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

Percentage Accurate: 75.0% → 89.0%

Time: 18.1s

Alternatives: 15

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{t_1}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_2 (- INFINITY))
     (* (/ y t) (/ z (fma y (/ b t) (+ a 1.0))))
     (if (<= t_2 5e+302) (/ t_1 (+ (+ 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);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / fma(y, (b / t), (a + 1.0)));
	} else if (t_2 <= 5e+302) {
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / fma(y, Float64(b / t), Float64(a + 1.0))));
	elseif (t_2 <= 5e+302)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / N[(y * N[(b / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+302], N[(t$95$1 / 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 41.5%

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

   2. Taylor expanded in x around 0 58.9%

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

      1. times-frac 76.8%

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

      2. associate-+r+ 76.8%

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

      3. +-commutative 76.8%

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

      4. +-commutative 76.8%

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

      5. associate-*l/ 76.8%

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

      6. *-commutative 76.8%

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

      7. fma-udef 76.8%

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

      8. +-commutative 76.8%

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

   4. Simplified 76.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5e302

   1. Initial program 92.0%

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

      1. associate-/l* 88.0%

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

      2. associate-/r/ 93.6%

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

   3. Applied egg-rr 93.6%

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

   if 5e302 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 18.8%

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

   2. Taylor expanded in y around inf 78.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{t_1}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_2 (- INFINITY))
     (/ (+ x (* y (/ z t))) (+ 1.0 (+ a (* y (/ b t)))))
     (if (<= t_2 5e+302) (/ t_1 (+ (+ 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);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (x + (y * (z / t))) / (1.0 + (a + (y * (b / t))));
	} else if (t_2 <= 5e+302) {
		tmp = t_1 / ((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);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + (y * (z / t))) / (1.0 + (a + (y * (b / t))));
	} else if (t_2 <= 5e+302) {
		tmp = t_1 / ((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)
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (x + (y * (z / t))) / (1.0 + (a + (y * (b / t))))
	elif t_2 <= 5e+302:
		tmp = t_1 / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	elseif (t_2 <= 5e+302)
		tmp = Float64(t_1 / 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);
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (x + (y * (z / t))) / (1.0 + (a + (y * (b / t))));
	elseif (t_2 <= 5e+302)
		tmp = t_1 / ((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[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+302], N[(t$95$1 / 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 41.5%

