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

Percentage Accurate: 75.7% → 91.2%

Time: 18.5s

Alternatives: 16

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.7% 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: 91.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t + t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a\right)}{z}}\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-316}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x}{b} - \frac{z}{b \cdot b}}{\frac{y}{t}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 (- INFINITY))
     (/ y (/ (+ t (* t (fma y (/ b t) a))) z))
     (if (<= t_1 -4e-316)
       t_1
       (if (<= t_1 0.0)
         (+ (/ z b) (/ (- (/ x b) (/ z (* b b))) (/ y t)))
         (if (<= t_1 2e+306) 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 <= -((double) INFINITY)) {
		tmp = y / ((t + (t * fma(y, (b / t), a))) / z);
	} else if (t_1 <= -4e-316) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + (((x / b) - (z / (b * b))) / (y / t));
	} else if (t_1 <= 2e+306) {
		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 <= Float64(-Inf))
		tmp = Float64(y / Float64(Float64(t + Float64(t * fma(y, Float64(b / t), a))) / z));
	elseif (t_1 <= -4e-316)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(x / b) - Float64(z / Float64(b * b))) / Float64(y / t)));
	elseif (t_1 <= 2e+306)
		tmp = t_1;
	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]}, If[LessEqual[t$95$1, (-Infinity)], N[(y / N[(N[(t + N[(t * N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e-316], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(x / b), $MachinePrecision] - N[(z / N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+306], t$95$1, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 24.4%

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

      1. *-commutative 24.4%

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

      2. associate-*l/ 54.0%

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

      3. *-commutative 54.0%

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

      4. associate-*l/ 53.5%

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

   3. Simplified 53.5%

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

   4. Taylor expanded in x around 0 61.0%

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

      1. associate-/l* 79.6%

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

      2. distribute-rgt-in 79.6%

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

      3. *-lft-identity 79.6%

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

      4. associate-*r/ 70.4%

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

      5. fma-def 70.4%

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

   6. Simplified 70.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -3.999999984e-316 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 99.7%

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

   if -3.999999984e-316 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-/l* 48.2%

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

      3. associate-*l/ 62.3%

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

      4. *-commutative 62.3%

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

      5. cancel-sign-sub 62.3%

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

      6. *-commutative 62.3%

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

      7. associate-*l/ 48.2%

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

      8. associate-+r- 48.2%

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

      9. associate-*l/ 62.3%

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

      10. *-commutative 62.3%

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

      11. cancel-sign-sub 62.3%

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

      12. *-commutative 62.3%

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

      13. associate-/r/ 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in a around 0 33.3%

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

   5. Taylor expanded in t around 0 62.1%

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

      1. *-commutative 62.1%

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

      2. associate-/r* 73.8%

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

      3. unpow2 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in y around -inf 78.0%

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

      1. mul-1-neg 78.0%

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

      2. associate-/l* 77.3%

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

      3. distribute-lft-out-- 77.3%

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

      4. unpow2 77.3%

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

   10. Simplified 77.3%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 10.4%

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

      1. *-commutative 10.4%

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

      2. associate-*l/ 14.9%

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

      3. *-commutative 14.9%

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

      4. associate-*l/ 25.7%

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

   3. Simplified 25.7%

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

   4. Taylor expanded in t around 0 88.9%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t + t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -4 \cdot 10^{-316}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x}{b} - \frac{z}{b \cdot b}}{\frac{y}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2: 88.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-316}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{z}{b} + t \cdot \left(\frac{\frac{x}{y}}{b} - \frac{z}{y \cdot \left(b \cdot b\right)}\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 -4e-316)
     t_1
     (if (<= t_1 0.0)
       (+ (/ z b) (* t (- (/ (/ x y) b) (/ z (* y (* b b))))))
       (if (<= t_1 2e+306) 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 <= -4e-316) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + (t * (((x / y) / b) - (z / (y * (b * b)))));
	} else if (t_1 <= 2e+306) {
		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 <= (-4d-316)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = (z / b) + (t * (((x / y) / b) - (z / (y * (b * b)))))
    else if (t_1 <= 2d+306) 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 <= -4e-316) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + (t * (((x / y) / b) - (z / (y * (b * b)))));
	} else if (t_1 <= 2e+306) {
		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 <= -4e-316:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (z / b) + (t * (((x / y) / b) - (z / (y * (b * b)))))
	elif t_1 <= 2e+306:
		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 <= -4e-316)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(Float64(x / y) / b) - Float64(z / Float64(y * Float64(b * b))))));
	elseif (t_1 <= 2e+306)
		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 <= -4e-316)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (z / b) + (t * (((x / y) / b) - (z / (y * (b * b)))));
	elseif (t_1 <= 2e+306)
		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, -4e-316], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(N[(x / y), $MachinePrecision] / b), $MachinePrecision] - N[(z / N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+306], 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))) < -3.999999984e-316 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 95.3%

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

   if -3.999999984e-316 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-/l* 48.2%

