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

Percentage Accurate: 76.4% → 90.1%

Time: 19.6s

Alternatives: 15

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.4% 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: 90.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := y \cdot \frac{\frac{z}{t}}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)} + \frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2
         (+
          (* y (/ (/ z t) (+ 1.0 (fma y (/ b t) a))))
          (/ x (+ (+ a 1.0) (* y (/ b t)))))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 5e+299) t_1 (if (<= t_1 INFINITY) t_2 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = (y * ((z / t) / (1.0 + fma(y, (b / t), a)))) + (x / ((a + 1.0) + (y * (b / t))));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 5e+299) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(Float64(y * Float64(Float64(z / t) / Float64(1.0 + fma(y, Float64(b / t), a)))) + Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t)))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 5e+299)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(z / t), $MachinePrecision] / N[(1.0 + N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 5e+299], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or 5.0000000000000003e299 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 23.0%

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

      1. *-commutative 23.0%

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

      2. associate-*l/ 65.2%

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

      3. *-commutative 65.2%

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

      4. associate-*l/ 65.2%

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

   3. Simplified 65.2%

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

   5. Taylor expanded in x around 0 39.4%

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

      1. +-commutative 39.4%

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

      2. associate-/r* 23.0%

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

      3. associate-*r/ 65.2%

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

      4. associate-+r+ 65.2%

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

      5. associate-*l/ 65.2%

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

      6. *-commutative 65.2%

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

      7. associate-+r+ 65.2%

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

      8. associate-*l/ 65.2%

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

      9. *-commutative 65.2%

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

   7. Simplified 65.2%

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

   8. Taylor expanded in z around 0 39.4%

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

      1. *-commutative 39.4%

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

      2. +-commutative 39.4%

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

      3. +-commutative 39.4%

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

      4. *-commutative 39.4%

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

      5. associate-*r/ 39.4%

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

      6. associate-+r+ 39.4%

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

      7. +-commutative 39.4%

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

      8. fma-udef 39.4%

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

      9. associate-*r/ 82.4%

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

      10. associate-/l/ 82.7%

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

      11. fma-udef 82.7%

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

      12. associate-+r+ 82.7%

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

      13. +-commutative 82.7%

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

      14. associate-+r+ 82.7%

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

      15. fma-def 82.7%

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

   10. Simplified 82.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000003e299

   1. Initial program 91.9%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.2%

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

      3. *-commutative 0.2%

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

      4. associate-*l/ 7.5%

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

   3. Simplified 7.5%

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

   5. Taylor expanded in t around 0 100.0%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)} + \frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)} + \frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+175}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 -2e+175)
     (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b)))))
     (if (<= t_1 5e+299) t_1 (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -2e+175) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= 5e+299) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
    if (t_1 <= (-2d+175)) then
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (y / (t / b))))
    else if (t_1 <= 5d+299) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -2e+175) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= 5e+299) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -2e+175:
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))))
	elif t_1 <= 5e+299:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= -2e+175)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	elseif (t_1 <= 5e+299)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -2e+175)
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	elseif (t_1 <= 5e+299)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+175], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+299], t$95$1, N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.9999999999999999e175

   1. Initial program 54.7%

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

      1. associate-/l* 83.4%

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

      2. associate-+l+ 83.4%

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

      3. associate-/l* 83.4%

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

   3. Simplified 83.4%

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

      1. associate-/r/ 88.7%

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

   6. Applied egg-rr 88.7%

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

   if -1.9999999999999999e175 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000003e299

   1. Initial program 91.6%

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

   if 5.0000000000000003e299 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 8.8%

