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

Percentage Accurate: 74.7% → 88.2%

Time: 11.6s

Alternatives: 13

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: 74.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t_2}{\left(a + 1\right) + t_1}\\ t_4 := 1 + \left(a + t_1\right)\\ \mathbf{if}\;t_3 \leq -1 \cdot 10^{-279}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot t_4} + \frac{x}{t_4}\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{t_2}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{a + \mathsf{fma}\left(\frac{y}{t}, b, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 (+ (+ a 1.0) t_1)))
        (t_4 (+ 1.0 (+ a t_1))))
   (if (<= t_3 -1e-279)
     (+ (/ (* y z) (* t t_4)) (/ x t_4))
     (if (<= t_3 0.0)
       (/ t_2 (+ (+ a 1.0) (/ y (/ t b))))
       (if (<= t_3 5e+302)
         (/ (fma (/ y t) z x) (+ a (fma (/ y t) b 1.0)))
         (/ 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);
	double t_3 = t_2 / ((a + 1.0) + t_1);
	double t_4 = 1.0 + (a + t_1);
	double tmp;
	if (t_3 <= -1e-279) {
		tmp = ((y * z) / (t * t_4)) + (x / t_4);
	} else if (t_3 <= 0.0) {
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	} else if (t_3 <= 5e+302) {
		tmp = fma((y / t), z, x) / (a + fma((y / t), b, 1.0));
	} 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(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / Float64(Float64(a + 1.0) + t_1))
	t_4 = Float64(1.0 + Float64(a + t_1))
	tmp = 0.0
	if (t_3 <= -1e-279)
		tmp = Float64(Float64(Float64(y * z) / Float64(t * t_4)) + Float64(x / t_4));
	elseif (t_3 <= 0.0)
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t_3 <= 5e+302)
		tmp = Float64(fma(Float64(y / t), z, x) / Float64(a + fma(Float64(y / t), b, 1.0)));
	else
		tmp = Float64(z / b);
	end
	return 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[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e-279], N[(N[(N[(y * z), $MachinePrecision] / N[(t * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x / t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+302], N[(N[(N[(y / t), $MachinePrecision] * z + x), $MachinePrecision] / N[(a + N[(N[(y / t), $MachinePrecision] * b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.00000000000000006e-279

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-/l* 93.0%

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

      3. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around 0 94.0%

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

   if -1.00000000000000006e-279 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 69.4%

