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

Percentage Accurate: 75.1% → 87.2%

Time: 13.5s

Alternatives: 15

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.2% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 44.3%

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

      1. *-commutative 44.3%

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

      2. associate-/l* 66.0%

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

      3. associate-*l/ 46.1%

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

   3. Simplified 46.1%

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

      1. clear-num 46.0%

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

      2. inv-pow 46.0%

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

      3. +-commutative 46.0%

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

      4. fma-def 46.0%

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

      5. +-commutative 46.0%

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

      6. div-inv 46.1%

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

      7. clear-num 46.1%

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

      8. fma-def 46.1%

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

   5. Applied egg-rr 46.1%

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

      1. unpow-1 46.1%

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

      2. +-commutative 46.1%

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

   7. Simplified 46.1%

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

   8. Taylor expanded in y around -inf 81.9%

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

      1. mul-1-neg 81.9%

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

      2. distribute-lft-out-- 77.4%

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

      3. associate-/l* 77.4%

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

      4. associate-*r* 77.4%

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

      5. unpow2 77.4%

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

   10. Simplified 77.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.9999999999999999e284

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 90.5%

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

      3. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

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

   1. Initial program 27.2%

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

      1. *-commutative 27.2%

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

      2. associate-/l* 32.4%

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

      3. associate-*l/ 29.6%

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

   3. Simplified 29.6%

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

   4. Taylor expanded in t around 0 89.7%

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

4. Final simplification 90.3%

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

Alternative 2: 86.4% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 44.3%

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

      1. *-commutative 44.3%

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

      2. associate-/l* 66.0%

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

      3. associate-*l/ 46.1%

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

   3. Simplified 46.1%

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

      1. clear-num 46.0%

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

      2. inv-pow 46.0%

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

      3. +-commutative 46.0%

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

      4. fma-def 46.0%

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

      5. +-commutative 46.0%

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

      6. div-inv 46.1%

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

      7. clear-num 46.1%

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

      8. fma-def 46.1%

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

   5. Applied egg-rr 46.1%

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

      1. unpow-1 46.1%

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

      2. +-commutative 46.1%

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

   7. Simplified 46.1%

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

   8. Taylor expanded in z around inf 65.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.9999999999999999e284

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 90.5%

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

      3. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

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

   1. Initial program 27.2%

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

      1. *-commutative 27.2%

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

      2. associate-/l* 32.4%

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

      3. associate-*l/ 29.6%

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

   3. Simplified 29.6%

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

   4. Taylor expanded in t around 0 89.7%

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

4. Final simplification 89.3%

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

Alternative 3: 79.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-218}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-273}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + 1}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-154}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* b (/ y t))))))
   (if (<= t -3.3e-159)
     t_1
     (if (<= t -4.3e-218)
       (/ z b)
       (if (<= t -1.35e-273)
         (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) 1.0))
         (if (<= t 4.8e-154) (/ z b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((a + 1.0) + (b * (y / t)));
	double tmp;
	if (t <= -3.3e-159) {
		tmp = t_1;
	} else if (t <= -4.3e-218) {
		tmp = z / b;
	} else if (t <= -1.35e-273) {
		tmp = (x + ((y * z) / t)) / (((y * b) / t) + 1.0);
	} else if (t <= 4.8e-154) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / ((a + 1.0d0) + (b * (y / t)))
    if (t <= (-3.3d-159)) then
        tmp = t_1
    else if (t <= (-4.3d-218)) then
        tmp = z / b
    else if (t <= (-1.35d-273)) then
        tmp = (x + ((y * z) / t)) / (((y * b) / t) + 1.0d0)
    else if (t <= 4.8d-154) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((a + 1.0) + (b * (y / t)));
	double tmp;
	if (t <= -3.3e-159) {
		tmp = t_1;
	} else if (t <= -4.3e-218) {
		tmp = z / b;
	} else if (t <= -1.35e-273) {
		tmp = (x + ((y * z) / t)) / (((y * b) / t) + 1.0);
	} else if (t <= 4.8e-154) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (b * (y / t)))
	tmp = 0
	if t <= -3.3e-159:
		tmp = t_1
	elif t <= -4.3e-218:
		tmp = z / b
	elif t <= -1.35e-273:
		tmp = (x + ((y * z) / t)) / (((y * b) / t) + 1.0)
	elif t <= 4.8e-154:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))))
	tmp = 0.0
	if (t <= -3.3e-159)
		tmp = t_1;
	elseif (t <= -4.3e-218)
		tmp = Float64(z / b);
	elseif (t <= -1.35e-273)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + 1.0));
	elseif (t <= 4.8e-154)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (b * (y / t)));
	tmp = 0.0;
	if (t <= -3.3e-159)
		tmp = t_1;
	elseif (t <= -4.3e-218)
		tmp = z / b;
	elseif (t <= -1.35e-273)
		tmp = (x + ((y * z) / t)) / (((y * b) / t) + 1.0);
	elseif (t <= 4.8e-154)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e-159], t$95$1, If[LessEqual[t, -4.3e-218], N[(z / b), $MachinePrecision], If[LessEqual[t, -1.35e-273], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-154], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3000000000000002e-159 or 4.79999999999999974e-154 < t