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

      1. *-commutative 8.8%

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

      2. associate-*l/ 21.7%

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

      3. *-commutative 21.7%

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

      4. associate-*l/ 26.2%

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

   3. Simplified 26.2%

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

   5. Taylor expanded in t around 0 78.1%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{+175}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-43}:\\ \;\;\;\;\frac{t\_1}{a + 1}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+95}:\\ \;\;\;\;\frac{t\_1}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+123}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+145}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ (+ z (/ t (/ y x))) b)))
   (if (<= y -4.5e+23)
     t_2
     (if (<= y 1.35e-43)
       (/ t_1 (+ a 1.0))
       (if (<= y 2.6e+95)
         (/ t_1 (+ 1.0 (/ (* y b) t)))
         (if (<= y 2.2e+123)
           (* (/ y t) (/ z (+ a 1.0)))
           (if (<= y 3e+145) (/ (* y z) (* t a)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = (z + (t / (y / x))) / b;
	double tmp;
	if (y <= -4.5e+23) {
		tmp = t_2;
	} else if (y <= 1.35e-43) {
		tmp = t_1 / (a + 1.0);
	} else if (y <= 2.6e+95) {
		tmp = t_1 / (1.0 + ((y * b) / t));
	} else if (y <= 2.2e+123) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 3e+145) {
		tmp = (y * z) / (t * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    t_2 = (z + (t / (y / x))) / b
    if (y <= (-4.5d+23)) then
        tmp = t_2
    else if (y <= 1.35d-43) then
        tmp = t_1 / (a + 1.0d0)
    else if (y <= 2.6d+95) then
        tmp = t_1 / (1.0d0 + ((y * b) / t))
    else if (y <= 2.2d+123) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= 3d+145) then
        tmp = (y * z) / (t * a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = (z + (t / (y / x))) / b;
	double tmp;
	if (y <= -4.5e+23) {
		tmp = t_2;
	} else if (y <= 1.35e-43) {
		tmp = t_1 / (a + 1.0);
	} else if (y <= 2.6e+95) {
		tmp = t_1 / (1.0 + ((y * b) / t));
	} else if (y <= 2.2e+123) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 3e+145) {
		tmp = (y * z) / (t * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = (z + (t / (y / x))) / b
	tmp = 0
	if y <= -4.5e+23:
		tmp = t_2
	elif y <= 1.35e-43:
		tmp = t_1 / (a + 1.0)
	elif y <= 2.6e+95:
		tmp = t_1 / (1.0 + ((y * b) / t))
	elif y <= 2.2e+123:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= 3e+145:
		tmp = (y * z) / (t * a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(Float64(z + Float64(t / Float64(y / x))) / b)
	tmp = 0.0
	if (y <= -4.5e+23)
		tmp = t_2;
	elseif (y <= 1.35e-43)
		tmp = Float64(t_1 / Float64(a + 1.0));
	elseif (y <= 2.6e+95)
		tmp = Float64(t_1 / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (y <= 2.2e+123)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= 3e+145)
		tmp = Float64(Float64(y * z) / Float64(t * a));
	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);
	t_2 = (z + (t / (y / x))) / b;
	tmp = 0.0;
	if (y <= -4.5e+23)
		tmp = t_2;
	elseif (y <= 1.35e-43)
		tmp = t_1 / (a + 1.0);
	elseif (y <= 2.6e+95)
		tmp = t_1 / (1.0 + ((y * b) / t));
	elseif (y <= 2.2e+123)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= 3e+145)
		tmp = (y * z) / (t * a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -4.5e+23], t$95$2, If[LessEqual[y, 1.35e-43], N[(t$95$1 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+95], N[(t$95$1 / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+123], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+145], N[(N[(y * z), $MachinePrecision] / N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.49999999999999979e23 or 3.0000000000000002e145 < y

   1. Initial program 46.2%

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

      1. *-commutative 46.2%

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

      2. associate-*l/ 55.4%

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

      3. *-commutative 55.4%

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

      4. associate-*l/ 60.5%

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

   3. Simplified 60.5%

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

   5. Taylor expanded in b around inf 31.1%

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

      1. times-frac 38.9%

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

      2. +-commutative 38.9%

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

      3. associate-*r/ 42.0%

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

      4. fma-udef 42.0%

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

   7. Simplified 42.0%

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

   8. Taylor expanded in t around 0 64.2%

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

      1. associate-/r* 64.9%

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

   10. Simplified 64.9%

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

   11. Taylor expanded in b around 0 66.0%

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

       1. associate-/l* 68.2%

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

   13. Simplified 68.2%

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

   if -4.49999999999999979e23 < y < 1.34999999999999996e-43

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-*l/ 88.5%

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

      3. *-commutative 88.5%

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

      4. associate-*l/ 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in b around 0 85.5%

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

   if 1.34999999999999996e-43 < y < 2.5999999999999999e95

   1. Initial program 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-*l/ 81.5%

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

      3. *-commutative 81.5%

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

      4. associate-*l/ 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in a around 0 66.6%