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

      1. associate-/l* 86.1%

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

   3. Simplified 86.1%

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

   if -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5e302

   1. Initial program 98.7%

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

      1. +-commutative 98.7%

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

      2. associate-*l/ 99.7%

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

      3. fma-def 99.7%

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

      4. associate-+l+ 99.7%

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

      5. +-commutative 99.7%

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

      6. associate-*l/ 99.7%

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

      7. fma-def 99.7%

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

   3. Simplified 99.7%

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

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

   1. Initial program 10.2%

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

      1. *-commutative 10.2%

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

      2. associate-/l* 10.4%

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

      3. associate-*l/ 1.2%

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

   3. Simplified 1.2%

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

   4. Taylor expanded in t around 0 92.8%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-279}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{a + \mathsf{fma}\left(\frac{y}{t}, b, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2: 86.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{if}\;t_2 \leq -2.5 \cdot 10^{-170}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{t_1}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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))))
        (t_3 (/ (+ x (/ z (/ t y))) (+ (+ a 1.0) (* b (/ y t))))))
   (if (<= t_2 -2.5e-170)
     t_3
     (if (<= t_2 0.0)
       (/ t_1 (+ (+ a 1.0) (* y (/ b t))))
       (if (<= t_2 5e+302) t_3 (/ 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 t_3 = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	double tmp;
	if (t_2 <= -2.5e-170) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= 5e+302) {
		tmp = t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    t_2 = t_1 / ((a + 1.0d0) + ((y * b) / t))
    t_3 = (x + (z / (t / y))) / ((a + 1.0d0) + (b * (y / t)))
    if (t_2 <= (-2.5d-170)) then
        tmp = t_3
    else if (t_2 <= 0.0d0) then
        tmp = t_1 / ((a + 1.0d0) + (y * (b / t)))
    else if (t_2 <= 5d+302) then
        tmp = t_3
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_3 = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	double tmp;
	if (t_2 <= -2.5e-170) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= 5e+302) {
		tmp = t_3;
	} 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))
	t_3 = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)))
	tmp = 0
	if t_2 <= -2.5e-170:
		tmp = t_3
	elif t_2 <= 0.0:
		tmp = t_1 / ((a + 1.0) + (y * (b / t)))
	elif t_2 <= 5e+302:
		tmp = t_3
	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)))
	t_3 = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))))
	tmp = 0.0
	if (t_2 <= -2.5e-170)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_2 <= 5e+302)
		tmp = t_3;
	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));
	t_3 = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	tmp = 0.0;
	if (t_2 <= -2.5e-170)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	elseif (t_2 <= 5e+302)
		tmp = t_3;
	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]}, Block[{t$95$3 = 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]}, If[LessEqual[t$95$2, -2.5e-170], t$95$3, If[LessEqual[t$95$2, 0.0], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+302], t$95$3, 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))) < -2.50000000000000005e-170 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5e302

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. associate-/l* 96.8%

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

      3. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   if -2.50000000000000005e-170 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 77.0%

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

      1. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

      1. div-inv 88.1%

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

      2. clear-num 88.1%

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

   5. Applied egg-rr 88.1%

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

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

   1. Initial program 10.2%

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

      1. *-commutative 10.2%

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

      2. associate-/l* 10.4%

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

      3. associate-*l/ 1.2%

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

   3. Simplified 1.2%

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

   4. Taylor expanded in t around 0 92.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2.5 \cdot 10^{-170}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3: 88.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t_2}{\left(a + 1\right) + t_1}\\ t_4 := 1 + \left(a + t_1\right)\\ \mathbf{if}\;t_3 \leq -1 \cdot 10^{-279}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot t_4} + \frac{x}{t_4}\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{t_2}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 (+ (+ a 1.0) t_1)))
        (t_4 (+ 1.0 (+ a t_1))))
   (if (<= t_3 -1e-279)
     (+ (/ (* y z) (* t t_4)) (/ x t_4))
     (if (<= t_3 0.0)
       (/ t_2 (+ (+ a 1.0) (/ y (/ t b))))
       (if (<= t_3 5e+302)
         (/ (+ 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);
	double t_3 = t_2 / ((a + 1.0) + t_1);
	double t_4 = 1.0 + (a + t_1);
	double tmp;
	if (t_3 <= -1e-279) {
		tmp = ((y * z) / (t * t_4)) + (x / t_4);
	} else if (t_3 <= 0.0) {
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	} else if (t_3 <= 5e+302) {
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (y * b) / t
    t_2 = x + ((y * z) / t)
    t_3 = t_2 / ((a + 1.0d0) + t_1)
    t_4 = 1.0d0 + (a + t_1)
    if (t_3 <= (-1d-279)) then
        tmp = ((y * z) / (t * t_4)) + (x / t_4)
    else if (t_3 <= 0.0d0) then
        tmp = t_2 / ((a + 1.0d0) + (y / (t / b)))
    else if (t_3 <= 5d+302) then
        tmp = (x + (z / (t / y))) / ((a + 1.0d0) + (b * (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 t_1 = (y * b) / t;
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / ((a + 1.0) + t_1);
	double t_4 = 1.0 + (a + t_1);
	double tmp;
	if (t_3 <= -1e-279) {
		tmp = ((y * z) / (t * t_4)) + (x / t_4);
	} else if (t_3 <= 0.0) {
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	} else if (t_3 <= 5e+302) {
		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_3 = t_2 / ((a + 1.0) + t_1)
	t_4 = 1.0 + (a + t_1)
	tmp = 0
	if t_3 <= -1e-279:
		tmp = ((y * z) / (t * t_4)) + (x / t_4)
	elif t_3 <= 0.0:
		tmp = t_2 / ((a + 1.0) + (y / (t / b)))
	elif t_3 <= 5e+302:
		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(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / Float64(Float64(a + 1.0) + t_1))
	t_4 = Float64(1.0 + Float64(a + t_1))
	tmp = 0.0
	if (t_3 <= -1e-279)
		tmp = Float64(Float64(Float64(y * z) / Float64(t * t_4)) + Float64(x / t_4));
	elseif (t_3 <= 0.0)
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t_3 <= 5e+302)
		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_3 = t_2 / ((a + 1.0) + t_1);
	t_4 = 1.0 + (a + t_1);
	tmp = 0.0;
	if (t_3 <= -1e-279)
		tmp = ((y * z) / (t * t_4)) + (x / t_4);
	elseif (t_3 <= 0.0)
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	elseif (t_3 <= 5e+302)
		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[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e-279], N[(N[(N[(y * z), $MachinePrecision] / N[(t * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x / t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+302], 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 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.00000000000000006e-279