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

      3. associate-*l/ 62.3%

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

      4. *-commutative 62.3%

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

      5. cancel-sign-sub 62.3%

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

      6. *-commutative 62.3%

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

      7. associate-*l/ 48.2%

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

      8. associate-+r- 48.2%

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

      9. associate-*l/ 62.3%

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

      10. *-commutative 62.3%

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

      11. cancel-sign-sub 62.3%

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

      12. *-commutative 62.3%

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

      13. associate-/r/ 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in a around 0 33.3%

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

   5. Taylor expanded in t around 0 62.1%

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

      1. *-commutative 62.1%

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

      2. associate-/r* 73.8%

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

      3. unpow2 73.8%

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

   7. Simplified 73.8%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 10.4%

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

      1. *-commutative 10.4%

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

      2. associate-*l/ 14.9%

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

      3. *-commutative 14.9%

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

      4. associate-*l/ 25.7%

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

   3. Simplified 25.7%

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

   4. Taylor expanded in t around 0 88.9%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -4 \cdot 10^{-316}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + t \cdot \left(\frac{\frac{x}{y}}{b} - \frac{z}{y \cdot \left(b \cdot b\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3: 88.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-316}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x}{b} - \frac{z}{b \cdot b}}{\frac{y}{t}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 -4e-316)
     t_1
     (if (<= t_1 0.0)
       (+ (/ z b) (/ (- (/ x b) (/ z (* b b))) (/ y t)))
       (if (<= t_1 2e+306) 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 <= -4e-316) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + (((x / b) - (z / (b * b))) / (y / t));
	} else if (t_1 <= 2e+306) {
		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 <= (-4d-316)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = (z / b) + (((x / b) - (z / (b * b))) / (y / t))
    else if (t_1 <= 2d+306) 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 <= -4e-316) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + (((x / b) - (z / (b * b))) / (y / t));
	} else if (t_1 <= 2e+306) {
		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 <= -4e-316:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (z / b) + (((x / b) - (z / (b * b))) / (y / t))
	elif t_1 <= 2e+306:
		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 <= -4e-316)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(x / b) - Float64(z / Float64(b * b))) / Float64(y / t)));
	elseif (t_1 <= 2e+306)
		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 <= -4e-316)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (z / b) + (((x / b) - (z / (b * b))) / (y / t));
	elseif (t_1 <= 2e+306)
		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, -4e-316], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(x / b), $MachinePrecision] - N[(z / N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+306], 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))) < -3.999999984e-316 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 95.3%

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

   if -3.999999984e-316 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-/l* 48.2%

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

      3. associate-*l/ 62.3%

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

      4. *-commutative 62.3%

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

      5. cancel-sign-sub 62.3%

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

      6. *-commutative 62.3%

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

      7. associate-*l/ 48.2%

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

      8. associate-+r- 48.2%

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

      9. associate-*l/ 62.3%

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

      10. *-commutative 62.3%

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

      11. cancel-sign-sub 62.3%

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

      12. *-commutative 62.3%

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

      13. associate-/r/ 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in a around 0 33.3%

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

   5. Taylor expanded in t around 0 62.1%

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

      1. *-commutative 62.1%

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

      2. associate-/r* 73.8%

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

      3. unpow2 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in y around -inf 78.0%

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

      1. mul-1-neg 78.0%

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

      2. associate-/l* 77.3%

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

      3. distribute-lft-out-- 77.3%

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

      4. unpow2 77.3%

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

   10. Simplified 77.3%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 10.4%

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

      1. *-commutative 10.4%

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

      2. associate-*l/ 14.9%

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

      3. *-commutative 14.9%

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

      4. associate-*l/ 25.7%

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

   3. Simplified 25.7%

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

   4. Taylor expanded in t around 0 88.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -4 \cdot 10^{-316}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x}{b} - \frac{z}{b \cdot b}}{\frac{y}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 4: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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+306) 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+306) {
		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+306) 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+306) {
		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+306:
		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+306)
		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+306)
		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+306], t$95$1, N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 86.8%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 10.4%

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

      1. *-commutative 10.4%

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

      2. associate-*l/ 14.9%

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

      3. *-commutative 14.9%

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

      4. associate-*l/ 25.7%

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

   3. Simplified 25.7%

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

   4. Taylor expanded in t around 0 88.9%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 5: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-164} \lor \neg \left(t \leq 2.1 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.5e-164) (not (<= t 2.1e-95)))
   (/ (+ 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 <= -3.5e-164) || !(t <= 2.1e-95)) {
		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 <= (-3.5d-164)) .or. (.not. (t <= 2.1d-95))) 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 <= -3.5e-164) || !(t <= 2.1e-95)) {
		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 <= -3.5e-164) or not (t <= 2.1e-95):
		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 <= -3.5e-164) || !(t <= 2.1e-95))
		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 <= -3.5e-164) || ~((t <= 2.1e-95)))
		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, -3.5e-164], N[Not[LessEqual[t, 2.1e-95]], $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 < -3.5e-164 or 2.1e-95 < t