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

      1. *-commutative 41.5%

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

      2. associate-/l* 59.0%

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

      3. +-commutative 59.0%

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

      4. associate-+l+ 59.0%

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

      5. associate-*r/ 59.0%

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

      6. *-commutative 59.0%

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

   3. Simplified 59.0%

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

      1. associate-/r/ 59.2%

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

   5. Applied egg-rr 59.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5e302

   1. Initial program 92.0%

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

      1. associate-/l* 88.0%

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

      2. associate-/r/ 93.6%

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

   3. Applied egg-rr 93.6%

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

   if 5e302 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 18.8%

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

   2. Taylor expanded in y around inf 78.8%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3: 55.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \frac{y \cdot b}{t}}\\ t_2 := x + z \cdot \frac{y}{t}\\ t_3 := \frac{t_2}{a}\\ \mathbf{if}\;a \leq -2100:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-216}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-110}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+45}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (/ (* y b) t))))
        (t_2 (+ x (* z (/ y t))))
        (t_3 (/ t_2 a)))
   (if (<= a -2100.0)
     t_3
     (if (<= a -1.35e-147)
       t_1
       (if (<= a 7.2e-216)
         t_2
         (if (<= a 1.8e-134)
           t_1
           (if (<= a 5e-110)
             (/ z b)
             (if (<= a 3.9e-63)
               (/ x (+ 1.0 (* b (/ y t))))
               (if (<= a 8.6e+45) (/ z b) t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + ((y * b) / t));
	double t_2 = x + (z * (y / t));
	double t_3 = t_2 / a;
	double tmp;
	if (a <= -2100.0) {
		tmp = t_3;
	} else if (a <= -1.35e-147) {
		tmp = t_1;
	} else if (a <= 7.2e-216) {
		tmp = t_2;
	} else if (a <= 1.8e-134) {
		tmp = t_1;
	} else if (a <= 5e-110) {
		tmp = z / b;
	} else if (a <= 3.9e-63) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (a <= 8.6e+45) {
		tmp = z / b;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x / (1.0d0 + ((y * b) / t))
    t_2 = x + (z * (y / t))
    t_3 = t_2 / a
    if (a <= (-2100.0d0)) then
        tmp = t_3
    else if (a <= (-1.35d-147)) then
        tmp = t_1
    else if (a <= 7.2d-216) then
        tmp = t_2
    else if (a <= 1.8d-134) then
        tmp = t_1
    else if (a <= 5d-110) then
        tmp = z / b
    else if (a <= 3.9d-63) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else if (a <= 8.6d+45) then
        tmp = z / b
    else
        tmp = t_3
    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 / (1.0 + ((y * b) / t));
	double t_2 = x + (z * (y / t));
	double t_3 = t_2 / a;
	double tmp;
	if (a <= -2100.0) {
		tmp = t_3;
	} else if (a <= -1.35e-147) {
		tmp = t_1;
	} else if (a <= 7.2e-216) {
		tmp = t_2;
	} else if (a <= 1.8e-134) {
		tmp = t_1;
	} else if (a <= 5e-110) {
		tmp = z / b;
	} else if (a <= 3.9e-63) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (a <= 8.6e+45) {
		tmp = z / b;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + ((y * b) / t))
	t_2 = x + (z * (y / t))
	t_3 = t_2 / a
	tmp = 0
	if a <= -2100.0:
		tmp = t_3
	elif a <= -1.35e-147:
		tmp = t_1
	elif a <= 7.2e-216:
		tmp = t_2
	elif a <= 1.8e-134:
		tmp = t_1
	elif a <= 5e-110:
		tmp = z / b
	elif a <= 3.9e-63:
		tmp = x / (1.0 + (b * (y / t)))
	elif a <= 8.6e+45:
		tmp = z / b
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)))
	t_2 = Float64(x + Float64(z * Float64(y / t)))
	t_3 = Float64(t_2 / a)
	tmp = 0.0
	if (a <= -2100.0)
		tmp = t_3;
	elseif (a <= -1.35e-147)
		tmp = t_1;
	elseif (a <= 7.2e-216)
		tmp = t_2;
	elseif (a <= 1.8e-134)
		tmp = t_1;
	elseif (a <= 5e-110)
		tmp = Float64(z / b);
	elseif (a <= 3.9e-63)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	elseif (a <= 8.6e+45)
		tmp = Float64(z / b);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + ((y * b) / t));
	t_2 = x + (z * (y / t));
	t_3 = t_2 / a;
	tmp = 0.0;
	if (a <= -2100.0)
		tmp = t_3;
	elseif (a <= -1.35e-147)
		tmp = t_1;
	elseif (a <= 7.2e-216)
		tmp = t_2;
	elseif (a <= 1.8e-134)
		tmp = t_1;
	elseif (a <= 5e-110)
		tmp = z / b;
	elseif (a <= 3.9e-63)
		tmp = x / (1.0 + (b * (y / t)));
	elseif (a <= 8.6e+45)
		tmp = z / b;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / a), $MachinePrecision]}, If[LessEqual[a, -2100.0], t$95$3, If[LessEqual[a, -1.35e-147], t$95$1, If[LessEqual[a, 7.2e-216], t$95$2, If[LessEqual[a, 1.8e-134], t$95$1, If[LessEqual[a, 5e-110], N[(z / b), $MachinePrecision], If[LessEqual[a, 3.9e-63], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e+45], N[(z / b), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2100 or 8.6000000000000006e45 < a

   1. Initial program 81.0%

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

      1. associate-/l* 77.6%

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

      2. associate-/r/ 80.6%

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

   3. Applied egg-rr 80.6%

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

   4. Taylor expanded in a around inf 68.5%

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

      1. associate-/l* 64.0%

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

      2. associate-/r/ 68.6%

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

   6. Simplified 68.6%

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

   if -2100 < a < -1.35e-147 or 7.1999999999999998e-216 < a < 1.79999999999999995e-134

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf 69.2%

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

   3. Taylor expanded in a around 0 69.2%

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

   if -1.35e-147 < a < 7.1999999999999998e-216

   1. Initial program 73.3%

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

   2. Taylor expanded in b around 0 55.6%

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

   3. Taylor expanded in a around 0 55.6%

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

      1. associate-/l* 61.0%

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

      2. associate-/r/ 62.9%

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

   5. Simplified 62.9%

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

   if 1.79999999999999995e-134 < a < 5e-110 or 3.90000000000000022e-63 < a < 8.6000000000000006e45

   1. Initial program 59.3%

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

   2. Taylor expanded in y around inf 58.0%

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

   if 5e-110 < a < 3.90000000000000022e-63

   1. Initial program 90.9%

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

   2. Taylor expanded in x around inf 82.4%

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

   3. Taylor expanded in a around 0 82.4%

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

      1. associate-*r/ 82.4%

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

   5. Simplified 82.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2100:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-147}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-216}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-134}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-110}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+45}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \end{array} \]