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-/l* 93.0%

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

      3. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around 0 94.0%

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

   if -1.00000000000000006e-279 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 69.4%

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

      1. associate-/l* 86.1%

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

   3. Simplified 86.1%

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

   if -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5e302

   1. Initial program 98.7%

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

      1. *-commutative 98.7%

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

      2. associate-/l* 99.7%

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

      3. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

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

   1. Initial program 10.2%

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

      1. *-commutative 10.2%

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

      2. associate-/l* 10.4%

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

      3. associate-*l/ 1.2%

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

   3. Simplified 1.2%

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

   4. Taylor expanded in t around 0 92.8%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-279}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 4: 79.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+259}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+139}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.8e+259)
   (/ z b)
   (if (<= y 3.7e+139)
     (/ (+ 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 tmp;
	if (y <= -8.8e+259) {
		tmp = z / b;
	} else if (y <= 3.7e+139) {
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (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 <= (-8.8d+259)) then
        tmp = z / b
    else if (y <= 3.7d+139) then
        tmp = (x + (z / (t / y))) / ((a + 1.0d0) + (b * (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 <= -8.8e+259) {
		tmp = z / b;
	} else if (y <= 3.7e+139) {
		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):
	tmp = 0
	if y <= -8.8e+259:
		tmp = z / b
	elif y <= 3.7e+139:
		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)
	tmp = 0.0
	if (y <= -8.8e+259)
		tmp = Float64(z / b);
	elseif (y <= 3.7e+139)
		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)
	tmp = 0.0;
	if (y <= -8.8e+259)
		tmp = z / b;
	elseif (y <= 3.7e+139)
		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_] := If[LessEqual[y, -8.8e+259], N[(z / b), $MachinePrecision], If[LessEqual[y, 3.7e+139], 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 2 regimes