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

   if 2.5999999999999999e95 < y < 2.19999999999999992e123

   1. Initial program 60.3%

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

      1. *-commutative 60.3%

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

      2. associate-*l/ 79.4%

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

      3. *-commutative 79.4%

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

      4. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in x around 0 42.1%

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

      1. associate-/r* 60.3%

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

      2. associate-*r/ 79.4%

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

      3. associate-+r+ 79.4%

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

      4. associate-*l/ 79.4%

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

      5. *-commutative 79.4%

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

   7. Simplified 79.4%

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

   8. Taylor expanded in y around 0 41.6%

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

      1. times-frac 79.8%

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

   10. Simplified 79.8%

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

   if 2.19999999999999992e123 < y < 3.0000000000000002e145

   1. Initial program 42.6%

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

      1. *-commutative 42.6%

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

      2. associate-*l/ 42.6%

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

      3. *-commutative 42.6%

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

      4. associate-*l/ 42.6%

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

   3. Simplified 42.6%

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

   5. Taylor expanded in x around 0 61.2%

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

      1. associate-/r* 42.6%

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

      2. associate-*r/ 42.6%

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

      3. associate-+r+ 42.6%

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

      4. associate-*l/ 42.6%

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

      5. *-commutative 42.6%

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

   7. Simplified 42.6%

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

   8. Taylor expanded in a around inf 80.5%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a \cdot t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-43}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+95}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+123}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+145}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+24} \lor \neg \left(y \leq 1.9 \cdot 10^{+192}\right):\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.45e+24) (not (<= y 1.9e+192)))
   (/ (+ z (/ t (/ y x))) b)
   (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e+24) || !(y <= 1.9e+192)) {
		tmp = (z + (t / (y / x))) / b;
	} else {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.45d+24)) .or. (.not. (y <= 1.9d+192))) then
        tmp = (z + (t / (y / x))) / b
    else
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (y / (t / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e+24) || !(y <= 1.9e+192)) {
		tmp = (z + (t / (y / x))) / b;
	} else {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.45e+24) or not (y <= 1.9e+192):
		tmp = (z + (t / (y / x))) / b
	else:
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.45e+24) || !(y <= 1.9e+192))
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / b);
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.45e+24) || ~((y <= 1.9e+192)))
		tmp = (z + (t / (y / x))) / b;
	else
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.45e+24], N[Not[LessEqual[y, 1.9e+192]], $MachinePrecision]], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4499999999999999e24 or 1.9e192 < y

   1. Initial program 44.6%

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

      1. *-commutative 44.6%

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

      2. associate-*l/ 52.8%

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

      3. *-commutative 52.8%

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

      4. associate-*l/ 57.4%

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

   3. Simplified 57.4%

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

   5. Taylor expanded in b around inf 31.2%

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

      1. times-frac 40.0%

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

      2. +-commutative 40.0%

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

      3. associate-*r/ 43.5%

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

      4. fma-udef 43.5%

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

   7. Simplified 43.5%

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

   8. Taylor expanded in t around 0 66.5%

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

      1. associate-/r* 67.3%

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

   10. Simplified 67.3%

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

   11. Taylor expanded in b around 0 68.5%

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

       1. associate-/l* 71.0%

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

   13. Simplified 71.0%

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

   if -1.4499999999999999e24 < y < 1.9e192

   1. Initial program 89.4%

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

      1. associate-/l* 85.0%

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

      2. associate-+l+ 85.0%

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

      3. associate-/l* 83.3%

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

   3. Simplified 83.3%

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

      1. associate-/r/ 87.7%

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

   6. Applied egg-rr 87.7%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+24} \lor \neg \left(y \leq 1.9 \cdot 10^{+192}\right):\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-150} \lor \neg \left(t \leq 4.2 \cdot 10^{-173}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.6e-150) (not (<= t 4.2e-173)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (+ (/ z b) (/ (* x t) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.6e-150) || !(t <= 4.2e-173)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.6d-150)) .or. (.not. (t <= 4.2d-173))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (z / b) + ((x * t) / (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.6e-150) || !(t <= 4.2e-173)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.6e-150) or not (t <= 4.2e-173):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.6e-150) || !(t <= 4.2e-173))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.6e-150) || ~((t <= 4.2e-173)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.6e-150], N[Not[LessEqual[t, 4.2e-173]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5999999999999999e-150 or 4.20000000000000003e-173 < t

