.6e-23:
		tmp = (x + ((y * z) * (1.0 / t))) / (a + 1.0)
	elif t <= 8.4e+40:
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -3.6e-85)
		tmp = t_1;
	elseif (t <= 1.9e-122)
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / b);
	elseif (t <= 4.6e-23)
		tmp = Float64(Float64(x + Float64(Float64(y * z) * Float64(1.0 / t))) / Float64(a + 1.0));
	elseif (t <= 8.4e+40)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -3.6e-85)
		tmp = t_1;
	elseif (t <= 1.9e-122)
		tmp = (z + (t / (y / x))) / b;
	elseif (t <= 4.6e-23)
		tmp = (x + ((y * z) * (1.0 / t))) / (a + 1.0);
	elseif (t <= 8.4e+40)
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e-85], t$95$1, If[LessEqual[t, 1.9e-122], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, 4.6e-23], N[(N[(x + N[(N[(y * z), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.4e+40], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.5999999999999998e-85 or 8.4000000000000004e40 < t

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

      2. associate-*l/ 89.6%

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

      3. *-commutative 89.6%

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

      4. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in b around 0 80.4%

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

   if -3.5999999999999998e-85 < t < 1.9e-122

   1. Initial program 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-*l/ 47.9%

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

      3. *-commutative 47.9%

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

      4. associate-*l/ 42.8%

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

   3. Simplified 42.8%

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

   4. Taylor expanded in y around inf 53.5%

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

      1. times-frac 48.4%

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

      2. associate-/l* 48.6%

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

      3. *-commutative 48.6%

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

      4. unpow2 48.6%

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

   6. Simplified 48.6%

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

   7. Taylor expanded in b around inf 72.0%

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

      1. associate-/l* 71.9%

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

   9. Simplified 71.9%

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

   if 1.9e-122 < t < 4.6000000000000002e-23

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*l/ 81.7%

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

      3. *-commutative 81.7%

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

      4. associate-*l/ 81.7%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in b around 0 81.0%

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

      1. div-inv 81.1%

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

   6. Applied egg-rr 81.1%

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

   if 4.6000000000000002e-23 < t < 8.4000000000000004e40

   1. Initial program 62.7%

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

      1. *-commutative 62.7%

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

      2. associate-*l/ 62.7%

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

      3. *-commutative 62.7%

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

      4. associate-*l/ 62.7%

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

   3. Simplified 62.7%

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

   4. Taylor expanded in x around 0 37.4%

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

      1. times-frac 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-*r/ 62.2%

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

   6. Simplified 62.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-85}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-122}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+40}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]

Alternative 5: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-176} \lor \neg \left(t \leq 1.5 \cdot 10^{-122}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.2e-176) (not (<= t 1.5e-122)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (/ (+ z (/ t (/ y x))) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.2e-176) || !(t <= 1.5e-122)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} 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 <= (-5.2d-176)) .or. (.not. (t <= 1.5d-122))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    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 <= -5.2e-176) || !(t <= 1.5e-122)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + (t / (y / x))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.2e-176) or not (t <= 1.5e-122):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (z + (t / (y / x))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.2e-176) || !(t <= 1.5e-122))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	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 <= -5.2e-176) || ~((t <= 1.5e-122)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (z + (t / (y / x))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.2e-176], N[Not[LessEqual[t, 1.5e-122]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.19999999999999984e-176 or 1.50000000000000002e-122 < t

   1. Initial program 80.8%

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

      1. *-commutative 80.8%

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

      2. associate-*l/ 83.3%

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

      3. *-commutative 83.3%

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

      4. associate-*l/ 86.7%

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

   3. Simplified 86.7%

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

   if -5.19999999999999984e-176 < t < 1.50000000000000002e-122

   1. Initial program 56.3%

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

      1. *-commutative 56.3%

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

      2. associate-*l/ 44.8%

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

      3. *-commutative 44.8%

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

      4. associate-*l/ 38.1%

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

   3. Simplified 38.1%

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

   4. Taylor expanded in y around inf 60.9%

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

      1. times-frac 54.2%

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

      2. associate-/l* 54.3%

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

      3. *-commutative 54.3%

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

      4. unpow2 54.3%

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

   6. Simplified 54.3%

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

   7. Taylor expanded in b around inf 76.6%

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

      1. associate-/l* 76.4%

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

   9. Simplified 76.4%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-176} \lor \neg \left(t \leq 1.5 \cdot 10^{-122}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]