   1. Initial program 83.7%

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

      1. *-commutative 83.7%

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

      2. associate-*l/ 84.9%

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

      3. *-commutative 84.9%

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

      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%

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

   if -3.5e-164 < t < 2.1e-95

   1. Initial program 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-*l/ 44.3%

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

      3. *-commutative 44.3%

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

      4. associate-*l/ 39.6%

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

   3. Simplified 39.6%

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

   4. Taylor expanded in b around inf 44.5%

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

      1. associate-/l* 41.9%

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

      2. associate-*r/ 38.3%

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

      3. *-commutative 38.3%

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

      4. associate-*l/ 41.9%

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

      5. associate-*r/ 31.5%

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

      6. fma-udef 31.5%

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

   6. Simplified 31.5%

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

   7. Taylor expanded in t around 0 72.6%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-164} \lor \neg \left(t \leq 2.1 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 6: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-166} \lor \neg \left(t \leq 1.45 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(\frac{y}{\frac{t}{b}} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3e-166) (not (<= t 1.45e-125)))
   (/ (+ x (/ z (/ t y))) (+ a (+ (/ y (/ t b)) 1.0)))
   (+ (/ 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 <= -3e-166) || !(t <= 1.45e-125)) {
		tmp = (x + (z / (t / y))) / (a + ((y / (t / b)) + 1.0));
	} 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 <= (-3d-166)) .or. (.not. (t <= 1.45d-125))) then
        tmp = (x + (z / (t / y))) / (a + ((y / (t / b)) + 1.0d0))
    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 <= -3e-166) || !(t <= 1.45e-125)) {
		tmp = (x + (z / (t / y))) / (a + ((y / (t / b)) + 1.0));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3e-166) or not (t <= 1.45e-125):
		tmp = (x + (z / (t / y))) / (a + ((y / (t / b)) + 1.0))
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3e-166) || !(t <= 1.45e-125))
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + Float64(Float64(y / Float64(t / b)) + 1.0)));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3e-166) || ~((t <= 1.45e-125)))
		tmp = (x + (z / (t / y))) / (a + ((y / (t / b)) + 1.0));
	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, -3e-166], N[Not[LessEqual[t, 1.45e-125]], $MachinePrecision]], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.0000000000000003e-166 or 1.4500000000000001e-125 < t

   1. Initial program 83.4%

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

      1. *-commutative 83.4%

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

      2. associate-/l* 85.6%

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

      3. associate-*l/ 90.8%

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

      4. *-commutative 90.8%

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

      5. cancel-sign-sub 90.8%

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

      6. *-commutative 90.8%

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

      7. associate-*l/ 85.6%

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

      8. associate-+r- 85.6%

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

      9. associate-*l/ 90.8%

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

      10. *-commutative 90.8%

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

      11. cancel-sign-sub 90.8%

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

      12. *-commutative 90.8%

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

      13. associate-/r/ 90.3%

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

   3. Simplified 90.3%

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

   if -3.0000000000000003e-166 < t < 1.4500000000000001e-125

   1. Initial program 48.3%

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

      1. *-commutative 48.3%

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

      2. associate-*l/ 42.8%

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

      3. *-commutative 42.8%

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

      4. associate-*l/ 38.9%

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

   3. Simplified 38.9%

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

   4. Taylor expanded in b around inf 47.1%

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

      1. associate-/l* 44.1%

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

      2. associate-*r/ 41.4%

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

      3. *-commutative 41.4%

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

      4. associate-*l/ 44.1%

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

      5. associate-*r/ 33.8%

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

      6. fma-udef 33.8%

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

   6. Simplified 33.8%

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

   7. Taylor expanded in t around 0 75.9%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-166} \lor \neg \left(t \leq 1.45 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(\frac{y}{\frac{t}{b}} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 7: 58.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+65}:\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) \cdot \frac{1}{a}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-11} \lor \neg \left(t \leq 1.05 \cdot 10^{-103}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -6.2e+145)
     t_1
     (if (<= t -6.8e+65)
       (* (+ x (* y (/ z t))) (/ 1.0 a))
       (if (or (<= t -1.15e-11) (not (<= t 1.05e-103)))
         t_1
         (+ (/ z b) (/ (* x t) (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -6.2e+145) {
		tmp = t_1;
	} else if (t <= -6.8e+65) {
		tmp = (x + (y * (z / t))) * (1.0 / a);
	} else if ((t <= -1.15e-11) || !(t <= 1.05e-103)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-6.2d+145)) then
        tmp = t_1
    else if (t <= (-6.8d+65)) then
        tmp = (x + (y * (z / t))) * (1.0d0 / a)
    else if ((t <= (-1.15d-11)) .or. (.not. (t <= 1.05d-103))) then
        tmp = t_1
    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 t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -6.2e+145) {
		tmp = t_1;
	} else if (t <= -6.8e+65) {
		tmp = (x + (y * (z / t))) * (1.0 / a);
	} else if ((t <= -1.15e-11) || !(t <= 1.05e-103)) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -6.2e+145:
		tmp = t_1
	elif t <= -6.8e+65:
		tmp = (x + (y * (z / t))) * (1.0 / a)
	elif (t <= -1.15e-11) or not (t <= 1.05e-103):
		tmp = t_1
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -6.2e+145)
		tmp = t_1;
	elseif (t <= -6.8e+65)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) * Float64(1.0 / a));
	elseif ((t <= -1.15e-11) || !(t <= 1.05e-103))
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -6.2e+145)
		tmp = t_1;
	elseif (t <= -6.8e+65)
		tmp = (x + (y * (z / t))) * (1.0 / a);
	elseif ((t <= -1.15e-11) || ~((t <= 1.05e-103)))
		tmp = t_1;
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+145], t$95$1, If[LessEqual[t, -6.8e+65], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.15e-11], N[Not[LessEqual[t, 1.05e-103]], $MachinePrecision]], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.19999999999999977e145 or -6.7999999999999999e65 < t < -1.15000000000000007e-11 or 1.05000000000000002e-103 < t