   1. Initial program 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-*l/ 86.1%

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

      3. *-commutative 86.1%

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

      4. associate-*l/ 88.0%

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

   3. Simplified 88.0%

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

   if -1.5999999999999999e-150 < t < 4.20000000000000003e-173

   1. Initial program 52.3%

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

      1. *-commutative 52.3%

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

      2. associate-*l/ 38.4%

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

      3. *-commutative 38.4%

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

      4. associate-*l/ 33.7%

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

   3. Simplified 33.7%

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

   5. Taylor expanded in b around inf 37.3%

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

      1. times-frac 24.7%

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

      2. +-commutative 24.7%

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

      3. associate-*r/ 24.7%

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

      4. fma-udef 24.7%

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

   7. Simplified 24.7%

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

   8. Taylor expanded in t around 0 70.1%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-150} \lor \neg \left(t \leq 4.2 \cdot 10^{-173}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-203} \lor \neg \left(t \leq 2.6 \cdot 10^{-175}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5e-203) (not (<= t 2.6e-175)))
   (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (/ y (/ t b)))))
   (+ (/ z b) (/ (/ (* x t) b) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5e-203) || !(t <= 2.6e-175)) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5d-203)) .or. (.not. (t <= 2.6d-175))) then
        tmp = (x + (y / (t / z))) / (a + (1.0d0 + (y / (t / b))))
    else
        tmp = (z / b) + (((x * t) / b) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5e-203) || !(t <= 2.6e-175)) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5e-203) or not (t <= 2.6e-175):
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))))
	else:
		tmp = (z / b) + (((x * t) / b) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5e-203) || !(t <= 2.6e-175))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(x * t) / b) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5e-203) || ~((t <= 2.6e-175)))
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	else
		tmp = (z / b) + (((x * t) / b) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5e-203], N[Not[LessEqual[t, 2.6e-175]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.0000000000000002e-203 or 2.6e-175 < t

   1. Initial program 81.8%

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

      1. associate-/l* 84.6%

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

      2. associate-+l+ 84.6%

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

      3. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

   if -5.0000000000000002e-203 < t < 2.6e-175

   1. Initial program 45.8%

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

      1. *-commutative 45.8%

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

      2. associate-*l/ 32.1%

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

      3. *-commutative 32.1%

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

      4. associate-*l/ 26.2%

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

   3. Simplified 26.2%

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

   5. Taylor expanded in b around inf 32.7%

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

      1. times-frac 18.8%

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

      2. +-commutative 18.8%

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

      3. associate-*r/ 18.8%

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

      4. fma-udef 18.8%

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

   7. Simplified 18.8%

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

   8. Taylor expanded in t around 0 72.2%

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

      1. associate-/r* 72.2%

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

   10. Simplified 72.2%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-203} \lor \neg \left(t \leq 2.6 \cdot 10^{-175}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-84}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ t (/ y x))) b)))
   (if (<= y -1.05e+22)
     t_1
     (if (<= y -4.6e-84)
       (* (/ y t) (/ z (+ a 1.0)))
       (if (<= y 4.5e+23) (/ x (+ 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 = (z + (t / (y / x))) / b;
	double tmp;
	if (y <= -1.05e+22) {
		tmp = t_1;
	} else if (y <= -4.6e-84) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 4.5e+23) {
		tmp = x / (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 = (z + (t / (y / x))) / b
    if (y <= (-1.05d+22)) then
        tmp = t_1
    else if (y <= (-4.6d-84)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= 4.5d+23) then
        tmp = x / (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 = (z + (t / (y / x))) / b;
	double tmp;
	if (y <= -1.05e+22) {
		tmp = t_1;
	} else if (y <= -4.6e-84) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 4.5e+23) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (t / (y / x))) / b
	tmp = 0
	if y <= -1.05e+22:
		tmp = t_1
	elif y <= -4.6e-84:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= 4.5e+23:
		tmp = x / (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(z + Float64(t / Float64(y / x))) / b)
	tmp = 0.0
	if (y <= -1.05e+22)
		tmp = t_1;
	elseif (y <= -4.6e-84)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= 4.5e+23)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = t_1;
	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 <= -1.05e+22)
		tmp = t_1;
	elseif (y <= -4.6e-84)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= 4.5e+23)
		tmp = x / (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[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -1.05e+22], t$95$1, If[LessEqual[y, -4.6e-84], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+23], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0499999999999999e22 or 4.49999999999999979e23 < y