   1. Initial program 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-/l* 86.5%

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

      3. associate-*l/ 88.0%

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

   3. Simplified 88.0%

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

      1. associate-/r/ 85.3%

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

   5. Applied egg-rr 85.3%

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

   if -3.3000000000000002e-159 < t < -4.3e-218 or -1.34999999999999992e-273 < t < 4.79999999999999974e-154

   1. Initial program 57.1%

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

      1. *-commutative 57.1%

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

      2. associate-/l* 55.5%

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

      3. associate-*l/ 46.4%

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

   3. Simplified 46.4%

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

   4. Taylor expanded in t around 0 75.5%

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

   if -4.3e-218 < t < -1.34999999999999992e-273

   1. Initial program 89.6%

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

      1. +-commutative 89.6%

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

      2. associate-*l/ 96.8%

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

      3. fma-def 96.8%

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

      4. associate-+l+ 96.8%

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

      5. +-commutative 96.8%

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

      6. associate-*l/ 96.5%

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

      7. fma-def 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in a around 0 75.8%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-159}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-218}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-273}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + 1}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-154}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 4: 55.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+266}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+159}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.9e+266)
   (/ (* y z) (* t (+ a 1.0)))
   (if (<= z -1.7e+212)
     (/ z b)
     (if (<= z -3.1e+159)
       (/ (+ x (/ (* y z) t)) a)
       (if (<= z 4e+42) (/ x (+ (+ a (/ (* y b) t)) 1.0)) (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.9e+266) {
		tmp = (y * z) / (t * (a + 1.0));
	} else if (z <= -1.7e+212) {
		tmp = z / b;
	} else if (z <= -3.1e+159) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (z <= 4e+42) {
		tmp = x / ((a + ((y * b) / t)) + 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 (z <= (-4.9d+266)) then
        tmp = (y * z) / (t * (a + 1.0d0))
    else if (z <= (-1.7d+212)) then
        tmp = z / b
    else if (z <= (-3.1d+159)) then
        tmp = (x + ((y * z) / t)) / a
    else if (z <= 4d+42) then
        tmp = x / ((a + ((y * b) / t)) + 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 (z <= -4.9e+266) {
		tmp = (y * z) / (t * (a + 1.0));
	} else if (z <= -1.7e+212) {
		tmp = z / b;
	} else if (z <= -3.1e+159) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (z <= 4e+42) {
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.9e+266:
		tmp = (y * z) / (t * (a + 1.0))
	elif z <= -1.7e+212:
		tmp = z / b
	elif z <= -3.1e+159:
		tmp = (x + ((y * z) / t)) / a
	elif z <= 4e+42:
		tmp = x / ((a + ((y * b) / t)) + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.9e+266)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(a + 1.0)));
	elseif (z <= -1.7e+212)
		tmp = Float64(z / b);
	elseif (z <= -3.1e+159)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	elseif (z <= 4e+42)
		tmp = Float64(x / Float64(Float64(a + Float64(Float64(y * b) / t)) + 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 (z <= -4.9e+266)
		tmp = (y * z) / (t * (a + 1.0));
	elseif (z <= -1.7e+212)
		tmp = z / b;
	elseif (z <= -3.1e+159)
		tmp = (x + ((y * z) / t)) / a;
	elseif (z <= 4e+42)
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.9e+266], N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e+212], N[(z / b), $MachinePrecision], If[LessEqual[z, -3.1e+159], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 4e+42], N[(x / N[(N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.9000000000000002e266

   1. Initial program 76.3%

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

      1. *-commutative 76.3%

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

      2. associate-/l* 76.3%

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

      3. associate-*l/ 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in b around 0 76.3%

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

   5. Taylor expanded in y around inf 75.8%

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

   if -4.9000000000000002e266 < z < -1.70000000000000018e212 or 4.00000000000000018e42 < z