Alternative 4: 54.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \frac{y \cdot b}{t}}\\ t_2 := x + z \cdot \frac{y}{t}\\ \mathbf{if}\;a \leq -8200:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+45}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (/ (* y b) t)))) (t_2 (+ x (* z (/ y t)))))
   (if (<= a -8200.0)
     (/ (+ x (/ (* y z) t)) a)
     (if (<= a -1.7e-151)
       t_1
       (if (<= a 2.7e-211)
         t_2
         (if (<= a 9.5e-135)
           t_1
           (if (<= a 6.6e-106)
             (/ z b)
             (if (<= a 1.6e-64)
               (/ x (+ 1.0 (* b (/ y t))))
               (if (<= a 8.6e+45) (/ z b) (/ t_2 a))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + ((y * b) / t));
	double t_2 = x + (z * (y / t));
	double tmp;
	if (a <= -8200.0) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (a <= -1.7e-151) {
		tmp = t_1;
	} else if (a <= 2.7e-211) {
		tmp = t_2;
	} else if (a <= 9.5e-135) {
		tmp = t_1;
	} else if (a <= 6.6e-106) {
		tmp = z / b;
	} else if (a <= 1.6e-64) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (a <= 8.6e+45) {
		tmp = z / b;
	} else {
		tmp = t_2 / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (1.0d0 + ((y * b) / t))
    t_2 = x + (z * (y / t))
    if (a <= (-8200.0d0)) then
        tmp = (x + ((y * z) / t)) / a
    else if (a <= (-1.7d-151)) then
        tmp = t_1
    else if (a <= 2.7d-211) then
        tmp = t_2
    else if (a <= 9.5d-135) then
        tmp = t_1
    else if (a <= 6.6d-106) then
        tmp = z / b
    else if (a <= 1.6d-64) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else if (a <= 8.6d+45) then
        tmp = z / b
    else
        tmp = t_2 / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + ((y * b) / t));
	double t_2 = x + (z * (y / t));
	double tmp;
	if (a <= -8200.0) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (a <= -1.7e-151) {
		tmp = t_1;
	} else if (a <= 2.7e-211) {
		tmp = t_2;
	} else if (a <= 9.5e-135) {
		tmp = t_1;
	} else if (a <= 6.6e-106) {
		tmp = z / b;
	} else if (a <= 1.6e-64) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (a <= 8.6e+45) {
		tmp = z / b;
	} else {
		tmp = t_2 / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + ((y * b) / t))
	t_2 = x + (z * (y / t))
	tmp = 0
	if a <= -8200.0:
		tmp = (x + ((y * z) / t)) / a
	elif a <= -1.7e-151:
		tmp = t_1
	elif a <= 2.7e-211:
		tmp = t_2
	elif a <= 9.5e-135:
		tmp = t_1
	elif a <= 6.6e-106:
		tmp = z / b
	elif a <= 1.6e-64:
		tmp = x / (1.0 + (b * (y / t)))
	elif a <= 8.6e+45:
		tmp = z / b
	else:
		tmp = t_2 / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)))
	t_2 = Float64(x + Float64(z * Float64(y / t)))
	tmp = 0.0
	if (a <= -8200.0)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	elseif (a <= -1.7e-151)
		tmp = t_1;
	elseif (a <= 2.7e-211)
		tmp = t_2;
	elseif (a <= 9.5e-135)
		tmp = t_1;
	elseif (a <= 6.6e-106)
		tmp = Float64(z / b);
	elseif (a <= 1.6e-64)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	elseif (a <= 8.6e+45)
		tmp = Float64(z / b);
	else
		tmp = Float64(t_2 / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + ((y * b) / t));
	t_2 = x + (z * (y / t));
	tmp = 0.0;
	if (a <= -8200.0)
		tmp = (x + ((y * z) / t)) / a;
	elseif (a <= -1.7e-151)
		tmp = t_1;
	elseif (a <= 2.7e-211)
		tmp = t_2;
	elseif (a <= 9.5e-135)
		tmp = t_1;
	elseif (a <= 6.6e-106)
		tmp = z / b;
	elseif (a <= 1.6e-64)
		tmp = x / (1.0 + (b * (y / t)));
	elseif (a <= 8.6e+45)
		tmp = z / b;
	else
		tmp = t_2 / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8200.0], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -1.7e-151], t$95$1, If[LessEqual[a, 2.7e-211], t$95$2, If[LessEqual[a, 9.5e-135], t$95$1, If[LessEqual[a, 6.6e-106], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.6e-64], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e+45], N[(z / b), $MachinePrecision], N[(t$95$2 / a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -8200