2. if y < -8.79999999999999965e259 or 3.69999999999999992e139 < y

   1. Initial program 40.6%

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

      1. *-commutative 40.6%

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

      2. associate-/l* 33.7%

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

      3. associate-*l/ 31.4%

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

   3. Simplified 31.4%

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

   4. Taylor expanded in t around 0 72.6%

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

   if -8.79999999999999965e259 < y < 3.69999999999999992e139

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-/l* 90.3%

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

      3. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+259}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+139}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 5: 64.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+179}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -7.7 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+55}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+158}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.6e+179)
   (/ z b)
   (if (<= y -7.7e-56)
     (/ x (+ (+ a 1.0) (/ y (/ t b))))
     (if (<= y 1.65e+55)
       (/ (+ x (/ (* y z) t)) (+ a 1.0))
       (if (<= y 1.75e+158) (/ x (+ (+ a 1.0) (* b (/ y t)))) (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.6e+179) {
		tmp = z / b;
	} else if (y <= -7.7e-56) {
		tmp = x / ((a + 1.0) + (y / (t / b)));
	} else if (y <= 1.65e+55) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 1.75e+158) {
		tmp = x / ((a + 1.0) + (b * (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 <= (-1.6d+179)) then
        tmp = z / b
    else if (y <= (-7.7d-56)) then
        tmp = x / ((a + 1.0d0) + (y / (t / b)))
    else if (y <= 1.65d+55) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (y <= 1.75d+158) then
        tmp = x / ((a + 1.0d0) + (b * (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 <= -1.6e+179) {
		tmp = z / b;
	} else if (y <= -7.7e-56) {
		tmp = x / ((a + 1.0) + (y / (t / b)));
	} else if (y <= 1.65e+55) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 1.75e+158) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.6e+179:
		tmp = z / b
	elif y <= -7.7e-56:
		tmp = x / ((a + 1.0) + (y / (t / b)))
	elif y <= 1.65e+55:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif y <= 1.75e+158:
		tmp = x / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.6e+179)
		tmp = Float64(z / b);
	elseif (y <= -7.7e-56)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (y <= 1.65e+55)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (y <= 1.75e+158)
		tmp = Float64(x / 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)
	tmp = 0.0;
	if (y <= -1.6e+179)
		tmp = z / b;
	elseif (y <= -7.7e-56)
		tmp = x / ((a + 1.0) + (y / (t / b)));
	elseif (y <= 1.65e+55)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (y <= 1.75e+158)
		tmp = x / ((a + 1.0) + (b * (y / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.6e+179], N[(z / b), $MachinePrecision], If[LessEqual[y, -7.7e-56], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+55], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+158], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6000000000000001e179 or 1.7500000000000001e158 < y

   1. Initial program 38.9%

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

      1. *-commutative 38.9%

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

      2. associate-/l* 35.5%

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

      3. associate-*l/ 38.0%

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

   3. Simplified 38.0%

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

   4. Taylor expanded in t around 0 72.4%

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

   if -1.6000000000000001e179 < y < -7.70000000000000037e-56

   1. Initial program 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-/l* 81.3%