Alternative 6: 60.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-63} \lor \neg \left(y \leq 1900000 \lor \neg \left(y \leq 8.5 \cdot 10^{+33}\right) \land y \leq 5.4 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.3e-63)
         (not (or (<= y 1900000.0) (and (not (<= y 8.5e+33)) (<= y 5.4e+73)))))
   (/ (+ z (/ t (/ y x))) b)
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e-63) || !((y <= 1900000.0) || (!(y <= 8.5e+33) && (y <= 5.4e+73)))) {
		tmp = (z + (t / (y / x))) / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.3d-63)) .or. (.not. (y <= 1900000.0d0) .or. (.not. (y <= 8.5d+33)) .and. (y <= 5.4d+73))) then
        tmp = (z + (t / (y / x))) / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e-63) || !((y <= 1900000.0) || (!(y <= 8.5e+33) && (y <= 5.4e+73)))) {
		tmp = (z + (t / (y / x))) / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.3e-63) or not ((y <= 1900000.0) or (not (y <= 8.5e+33) and (y <= 5.4e+73))):
		tmp = (z + (t / (y / x))) / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.3e-63) || !((y <= 1900000.0) || (!(y <= 8.5e+33) && (y <= 5.4e+73))))
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.3e-63) || ~(((y <= 1900000.0) || (~((y <= 8.5e+33)) && (y <= 5.4e+73)))))
		tmp = (z + (t / (y / x))) / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.3e-63], N[Not[Or[LessEqual[y, 1900000.0], And[N[Not[LessEqual[y, 8.5e+33]], $MachinePrecision], LessEqual[y, 5.4e+73]]]], $MachinePrecision]], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e-63 or 1.9e6 < y < 8.4999999999999998e33 or 5.3999999999999998e73 < y

   1. Initial program 56.5%

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

      1. *-commutative 56.5%

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

      2. associate-*l/ 60.2%

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

      3. *-commutative 60.2%

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

      4. associate-*l/ 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in y around inf 41.6%