   1. Initial program 59.2%

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

      1. *-commutative 59.2%

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

      2. associate-/l* 64.2%

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

      3. associate-*l/ 61.2%

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

   3. Simplified 61.2%

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

   4. Taylor expanded in t around 0 56.5%

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

   if -1.70000000000000018e212 < z < -3.0999999999999998e159

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 100.0%

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

      3. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around inf 67.4%

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

   if -3.0999999999999998e159 < z < 4.00000000000000018e42

   1. Initial program 85.2%

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

      1. *-commutative 85.2%

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

      2. associate-/l* 86.2%

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

      3. associate-*l/ 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in x around inf 70.3%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+266}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+159}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 5: 69.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{-15}:\\ \;\;\;\;\left(x + \frac{z}{\frac{t}{y}}\right) \cdot \frac{1}{a + 1}\\ \mathbf{elif}\;a \leq 1750:\\ \;\;\;\;\frac{t_1}{\frac{y \cdot b}{t} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))))
   (if (<= a -6.2e-15)
     (* (+ x (/ z (/ t y))) (/ 1.0 (+ a 1.0)))
     (if (<= a 1750.0) (/ t_1 (+ (/ (* y b) t) 1.0)) (/ t_1 (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if (a <= -6.2e-15) {
		tmp = (x + (z / (t / y))) * (1.0 / (a + 1.0));
	} else if (a <= 1750.0) {
		tmp = t_1 / (((y * b) / t) + 1.0);
	} else {
		tmp = t_1 / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    if (a <= (-6.2d-15)) then
        tmp = (x + (z / (t / y))) * (1.0d0 / (a + 1.0d0))
    else if (a <= 1750.0d0) then
        tmp = t_1 / (((y * b) / t) + 1.0d0)
    else
        tmp = t_1 / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if (a <= -6.2e-15) {
		tmp = (x + (z / (t / y))) * (1.0 / (a + 1.0));
	} else if (a <= 1750.0) {
		tmp = t_1 / (((y * b) / t) + 1.0);
	} else {
		tmp = t_1 / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	tmp = 0
	if a <= -6.2e-15:
		tmp = (x + (z / (t / y))) * (1.0 / (a + 1.0))
	elif a <= 1750.0:
		tmp = t_1 / (((y * b) / t) + 1.0)
	else:
		tmp = t_1 / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (a <= -6.2e-15)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) * Float64(1.0 / Float64(a + 1.0)));
	elseif (a <= 1750.0)
		tmp = Float64(t_1 / Float64(Float64(Float64(y * b) / t) + 1.0));
	else
		tmp = Float64(t_1 / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	tmp = 0.0;
	if (a <= -6.2e-15)
		tmp = (x + (z / (t / y))) * (1.0 / (a + 1.0));
	elseif (a <= 1750.0)
		tmp = t_1 / (((y * b) / t) + 1.0);
	else
		tmp = t_1 / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e-15], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1750.0], N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.1999999999999998e-15

   1. Initial program 71.1%

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

      1. associate-/l* 68.6%

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

   3. Simplified 68.6%

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

      1. div-inv 68.5%

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

      2. associate-/l* 71.4%

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

      3. associate-/r/ 70.9%

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

      4. +-commutative 70.9%

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

      5. fma-def 70.9%

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

   5. Applied egg-rr 70.9%

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

   6. Taylor expanded in y around 0 65.5%

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

      1. associate-/r/ 67.2%

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

   8. Applied egg-rr 67.2%

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

      1. *-commutative 67.2%

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

      2. clear-num 67.2%

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

      3. un-div-inv 67.2%

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

   10. Applied egg-rr 67.2%

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

   if -6.1999999999999998e-15 < a < 1750

   1. Initial program 81.5%

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

      1. +-commutative 81.5%

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

      2. associate-*l/ 83.1%

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

      3. fma-def 83.1%

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

      4. associate-+l+ 83.1%

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

      5. +-commutative 83.1%

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

      6. associate-*l/ 83.0%

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

      7. fma-def 83.0%

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

   3. Simplified 83.0%

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

   4. Taylor expanded in a around 0 81.0%

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

   if 1750 < a

   1. Initial program 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-/l* 76.8%

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

      3. associate-*l/ 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in b around 0 69.2%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-15}:\\ \;\;\;\;\left(x + \frac{z}{\frac{t}{y}}\right) \cdot \frac{1}{a + 1}\\ \mathbf{elif}\;a \leq 1750:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]