   1. Initial program 79.2%

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

   2. Taylor expanded in a around inf 63.7%

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

   if -8200 < a < -1.7000000000000001e-151 or 2.6999999999999999e-211 < a < 9.50000000000000007e-135

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf 69.2%

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

   3. Taylor expanded in a around 0 69.2%

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

   if -1.7000000000000001e-151 < a < 2.6999999999999999e-211

   1. Initial program 73.3%

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

   2. Taylor expanded in b around 0 55.6%

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

   3. Taylor expanded in a around 0 55.6%

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

      1. associate-/l* 61.0%

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

      2. associate-/r/ 62.9%

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

   5. Simplified 62.9%

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

   if 9.50000000000000007e-135 < a < 6.60000000000000031e-106 or 1.59999999999999988e-64 < a < 8.6000000000000006e45

   1. Initial program 59.3%

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

   2. Taylor expanded in y around inf 58.0%

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

   if 6.60000000000000031e-106 < a < 1.59999999999999988e-64

   1. Initial program 90.9%

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

   2. Taylor expanded in x around inf 82.4%

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

   3. Taylor expanded in a around 0 82.4%

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

      1. associate-*r/ 82.4%

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

   5. Simplified 82.4%

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

   if 8.6000000000000006e45 < a

   1. Initial program 83.2%

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

      1. associate-/l* 75.8%

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

      2. associate-/r/ 83.1%

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

   3. Applied egg-rr 83.1%

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

   4. Taylor expanded in a around inf 74.7%

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

      1. associate-/l* 70.9%

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

      2. associate-/r/ 76.7%

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

   6. Simplified 76.7%

      \[\leadsto \color{blue}{\frac{x + \frac{y}{t} \cdot z}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8200:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-151}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-211}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+45}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \end{array} \]

Alternative 5: 79.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-174} \lor \neg \left(t \leq 3.2 \cdot 10^{-207}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3e-174) (not (<= t 3.2e-207)))
   (/ (+ x (* z (/ y t))) (+ 1.0 (+ a (* y (/ b t)))))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3e-174) || !(t <= 3.2e-207)) {
		tmp = (x + (z * (y / t))) / (1.0 + (a + (y * (b / 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 ((t <= (-3d-174)) .or. (.not. (t <= 3.2d-207))) then
        tmp = (x + (z * (y / t))) / (1.0d0 + (a + (y * (b / 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 ((t <= -3e-174) || !(t <= 3.2e-207)) {
		tmp = (x + (z * (y / t))) / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3e-174) or not (t <= 3.2e-207):
		tmp = (x + (z * (y / t))) / (1.0 + (a + (y * (b / t))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3e-174) || !(t <= 3.2e-207))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(1.0 + Float64(a + Float64(y * Float64(b / 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 ((t <= -3e-174) || ~((t <= 3.2e-207)))
		tmp = (x + (z * (y / t))) / (1.0 + (a + (y * (b / t))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3e-174], N[Not[LessEqual[t, 3.2e-207]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.00000000000000021e-174 or 3.2000000000000003e-207 < t