   1. Initial program 49.0%

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

      1. *-commutative 49.0%

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

      2. associate-*l/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*l/ 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in b around inf 32.9%

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

      1. times-frac 38.3%

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

      2. +-commutative 38.3%

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

      3. associate-*r/ 40.8%

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

      4. fma-udef 40.9%

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

   7. Simplified 40.9%

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

   8. Taylor expanded in t around 0 60.9%

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

      1. associate-/r* 62.2%

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

   10. Simplified 62.2%

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

   11. Taylor expanded in b around 0 63.3%

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

       1. associate-/l* 65.0%

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

   13. Simplified 65.0%

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

   if -1.0499999999999999e22 < y < -4.59999999999999961e-84

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*l/ 91.0%

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

      3. *-commutative 91.0%

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

      4. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around 0 59.1%

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

      1. associate-/r* 63.2%

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

      2. associate-*r/ 63.2%

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

      3. associate-+r+ 63.2%

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

      4. associate-*l/ 63.2%

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

      5. *-commutative 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in y around 0 59.1%

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

      1. times-frac 67.6%

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

   10. Simplified 67.6%

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

   if -4.59999999999999961e-84 < y < 4.49999999999999979e23

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      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/ 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in x around inf 76.5%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+22}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-84}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-98}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ t (/ y x))) b)))
   (if (<= y -9e+20)
     t_1
     (if (<= y -1.35e-98)
       (* (/ y t) (/ z (+ a 1.0)))
       (if (<= y 4.1e+21) (/ x (+ a 1.0)) t_1)))))

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 <= -9e+20) {
		tmp = t_1;
	} else if (y <= -1.35e-98) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 4.1e+21) {
		tmp = x / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + (t / (y / x))) / b
    if (y <= (-9d+20)) then
        tmp = t_1
    else if (y <= (-1.35d-98)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= 4.1d+21) then
        tmp = x / (a + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t / (y / x))) / b;
	double tmp;
	if (y <= -9e+20) {
		tmp = t_1;
	} else if (y <= -1.35e-98) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 4.1e+21) {
		tmp = x / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (t / (y / x))) / b
	tmp = 0
	if y <= -9e+20:
		tmp = t_1
	elif y <= -1.35e-98:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= 4.1e+21:
		tmp = x / (a + 1.0)
	else:
		tmp = t_1
	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 <= -9e+20)
		tmp = t_1;
	elseif (y <= -1.35e-98)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= 4.1e+21)
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (t / (y / x))) / b;
	tmp = 0.0;
	if (y <= -9e+20)
		tmp = t_1;
	elseif (y <= -1.35e-98)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= 4.1e+21)
		tmp = x / (a + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -9e+20], t$95$1, If[LessEqual[y, -1.35e-98], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+21], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9e20 or 4.1e21 < y

   1. Initial program 49.0%

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

      1. *-commutative 49.0%

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

      2. associate-*l/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*l/ 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in b around inf 32.9%

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

      1. times-frac 38.3%

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

      2. +-commutative 38.3%

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

      3. associate-*r/ 40.8%

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

      4. fma-udef 40.9%

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

   7. Simplified 40.9%

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

   8. Taylor expanded in t around 0 60.9%

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

      1. associate-/r* 62.2%

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

   10. Simplified 62.2%

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

   11. Taylor expanded in b around 0 63.3%

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

       1. associate-/l* 65.0%

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

   13. Simplified 65.0%

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

   if -9e20 < y < -1.3499999999999999e-98

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*l/ 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*l/ 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in x around 0 58.5%

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

      1. associate-/r* 62.3%

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

      2. associate-*r/ 58.5%

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

      3. associate-+r+ 58.5%

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

      4. associate-*l/ 58.5%

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

      5. *-commutative 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in y around 0 58.4%