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-*l/ 85.0%

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

      3. *-commutative 85.0%

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

      4. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in t around inf 63.6%

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

   if -6.19999999999999977e145 < t < -6.7999999999999999e65

   1. Initial program 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-*l/ 87.0%

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

      3. *-commutative 87.0%

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

      4. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

      1. associate-*l/ 74.4%

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

      2. *-commutative 74.4%

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

      3. associate-/l* 87.0%

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

      4. clear-num 87.1%

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

   5. Applied egg-rr 87.1%

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

      1. div-inv 86.8%

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

      2. associate-/r/ 87.0%

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

      3. clear-num 87.1%

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

      4. associate-+l+ 87.1%

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

      5. *-commutative 87.1%

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

   7. Applied egg-rr 87.1%

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

   8. Taylor expanded in a around inf 62.0%

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

   if -1.15000000000000007e-11 < t < 1.05000000000000002e-103

   1. Initial program 58.3%

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

      1. *-commutative 58.3%

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

      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/ 50.1%

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

   3. Simplified 50.1%

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

   4. Taylor expanded in b around inf 45.5%

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

      1. associate-/l* 43.4%

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

      2. associate-*r/ 41.5%

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

      3. *-commutative 41.5%

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

      4. associate-*l/ 43.4%

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

      5. associate-*r/ 34.3%

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

      6. fma-udef 34.3%

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

   6. Simplified 34.3%

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

   7. Taylor expanded in t around 0 70.2%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+65}:\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) \cdot \frac{1}{a}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-11} \lor \neg \left(t \leq 1.05 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 8: 63.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{+61}:\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) \cdot \frac{1}{a}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-14} \lor \neg \left(t \leq 1.5 \cdot 10^{-112}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -6.2e+145)
     t_1
     (if (<= t -3.15e+61)
       (* (+ x (* y (/ z t))) (/ 1.0 a))
       (if (or (<= t -6e-14) (not (<= t 1.5e-112)))
         t_1
         (+ (/ z b) (/ (* x t) (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -6.2e+145) {
		tmp = t_1;
	} else if (t <= -3.15e+61) {
		tmp = (x + (y * (z / t))) * (1.0 / a);
	} else if ((t <= -6e-14) || !(t <= 1.5e-112)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((a + 1.0d0) + (y * (b / t)))
    if (t <= (-6.2d+145)) then
        tmp = t_1
    else if (t <= (-3.15d+61)) then
        tmp = (x + (y * (z / t))) * (1.0d0 / a)
    else if ((t <= (-6d-14)) .or. (.not. (t <= 1.5d-112))) then
        tmp = t_1
    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 t_1 = x / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -6.2e+145) {
		tmp = t_1;
	} else if (t <= -3.15e+61) {
		tmp = (x + (y * (z / t))) * (1.0 / a);
	} else if ((t <= -6e-14) || !(t <= 1.5e-112)) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a + 1.0) + (y * (b / t)))
	tmp = 0
	if t <= -6.2e+145:
		tmp = t_1
	elif t <= -3.15e+61:
		tmp = (x + (y * (z / t))) * (1.0 / a)
	elif (t <= -6e-14) or not (t <= 1.5e-112):
		tmp = t_1
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -6.2e+145)
		tmp = t_1;
	elseif (t <= -3.15e+61)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) * Float64(1.0 / a));
	elseif ((t <= -6e-14) || !(t <= 1.5e-112))
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / ((a + 1.0) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -6.2e+145)
		tmp = t_1;
	elseif (t <= -3.15e+61)
		tmp = (x + (y * (z / t))) * (1.0 / a);
	elseif ((t <= -6e-14) || ~((t <= 1.5e-112)))
		tmp = t_1;
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+145], t$95$1, If[LessEqual[t, -3.15e+61], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -6e-14], N[Not[LessEqual[t, 1.5e-112]], $MachinePrecision]], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.19999999999999977e145 or -3.14999999999999988e61 < t < -5.9999999999999997e-14 or 1.5e-112 < t