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

      3. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in x around inf 67.9%

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

   5. Taylor expanded in y around 0 67.9%

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

      1. associate-/l* 68.0%

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

   7. Simplified 68.0%

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

   if -7.70000000000000037e-56 < y < 1.65e55

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

      2. associate-/l* 97.8%

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

      3. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in b around 0 77.9%

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

   if 1.65e55 < y < 1.7500000000000001e158

   1. Initial program 54.4%

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

      1. *-commutative 54.4%

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

      2. associate-/l* 57.6%

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

      3. associate-*l/ 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in x around inf 82.6%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+179}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -7.7 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+55}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+158}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 6: 42.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-246}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.0)
   (/ x a)
   (if (<= a -1.75e-133)
     x
     (if (<= a -1.05e-246)
       (/ z b)
       (if (<= a 2.8e-193)
         x
         (if (<= a 1.6e-110)
           (/ z b)
           (if (<= a 1.1e-56) x (if (<= a 6.8e+19) (/ z b) (/ x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= -1.75e-133) {
		tmp = x;
	} else if (a <= -1.05e-246) {
		tmp = z / b;
	} else if (a <= 2.8e-193) {
		tmp = x;
	} else if (a <= 1.6e-110) {
		tmp = z / b;
	} else if (a <= 1.1e-56) {
		tmp = x;
	} else if (a <= 6.8e+19) {
		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 <= (-1.0d0)) then
        tmp = x / a
    else if (a <= (-1.75d-133)) then
        tmp = x
    else if (a <= (-1.05d-246)) then
        tmp = z / b
    else if (a <= 2.8d-193) then
        tmp = x
    else if (a <= 1.6d-110) then
        tmp = z / b
    else if (a <= 1.1d-56) then
        tmp = x
    else if (a <= 6.8d+19) 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 <= -1.0) {
		tmp = x / a;
	} else if (a <= -1.75e-133) {
		tmp = x;
	} else if (a <= -1.05e-246) {
		tmp = z / b;
	} else if (a <= 2.8e-193) {
		tmp = x;
	} else if (a <= 1.6e-110) {
		tmp = z / b;
	} else if (a <= 1.1e-56) {
		tmp = x;
	} else if (a <= 6.8e+19) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.0:
		tmp = x / a
	elif a <= -1.75e-133:
		tmp = x
	elif a <= -1.05e-246:
		tmp = z / b
	elif a <= 2.8e-193:
		tmp = x
	elif a <= 1.6e-110:
		tmp = z / b
	elif a <= 1.1e-56:
		tmp = x
	elif a <= 6.8e+19:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.0)
		tmp = Float64(x / a);
	elseif (a <= -1.75e-133)
		tmp = x;
	elseif (a <= -1.05e-246)
		tmp = Float64(z / b);
	elseif (a <= 2.8e-193)
		tmp = x;
	elseif (a <= 1.6e-110)
		tmp = Float64(z / b);
	elseif (a <= 1.1e-56)
		tmp = x;
	elseif (a <= 6.8e+19)
		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 <= -1.0)
		tmp = x / a;
	elseif (a <= -1.75e-133)
		tmp = x;
	elseif (a <= -1.05e-246)
		tmp = z / b;
	elseif (a <= 2.8e-193)
		tmp = x;
	elseif (a <= 1.6e-110)
		tmp = z / b;
	elseif (a <= 1.1e-56)
		tmp = x;
	elseif (a <= 6.8e+19)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.0], N[(x / a), $MachinePrecision], If[LessEqual[a, -1.75e-133], x, If[LessEqual[a, -1.05e-246], N[(z / b), $MachinePrecision], If[LessEqual[a, 2.8e-193], x, If[LessEqual[a, 1.6e-110], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.1e-56], x, If[LessEqual[a, 6.8e+19], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1 or 6.8e19 < a