Alternative 6: 54.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-62} \lor \neg \left(t \leq 1.5 \cdot 10^{-107} \lor \neg \left(t \leq 2.8 \cdot 10^{-76}\right) \land t \leq 13.5\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -3.8e+23)
     t_1
     (if (<= t -3.8e-53)
       (* (/ y t) (/ z a))
       (if (or (<= t -1.62e-62)
               (not
                (or (<= t 1.5e-107) (and (not (<= t 2.8e-76)) (<= t 13.5)))))
         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 <= -3.8e+23) {
		tmp = t_1;
	} else if (t <= -3.8e-53) {
		tmp = (y / t) * (z / a);
	} else if ((t <= -1.62e-62) || !((t <= 1.5e-107) || (!(t <= 2.8e-76) && (t <= 13.5)))) {
		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 <= (-3.8d+23)) then
        tmp = t_1
    else if (t <= (-3.8d-53)) then
        tmp = (y / t) * (z / a)
    else if ((t <= (-1.62d-62)) .or. (.not. (t <= 1.5d-107) .or. (.not. (t <= 2.8d-76)) .and. (t <= 13.5d0))) 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 <= -3.8e+23) {
		tmp = t_1;
	} else if (t <= -3.8e-53) {
		tmp = (y / t) * (z / a);
	} else if ((t <= -1.62e-62) || !((t <= 1.5e-107) || (!(t <= 2.8e-76) && (t <= 13.5)))) {
		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 <= -3.8e+23:
		tmp = t_1
	elif t <= -3.8e-53:
		tmp = (y / t) * (z / a)
	elif (t <= -1.62e-62) or not ((t <= 1.5e-107) or (not (t <= 2.8e-76) and (t <= 13.5))):
		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 <= -3.8e+23)
		tmp = t_1;
	elseif (t <= -3.8e-53)
		tmp = Float64(Float64(y / t) * Float64(z / a));
	elseif ((t <= -1.62e-62) || !((t <= 1.5e-107) || (!(t <= 2.8e-76) && (t <= 13.5))))
		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 <= -3.8e+23)
		tmp = t_1;
	elseif (t <= -3.8e-53)
		tmp = (y / t) * (z / a);
	elseif ((t <= -1.62e-62) || ~(((t <= 1.5e-107) || (~((t <= 2.8e-76)) && (t <= 13.5)))))
		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, -3.8e+23], t$95$1, If[LessEqual[t, -3.8e-53], N[(N[(y / t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.62e-62], N[Not[Or[LessEqual[t, 1.5e-107], And[N[Not[LessEqual[t, 2.8e-76]], $MachinePrecision], LessEqual[t, 13.5]]]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.79999999999999975e23 or -3.7999999999999998e-53 < t < -1.6199999999999999e-62 or 1.4999999999999999e-107 < t < 2.8000000000000001e-76 or 13.5 < t

   1. Initial program 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-/l* 90.1%

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

      3. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in t around inf 68.6%

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

   if -3.79999999999999975e23 < t < -3.7999999999999998e-53

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

      2. associate-/l* 85.3%

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

      3. associate-*l/ 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in a around inf 47.1%

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

   5. Taylor expanded in y around inf 42.2%

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

      1. *-commutative 42.2%

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

      2. times-frac 41.8%

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

   7. Simplified 41.8%

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

   if -1.6199999999999999e-62 < t < 1.4999999999999999e-107 or 2.8000000000000001e-76 < t < 13.5

   1. Initial program 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-/l* 66.1%

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

      3. associate-*l/ 61.1%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in t around 0 63.9%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-62} \lor \neg \left(t \leq 1.5 \cdot 10^{-107} \lor \neg \left(t \leq 2.8 \cdot 10^{-76}\right) \land t \leq 13.5\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 7: 54.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-107} \lor \neg \left(t \leq 1.05 \cdot 10^{-75}\right) \land t \leq 25.5:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -4.4e+23)
     t_1
     (if (<= t -4.6e-55)
       (* (/ y t) (/ z a))
       (if (<= t -7.8e-63)
         (+ x (/ (* y z) t))
         (if (or (<= t 1.6e-107) (and (not (<= t 1.05e-75)) (<= t 25.5)))
           (/ z b)
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -4.4e+23) {
		tmp = t_1;
	} else if (t <= -4.6e-55) {
		tmp = (y / t) * (z / a);
	} else if (t <= -7.8e-63) {
		tmp = x + ((y * z) / t);
	} else if ((t <= 1.6e-107) || (!(t <= 1.05e-75) && (t <= 25.5))) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-4.4d+23)) then
        tmp = t_1
    else if (t <= (-4.6d-55)) then
        tmp = (y / t) * (z / a)
    else if (t <= (-7.8d-63)) then
        tmp = x + ((y * z) / t)
    else if ((t <= 1.6d-107) .or. (.not. (t <= 1.05d-75)) .and. (t <= 25.5d0)) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -4.4e+23) {
		tmp = t_1;
	} else if (t <= -4.6e-55) {
		tmp = (y / t) * (z / a);
	} else if (t <= -7.8e-63) {
		tmp = x + ((y * z) / t);
	} else if ((t <= 1.6e-107) || (!(t <= 1.05e-75) && (t <= 25.5))) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -4.4e+23:
		tmp = t_1
	elif t <= -4.6e-55:
		tmp = (y / t) * (z / a)
	elif t <= -7.8e-63:
		tmp = x + ((y * z) / t)
	elif (t <= 1.6e-107) or (not (t <= 1.05e-75) and (t <= 25.5)):
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -4.4e+23)
		tmp = t_1;
	elseif (t <= -4.6e-55)
		tmp = Float64(Float64(y / t) * Float64(z / a));
	elseif (t <= -7.8e-63)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif ((t <= 1.6e-107) || (!(t <= 1.05e-75) && (t <= 25.5)))
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -4.4e+23)
		tmp = t_1;
	elseif (t <= -4.6e-55)
		tmp = (y / t) * (z / a);
	elseif (t <= -7.8e-63)
		tmp = x + ((y * z) / t);
	elseif ((t <= 1.6e-107) || (~((t <= 1.05e-75)) && (t <= 25.5)))
		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[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+23], t$95$1, If[LessEqual[t, -4.6e-55], N[(N[(y / t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.8e-63], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.6e-107], And[N[Not[LessEqual[t, 1.05e-75]], $MachinePrecision], LessEqual[t, 25.5]]], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.40000000000000017e23 or 1.60000000000000006e-107 < t < 1.0500000000000001e-75 or 25.5 < t