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*l/ 85.1%

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

      3. *-commutative 85.1%

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

      4. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in x around inf 70.9%

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

   if -6.19999999999999977e145 < t < -3.14999999999999988e61

   1. Initial program 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-*l/ 87.0%

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

      3. *-commutative 87.0%

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

      4. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

      1. associate-*l/ 74.4%

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

      2. *-commutative 74.4%

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

      3. associate-/l* 87.0%

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

      4. clear-num 87.1%

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

   5. Applied egg-rr 87.1%

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

      1. div-inv 86.8%

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

      2. associate-/r/ 87.0%

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

      3. clear-num 87.1%

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

      4. associate-+l+ 87.1%

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

      5. *-commutative 87.1%

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

   7. Applied egg-rr 87.1%

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

   8. Taylor expanded in a around inf 62.0%

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

   if -5.9999999999999997e-14 < t < 1.5e-112

   1. Initial program 57.9%

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

      1. *-commutative 57.9%

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

      2. associate-*l/ 52.3%

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

      3. *-commutative 52.3%

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

      4. associate-*l/ 49.6%

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

   3. Simplified 49.6%

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

   4. Taylor expanded in b around inf 45.0%

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

      1. associate-/l* 42.8%

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

      2. associate-*r/ 41.0%

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

      3. *-commutative 41.0%

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

      4. associate-*l/ 42.8%

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

      5. associate-*r/ 34.7%

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

      6. fma-udef 34.7%

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

   6. Simplified 34.7%

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

   7. Taylor expanded in t around 0 69.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{+61}:\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) \cdot \frac{1}{a}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-14} \lor \neg \left(t \leq 1.5 \cdot 10^{-112}\right):\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 9: 66.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{t}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+126}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + t_1}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+65}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \left(t_1 + 1\right)}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-71} \lor \neg \left(t \leq 5 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (/ b t))))
   (if (<= t -2.7e+126)
     (/ x (+ (+ a 1.0) t_1))
     (if (<= t -1.7e+65)
       (* (/ y t) (/ z (+ a (+ t_1 1.0))))
       (if (or (<= t -2.4e-71) (not (<= t 5e-105)))
         (/ (+ x (/ (* y z) t)) (+ a 1.0))
         (+ (/ z b) (/ (* x t) (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / t);
	double tmp;
	if (t <= -2.7e+126) {
		tmp = x / ((a + 1.0) + t_1);
	} else if (t <= -1.7e+65) {
		tmp = (y / t) * (z / (a + (t_1 + 1.0)));
	} else if ((t <= -2.4e-71) || !(t <= 5e-105)) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (b / t)
    if (t <= (-2.7d+126)) then
        tmp = x / ((a + 1.0d0) + t_1)
    else if (t <= (-1.7d+65)) then
        tmp = (y / t) * (z / (a + (t_1 + 1.0d0)))
    else if ((t <= (-2.4d-71)) .or. (.not. (t <= 5d-105))) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    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 t_1 = y * (b / t);
	double tmp;
	if (t <= -2.7e+126) {
		tmp = x / ((a + 1.0) + t_1);
	} else if (t <= -1.7e+65) {
		tmp = (y / t) * (z / (a + (t_1 + 1.0)));
	} else if ((t <= -2.4e-71) || !(t <= 5e-105)) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b / t)
	tmp = 0
	if t <= -2.7e+126:
		tmp = x / ((a + 1.0) + t_1)
	elif t <= -1.7e+65:
		tmp = (y / t) * (z / (a + (t_1 + 1.0)))
	elif (t <= -2.4e-71) or not (t <= 5e-105):
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b / t))
	tmp = 0.0
	if (t <= -2.7e+126)
		tmp = Float64(x / Float64(Float64(a + 1.0) + t_1));
	elseif (t <= -1.7e+65)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + Float64(t_1 + 1.0))));
	elseif ((t <= -2.4e-71) || !(t <= 5e-105))
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b / t);
	tmp = 0.0;
	if (t <= -2.7e+126)
		tmp = x / ((a + 1.0) + t_1);
	elseif (t <= -1.7e+65)
		tmp = (y / t) * (z / (a + (t_1 + 1.0)));
	elseif ((t <= -2.4e-71) || ~((t <= 5e-105)))
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+126], N[(x / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e+65], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + N[(t$95$1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.4e-71], N[Not[LessEqual[t, 5e-105]], $MachinePrecision]], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.70000000000000002e126

   1. Initial program 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-*l/ 84.4%

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

      3. *-commutative 84.4%

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

      4. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around inf 81.0%

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

   if -2.70000000000000002e126 < t < -1.7e65

   1. Initial program 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-*l/ 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*l/ 82.5%