   1. Initial program 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-/l* 83.2%

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

      3. +-commutative 83.2%

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

      4. associate-+l+ 83.2%

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

      5. associate-*r/ 85.3%

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

      6. *-commutative 85.3%

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

   3. Simplified 85.3%

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

      1. div-inv 84.8%

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

      2. clear-num 84.9%

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

   5. Applied egg-rr 84.9%

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

   if -3.00000000000000021e-174 < t < 3.2000000000000003e-207

   1. Initial program 61.9%

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

   2. Taylor expanded in y around inf 61.6%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-174} \lor \neg \left(t \leq 3.2 \cdot 10^{-207}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 6: 79.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \left(a + y \cdot \frac{b}{t}\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-173}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t_1}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-229}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ 1.0 (+ a (* y (/ b t))))))
   (if (<= t -1.05e-173)
     (/ (+ x (* z (/ y t))) t_1)
     (if (<= t 7.5e-229) (/ z b) (/ (+ x (* y (/ z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + (a + (y * (b / t)));
	double tmp;
	if (t <= -1.05e-173) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t <= 7.5e-229) {
		tmp = z / b;
	} else {
		tmp = (x + (y * (z / t))) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + (a + (y * (b / t)))
    if (t <= (-1.05d-173)) then
        tmp = (x + (z * (y / t))) / t_1
    else if (t <= 7.5d-229) then
        tmp = z / b
    else
        tmp = (x + (y * (z / t))) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + (a + (y * (b / t)));
	double tmp;
	if (t <= -1.05e-173) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t <= 7.5e-229) {
		tmp = z / b;
	} else {
		tmp = (x + (y * (z / t))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 + (a + (y * (b / t)))
	tmp = 0
	if t <= -1.05e-173:
		tmp = (x + (z * (y / t))) / t_1
	elif t <= 7.5e-229:
		tmp = z / b
	else:
		tmp = (x + (y * (z / t))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -1.05e-173)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	elseif (t <= 7.5e-229)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 + (a + (y * (b / t)));
	tmp = 0.0;
	if (t <= -1.05e-173)
		tmp = (x + (z * (y / t))) / t_1;
	elseif (t <= 7.5e-229)
		tmp = z / b;
	else
		tmp = (x + (y * (z / t))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e-173], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 7.5e-229], N[(z / b), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05000000000000001e-173

   1. Initial program 80.2%

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

      1. *-commutative 80.2%

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

      2. associate-/l* 81.0%

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

      3. +-commutative 81.0%

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

      4. associate-+l+ 81.0%

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

      5. associate-*r/ 82.5%

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

      6. *-commutative 82.5%

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

   3. Simplified 82.5%

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

      1. div-inv 82.6%

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

      2. clear-num 82.6%

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

   5. Applied egg-rr 82.6%

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

   if -1.05000000000000001e-173 < t < 7.4999999999999999e-229

   1. Initial program 60.3%

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

   2. Taylor expanded in y around inf 62.0%

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

   if 7.4999999999999999e-229 < t

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-/l* 84.9%

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

      3. +-commutative 84.9%

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

      4. associate-+l+ 84.9%

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

      5. associate-*r/ 87.7%

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

      6. *-commutative 87.7%

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

   3. Simplified 87.7%

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

      1. associate-/r/ 88.5%

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

   5. Applied egg-rr 88.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-173}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-229}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \]

Alternative 7: 61.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+176}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+36}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{z}}{y}}}{a + 1}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ a 1.0))))
   (if (<= z -6.4e+221)
     t_1
     (if (<= z -7.5e+176)
       (/ z b)
       (if (<= z -1.05e+36)
         (/ (+ x (/ 1.0 (/ (/ t z) y))) (+ a 1.0))
         (if (<= z 3.7e-84) (/ x (+ 1.0 (+ a (/ (* y b) t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (a + 1.0);
	double tmp;
	if (z <= -6.4e+221) {
		tmp = t_1;
	} else if (z <= -7.5e+176) {
		tmp = z / b;
	} else if (z <= -1.05e+36) {
		tmp = (x + (1.0 / ((t / z) / y))) / (a + 1.0);
	} else if (z <= 3.7e-84) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / (a + 1.0d0)
    if (z <= (-6.4d+221)) then
        tmp = t_1
    else if (z <= (-7.5d+176)) then
        tmp = z / b
    else if (z <= (-1.05d+36)) then
        tmp = (x + (1.0d0 / ((t / z) / y))) / (a + 1.0d0)
    else if (z <= 3.7d-84) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (a + 1.0);
	double tmp;
	if (z <= -6.4e+221) {
		tmp = t_1;
	} else if (z <= -7.5e+176) {
		tmp = z / b;
	} else if (z <= -1.05e+36) {
		tmp = (x + (1.0 / ((t / z) / y))) / (a + 1.0);
	} else if (z <= 3.7e-84) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (a + 1.0)
	tmp = 0
	if z <= -6.4e+221:
		tmp = t_1
	elif z <= -7.5e+176:
		tmp = z / b
	elif z <= -1.05e+36:
		tmp = (x + (1.0 / ((t / z) / y))) / (a + 1.0)
	elif z <= 3.7e-84:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0))
	tmp = 0.0
	if (z <= -6.4e+221)
		tmp = t_1;
	elseif (z <= -7.5e+176)
		tmp = Float64(z / b);
	elseif (z <= -1.05e+36)
		tmp = Float64(Float64(x + Float64(1.0 / Float64(Float64(t / z) / y))) / Float64(a + 1.0));
	elseif (z <= 3.7e-84)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (a + 1.0);
	tmp = 0.0;
	if (z <= -6.4e+221)
		tmp = t_1;
	elseif (z <= -7.5e+176)
		tmp = z / b;
	elseif (z <= -1.05e+36)
		tmp = (x + (1.0 / ((t / z) / y))) / (a + 1.0);
	elseif (z <= 3.7e-84)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e+221], t$95$1, If[LessEqual[z, -7.5e+176], N[(z / b), $MachinePrecision], If[LessEqual[z, -1.05e+36], N[(N[(x + N[(1.0 / N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-84], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.4e221 or 3.6999999999999999e-84 < z