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

      1. times-frac 44.5%

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

      2. associate-/l* 47.7%

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

      3. *-commutative 47.7%

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

      4. unpow2 47.7%

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

   6. Simplified 47.7%

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

   7. Taylor expanded in b around inf 55.7%

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

      1. associate-/l* 61.7%

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

   9. Simplified 61.7%

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

   if -2.3e-63 < y < 1.9e6 or 8.4999999999999998e33 < y < 5.3999999999999998e73

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

      2. associate-*l/ 89.9%

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

      3. *-commutative 89.9%

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

      4. associate-*l/ 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in t around inf 73.9%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-63} \lor \neg \left(y \leq 1900000 \lor \neg \left(y \leq 8.5 \cdot 10^{+33}\right) \land y \leq 5.4 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 7: 62.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 800000:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+33} \lor \neg \left(y \leq 1.95 \cdot 10^{+73}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ t (/ y x))) b)))
   (if (<= y -2.9e-63)
     t_1
     (if (<= y 800000.0)
       (/ x (+ 1.0 (+ a (* y (/ b t)))))
       (if (or (<= y 8.5e+33) (not (<= y 1.95e+73))) t_1 (/ x (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t / (y / x))) / b;
	double tmp;
	if (y <= -2.9e-63) {
		tmp = t_1;
	} else if (y <= 800000.0) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if ((y <= 8.5e+33) || !(y <= 1.95e+73)) {
		tmp = t_1;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + (t / (y / x))) / b
    if (y <= (-2.9d-63)) then
        tmp = t_1
    else if (y <= 800000.0d0) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    else if ((y <= 8.5d+33) .or. (.not. (y <= 1.95d+73))) then
        tmp = t_1
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t / (y / x))) / b;
	double tmp;
	if (y <= -2.9e-63) {
		tmp = t_1;
	} else if (y <= 800000.0) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if ((y <= 8.5e+33) || !(y <= 1.95e+73)) {
		tmp = t_1;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (t / (y / x))) / b
	tmp = 0
	if y <= -2.9e-63:
		tmp = t_1
	elif y <= 800000.0:
		tmp = x / (1.0 + (a + (y * (b / t))))
	elif (y <= 8.5e+33) or not (y <= 1.95e+73):
		tmp = t_1
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(t / Float64(y / x))) / b)
	tmp = 0.0
	if (y <= -2.9e-63)
		tmp = t_1;
	elseif (y <= 800000.0)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	elseif ((y <= 8.5e+33) || !(y <= 1.95e+73))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (t / (y / x))) / b;
	tmp = 0.0;
	if (y <= -2.9e-63)
		tmp = t_1;
	elseif (y <= 800000.0)
		tmp = x / (1.0 + (a + (y * (b / t))));
	elseif ((y <= 8.5e+33) || ~((y <= 1.95e+73)))
		tmp = t_1;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -2.9e-63], t$95$1, If[LessEqual[y, 800000.0], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.5e+33], N[Not[LessEqual[y, 1.95e+73]], $MachinePrecision]], t$95$1, N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.89999999999999975e-63 or 8e5 < y < 8.4999999999999998e33 or 1.95e73 < y

   1. Initial program 56.5%

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

      1. *-commutative 56.5%

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

      2. associate-*l/ 60.2%

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

      3. *-commutative 60.2%

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

      4. associate-*l/ 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in y around inf 41.6%

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

      1. times-frac 44.5%

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

      2. associate-/l* 47.7%

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

      3. *-commutative 47.7%

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

      4. unpow2 47.7%

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

   6. Simplified 47.7%

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

   7. Taylor expanded in b around inf 55.7%

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

      1. associate-/l* 61.7%

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

   9. Simplified 61.7%

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

   if -2.89999999999999975e-63 < y < 8e5

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-*l/ 89.1%

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

      3. *-commutative 89.1%

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

      4. associate-*l/ 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in x around inf 79.6%

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

      1. *-commutative 79.6%

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

      2. associate-*r/ 76.2%

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

   6. Simplified 76.2%

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

   if 8.4999999999999998e33 < y < 1.95e73

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 71.6%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-63}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;y \leq 800000:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+33} \lor \neg \left(y \leq 1.95 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 8: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{if}\;y \leq -6 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 30000000:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+33} \lor \neg \left(y \leq 4.3 \cdot 10^{+74}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ t (/ y x))) b)))
   (if (<= y -6e-24)
     t_1
     (if (<= y 30000000.0)
       (/ x (+ 1.0 (+ a (/ (* y b) t))))
       (if (or (<= y 8.2e+33) (not (<= y 4.3e+74))) t_1 (/ x (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t / (y / x))) / b;
	double tmp;
	if (y <= -6e-24) {
		tmp = t_1;
	} else if (y <= 30000000.0) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if ((y <= 8.2e+33) || !(y <= 4.3e+74)) {
		tmp = t_1;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + (t / (y / x))) / b
    if (y <= (-6d-24)) then
        tmp = t_1
    else if (y <= 30000000.0d0) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if ((y <= 8.2d+33) .or. (.not. (y <= 4.3d+74))) then
        tmp = t_1
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t / (y / x))) / b;
	double tmp;
	if (y <= -6e-24) {
		tmp = t_1;
	} else if (y <= 30000000.0) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if ((y <= 8.2e+33) || !(y <= 4.3e+74)) {
		tmp = t_1;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (t / (y / x))) / b
	tmp = 0
	if y <= -6e-24:
		tmp = t_1
	elif y <= 30000000.0:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif (y <= 8.2e+33) or not (y <= 4.3e+74):
		tmp = t_1
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(t / Float64(y / x))) / b)
	tmp = 0.0
	if (y <= -6e-24)
		tmp = t_1;
	elseif (y <= 30000000.0)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif ((y <= 8.2e+33) || !(y <= 4.3e+74))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (t / (y / x))) / b;
	tmp = 0.0;
	if (y <= -6e-24)
		tmp = t_1;
	elseif (y <= 30000000.0)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif ((y <= 8.2e+33) || ~((y <= 4.3e+74)))
		tmp = t_1;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -6e-24], t$95$1, If[LessEqual[y, 30000000.0], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.2e+33], N[Not[LessEqual[y, 4.3e+74]], $MachinePrecision]], t$95$1, N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999991e-24 or 3e7 < y < 8.1999999999999999e33 or 4.30000000000000001e74 < y