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

      1. times-frac 66.2%

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

   10. Simplified 66.2%

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

   if -1.3499999999999999e-98 < y < 4.1e21

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. associate-*l/ 88.1%

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

      3. *-commutative 88.1%

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

      4. associate-*l/ 84.7%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around inf 69.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+20}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-98}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.2e+19)
   (/ z b)
   (if (<= y -9e-163)
     (/ x a)
     (if (<= y -6e-300) x (if (<= y 3.2e+21) (/ x a) (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.2e+19) {
		tmp = z / b;
	} else if (y <= -9e-163) {
		tmp = x / a;
	} else if (y <= -6e-300) {
		tmp = x;
	} else if (y <= 3.2e+21) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7.2d+19)) then
        tmp = z / b
    else if (y <= (-9d-163)) then
        tmp = x / a
    else if (y <= (-6d-300)) then
        tmp = x
    else if (y <= 3.2d+21) then
        tmp = x / a
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.2e+19) {
		tmp = z / b;
	} else if (y <= -9e-163) {
		tmp = x / a;
	} else if (y <= -6e-300) {
		tmp = x;
	} else if (y <= 3.2e+21) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.2e+19:
		tmp = z / b
	elif y <= -9e-163:
		tmp = x / a
	elif y <= -6e-300:
		tmp = x
	elif y <= 3.2e+21:
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.2e+19)
		tmp = Float64(z / b);
	elseif (y <= -9e-163)
		tmp = Float64(x / a);
	elseif (y <= -6e-300)
		tmp = x;
	elseif (y <= 3.2e+21)
		tmp = Float64(x / a);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.2e+19)
		tmp = z / b;
	elseif (y <= -9e-163)
		tmp = x / a;
	elseif (y <= -6e-300)
		tmp = x;
	elseif (y <= 3.2e+21)
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.2e+19], N[(z / b), $MachinePrecision], If[LessEqual[y, -9e-163], N[(x / a), $MachinePrecision], If[LessEqual[y, -6e-300], x, If[LessEqual[y, 3.2e+21], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.2e19 or 3.2e21 < y

   1. Initial program 49.0%

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

      1. *-commutative 49.0%

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

      2. associate-*l/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*l/ 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in t around 0 57.8%

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

   if -7.2e19 < y < -8.9999999999999995e-163 or -6.00000000000000048e-300 < y < 3.2e21

   1. Initial program 97.0%

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

      1. *-commutative 97.0%

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

      2. associate-*l/ 87.8%

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

      3. *-commutative 87.8%

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

      4. associate-*l/ 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in x around inf 66.1%

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

   6. Taylor expanded in a around inf 43.7%

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

   if -8.9999999999999995e-163 < y < -6.00000000000000048e-300

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      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/ 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in x around inf 69.7%

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

   6. Taylor expanded in a around 0 48.1%

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

   7. Taylor expanded in b around 0 42.8%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+23} \lor \neg \left(y \leq 9.5 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.15e+23) (not (<= y 9.5e+27)))
   (/ (+ z (/ t (/ y x))) b)
   (/ (+ x (/ (* y z) t)) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e+23) || !(y <= 9.5e+27)) {
		tmp = (z + (t / (y / x))) / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.15d+23)) .or. (.not. (y <= 9.5d+27))) then
        tmp = (z + (t / (y / x))) / b
    else
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e+23) || !(y <= 9.5e+27)) {
		tmp = (z + (t / (y / x))) / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.15e+23) or not (y <= 9.5e+27):
		tmp = (z + (t / (y / x))) / b
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.15e+23) || !(y <= 9.5e+27))
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / b);
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.15e+23) || ~((y <= 9.5e+27)))
		tmp = (z + (t / (y / x))) / b;
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.15e+23], N[Not[LessEqual[y, 9.5e+27]], $MachinePrecision]], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e23 or 9.4999999999999997e27 < y

   1. Initial program 49.0%

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

      1. *-commutative 49.0%

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

      2. associate-*l/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*l/ 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in b around inf 32.9%