   1. Initial program 78.1%

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

   2. Taylor expanded in b around 0 65.7%

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

   if -6.4e221 < z < -7.499999999999999e176

   1. Initial program 3.5%

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

   2. Taylor expanded in y around inf 100.0%

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

   if -7.499999999999999e176 < z < -1.05000000000000002e36

   1. Initial program 63.0%

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

   2. Taylor expanded in b around 0 52.8%

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

      1. associate-/l* 62.8%

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

      2. clear-num 62.8%

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

      3. inv-pow 62.8%

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

   4. Applied egg-rr 62.8%

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

      1. unpow-1 62.8%

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

   6. Simplified 62.8%

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

   if -1.05000000000000002e36 < z < 3.6999999999999999e-84

   1. Initial program 86.7%

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

   2. Taylor expanded in x around inf 78.7%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+221}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+176}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+36}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{z}}{y}}}{a + 1}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]

Alternative 8: 59.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \left(a + \frac{y \cdot b}{t}\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+23} \lor \neg \left(x \leq 2.6 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ 1.0 (+ a (/ (* y b) t)))))
   (if (or (<= x -2.3e+23) (not (<= x 2.6e-29)))
     (/ x t_1)
     (/ (* y z) (* t t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + (a + ((y * b) / t));
	double tmp;
	if ((x <= -2.3e+23) || !(x <= 2.6e-29)) {
		tmp = x / t_1;
	} else {
		tmp = (y * z) / (t * t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + (a + ((y * b) / t))
    if ((x <= (-2.3d+23)) .or. (.not. (x <= 2.6d-29))) then
        tmp = x / t_1
    else
        tmp = (y * z) / (t * t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + (a + ((y * b) / t));
	double tmp;
	if ((x <= -2.3e+23) || !(x <= 2.6e-29)) {
		tmp = x / t_1;
	} else {
		tmp = (y * z) / (t * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 + (a + ((y * b) / t))
	tmp = 0
	if (x <= -2.3e+23) or not (x <= 2.6e-29):
		tmp = x / t_1
	else:
		tmp = (y * z) / (t * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if ((x <= -2.3e+23) || !(x <= 2.6e-29))
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(y * z) / Float64(t * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 + (a + ((y * b) / t));
	tmp = 0.0;
	if ((x <= -2.3e+23) || ~((x <= 2.6e-29)))
		tmp = x / t_1;
	else
		tmp = (y * z) / (t * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -2.3e+23], N[Not[LessEqual[x, 2.6e-29]], $MachinePrecision]], N[(x / t$95$1), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e23 or 2.6000000000000002e-29 < x

   1. Initial program 81.5%

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

   2. Taylor expanded in x around inf 74.0%

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

   if -2.3e23 < x < 2.6000000000000002e-29

   1. Initial program 75.5%

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

   2. Taylor expanded in x around 0 64.8%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+23} \lor \neg \left(x \leq 2.6 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \end{array} \]

Alternative 9: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+182}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+64}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+258}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.05e+182)
   (/ z b)
   (if (<= b 2.3e+64)
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (if (<= b 3.8e+258) (/ z b) (/ x (+ 1.0 (+ a (/ (* y b) t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.05e+182) {
		tmp = z / b;
	} else if (b <= 2.3e+64) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (b <= 3.8e+258) {
		tmp = z / b;
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.05d+182)) then
        tmp = z / b
    else if (b <= 2.3d+64) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (b <= 3.8d+258) then
        tmp = z / b
    else
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.05e+182) {
		tmp = z / b;
	} else if (b <= 2.3e+64) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (b <= 3.8e+258) {
		tmp = z / b;
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.05e+182:
		tmp = z / b
	elif b <= 2.3e+64:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif b <= 3.8e+258:
		tmp = z / b
	else:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.05e+182)
		tmp = Float64(z / b);
	elseif (b <= 2.3e+64)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (b <= 3.8e+258)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.05e+182)
		tmp = z / b;
	elseif (b <= 2.3e+64)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (b <= 3.8e+258)
		tmp = z / b;
	else
		tmp = x / (1.0 + (a + ((y * b) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.05e+182], N[(z / b), $MachinePrecision], If[LessEqual[b, 2.3e+64], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+258], N[(z / b), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.0499999999999999e182 or 2.3e64 < b < 3.80000000000000009e258