   1. Initial program 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-/l* 90.6%

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

      3. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in t around inf 69.2%

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

   if -4.40000000000000017e23 < t < -4.60000000000000023e-55

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

      2. associate-/l* 85.3%

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

      3. associate-*l/ 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in a around inf 47.1%

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

   5. Taylor expanded in y around inf 42.2%

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

      1. *-commutative 42.2%

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

      2. times-frac 41.8%

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

   7. Simplified 41.8%

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

   if -4.60000000000000023e-55 < t < -7.80000000000000044e-63

   1. Initial program 76.5%

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

      1. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

      1. div-inv 76.5%

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

      2. associate-/l* 76.5%

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

      3. associate-/r/ 76.5%

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

      4. +-commutative 76.5%

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

      5. fma-def 76.5%

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

   5. Applied egg-rr 76.5%

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

   6. Taylor expanded in y around 0 75.5%

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

   7. Taylor expanded in a around 0 51.3%

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

   if -7.80000000000000044e-63 < t < 1.60000000000000006e-107 or 1.0500000000000001e-75 < t < 25.5

   1. Initial program 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-/l* 66.1%

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

      3. associate-*l/ 61.1%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in t around 0 63.9%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-107} \lor \neg \left(t \leq 1.05 \cdot 10^{-75}\right) \land t \leq 25.5:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 8: 54.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-53}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot a}\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-61}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-108} \lor \neg \left(t \leq 1.1 \cdot 10^{-72}\right) \land t \leq 14.5:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -1.05e+23)
     t_1
     (if (<= t -2.9e-53)
       (/ (* y z) (* t a))
       (if (<= t -1.52e-61)
         (+ x (/ (* y z) t))
         (if (or (<= t 8.6e-108) (and (not (<= t 1.1e-72)) (<= t 14.5)))
           (/ z b)
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.05e+23) {
		tmp = t_1;
	} else if (t <= -2.9e-53) {
		tmp = (y * z) / (t * a);
	} else if (t <= -1.52e-61) {
		tmp = x + ((y * z) / t);
	} else if ((t <= 8.6e-108) || (!(t <= 1.1e-72) && (t <= 14.5))) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-1.05d+23)) then
        tmp = t_1
    else if (t <= (-2.9d-53)) then
        tmp = (y * z) / (t * a)
    else if (t <= (-1.52d-61)) then
        tmp = x + ((y * z) / t)
    else if ((t <= 8.6d-108) .or. (.not. (t <= 1.1d-72)) .and. (t <= 14.5d0)) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.05e+23) {
		tmp = t_1;
	} else if (t <= -2.9e-53) {
		tmp = (y * z) / (t * a);
	} else if (t <= -1.52e-61) {
		tmp = x + ((y * z) / t);
	} else if ((t <= 8.6e-108) || (!(t <= 1.1e-72) && (t <= 14.5))) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -1.05e+23:
		tmp = t_1
	elif t <= -2.9e-53:
		tmp = (y * z) / (t * a)
	elif t <= -1.52e-61:
		tmp = x + ((y * z) / t)
	elif (t <= 8.6e-108) or (not (t <= 1.1e-72) and (t <= 14.5)):
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.05e+23)
		tmp = t_1;
	elseif (t <= -2.9e-53)
		tmp = Float64(Float64(y * z) / Float64(t * a));
	elseif (t <= -1.52e-61)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif ((t <= 8.6e-108) || (!(t <= 1.1e-72) && (t <= 14.5)))
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.05e+23)
		tmp = t_1;
	elseif (t <= -2.9e-53)
		tmp = (y * z) / (t * a);
	elseif (t <= -1.52e-61)
		tmp = x + ((y * z) / t);
	elseif ((t <= 8.6e-108) || (~((t <= 1.1e-72)) && (t <= 14.5)))
		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[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+23], t$95$1, If[LessEqual[t, -2.9e-53], N[(N[(y * z), $MachinePrecision] / N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.52e-61], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 8.6e-108], And[N[Not[LessEqual[t, 1.1e-72]], $MachinePrecision], LessEqual[t, 14.5]]], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.0500000000000001e23 or 8.6000000000000001e-108 < t < 1.10000000000000001e-72 or 14.5 < t

   1. Initial program 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-/l* 90.6%

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

      3. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in t around inf 69.2%

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

   if -1.0500000000000001e23 < t < -2.8999999999999998e-53

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

      2. associate-/l* 85.3%

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

      3. associate-*l/ 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in a around inf 47.1%