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

   3. Simplified 82.5%

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

      1. associate-*l/ 65.1%

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

      2. *-commutative 65.1%

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

      3. associate-/l* 82.3%

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

      4. clear-num 82.5%

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

   5. Applied egg-rr 82.5%

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

   6. Taylor expanded in x around 0 56.0%

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

      1. times-frac 81.8%

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

      2. associate-+r+ 81.8%

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

      3. associate-*r/ 90.7%

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

      4. +-commutative 90.7%

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

   8. Simplified 90.7%

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

   if -1.7e65 < t < -2.4e-71 or 4.99999999999999963e-105 < t

   1. Initial program 87.8%

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

      1. *-commutative 87.8%

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

      2. associate-*l/ 85.5%

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

      3. *-commutative 85.5%

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

      4. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in b around 0 79.1%

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

   if -2.4e-71 < t < 4.99999999999999963e-105

   1. Initial program 54.1%

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

      1. *-commutative 54.1%

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

      2. associate-*l/ 48.8%

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

      3. *-commutative 48.8%

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

      4. associate-*l/ 45.8%

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

   3. Simplified 45.8%

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

   4. Taylor expanded in b around inf 48.0%

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

      1. associate-/l* 45.6%

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

      2. associate-*r/ 43.5%

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

      3. *-commutative 43.5%

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

      4. associate-*l/ 45.6%

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

      5. associate-*r/ 35.4%

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

      6. fma-udef 35.4%

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

   6. Simplified 35.4%

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

   7. Taylor expanded in t around 0 74.7%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+126}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+65}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \left(y \cdot \frac{b}{t} + 1\right)}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-71} \lor \neg \left(t \leq 5 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 10: 67.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+181}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-71} \lor \neg \left(t \leq 5.5 \cdot 10^{-109}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.45e+181)
   (/ x (+ (+ a 1.0) (* y (/ b t))))
   (if (or (<= t -2.8e-71) (not (<= t 5.5e-109)))
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (+ (/ z b) (/ (* x t) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.45e+181) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if ((t <= -2.8e-71) || !(t <= 5.5e-109)) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} 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 <= (-1.45d+181)) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    else if ((t <= (-2.8d-71)) .or. (.not. (t <= 5.5d-109))) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    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 <= -1.45e+181) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if ((t <= -2.8e-71) || !(t <= 5.5e-109)) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.45e+181:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	elif (t <= -2.8e-71) or not (t <= 5.5e-109):
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.45e+181)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif ((t <= -2.8e-71) || !(t <= 5.5e-109))
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.45e+181)
		tmp = x / ((a + 1.0) + (y * (b / t)));
	elseif ((t <= -2.8e-71) || ~((t <= 5.5e-109)))
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.45e+181], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.8e-71], N[Not[LessEqual[t, 5.5e-109]], $MachinePrecision]], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.45e181

   1. Initial program 65.8%

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

      1. *-commutative 65.8%

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

      2. associate-*l/ 75.8%

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

      3. *-commutative 75.8%

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

      4. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in x around inf 76.8%

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

   if -1.45e181 < t < -2.8e-71 or 5.5000000000000003e-109 < t

   1. Initial program 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-*l/ 86.4%

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

      3. *-commutative 86.4%

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

      4. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in b around 0 77.6%

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

   if -2.8e-71 < t < 5.5000000000000003e-109

   1. Initial program 54.1%

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

      1. *-commutative 54.1%

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

      2. associate-*l/ 48.8%

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

      3. *-commutative 48.8%

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

      4. associate-*l/ 45.8%

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

   3. Simplified 45.8%

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

   4. Taylor expanded in b around inf 48.0%

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

      1. associate-/l* 45.6%

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

      2. associate-*r/ 43.5%

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

      3. *-commutative 43.5%

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

      4. associate-*l/ 45.6%

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

      5. associate-*r/ 35.4%

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

      6. fma-udef 35.4%

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

   6. Simplified 35.4%

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

   7. Taylor expanded in t around 0 74.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+181}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-71} \lor \neg \left(t \leq 5.5 \cdot 10^{-109}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 11: 54.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+65}:\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) \cdot \frac{1}{a}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-12} \lor \neg \left(t \leq 1.05 \cdot 10^{-103}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -6.2e+145)
     t_1
     (if (<= t -2.2e+65)
       (* (+ x (* y (/ z t))) (/ 1.0 a))
       (if (or (<= t -4.5e-12) (not (<= t 1.05e-103))) t_1 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -6.2e+145) {
		tmp = t_1;
	} else if (t <= -2.2e+65) {
		tmp = (x + (y * (z / t))) * (1.0 / a);
	} else if ((t <= -4.5e-12) || !(t <= 1.05e-103)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-6.2d+145)) then
        tmp = t_1
    else if (t <= (-2.2d+65)) then
        tmp = (x + (y * (z / t))) * (1.0d0 / a)
    else if ((t <= (-4.5d-12)) .or. (.not. (t <= 1.05d-103))) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -6.2e+145) {
		tmp = t_1;
	} else if (t <= -2.2e+65) {
		tmp = (x + (y * (z / t))) * (1.0 / a);
	} else if ((t <= -4.5e-12) || !(t <= 1.05e-103)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -6.2e+145:
		tmp = t_1
	elif t <= -2.2e+65:
		tmp = (x + (y * (z / t))) * (1.0 / a)
	elif (t <= -4.5e-12) or not (t <= 1.05e-103):
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -6.2e+145)
		tmp = t_1;
	elseif (t <= -2.2e+65)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) * Float64(1.0 / a));
	elseif ((t <= -4.5e-12) || !(t <= 1.05e-103))
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -6.2e+145)
		tmp = t_1;
	elseif (t <= -2.2e+65)
		tmp = (x + (y * (z / t))) * (1.0 / a);
	elseif ((t <= -4.5e-12) || ~((t <= 1.05e-103)))
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+145], t$95$1, If[LessEqual[t, -2.2e+65], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -4.5e-12], N[Not[LessEqual[t, 1.05e-103]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.19999999999999977e145 or -2.1999999999999998e65 < t < -4.49999999999999981e-12 or 1.05000000000000002e-103 < t