   1. Initial program 82.6%

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

      1. *-commutative 82.6%

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

      2. associate-/l* 78.8%

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

      3. associate-*l/ 80.3%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in t around inf 53.0%

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

   5. Taylor expanded in a around inf 53.0%

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

   if -1 < a < -1.75000000000000001e-133 or -1.04999999999999997e-246 < a < 2.8000000000000002e-193 or 1.60000000000000014e-110 < a < 1.10000000000000002e-56

   1. Initial program 77.8%

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

      1. +-commutative 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*r/ 80.1%

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

      4. fma-def 80.1%

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

      5. associate-+l+ 80.1%

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

      6. +-commutative 80.1%

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

      7. associate-*r/ 83.5%

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

      8. fma-def 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in a around 0 76.4%

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

   5. Taylor expanded in y around 0 56.2%

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

   if -1.75000000000000001e-133 < a < -1.04999999999999997e-246 or 2.8000000000000002e-193 < a < 1.60000000000000014e-110 or 1.10000000000000002e-56 < a < 6.8e19

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-/l* 76.6%

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

      3. associate-*l/ 74.5%

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

   3. Simplified 74.5%

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

   4. Taylor expanded in t around 0 55.2%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-246}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 7: 42.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-133}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-249}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-199}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-108}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.0)
   (/ x a)
   (if (<= a -1.45e-133)
     (- x (* x a))
     (if (<= a -4.6e-249)
       (/ z b)
       (if (<= a 2.05e-199)
         x
         (if (<= a 2.3e-108)
           (/ z b)
           (if (<= a 2.2e-55) x (if (<= a 5.5e+18) (/ z b) (/ x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= -1.45e-133) {
		tmp = x - (x * a);
	} else if (a <= -4.6e-249) {
		tmp = z / b;
	} else if (a <= 2.05e-199) {
		tmp = x;
	} else if (a <= 2.3e-108) {
		tmp = z / b;
	} else if (a <= 2.2e-55) {
		tmp = x;
	} else if (a <= 5.5e+18) {
		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 <= (-1.0d0)) then
        tmp = x / a
    else if (a <= (-1.45d-133)) then
        tmp = x - (x * a)
    else if (a <= (-4.6d-249)) then
        tmp = z / b
    else if (a <= 2.05d-199) then
        tmp = x
    else if (a <= 2.3d-108) then
        tmp = z / b
    else if (a <= 2.2d-55) then
        tmp = x
    else if (a <= 5.5d+18) 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 <= -1.0) {
		tmp = x / a;
	} else if (a <= -1.45e-133) {
		tmp = x - (x * a);
	} else if (a <= -4.6e-249) {
		tmp = z / b;
	} else if (a <= 2.05e-199) {
		tmp = x;
	} else if (a <= 2.3e-108) {
		tmp = z / b;
	} else if (a <= 2.2e-55) {
		tmp = x;
	} else if (a <= 5.5e+18) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.0:
		tmp = x / a
	elif a <= -1.45e-133:
		tmp = x - (x * a)
	elif a <= -4.6e-249:
		tmp = z / b
	elif a <= 2.05e-199:
		tmp = x
	elif a <= 2.3e-108:
		tmp = z / b
	elif a <= 2.2e-55:
		tmp = x
	elif a <= 5.5e+18:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.0)
		tmp = Float64(x / a);
	elseif (a <= -1.45e-133)
		tmp = Float64(x - Float64(x * a));
	elseif (a <= -4.6e-249)
		tmp = Float64(z / b);
	elseif (a <= 2.05e-199)
		tmp = x;
	elseif (a <= 2.3e-108)
		tmp = Float64(z / b);
	elseif (a <= 2.2e-55)
		tmp = x;
	elseif (a <= 5.5e+18)
		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 <= -1.0)
		tmp = x / a;
	elseif (a <= -1.45e-133)
		tmp = x - (x * a);
	elseif (a <= -4.6e-249)
		tmp = z / b;
	elseif (a <= 2.05e-199)
		tmp = x;
	elseif (a <= 2.3e-108)
		tmp = z / b;
	elseif (a <= 2.2e-55)
		tmp = x;
	elseif (a <= 5.5e+18)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.0], N[(x / a), $MachinePrecision], If[LessEqual[a, -1.45e-133], N[(x - N[(x * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.6e-249], N[(z / b), $MachinePrecision], If[LessEqual[a, 2.05e-199], x, If[LessEqual[a, 2.3e-108], N[(z / b), $MachinePrecision], If[LessEqual[a, 2.2e-55], x, If[LessEqual[a, 5.5e+18], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1 or 5.5e18 < a

   1. Initial program 82.6%

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

      1. *-commutative 82.6%

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

      2. associate-/l* 78.8%

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

      3. associate-*l/ 80.3%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in t around inf 53.0%

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

   5. Taylor expanded in a around inf 53.0%

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

   if -1 < a < -1.4499999999999999e-133

   1. Initial program 74.6%

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

      1. *-commutative 74.6%

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

      2. associate-/l* 74.8%

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

      3. associate-*l/ 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in t around inf 50.0%

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

   5. Taylor expanded in a around 0 47.1%

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

      1. +-commutative 47.1%

         \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot x\right)} \]

      2. mul-1-neg 47.1%

         \[\leadsto x + \color{blue}{\left(-a \cdot x\right)} \]

      3. unsub-neg 47.1%

         \[\leadsto \color{blue}{x - a \cdot x} \]

   7. Simplified 47.1%

      \[\leadsto \color{blue}{x - a \cdot x} \]

   if -1.4499999999999999e-133 < a < -4.5999999999999996e-249 or 2.05000000000000011e-199 < a < 2.29999999999999996e-108 or 2.2e-55 < a < 5.5e18

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-/l* 76.6%

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

      3. associate-*l/ 74.5%

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

   3. Simplified 74.5%

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

   4. Taylor expanded in t around 0 55.2%

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

   if -4.5999999999999996e-249 < a < 2.05000000000000011e-199 or 2.29999999999999996e-108 < a < 2.2e-55

   1. Initial program 79.4%

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

      1. +-commutative 79.4%

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

      2. *-commutative 79.4%

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

      3. associate-*r/ 82.6%

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

      4. fma-def 82.6%

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

      5. associate-+l+ 82.6%

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

      6. +-commutative 82.6%

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

      7. associate-*r/ 84.4%

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

      8. fma-def 84.4%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in a around 0 79.4%

