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

Percentage Accurate: 75.7% → 90.5%

Time: 18.0s

Alternatives: 17

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1 + \left(a + 1\right)}\\ t_3 := 1 + \left(a + t\_1\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-307}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{y}{t \cdot t\_3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (/ (+ x (/ (* y z) t)) (+ t_1 (+ a 1.0))))
        (t_3 (+ 1.0 (+ a t_1))))
   (if (<= t_2 -2e-307)
     t_2
     (if (<= t_2 0.0)
       (+ (/ z b) (* t (/ (/ x b) y)))
       (if (<= t_2 2e+295)
         t_2
         (if (<= t_2 INFINITY)
           (* z (+ (/ x (* z t_3)) (/ y (* t t_3))))
           (/ (+ z (* t (/ x y))) b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double t_3 = 1.0 + (a + t_1);
	double tmp;
	if (t_2 <= -2e-307) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else if (t_2 <= 2e+295) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	} else {
		tmp = (z + (t * (x / y))) / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double t_3 = 1.0 + (a + t_1);
	double tmp;
	if (t_2 <= -2e-307) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else if (t_2 <= 2e+295) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	} else {
		tmp = (z + (t * (x / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0))
	t_3 = 1.0 + (a + t_1)
	tmp = 0
	if t_2 <= -2e-307:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (z / b) + (t * ((x / b) / y))
	elif t_2 <= 2e+295:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)))
	else:
		tmp = (z + (t * (x / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(t_1 + Float64(a + 1.0)))
	t_3 = Float64(1.0 + Float64(a + t_1))
	tmp = 0.0
	if (t_2 <= -2e-307)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	elseif (t_2 <= 2e+295)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_3)) + Float64(y / Float64(t * t_3))));
	else
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	t_3 = 1.0 + (a + t_1);
	tmp = 0.0;
	if (t_2 <= -2e-307)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (z / b) + (t * ((x / b) / y));
	elseif (t_2 <= 2e+295)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	else
		tmp = (z + (t * (x / y))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-307], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+295], t$95$2, If[LessEqual[t$95$2, Infinity], N[(z * N[(N[(x / N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999982e-307 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2e295

   1. Initial program 97.3%

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

   if -1.99999999999999982e-307 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 55.5%

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

      1. associate-/l* 55.3%

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

      2. associate-/l* 70.1%

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

   3. Simplified 70.1%

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

   5. Taylor expanded in b around inf 60.1%

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

   6. Taylor expanded in y around inf 60.1%

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

   7. Taylor expanded in y around inf 67.4%

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

      1. associate-/l* 67.8%

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

      2. associate-/r* 83.7%

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

   9. Simplified 83.7%

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

   if 2e295 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 33.4%

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

      1. associate-/l* 55.6%

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

      2. associate-/l* 55.6%

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

   3. Simplified 55.6%

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

   5. Taylor expanded in z around inf 94.2%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

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

      1. associate-/l* 0.3%

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

      2. associate-/l* 9.2%

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

   3. Simplified 9.2%

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

   5. Taylor expanded in b around inf 5.5%

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

   6. Taylor expanded in y around inf 32.7%

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

   7. Taylor expanded in b around 0 95.6%

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

      1. *-un-lft-identity 95.6%

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

      2. associate-/l* 100.0%

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

   9. Applied egg-rr 100.0%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-307}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+297}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 -2e-307)
     t_1
     (if (<= t_1 0.0)
       (+ (/ z b) (* t (/ (/ x b) y)))
       (if (<= t_1 4e+297) t_1 (/ (+ z (* t (/ x y))) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -2e-307) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else if (t_1 <= 4e+297) {
		tmp = t_1;
	} else {
		tmp = (z + (t * (x / y))) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0d0))
    if (t_1 <= (-2d-307)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = (z / b) + (t * ((x / b) / y))
    else if (t_1 <= 4d+297) then
        tmp = t_1
    else
        tmp = (z + (t * (x / y))) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -2e-307) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else if (t_1 <= 4e+297) {
		tmp = t_1;
	} else {
		tmp = (z + (t * (x / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_1 <= -2e-307:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (z / b) + (t * ((x / b) / y))
	elif t_1 <= 4e+297:
		tmp = t_1
	else:
		tmp = (z + (t * (x / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= -2e-307)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	elseif (t_1 <= 4e+297)
		tmp = t_1;
	else
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_1 <= -2e-307)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (z / b) + (t * ((x / b) / y));
	elseif (t_1 <= 4e+297)
		tmp = t_1;
	else
		tmp = (z + (t * (x / y))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-307], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+297], t$95$1, N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999982e-307 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.0000000000000001e297