   1. Initial program 59.2%

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

   2. Taylor expanded in y around inf 66.0%

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

   if -1.0499999999999999e182 < b < 2.3e64

   1. Initial program 84.9%

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

   2. Taylor expanded in b around 0 71.7%

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

   if 3.80000000000000009e258 < b

   1. Initial program 80.2%

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

   2. Taylor expanded in x around inf 80.6%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+182}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+64}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+258}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]

Alternative 10: 55.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+176}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.2e+176)
   (/ z b)
   (if (<= z 1.5e+95)
     (/ x (+ 1.0 (+ a (/ (* y b) t))))
     (* (/ y t) (/ z (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.2e+176) {
		tmp = z / b;
	} else if (z <= 1.5e+95) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = (y / t) * (z / (a + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.2d+176)) then
        tmp = z / b
    else if (z <= 1.5d+95) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = (y / t) * (z / (a + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.2e+176) {
		tmp = z / b;
	} else if (z <= 1.5e+95) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = (y / t) * (z / (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.2e+176:
		tmp = z / b
	elif z <= 1.5e+95:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = (y / t) * (z / (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.2e+176)
		tmp = Float64(z / b);
	elseif (z <= 1.5e+95)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.2e+176)
		tmp = z / b;
	elseif (z <= 1.5e+95)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = (y / t) * (z / (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.2e+176], N[(z / b), $MachinePrecision], If[LessEqual[z, 1.5e+95], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1999999999999998e176

   1. Initial program 68.2%

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

   2. Taylor expanded in y around inf 48.3%

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

   if -3.1999999999999998e176 < z < 1.49999999999999996e95

   1. Initial program 82.8%

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

   2. Taylor expanded in x around inf 70.9%

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

   if 1.49999999999999996e95 < z

   1. Initial program 68.3%

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

   2. Taylor expanded in b around 0 58.3%

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

   3. Taylor expanded in x around 0 44.7%

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

      1. times-frac 52.5%

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

   5. Simplified 52.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+176}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \end{array} \]

Alternative 11: 54.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{+201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+167}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a + 1}\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-115} \lor \neg \left(t \leq 5.8 \cdot 10^{-17}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -2.15e+201)
     t_1
     (if (<= t -1.3e+167)
       (* (/ z t) (/ y (+ a 1.0)))
       (if (or (<= t -7.4e-115) (not (<= t 5.8e-17))) t_1 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -2.15e+201) {
		tmp = t_1;
	} else if (t <= -1.3e+167) {
		tmp = (z / t) * (y / (a + 1.0));
	} else if ((t <= -7.4e-115) || !(t <= 5.8e-17)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-2.15d+201)) then
        tmp = t_1
    else if (t <= (-1.3d+167)) then
        tmp = (z / t) * (y / (a + 1.0d0))
    else if ((t <= (-7.4d-115)) .or. (.not. (t <= 5.8d-17))) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -2.15e+201) {
		tmp = t_1;
	} else if (t <= -1.3e+167) {
		tmp = (z / t) * (y / (a + 1.0));
	} else if ((t <= -7.4e-115) || !(t <= 5.8e-17)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -2.15e+201:
		tmp = t_1
	elif t <= -1.3e+167:
		tmp = (z / t) * (y / (a + 1.0))
	elif (t <= -7.4e-115) or not (t <= 5.8e-17):
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -2.15e+201)
		tmp = t_1;
	elseif (t <= -1.3e+167)
		tmp = Float64(Float64(z / t) * Float64(y / Float64(a + 1.0)));
	elseif ((t <= -7.4e-115) || !(t <= 5.8e-17))
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -2.15e+201)
		tmp = t_1;
	elseif (t <= -1.3e+167)
		tmp = (z / t) * (y / (a + 1.0));
	elseif ((t <= -7.4e-115) || ~((t <= 5.8e-17)))
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.15e+201], t$95$1, If[LessEqual[t, -1.3e+167], N[(N[(z / t), $MachinePrecision] * N[(y / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -7.4e-115], N[Not[LessEqual[t, 5.8e-17]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.14999999999999995e201 or -1.3000000000000001e167 < t < -7.4e-115 or 5.8000000000000006e-17 < t