   1. Initial program 55.2%

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

      1. *-commutative 55.2%

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

      2. associate-*l/ 58.9%

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

      3. *-commutative 58.9%

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

      4. associate-*l/ 64.1%

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

   3. Simplified 64.1%

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

   4. Taylor expanded in y around inf 42.1%

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

      1. times-frac 45.9%

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

      2. associate-/l* 49.1%

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

      3. *-commutative 49.1%

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

      4. unpow2 49.1%

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

   6. Simplified 49.1%

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

   7. Taylor expanded in b around inf 56.6%

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

      1. associate-/l* 62.7%

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

   9. Simplified 62.7%

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

   if -5.99999999999999991e-24 < y < 3e7

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

      2. associate-*l/ 89.4%

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

      3. *-commutative 89.4%

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

      4. associate-*l/ 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in x around inf 78.6%

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

   if 8.1999999999999999e33 < y < 4.30000000000000001e74

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 71.6%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-24}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;y \leq 30000000:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+33} \lor \neg \left(y \leq 4.3 \cdot 10^{+74}\right):\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 9: 40.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-268}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 1700:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+34}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.5e-13)
   (/ z b)
   (if (<= y 4.6e-268)
     (/ x a)
     (if (<= y 1700.0)
       x
       (if (<= y 1e+34)
         (/ z b)
         (if (<= y 8e+56) x (if (<= y 3.1e+90) (/ x a) (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.5e-13) {
		tmp = z / b;
	} else if (y <= 4.6e-268) {
		tmp = x / a;
	} else if (y <= 1700.0) {
		tmp = x;
	} else if (y <= 1e+34) {
		tmp = z / b;
	} else if (y <= 8e+56) {
		tmp = x;
	} else if (y <= 3.1e+90) {
		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 <= (-1.5d-13)) then
        tmp = z / b
    else if (y <= 4.6d-268) then
        tmp = x / a
    else if (y <= 1700.0d0) then
        tmp = x
    else if (y <= 1d+34) then
        tmp = z / b
    else if (y <= 8d+56) then
        tmp = x
    else if (y <= 3.1d+90) 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 <= -1.5e-13) {
		tmp = z / b;
	} else if (y <= 4.6e-268) {
		tmp = x / a;
	} else if (y <= 1700.0) {
		tmp = x;
	} else if (y <= 1e+34) {
		tmp = z / b;
	} else if (y <= 8e+56) {
		tmp = x;
	} else if (y <= 3.1e+90) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.5e-13:
		tmp = z / b
	elif y <= 4.6e-268:
		tmp = x / a
	elif y <= 1700.0:
		tmp = x
	elif y <= 1e+34:
		tmp = z / b
	elif y <= 8e+56:
		tmp = x
	elif y <= 3.1e+90:
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.5e-13)
		tmp = Float64(z / b);
	elseif (y <= 4.6e-268)
		tmp = Float64(x / a);
	elseif (y <= 1700.0)
		tmp = x;
	elseif (y <= 1e+34)
		tmp = Float64(z / b);
	elseif (y <= 8e+56)
		tmp = x;
	elseif (y <= 3.1e+90)
		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 <= -1.5e-13)
		tmp = z / b;
	elseif (y <= 4.6e-268)
		tmp = x / a;
	elseif (y <= 1700.0)
		tmp = x;
	elseif (y <= 1e+34)
		tmp = z / b;
	elseif (y <= 8e+56)
		tmp = x;
	elseif (y <= 3.1e+90)
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.5e-13], N[(z / b), $MachinePrecision], If[LessEqual[y, 4.6e-268], N[(x / a), $MachinePrecision], If[LessEqual[y, 1700.0], x, If[LessEqual[y, 1e+34], N[(z / b), $MachinePrecision], If[LessEqual[y, 8e+56], x, If[LessEqual[y, 3.1e+90], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.49999999999999992e-13 or 1700 < y < 9.99999999999999946e33 or 3.09999999999999988e90 < y