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-*l/ 85.0%

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

      3. *-commutative 85.0%

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

      4. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in t around inf 63.6%

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

   if -6.19999999999999977e145 < t < -2.1999999999999998e65

   1. Initial program 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-*l/ 87.0%

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

      3. *-commutative 87.0%

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

      4. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

      1. associate-*l/ 74.4%

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

      2. *-commutative 74.4%

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

      3. associate-/l* 87.0%

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

      4. clear-num 87.1%

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

   5. Applied egg-rr 87.1%

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

      1. div-inv 86.8%

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

      2. associate-/r/ 87.0%

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

      3. clear-num 87.1%

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

      4. associate-+l+ 87.1%

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

      5. *-commutative 87.1%

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

   7. Applied egg-rr 87.1%

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

   8. Taylor expanded in a around inf 62.0%

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

   if -4.49999999999999981e-12 < t < 1.05000000000000002e-103

   1. Initial program 58.3%

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

      1. *-commutative 58.3%

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

      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/ 50.1%

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

   3. Simplified 50.1%

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

   4. Taylor expanded in t around 0 60.3%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+65}:\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) \cdot \frac{1}{a}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-12} \lor \neg \left(t \leq 1.05 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 12: 53.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+123} \lor \neg \left(t \leq -4.6 \cdot 10^{+66} \lor \neg \left(t \leq -4.4 \cdot 10^{-14}\right) \land t \leq 1.05 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.9e+123)
         (not
          (or (<= t -4.6e+66) (and (not (<= t -4.4e-14)) (<= t 1.05e-103)))))
   (/ x (+ a 1.0))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.9e+123) || !((t <= -4.6e+66) || (!(t <= -4.4e-14) && (t <= 1.05e-103)))) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.9d+123)) .or. (.not. (t <= (-4.6d+66)) .or. (.not. (t <= (-4.4d-14))) .and. (t <= 1.05d-103))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.9e+123) || !((t <= -4.6e+66) || (!(t <= -4.4e-14) && (t <= 1.05e-103)))) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.9e+123) or not ((t <= -4.6e+66) or (not (t <= -4.4e-14) and (t <= 1.05e-103))):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.9e+123) || !((t <= -4.6e+66) || (!(t <= -4.4e-14) && (t <= 1.05e-103))))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.9e+123) || ~(((t <= -4.6e+66) || (~((t <= -4.4e-14)) && (t <= 1.05e-103)))))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.9e+123], N[Not[Or[LessEqual[t, -4.6e+66], And[N[Not[LessEqual[t, -4.4e-14]], $MachinePrecision], LessEqual[t, 1.05e-103]]]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9000000000000001e123 or -4.6e66 < t < -4.4000000000000002e-14 or 1.05000000000000002e-103 < t

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-*l/ 85.4%

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

      3. *-commutative 85.4%

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

      4. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in t around inf 64.6%

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

   if -2.9000000000000001e123 < t < -4.6e66 or -4.4000000000000002e-14 < t < 1.05000000000000002e-103

   1. Initial program 59.0%

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

      1. *-commutative 59.0%

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

      2. associate-*l/ 55.6%

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

      3. *-commutative 55.6%

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

      4. associate-*l/ 53.1%

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

   3. Simplified 53.1%

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

   4. Taylor expanded in t around 0 59.0%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+123} \lor \neg \left(t \leq -4.6 \cdot 10^{+66} \lor \neg \left(t \leq -4.4 \cdot 10^{-14}\right) \land t \leq 1.05 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 13: 54.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+62}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-12} \lor \neg \left(t \leq 10^{-103}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -2.05e+149)
     t_1
     (if (<= t -1.4e+62)
       (/ (+ x (* y (/ z t))) a)
       (if (or (<= t -3.1e-12) (not (<= t 1e-103))) t_1 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -2.05e+149) {
		tmp = t_1;
	} else if (t <= -1.4e+62) {
		tmp = (x + (y * (z / t))) / a;
	} else if ((t <= -3.1e-12) || !(t <= 1e-103)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-2.05d+149)) then
        tmp = t_1
    else if (t <= (-1.4d+62)) then
        tmp = (x + (y * (z / t))) / a
    else if ((t <= (-3.1d-12)) .or. (.not. (t <= 1d-103))) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -2.05e+149) {
		tmp = t_1;
	} else if (t <= -1.4e+62) {
		tmp = (x + (y * (z / t))) / a;
	} else if ((t <= -3.1e-12) || !(t <= 1e-103)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -2.05e+149:
		tmp = t_1
	elif t <= -1.4e+62:
		tmp = (x + (y * (z / t))) / a
	elif (t <= -3.1e-12) or not (t <= 1e-103):
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -2.05e+149)
		tmp = t_1;
	elseif (t <= -1.4e+62)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	elseif ((t <= -3.1e-12) || !(t <= 1e-103))
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -2.05e+149)
		tmp = t_1;
	elseif (t <= -1.4e+62)
		tmp = (x + (y * (z / t))) / a;
	elseif ((t <= -3.1e-12) || ~((t <= 1e-103)))
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.05e+149], t$95$1, If[LessEqual[t, -1.4e+62], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[Or[LessEqual[t, -3.1e-12], N[Not[LessEqual[t, 1e-103]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0499999999999998e149 or -1.40000000000000007e62 < t < -3.1000000000000001e-12 or 9.99999999999999958e-104 < t