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

   5. Taylor expanded in y around inf 42.2%

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

      1. *-commutative 42.2%

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

   7. Simplified 42.2%

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

   if -2.8999999999999998e-53 < t < -1.52000000000000003e-61

   1. Initial program 76.5%

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

      1. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

      1. div-inv 76.5%

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

      2. associate-/l* 76.5%

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

      3. associate-/r/ 76.5%

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

      4. +-commutative 76.5%

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

      5. fma-def 76.5%

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

   5. Applied egg-rr 76.5%

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

   6. Taylor expanded in y around 0 75.5%

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

   7. Taylor expanded in a around 0 51.3%

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

   if -1.52000000000000003e-61 < t < 8.6000000000000001e-108 or 1.10000000000000001e-72 < t < 14.5

   1. Initial program 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-/l* 66.1%

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

      3. associate-*l/ 61.1%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in t around 0 63.9%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-53}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot a}\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-61}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-108} \lor \neg \left(t \leq 1.1 \cdot 10^{-72}\right) \land t \leq 14.5:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 9: 66.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+119}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+106}:\\ \;\;\;\;\frac{1}{a + 1} \cdot \left(x + z \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.25e+119)
   (/ z b)
   (if (<= y 3.1e+106) (* (/ 1.0 (+ a 1.0)) (+ x (* z (/ y t)))) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.25e+119) {
		tmp = z / b;
	} else if (y <= 3.1e+106) {
		tmp = (1.0 / (a + 1.0)) * (x + (z * (y / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.25d+119)) then
        tmp = z / b
    else if (y <= 3.1d+106) then
        tmp = (1.0d0 / (a + 1.0d0)) * (x + (z * (y / t)))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.25e+119) {
		tmp = z / b;
	} else if (y <= 3.1e+106) {
		tmp = (1.0 / (a + 1.0)) * (x + (z * (y / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.25e+119:
		tmp = z / b
	elif y <= 3.1e+106:
		tmp = (1.0 / (a + 1.0)) * (x + (z * (y / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.25e+119)
		tmp = Float64(z / b);
	elseif (y <= 3.1e+106)
		tmp = Float64(Float64(1.0 / Float64(a + 1.0)) * Float64(x + Float64(z * Float64(y / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.25e+119)
		tmp = z / b;
	elseif (y <= 3.1e+106)
		tmp = (1.0 / (a + 1.0)) * (x + (z * (y / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.25e+119], N[(z / b), $MachinePrecision], If[LessEqual[y, 3.1e+106], N[(N[(1.0 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision] * N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2500000000000001e119 or 3.0999999999999999e106 < y

   1. Initial program 45.2%

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

      1. *-commutative 45.2%

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

      2. associate-/l* 50.6%

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

      3. associate-*l/ 49.9%

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

   3. Simplified 49.9%

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

   4. Taylor expanded in t around 0 64.9%

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

   if -2.2500000000000001e119 < y < 3.0999999999999999e106

   1. Initial program 90.1%

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

      1. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

      1. div-inv 83.4%

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

      2. associate-/l* 79.9%

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

      3. associate-/r/ 83.6%

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

      4. +-commutative 83.6%

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

      5. fma-def 83.6%

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

   5. Applied egg-rr 83.6%

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

   6. Taylor expanded in y around 0 70.8%

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

      1. associate-/r/ 73.7%

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

   8. Applied egg-rr 73.7%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+119}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+106}:\\ \;\;\;\;\frac{1}{a + 1} \cdot \left(x + z \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 10: 53.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{a + 1} \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-107} \lor \neg \left(t \leq 2.9 \cdot 10^{-74}\right) \land t \leq 210:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -1.95e+24)
     t_1
     (if (<= t -7e-157)
       (* (/ z (+ a 1.0)) (/ y t))
       (if (or (<= t 1.75e-107) (and (not (<= t 2.9e-74)) (<= t 210.0)))
         (/ z b)
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.95e+24) {
		tmp = t_1;
	} else if (t <= -7e-157) {
		tmp = (z / (a + 1.0)) * (y / t);
	} else if ((t <= 1.75e-107) || (!(t <= 2.9e-74) && (t <= 210.0))) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-1.95d+24)) then
        tmp = t_1
    else if (t <= (-7d-157)) then
        tmp = (z / (a + 1.0d0)) * (y / t)
    else if ((t <= 1.75d-107) .or. (.not. (t <= 2.9d-74)) .and. (t <= 210.0d0)) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.95e+24) {
		tmp = t_1;
	} else if (t <= -7e-157) {
		tmp = (z / (a + 1.0)) * (y / t);
	} else if ((t <= 1.75e-107) || (!(t <= 2.9e-74) && (t <= 210.0))) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -1.95e+24:
		tmp = t_1
	elif t <= -7e-157:
		tmp = (z / (a + 1.0)) * (y / t)
	elif (t <= 1.75e-107) or (not (t <= 2.9e-74) and (t <= 210.0)):
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.95e+24)
		tmp = t_1;
	elseif (t <= -7e-157)
		tmp = Float64(Float64(z / Float64(a + 1.0)) * Float64(y / t));
	elseif ((t <= 1.75e-107) || (!(t <= 2.9e-74) && (t <= 210.0)))
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.95e+24)
		tmp = t_1;
	elseif (t <= -7e-157)
		tmp = (z / (a + 1.0)) * (y / t);
	elseif ((t <= 1.75e-107) || (~((t <= 2.9e-74)) && (t <= 210.0)))
		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[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.95e+24], t$95$1, If[LessEqual[t, -7e-157], N[(N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.75e-107], And[N[Not[LessEqual[t, 2.9e-74]], $MachinePrecision], LessEqual[t, 210.0]]], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9499999999999999e24 or 1.74999999999999993e-107 < t < 2.9e-74 or 210 < t