   1. Initial program 54.5%

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

      1. *-commutative 54.5%

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

      2. associate-*l/ 58.4%

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

      3. *-commutative 58.4%

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

      4. associate-*l/ 63.8%

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

   3. Simplified 63.8%

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

   4. Taylor expanded in t around 0 54.8%

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

   if -1.49999999999999992e-13 < y < 4.60000000000000021e-268 or 8.00000000000000074e56 < y < 3.09999999999999988e90

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

      2. associate-*l/ 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in x around inf 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-*r/ 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in a around inf 49.3%

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

   if 4.60000000000000021e-268 < y < 1700 or 9.99999999999999946e33 < y < 8.00000000000000074e56

   1. Initial program 93.7%

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

      1. *-commutative 93.7%

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

      2. associate-*l/ 92.4%

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

      3. *-commutative 92.4%

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

      4. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

      1. clear-num 89.4%

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

      2. associate-*l/ 91.0%

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

      3. *-commutative 91.0%

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

      4. associate-*l/ 92.4%

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

      5. *-commutative 92.4%

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

      6. inv-pow 92.4%

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

      7. +-commutative 92.4%

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

      8. *-commutative 92.4%

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

      9. associate-*l/ 89.3%

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

      10. *-commutative 89.3%

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

      11. fma-def 89.3%

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

      12. +-commutative 89.3%

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

      13. *-commutative 89.3%

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

      14. associate-*l/ 89.4%

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

      15. fma-def 89.4%

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

   5. Applied egg-rr 89.4%

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

      1. unpow-1 89.4%

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

      2. +-commutative 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in y around 0 69.7%

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

   9. Taylor expanded in a around 0 49.2%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-268}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 1700:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+34}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 10: 54.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a \leq -1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-88}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+48}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) a)))
   (if (<= a -1.0)
     t_1
     (if (<= a 2.35e-88)
       (+ x (* z (/ y t)))
       (if (<= a 3.9e+48) (/ z b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -1.0) {
		tmp = t_1;
	} else if (a <= 2.35e-88) {
		tmp = x + (z * (y / t));
	} else if (a <= 3.9e+48) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / a
    if (a <= (-1.0d0)) then
        tmp = t_1
    else if (a <= 2.35d-88) then
        tmp = x + (z * (y / t))
    else if (a <= 3.9d+48) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -1.0) {
		tmp = t_1;
	} else if (a <= 2.35e-88) {
		tmp = x + (z * (y / t));
	} else if (a <= 3.9e+48) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / a
	tmp = 0
	if a <= -1.0:
		tmp = t_1
	elif a <= 2.35e-88:
		tmp = x + (z * (y / t))
	elif a <= 3.9e+48:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / a)
	tmp = 0.0
	if (a <= -1.0)
		tmp = t_1;
	elseif (a <= 2.35e-88)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (a <= 3.9e+48)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / a;
	tmp = 0.0;
	if (a <= -1.0)
		tmp = t_1;
	elseif (a <= 2.35e-88)
		tmp = x + (z * (y / t));
	elseif (a <= 3.9e+48)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -1.0], t$95$1, If[LessEqual[a, 2.35e-88], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e+48], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1 or 3.9000000000000001e48 < a

   1. Initial program 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-*l/ 70.7%

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

      3. *-commutative 70.7%

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

      4. associate-*l/ 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in a around inf 63.0%