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

      1. times-frac 38.3%

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

      2. +-commutative 38.3%

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

      3. associate-*r/ 40.8%

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

      4. fma-udef 40.9%

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

   7. Simplified 40.9%

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

   8. Taylor expanded in t around 0 60.9%

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

      1. associate-/r* 62.2%

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

   10. Simplified 62.2%

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

   11. Taylor expanded in b around 0 63.3%

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

       1. associate-/l* 65.0%

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

   13. Simplified 65.0%

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

   if -1.15e23 < y < 9.4999999999999997e27

   1. Initial program 97.1%

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

      1. *-commutative 97.1%

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

      2. associate-*l/ 88.1%

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

      3. *-commutative 88.1%

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

      4. associate-*l/ 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in b around 0 83.9%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+23} \lor \neg \left(y \leq 9.5 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-97}:\\ \;\;\;\;z \cdot \frac{y}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.5e+23)
   (/ z b)
   (if (<= y -2.25e-97)
     (* z (/ y (* t (+ a 1.0))))
     (if (<= y 5.6e+22) (/ 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 <= -9.5e+23) {
		tmp = z / b;
	} else if (y <= -2.25e-97) {
		tmp = z * (y / (t * (a + 1.0)));
	} else if (y <= 5.6e+22) {
		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 <= (-9.5d+23)) then
        tmp = z / b
    else if (y <= (-2.25d-97)) then
        tmp = z * (y / (t * (a + 1.0d0)))
    else if (y <= 5.6d+22) 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 <= -9.5e+23) {
		tmp = z / b;
	} else if (y <= -2.25e-97) {
		tmp = z * (y / (t * (a + 1.0)));
	} else if (y <= 5.6e+22) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.5e+23:
		tmp = z / b
	elif y <= -2.25e-97:
		tmp = z * (y / (t * (a + 1.0)))
	elif y <= 5.6e+22:
		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 <= -9.5e+23)
		tmp = Float64(z / b);
	elseif (y <= -2.25e-97)
		tmp = Float64(z * Float64(y / Float64(t * Float64(a + 1.0))));
	elseif (y <= 5.6e+22)
		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 <= -9.5e+23)
		tmp = z / b;
	elseif (y <= -2.25e-97)
		tmp = z * (y / (t * (a + 1.0)));
	elseif (y <= 5.6e+22)
		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, -9.5e+23], N[(z / b), $MachinePrecision], If[LessEqual[y, -2.25e-97], N[(z * N[(y / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+22], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000038e23 or 5.6e22 < y

   1. Initial program 49.0%

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

      1. *-commutative 49.0%

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

      2. associate-*l/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*l/ 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in t around 0 57.8%

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

   if -9.50000000000000038e23 < y < -2.25000000000000005e-97

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*l/ 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*l/ 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in x around 0 58.5%

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

      1. associate-/r* 62.3%

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

      2. associate-*r/ 58.5%

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

      3. associate-+r+ 58.5%

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

      4. associate-*l/ 58.5%

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

      5. *-commutative 58.5%

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

   7. Simplified 58.5%

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

      1. associate-*r/ 58.5%

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

   9. Applied egg-rr 58.5%

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

   10. Taylor expanded in y around 0 58.4%

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

       1. *-commutative 58.4%

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

       2. associate-*r/ 58.5%

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

   12. Simplified 58.5%

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

   if -2.25000000000000005e-97 < y < 5.6e22

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. associate-*l/ 88.1%

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

      3. *-commutative 88.1%

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

      4. associate-*l/ 84.7%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around inf 69.3%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-97}:\\ \;\;\;\;z \cdot \frac{y}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-98}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.7e+21)
   (/ z b)
   (if (<= y -3.5e-98)
     (* (/ y t) (/ z (+ a 1.0)))
     (if (<= y 5.8e+23) (/ 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 <= -2.7e+21) {
		tmp = z / b;
	} else if (y <= -3.5e-98) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 5.8e+23) {
		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 <= (-2.7d+21)) then
        tmp = z / b
    else if (y <= (-3.5d-98)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (y <= 5.8d+23) 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 <= -2.7e+21) {
		tmp = z / b;
	} else if (y <= -3.5e-98) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (y <= 5.8e+23) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.7e+21:
		tmp = z / b
	elif y <= -3.5e-98:
		tmp = (y / t) * (z / (a + 1.0))
	elif y <= 5.8e+23:
		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 <= -2.7e+21)
		tmp = Float64(z / b);
	elseif (y <= -3.5e-98)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (y <= 5.8e+23)
		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 <= -2.7e+21)
		tmp = z / b;
	elseif (y <= -3.5e-98)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (y <= 5.8e+23)
		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, -2.7e+21], N[(z / b), $MachinePrecision], If[LessEqual[y, -3.5e-98], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+23], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e21 or 5.80000000000000025e23 < y