   1. Initial program 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-/l* 90.6%

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

      3. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in t around inf 69.2%

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

   if -1.9499999999999999e24 < t < -7.0000000000000004e-157

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-/l* 79.6%

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

      3. associate-*l/ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in b around 0 61.3%

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

   5. Taylor expanded in y around inf 49.0%

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

      1. times-frac 49.0%

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

   7. Simplified 49.0%

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

   if -7.0000000000000004e-157 < t < 1.74999999999999993e-107 or 2.9e-74 < t < 210

   1. Initial program 65.5%

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

      1. *-commutative 65.5%

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

      2. associate-/l* 65.2%

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

      3. associate-*l/ 59.3%

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

   3. Simplified 59.3%

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

   4. Taylor expanded in t around 0 66.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{a + 1} \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-107} \lor \neg \left(t \leq 2.9 \cdot 10^{-74}\right) \land t \leq 210:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 11: 53.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-155}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-108} \lor \neg \left(t \leq 5 \cdot 10^{-76}\right) \land t \leq 88:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -1.1e+25)
     t_1
     (if (<= t -5.2e-155)
       (/ (* y z) (* t (+ a 1.0)))
       (if (or (<= t 2.6e-108) (and (not (<= t 5e-76)) (<= t 88.0)))
         (/ z b)
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.1e+25) {
		tmp = t_1;
	} else if (t <= -5.2e-155) {
		tmp = (y * z) / (t * (a + 1.0));
	} else if ((t <= 2.6e-108) || (!(t <= 5e-76) && (t <= 88.0))) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-1.1d+25)) then
        tmp = t_1
    else if (t <= (-5.2d-155)) then
        tmp = (y * z) / (t * (a + 1.0d0))
    else if ((t <= 2.6d-108) .or. (.not. (t <= 5d-76)) .and. (t <= 88.0d0)) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.1e+25) {
		tmp = t_1;
	} else if (t <= -5.2e-155) {
		tmp = (y * z) / (t * (a + 1.0));
	} else if ((t <= 2.6e-108) || (!(t <= 5e-76) && (t <= 88.0))) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -1.1e+25:
		tmp = t_1
	elif t <= -5.2e-155:
		tmp = (y * z) / (t * (a + 1.0))
	elif (t <= 2.6e-108) or (not (t <= 5e-76) and (t <= 88.0)):
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.1e+25)
		tmp = t_1;
	elseif (t <= -5.2e-155)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(a + 1.0)));
	elseif ((t <= 2.6e-108) || (!(t <= 5e-76) && (t <= 88.0)))
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.1e+25)
		tmp = t_1;
	elseif (t <= -5.2e-155)
		tmp = (y * z) / (t * (a + 1.0));
	elseif ((t <= 2.6e-108) || (~((t <= 5e-76)) && (t <= 88.0)))
		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[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+25], t$95$1, If[LessEqual[t, -5.2e-155], N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 2.6e-108], And[N[Not[LessEqual[t, 5e-76]], $MachinePrecision], LessEqual[t, 88.0]]], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e25 or 2.59999999999999984e-108 < t < 4.9999999999999998e-76 or 88 < t

   1. Initial program 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-/l* 90.6%

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

      3. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in t around inf 69.2%

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

   if -1.1e25 < t < -5.20000000000000016e-155

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-/l* 79.6%

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

      3. associate-*l/ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in b around 0 61.3%

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

   5. Taylor expanded in y around inf 49.0%

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

   if -5.20000000000000016e-155 < t < 2.59999999999999984e-108 or 4.9999999999999998e-76 < t < 88