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

   5. Taylor expanded in y around 0 61.2%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-133}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-249}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-199}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-108}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 8: 52.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+152}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+158}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.02e+152)
   (/ z b)
   (if (<= y 1.05e-73)
     (/ x (+ a 1.0))
     (if (<= y 2.15e+158) (/ x (+ 1.0 (* y (/ b t)))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.02e+152) {
		tmp = z / b;
	} else if (y <= 1.05e-73) {
		tmp = x / (a + 1.0);
	} else if (y <= 2.15e+158) {
		tmp = x / (1.0 + (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 (y <= (-1.02d+152)) then
        tmp = z / b
    else if (y <= 1.05d-73) then
        tmp = x / (a + 1.0d0)
    else if (y <= 2.15d+158) then
        tmp = x / (1.0d0 + (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 (y <= -1.02e+152) {
		tmp = z / b;
	} else if (y <= 1.05e-73) {
		tmp = x / (a + 1.0);
	} else if (y <= 2.15e+158) {
		tmp = x / (1.0 + (y * (b / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.02e+152:
		tmp = z / b
	elif y <= 1.05e-73:
		tmp = x / (a + 1.0)
	elif y <= 2.15e+158:
		tmp = x / (1.0 + (y * (b / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.02e+152)
		tmp = Float64(z / b);
	elseif (y <= 1.05e-73)
		tmp = Float64(x / Float64(a + 1.0));
	elseif (y <= 2.15e+158)
		tmp = Float64(x / Float64(1.0 + 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 (y <= -1.02e+152)
		tmp = z / b;
	elseif (y <= 1.05e-73)
		tmp = x / (a + 1.0);
	elseif (y <= 2.15e+158)
		tmp = x / (1.0 + (y * (b / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.02e+152], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.05e-73], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+158], N[(x / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.01999999999999999e152 or 2.15e158 < y

   1. Initial program 42.1%

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

      1. *-commutative 42.1%

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

      2. associate-/l* 37.4%

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

      3. associate-*l/ 39.8%

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

   3. Simplified 39.8%

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

   4. Taylor expanded in t around 0 68.5%

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

   if -1.01999999999999999e152 < y < 1.0499999999999999e-73

   1. Initial program 94.1%

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

      1. *-commutative 94.1%

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

      2. associate-/l* 95.3%

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

      3. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around inf 62.5%

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

   if 1.0499999999999999e-73 < y < 2.15e158

   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. *-commutative 81.0%

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

      2. associate-/l* 82.1%

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

      3. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in x around inf 71.5%

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

   5. Taylor expanded in y around 0 66.5%

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

   6. Taylor expanded in a around 0 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-*l/ 57.3%

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

      3. *-commutative 57.3%

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

   8. Simplified 57.3%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+152}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+158}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 9: 60.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+181} \lor \neg \left(y \leq 1.35 \cdot 10^{+160}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.1e+181) (not (<= y 1.35e+160)))
   (/ 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 ((y <= -3.1e+181) || !(y <= 1.35e+160)) {
		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 ((y <= (-3.1d+181)) .or. (.not. (y <= 1.35d+160))) 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 ((y <= -3.1e+181) || !(y <= 1.35e+160)) {
		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 (y <= -3.1e+181) or not (y <= 1.35e+160):
		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 ((y <= -3.1e+181) || !(y <= 1.35e+160))
		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 ((y <= -3.1e+181) || ~((y <= 1.35e+160)))
		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[Or[LessEqual[y, -3.1e+181], N[Not[LessEqual[y, 1.35e+160]], $MachinePrecision]], 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 2 regimes

2. if y < -3.09999999999999989e181 or 1.35e160 < y

   1. Initial program 38.9%

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

      1. *-commutative 38.9%

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

      2. associate-/l* 35.5%

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

      3. associate-*l/ 38.0%

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

   3. Simplified 38.0%

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

   4. Taylor expanded in t around 0 72.4%

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

   if -3.09999999999999989e181 < y < 1.35e160

   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* 91.8%

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

      3. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around inf 71.2%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+181} \lor \neg \left(y \leq 1.35 \cdot 10^{+160}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]