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

   if -1 < a < 2.35e-88

   1. Initial program 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-*l/ 81.1%

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

      3. *-commutative 81.1%

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

      4. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in b around 0 62.7%

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

   5. Taylor expanded in a around 0 62.4%

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

      1. associate-*l/ 62.7%

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

      2. *-commutative 62.7%

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

   7. Simplified 62.7%

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

   if 2.35e-88 < a < 3.9000000000000001e48

   1. Initial program 58.2%

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

      1. *-commutative 58.2%

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

      2. associate-*l/ 62.3%

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

      3. *-commutative 62.3%

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

      4. associate-*l/ 66.6%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in t around 0 61.0%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-88}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+48}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]

Alternative 11: 68.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-85} \lor \neg \left(t \leq 4.8 \cdot 10^{-132}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.5e-85) (not (<= t 4.8e-132)))
   (/ (+ x (* y (/ z t))) (+ 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 <= -3.5e-85) || !(t <= 4.8e-132)) {
		tmp = (x + (y * (z / t))) / (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 <= (-3.5d-85)) .or. (.not. (t <= 4.8d-132))) then
        tmp = (x + (y * (z / t))) / (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 <= -3.5e-85) || !(t <= 4.8e-132)) {
		tmp = (x + (y * (z / t))) / (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 <= -3.5e-85) or not (t <= 4.8e-132):
		tmp = (x + (y * (z / t))) / (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 <= -3.5e-85) || !(t <= 4.8e-132))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / 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 <= -3.5e-85) || ~((t <= 4.8e-132)))
		tmp = (x + (y * (z / t))) / (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, -3.5e-85], N[Not[LessEqual[t, 4.8e-132]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 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 < -3.49999999999999978e-85 or 4.80000000000000031e-132 < t

   1. Initial program 82.6%

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

      1. *-commutative 82.6%

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

      2. associate-*l/ 85.9%

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

      3. *-commutative 85.9%

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

      4. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in b around 0 76.0%

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

   if -3.49999999999999978e-85 < t < 4.80000000000000031e-132

   1. Initial program 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-*l/ 47.9%

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

      3. *-commutative 47.9%

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

      4. associate-*l/ 42.8%

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

   3. Simplified 42.8%

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

   4. Taylor expanded in y around inf 53.5%

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

      1. times-frac 48.4%

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

      2. associate-/l* 48.6%

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

      3. *-commutative 48.6%

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

      4. unpow2 48.6%

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

   6. Simplified 48.6%

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

   7. Taylor expanded in b around inf 72.0%

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

      1. associate-/l* 71.9%

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

   9. Simplified 71.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-85} \lor \neg \left(t \leq 4.8 \cdot 10^{-132}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]

Alternative 12: 55.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 25000000 \lor \neg \left(y \leq 8 \cdot 10^{+33}\right) \land y \leq 8.1 \cdot 10^{+74}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.2e-22)
   (/ z b)
   (if (or (<= y 25000000.0) (and (not (<= y 8e+33)) (<= y 8.1e+74)))
     (/ x (+ a 1.0))
     (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.2e-22) {
		tmp = z / b;
	} else if ((y <= 25000000.0) || (!(y <= 8e+33) && (y <= 8.1e+74))) {
		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 (y <= (-2.2d-22)) then
        tmp = z / b
    else if ((y <= 25000000.0d0) .or. (.not. (y <= 8d+33)) .and. (y <= 8.1d+74)) 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 (y <= -2.2e-22) {
		tmp = z / b;
	} else if ((y <= 25000000.0) || (!(y <= 8e+33) && (y <= 8.1e+74))) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.2e-22:
		tmp = z / b
	elif (y <= 25000000.0) or (not (y <= 8e+33) and (y <= 8.1e+74)):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.2e-22)
		tmp = Float64(z / b);
	elseif ((y <= 25000000.0) || (!(y <= 8e+33) && (y <= 8.1e+74)))
		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 (y <= -2.2e-22)
		tmp = z / b;
	elseif ((y <= 25000000.0) || (~((y <= 8e+33)) && (y <= 8.1e+74)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.2e-22], N[(z / b), $MachinePrecision], If[Or[LessEqual[y, 25000000.0], And[N[Not[LessEqual[y, 8e+33]], $MachinePrecision], LessEqual[y, 8.1e+74]]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2000000000000001e-22 or 2.5e7 < y < 7.9999999999999996e33 or 8.1000000000000003e74 < y