   1. Initial program 84.4%

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

   2. Taylor expanded in y around 0 59.0%

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

   if -2.14999999999999995e201 < t < -1.3000000000000001e167

   1. Initial program 82.9%

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

   2. Taylor expanded in b around 0 74.2%

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

   3. Taylor expanded in x around 0 57.0%

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

      1. *-commutative 57.0%

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

      2. times-frac 82.7%

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

   5. Applied egg-rr 82.7%

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

   if -7.4e-115 < t < 5.8000000000000006e-17

   1. Initial program 68.6%

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

   2. Taylor expanded in y around inf 55.1%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+201}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+167}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a + 1}\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-115} \lor \neg \left(t \leq 5.8 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 12: 41.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -2.173 \cdot 10^{-296}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.02e+125)
   (/ x a)
   (if (<= a -2.173e-296)
     (/ z b)
     (if (<= a 1.1e-134) x (if (<= a 6.6e+95) (/ z b) (/ x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.02e+125) {
		tmp = x / a;
	} else if (a <= -2.173e-296) {
		tmp = z / b;
	} else if (a <= 1.1e-134) {
		tmp = x;
	} else if (a <= 6.6e+95) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.02d+125)) then
        tmp = x / a
    else if (a <= (-2.173d-296)) then
        tmp = z / b
    else if (a <= 1.1d-134) then
        tmp = x
    else if (a <= 6.6d+95) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.02e+125) {
		tmp = x / a;
	} else if (a <= -2.173e-296) {
		tmp = z / b;
	} else if (a <= 1.1e-134) {
		tmp = x;
	} else if (a <= 6.6e+95) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.02e+125:
		tmp = x / a
	elif a <= -2.173e-296:
		tmp = z / b
	elif a <= 1.1e-134:
		tmp = x
	elif a <= 6.6e+95:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.02e+125)
		tmp = Float64(x / a);
	elseif (a <= -2.173e-296)
		tmp = Float64(z / b);
	elseif (a <= 1.1e-134)
		tmp = x;
	elseif (a <= 6.6e+95)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.02e+125)
		tmp = x / a;
	elseif (a <= -2.173e-296)
		tmp = z / b;
	elseif (a <= 1.1e-134)
		tmp = x;
	elseif (a <= 6.6e+95)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.02e+125], N[(x / a), $MachinePrecision], If[LessEqual[a, -2.173e-296], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.1e-134], x, If[LessEqual[a, 6.6e+95], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.02e125 or 6.5999999999999997e95 < a

   1. Initial program 83.5%

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

   2. Taylor expanded in y around 0 61.5%

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

   3. Taylor expanded in a around inf 61.5%

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

   if -1.02e125 < a < -2.173e-296 or 1.1e-134 < a < 6.5999999999999997e95

   1. Initial program 73.5%

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

   2. Taylor expanded in y around inf 44.2%

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

   if -2.173e-296 < a < 1.1e-134

   1. Initial program 83.0%

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

   2. Taylor expanded in y around 0 43.3%

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

   3. Taylor expanded in a around 0 43.3%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -2.173 \cdot 10^{-296}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 13: 55.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.1 \cdot 10^{-115} \lor \neg \left(t \leq 2.15 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.1e-115) (not (<= t 2.15e-15))) (/ 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 <= -7.1e-115) || !(t <= 2.15e-15)) {
		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 <= (-7.1d-115)) .or. (.not. (t <= 2.15d-15))) 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 <= -7.1e-115) || !(t <= 2.15e-15)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.1e-115) or not (t <= 2.15e-15):
		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 <= -7.1e-115) || !(t <= 2.15e-15))
		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 <= -7.1e-115) || ~((t <= 2.15e-15)))
		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, -7.1e-115], N[Not[LessEqual[t, 2.15e-15]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.0999999999999998e-115 or 2.1499999999999998e-15 < t

   1. Initial program 84.3%

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

   2. Taylor expanded in y around 0 57.0%

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

   if -7.0999999999999998e-115 < t < 2.1499999999999998e-15

   1. Initial program 68.6%

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

   2. Taylor expanded in y around inf 55.1%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.1 \cdot 10^{-115} \lor \neg \left(t \leq 2.15 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 14: 41.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.12 \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -0.12) (not (<= a 1.0))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -0.12) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-0.12d0)) .or. (.not. (a <= 1.0d0))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -0.12) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -0.12) or not (a <= 1.0):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -0.12) || !(a <= 1.0))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -0.12) || ~((a <= 1.0)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -0.12], N[Not[LessEqual[a, 1.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -0.12 or 1 < a

   1. Initial program 80.2%

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

   2. Taylor expanded in y around 0 51.1%

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

   3. Taylor expanded in a around inf 50.1%

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

   if -0.12 < a < 1

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0 33.9%

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

   3. Taylor expanded in a around 0 33.9%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.12 \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 19.8% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.5%

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

2. Taylor expanded in y around 0 42.2%

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

3. Taylor expanded in a around 0 19.3%

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

4. Final simplification 19.3%

   \[\leadsto x \]

Developer target: 79.5% 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 2023334 
(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))))