Alternative 10: 60.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+180}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+159}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1e+180)
   (/ z b)
   (if (<= y 2.5e+159) (/ x (+ (+ a 1.0) (* b (/ y t)))) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1e+180) {
		tmp = z / b;
	} else if (y <= 2.5e+159) {
		tmp = x / ((a + 1.0) + (b * (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 <= (-1d+180)) then
        tmp = z / b
    else if (y <= 2.5d+159) then
        tmp = x / ((a + 1.0d0) + (b * (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 <= -1e+180) {
		tmp = z / b;
	} else if (y <= 2.5e+159) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1e+180:
		tmp = z / b
	elif y <= 2.5e+159:
		tmp = x / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1e+180)
		tmp = Float64(z / b);
	elseif (y <= 2.5e+159)
		tmp = Float64(x / 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)
	tmp = 0.0;
	if (y <= -1e+180)
		tmp = z / b;
	elseif (y <= 2.5e+159)
		tmp = x / ((a + 1.0) + (b * (y / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1e+180], N[(z / b), $MachinePrecision], If[LessEqual[y, 2.5e+159], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1e180 or 2.50000000000000002e159 < y

   1. Initial program 38.9%

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

      1. *-commutative 38.9%

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

      2. associate-/l* 35.5%

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

      3. associate-*l/ 38.0%

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

   3. Simplified 38.0%

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

   4. Taylor expanded in t around 0 72.4%

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

   if -1e180 < y < 2.50000000000000002e159

   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* 91.8%

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

      3. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around inf 72.2%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+180}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+159}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 11: 54.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+152}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.9e+152) (/ z b) (if (<= y 1.2e+84) (/ x (+ a 1.0)) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.9e+152) {
		tmp = z / b;
	} else if (y <= 1.2e+84) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.9d+152)) then
        tmp = z / b
    else if (y <= 1.2d+84) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.9e+152) {
		tmp = z / b;
	} else if (y <= 1.2e+84) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.9e+152:
		tmp = z / b
	elif y <= 1.2e+84:
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.9e+152)
		tmp = Float64(z / b);
	elseif (y <= 1.2e+84)
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.9e+152)
		tmp = z / b;
	elseif (y <= 1.2e+84)
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.9e+152], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.2e+84], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8999999999999998e152 or 1.2e84 < y

   1. Initial program 41.9%

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

      1. *-commutative 41.9%

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

      2. associate-/l* 37.0%

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

      3. associate-*l/ 41.7%

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

   3. Simplified 41.7%

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

   4. Taylor expanded in t around 0 64.0%

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

   if -2.8999999999999998e152 < y < 1.2e84

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-/l* 95.5%

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

      3. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around inf 59.7%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+152}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 12: 41.0% accurate, 2.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if a < -1 or 1 < a

   1. Initial program 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* 78.6%

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

      3. associate-*l/ 79.1%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in t around inf 51.8%

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

   5. Taylor expanded in a around inf 51.8%

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

   if -1 < a < 1

   1. Initial program 76.1%

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

      1. +-commutative 76.1%

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

      2. *-commutative 76.1%

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

      3. associate-*r/ 79.0%

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

      4. fma-def 79.0%

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

      5. associate-+l+ 79.0%

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

      6. +-commutative 79.0%

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

      7. associate-*r/ 79.8%

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

      8. fma-def 79.8%

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

   3. Simplified 79.8%

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

   4. Taylor expanded in a around 0 73.6%

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

   5. Taylor expanded in y around 0 41.4%

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

4. Final simplification 46.4%

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

Alternative 13: 20.0% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.1%

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

   1. +-commutative 79.1%

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

   2. *-commutative 79.1%

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

   3. associate-*r/ 78.8%

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

   4. fma-def 78.8%

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

   5. associate-+l+ 78.8%

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

   6. +-commutative 78.8%

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

   7. associate-*r/ 75.9%

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

   8. fma-def 75.9%

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

3. Simplified 75.9%

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

4. Taylor expanded in a around 0 48.7%

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

5. Taylor expanded in y around 0 23.3%

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

6. Final simplification 23.3%

   \[\leadsto x \]

Developer target: 78.4% 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 2023257 
(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))))