   1. Initial program 55.2%

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

      1. *-commutative 55.2%

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

      2. associate-*l/ 58.9%

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

      3. *-commutative 58.9%

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

      4. associate-*l/ 64.1%

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

   3. Simplified 64.1%

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

   4. Taylor expanded in t around 0 54.0%

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

   if -2.2000000000000001e-22 < y < 2.5e7 or 7.9999999999999996e33 < y < 8.1000000000000003e74

   1. Initial program 95.4%

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

      1. *-commutative 95.4%

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

      2. associate-*l/ 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*l/ 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in t around inf 72.4%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 25000000 \lor \neg \left(y \leq 8 \cdot 10^{+33}\right) \land y \leq 8.1 \cdot 10^{+74}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 13: 40.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 0.88:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.0) (/ x a) (if (<= a 0.88) x (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= 0.88) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.0d0)) then
        tmp = x / a
    else if (a <= 0.88d0) then
        tmp = x
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= 0.88) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.0:
		tmp = x / a
	elif a <= 0.88:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.0)
		tmp = Float64(x / a);
	elseif (a <= 0.88)
		tmp = x;
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.0)
		tmp = x / a;
	elseif (a <= 0.88)
		tmp = x;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.0], N[(x / a), $MachinePrecision], If[LessEqual[a, 0.88], x, N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 0.880000000000000004 < a

   1. Initial program 69.3%

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

      1. *-commutative 69.3%

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

      2. associate-*l/ 69.3%

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

      3. *-commutative 69.3%

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

      4. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in x around inf 53.4%

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

      1. *-commutative 53.4%

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

      2. associate-*r/ 54.2%

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

   6. Simplified 54.2%

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

   7. Taylor expanded in a around inf 47.8%

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

   if -1 < a < 0.880000000000000004

   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/ 79.9%

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

      3. *-commutative 79.9%

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

      4. associate-*l/ 78.5%

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

   3. Simplified 78.5%

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

      1. clear-num 78.3%

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

      2. associate-*l/ 79.8%

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

      3. *-commutative 79.8%

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

      4. associate-*l/ 81.2%

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

      5. *-commutative 81.2%

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

      6. inv-pow 81.2%

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

      7. +-commutative 81.2%

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

      8. *-commutative 81.2%

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

      9. associate-*l/ 78.3%

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

      10. *-commutative 78.3%

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

      11. fma-def 78.3%

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

      12. +-commutative 78.3%

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

      13. *-commutative 78.3%

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

      14. associate-*l/ 78.3%

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

      15. fma-def 78.3%

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

   5. Applied egg-rr 78.3%

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

      1. unpow-1 78.3%

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

      2. +-commutative 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in y around 0 40.1%

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

   9. Taylor expanded in a around 0 39.3%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 0.88:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 14: 19.3% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.3%

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

   1. *-commutative 75.3%

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

   2. associate-*l/ 74.6%

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

   3. *-commutative 74.6%

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

   4. associate-*l/ 75.7%

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

3. Simplified 75.7%

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

   1. clear-num 75.3%

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

   2. associate-*l/ 74.1%

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

   3. *-commutative 74.1%

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

   4. associate-*l/ 74.9%

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

   5. *-commutative 74.9%

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

   6. inv-pow 74.9%

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

   7. +-commutative 74.9%

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

   8. *-commutative 74.9%

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

   9. associate-*l/ 74.2%

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

   10. *-commutative 74.2%

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

   11. fma-def 74.2%

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

   12. +-commutative 74.2%

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

   13. *-commutative 74.2%

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

   14. associate-*l/ 75.3%

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

   15. fma-def 75.3%

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

5. Applied egg-rr 75.3%

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

   1. unpow-1 75.3%

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

   2. +-commutative 75.3%

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

7. Simplified 75.3%

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

8. Taylor expanded in y around 0 43.9%

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

9. Taylor expanded in a around 0 21.4%

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

10. Final simplification 21.4%

    \[\leadsto x \]

Developer target: 79.6% 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 2023290 
(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))))