   1. Initial program 49.0%

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

      1. *-commutative 49.0%

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

      2. associate-*l/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*l/ 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in t around 0 57.8%

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

   if -2.7e21 < y < -3.5000000000000002e-98

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*l/ 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*l/ 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in x around 0 58.5%

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

      1. associate-/r* 62.3%

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

      2. associate-*r/ 58.5%

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

      3. associate-+r+ 58.5%

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

      4. associate-*l/ 58.5%

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

      5. *-commutative 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in y around 0 58.4%

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

      1. times-frac 66.2%

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

   10. Simplified 66.2%

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

   if -3.5000000000000002e-98 < y < 5.80000000000000025e23

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. associate-*l/ 88.1%

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

      3. *-commutative 88.1%

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

      4. associate-*l/ 84.7%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around inf 69.3%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-98}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+22} \lor \neg \left(y \leq 3 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.9e+22) (not (<= y 3e+27))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.9e+22) || !(y <= 3e+27)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.9d+22)) .or. (.not. (y <= 3d+27))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.9e+22) || !(y <= 3e+27)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.9e+22) or not (y <= 3e+27):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.9e+22) || !(y <= 3e+27))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.9e+22) || ~((y <= 3e+27)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.9e+22], N[Not[LessEqual[y, 3e+27]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e22 or 2.99999999999999976e27 < y

   1. Initial program 49.0%

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

      1. *-commutative 49.0%

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

      2. associate-*l/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*l/ 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in t around 0 57.8%

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

   if -2.9e22 < y < 2.99999999999999976e27

   1. Initial program 97.1%

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

      1. *-commutative 97.1%

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

      2. associate-*l/ 88.1%

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

      3. *-commutative 88.1%

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

      4. associate-*l/ 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in t around inf 62.1%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+22} \lor \neg \left(y \leq 3 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-8} \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.45e-8) (not (<= a 1.0))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.45e-8) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.45d-8)) .or. (.not. (a <= 1.0d0))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.45e-8) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.45e-8) or not (a <= 1.0):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.45e-8) || !(a <= 1.0))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.45e-8) || ~((a <= 1.0)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.45e-8], N[Not[LessEqual[a, 1.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -2.4500000000000001e-8 or 1 < a

   1. Initial program 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-*l/ 72.4%

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

      3. *-commutative 72.4%

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

      4. associate-*l/ 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in x around inf 54.3%

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

   6. Taylor expanded in a around inf 47.7%

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

   if -2.4500000000000001e-8 < a < 1

   1. Initial program 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*l/ 77.2%

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

      3. *-commutative 77.2%

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

      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. Add Preprocessing

   5. Taylor expanded in x around inf 49.9%

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

   6. Taylor expanded in a around 0 51.9%

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

   7. Taylor expanded in b around 0 36.1%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-8} \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 20.0% 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 74.9%

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

   1. *-commutative 74.9%

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

   2. associate-*l/ 74.5%

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

   3. *-commutative 74.5%

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

   4. associate-*l/ 74.9%

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

3. Simplified 74.9%

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

5. Taylor expanded in x around inf 52.3%

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

6. Taylor expanded in a around 0 30.9%

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

7. Taylor expanded in b around 0 18.5%

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

8. Final simplification 18.5%

   \[\leadsto x \]
9. Add Preprocessing

Developer target: 79.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))
   (if (< t -1.3659085366310088e-271)
     t_1
     (if (< t 3.036967103737246e-130) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 * ((x + ((y / t) * z)) * (1.0d0 / ((a + 1.0d0) + ((y / t) * b))))
    if (t < (-1.3659085366310088d-271)) then
        tmp = t_1
    else if (t < 3.036967103737246d-130) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))))
	tmp = 0
	if t < -1.3659085366310088e-271:
		tmp = t_1
	elif t < 3.036967103737246e-130:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 * Float64(Float64(x + Float64(Float64(y / t) * z)) * Float64(1.0 / Float64(Float64(a + 1.0) + Float64(Float64(y / t) * b)))))
	tmp = 0.0
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	tmp = 0.0;
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 * N[(N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.3659085366310088e-271], t$95$1, If[Less[t, 3.036967103737246e-130], N[(z / b), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024029 
(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))))