   1. Initial program 65.5%

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

      1. *-commutative 65.5%

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

      2. associate-/l* 65.2%

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

      3. associate-*l/ 59.3%

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

   3. Simplified 59.3%

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

   4. Taylor expanded in t around 0 66.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-155}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-108} \lor \neg \left(t \leq 5 \cdot 10^{-76}\right) \land t \leq 88:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 12: 61.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+56}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.2e+109)
   (/ z b)
   (if (<= b 2.95e+56) (/ (+ x (/ (* y z) t)) (+ a 1.0)) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e+109) {
		tmp = z / b;
	} else if (b <= 2.95e+56) {
		tmp = (x + ((y * z) / t)) / (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 (b <= (-5.2d+109)) then
        tmp = z / b
    else if (b <= 2.95d+56) then
        tmp = (x + ((y * z) / t)) / (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 (b <= -5.2e+109) {
		tmp = z / b;
	} else if (b <= 2.95e+56) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.2e+109:
		tmp = z / b
	elif b <= 2.95e+56:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.2e+109)
		tmp = Float64(z / b);
	elseif (b <= 2.95e+56)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / 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 (b <= -5.2e+109)
		tmp = z / b;
	elseif (b <= 2.95e+56)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.2e+109], N[(z / b), $MachinePrecision], If[LessEqual[b, 2.95e+56], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.1999999999999997e109 or 2.9500000000000001e56 < b

   1. Initial program 61.6%

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

      1. *-commutative 61.6%

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

      2. associate-/l* 61.5%

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

      3. associate-*l/ 64.6%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in t around 0 58.8%

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

   if -5.1999999999999997e109 < b < 2.9500000000000001e56

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

      2. associate-/l* 90.0%

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

      3. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in b around 0 78.3%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+56}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 13: 55.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.55 \cdot 10^{+27} \lor \neg \left(t \leq 1.75 \cdot 10^{-107}\right) \land \left(t \leq 9.6 \cdot 10^{-74} \lor \neg \left(t \leq 15.2\right)\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.55e+27)
         (and (not (<= t 1.75e-107)) (or (<= t 9.6e-74) (not (<= t 15.2)))))
   (/ 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 <= -4.55e+27) || (!(t <= 1.75e-107) && ((t <= 9.6e-74) || !(t <= 15.2)))) {
		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 <= (-4.55d+27)) .or. (.not. (t <= 1.75d-107)) .and. (t <= 9.6d-74) .or. (.not. (t <= 15.2d0))) 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 <= -4.55e+27) || (!(t <= 1.75e-107) && ((t <= 9.6e-74) || !(t <= 15.2)))) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.55e+27) or (not (t <= 1.75e-107) and ((t <= 9.6e-74) or not (t <= 15.2))):
		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 <= -4.55e+27) || (!(t <= 1.75e-107) && ((t <= 9.6e-74) || !(t <= 15.2))))
		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 <= -4.55e+27) || (~((t <= 1.75e-107)) && ((t <= 9.6e-74) || ~((t <= 15.2)))))
		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, -4.55e+27], And[N[Not[LessEqual[t, 1.75e-107]], $MachinePrecision], Or[LessEqual[t, 9.6e-74], N[Not[LessEqual[t, 15.2]], $MachinePrecision]]]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.55000000000000002e27 or 1.74999999999999993e-107 < t < 9.5999999999999996e-74 or 15.199999999999999 < t

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-/l* 91.3%

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

      3. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in t around inf 69.7%

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

   if -4.55000000000000002e27 < t < 1.74999999999999993e-107 or 9.5999999999999996e-74 < t < 15.199999999999999

   1. Initial program 69.1%

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

      1. *-commutative 69.1%

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

      2. associate-/l* 68.8%

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

      3. associate-*l/ 64.7%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in t around 0 56.4%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.55 \cdot 10^{+27} \lor \neg \left(t \leq 1.75 \cdot 10^{-107}\right) \land \left(t \leq 9.6 \cdot 10^{-74} \lor \neg \left(t \leq 15.2\right)\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 14: 42.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+27} \lor \neg \left(t \leq 15\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.6e+27) (not (<= t 15.0))) (/ x a) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.6e+27) || !(t <= 15.0)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.6d+27)) .or. (.not. (t <= 15.0d0))) then
        tmp = x / a
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.6e+27) || !(t <= 15.0)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.6e+27) or not (t <= 15.0):
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.6e+27) || !(t <= 15.0))
		tmp = Float64(x / a);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.6e+27) || ~((t <= 15.0)))
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.6e+27], N[Not[LessEqual[t, 15.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6000000000000001e27 or 15 < t

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

      2. associate-/l* 90.5%

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

      3. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in a around inf 43.6%

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

   5. Taylor expanded in y around 0 38.9%

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

   if -4.6000000000000001e27 < t < 15

   1. Initial program 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-/l* 71.2%

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

      3. associate-*l/ 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in t around 0 52.9%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+27} \lor \neg \left(t \leq 15\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 15: 25.2% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.6%

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

   1. *-commutative 77.6%

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

   2. associate-/l* 79.7%

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

   3. associate-*l/ 78.7%

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

3. Simplified 78.7%

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

4. Taylor expanded in a around inf 37.2%

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

5. Taylor expanded in y around 0 26.0%

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

6. Final simplification 26.0%

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

Developer target: 79.3% 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 2023171 
(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))))