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-*l/ 84.9%

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

      3. *-commutative 84.9%

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

      4. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in t around inf 63.3%

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

   if -2.0499999999999998e149 < t < -1.40000000000000007e62

   1. Initial program 75.9%

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

      1. *-commutative 75.9%

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

      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/ 87.9%

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

   3. Simplified 87.9%

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

      1. associate-*l/ 76.0%

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

      2. *-commutative 76.0%

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

      3. associate-/l* 87.8%

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

      4. clear-num 87.9%

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

   5. Applied egg-rr 87.9%

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

   6. Taylor expanded in a around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. associate-*r/ 64.3%

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

   8. Simplified 64.3%

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

   if -3.1000000000000001e-12 < t < 9.99999999999999958e-104

   1. Initial program 58.3%

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

      1. *-commutative 58.3%

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

      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/ 50.1%

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

   3. Simplified 50.1%

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

   4. Taylor expanded in t around 0 60.3%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+149}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+62}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-12} \lor \neg \left(t \leq 10^{-103}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 14: 41.0% accurate, 2.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if a < -1 or 1 < a

   1. Initial program 77.2%

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

      1. *-commutative 77.2%

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

      2. associate-/l* 77.7%

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

      3. associate-*l/ 80.4%

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

      4. *-commutative 80.4%

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

      5. cancel-sign-sub 80.4%

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

      6. *-commutative 80.4%

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

      7. associate-*l/ 77.7%

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

      8. associate-+r- 77.7%

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

      9. associate-*l/ 80.4%

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

      10. *-commutative 80.4%

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

      11. cancel-sign-sub 80.4%

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

      12. *-commutative 80.4%

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

      13. associate-/r/ 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in x around inf 52.7%

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

   5. Taylor expanded in a around inf 44.8%

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

   if -1 < a < 1

   1. Initial program 69.2%

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

      1. *-commutative 69.2%

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

      2. associate-/l* 68.5%

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

      3. associate-*l/ 72.3%

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

      4. *-commutative 72.3%

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

      5. cancel-sign-sub 72.3%

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

      6. *-commutative 72.3%

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

      7. associate-*l/ 68.5%

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

      8. associate-+r- 68.5%

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

      9. associate-*l/ 72.3%

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

      10. *-commutative 72.3%

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

      11. cancel-sign-sub 72.3%

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

      12. *-commutative 72.3%

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

      13. associate-/r/ 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in x around inf 45.9%

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

   5. Taylor expanded in a around 0 44.5%

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

   6. Taylor expanded in y around 0 36.8%

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

4. Final simplification 40.9%

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

Alternative 15: 40.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.3e+123) (/ x a) (if (<= t 2.7e-95) (/ z b) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.3e+123) {
		tmp = x / a;
	} else if (t <= 2.7e-95) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.3d+123)) then
        tmp = x / a
    else if (t <= 2.7d-95) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.3e+123) {
		tmp = x / a;
	} else if (t <= 2.7e-95) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.3e+123:
		tmp = x / a
	elif t <= 2.7e-95:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.3e+123)
		tmp = Float64(x / a);
	elseif (t <= 2.7e-95)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.3e+123)
		tmp = x / a;
	elseif (t <= 2.7e-95)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.3e+123], N[(x / a), $MachinePrecision], If[LessEqual[t, 2.7e-95], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.30000000000000003e123 or 2.7e-95 < t

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-/l* 88.3%

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

      3. associate-*l/ 95.7%

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

      4. *-commutative 95.7%

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

      5. cancel-sign-sub 95.7%

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

      6. *-commutative 95.7%

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

      7. associate-*l/ 88.3%

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

      8. associate-+r- 88.3%

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

      9. associate-*l/ 95.7%

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

      10. *-commutative 95.7%

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

      11. cancel-sign-sub 95.7%

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

      12. *-commutative 95.7%

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

      13. associate-/r/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around inf 69.5%

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

   5. Taylor expanded in a around inf 39.5%

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

   if -3.30000000000000003e123 < t < 2.7e-95

   1. Initial program 62.5%

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

      1. *-commutative 62.5%

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

      2. associate-*l/ 58.3%

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

      3. *-commutative 58.3%

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

      4. associate-*l/ 56.3%

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

   3. Simplified 56.3%

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

   4. Taylor expanded in t around 0 53.8%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 16: 19.6% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.4%

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

   1. *-commutative 73.4%

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

   2. associate-/l* 73.3%

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

   3. associate-*l/ 76.5%

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

   4. *-commutative 76.5%

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

   5. cancel-sign-sub 76.5%

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

   6. *-commutative 76.5%

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

   7. associate-*l/ 73.3%

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

   8. associate-+r- 73.3%

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

   9. associate-*l/ 76.5%

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

   10. *-commutative 76.5%

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

   11. cancel-sign-sub 76.5%

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

   12. *-commutative 76.5%

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

   13. associate-/r/ 75.2%

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

3. Simplified 75.2%

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

4. Taylor expanded in x around inf 49.4%

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

5. Taylor expanded in a around 0 29.2%

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

6. Taylor expanded in y around 0 19.6%

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

7. Final simplification 19.6%

   \[\leadsto x \]

Developer target: 78.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(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))))