   1. Initial program 97.3%

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

   if -1.99999999999999982e-307 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 55.5%

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

      1. associate-/l* 55.3%

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

      2. associate-/l* 70.1%

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

   3. Simplified 70.1%

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

   5. Taylor expanded in b around inf 60.1%

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

   6. Taylor expanded in y around inf 60.1%

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

   7. Taylor expanded in y around inf 67.4%

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

      1. associate-/l* 67.8%

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

      2. associate-/r* 83.7%

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

   9. Simplified 83.7%

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

   if 4.0000000000000001e297 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 12.3%

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

      1. associate-/l* 22.4%

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

      2. associate-/l* 27.6%

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

   3. Simplified 27.6%

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

   5. Taylor expanded in b around inf 14.7%

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

   6. Taylor expanded in y around inf 40.5%

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

   7. Taylor expanded in b around 0 79.4%

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

      1. *-un-lft-identity 79.4%

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

      2. associate-/l* 81.9%

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

   9. Applied egg-rr 81.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-307}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 4 \cdot 10^{+297}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 55.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+84}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot \frac{z}{a}}{t}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.4e+84)
   (/ z b)
   (if (<= y 6e-66)
     (/ x (+ a 1.0))
     (if (<= y 4.5e-27)
       (/ (* y (/ z a)) t)
       (if (<= y 5e+17)
         (/ x (+ 1.0 (/ (* y b) t)))
         (if (<= y 1.55e+38) (/ (* y (/ z t)) (+ a 1.0)) (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.4e+84) {
		tmp = z / b;
	} else if (y <= 6e-66) {
		tmp = x / (a + 1.0);
	} else if (y <= 4.5e-27) {
		tmp = (y * (z / a)) / t;
	} else if (y <= 5e+17) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (y <= 1.55e+38) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.4d+84)) then
        tmp = z / b
    else if (y <= 6d-66) then
        tmp = x / (a + 1.0d0)
    else if (y <= 4.5d-27) then
        tmp = (y * (z / a)) / t
    else if (y <= 5d+17) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (y <= 1.55d+38) then
        tmp = (y * (z / t)) / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.4e+84) {
		tmp = z / b;
	} else if (y <= 6e-66) {
		tmp = x / (a + 1.0);
	} else if (y <= 4.5e-27) {
		tmp = (y * (z / a)) / t;
	} else if (y <= 5e+17) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (y <= 1.55e+38) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.4e+84:
		tmp = z / b
	elif y <= 6e-66:
		tmp = x / (a + 1.0)
	elif y <= 4.5e-27:
		tmp = (y * (z / a)) / t
	elif y <= 5e+17:
		tmp = x / (1.0 + ((y * b) / t))
	elif y <= 1.55e+38:
		tmp = (y * (z / t)) / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.4e+84)
		tmp = Float64(z / b);
	elseif (y <= 6e-66)
		tmp = Float64(x / Float64(a + 1.0));
	elseif (y <= 4.5e-27)
		tmp = Float64(Float64(y * Float64(z / a)) / t);
	elseif (y <= 5e+17)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (y <= 1.55e+38)
		tmp = Float64(Float64(y * Float64(z / t)) / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.4e+84)
		tmp = z / b;
	elseif (y <= 6e-66)
		tmp = x / (a + 1.0);
	elseif (y <= 4.5e-27)
		tmp = (y * (z / a)) / t;
	elseif (y <= 5e+17)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (y <= 1.55e+38)
		tmp = (y * (z / t)) / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.4e+84], N[(z / b), $MachinePrecision], If[LessEqual[y, 6e-66], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-27], N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 5e+17], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+38], N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.3999999999999997e84 or 1.55000000000000009e38 < y

   1. Initial program 51.8%

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

      1. associate-/l* 56.2%

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

      2. associate-/l* 63.8%

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

   3. Simplified 63.8%

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

   5. Taylor expanded in y around inf 61.9%

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

   if -4.3999999999999997e84 < y < 6.0000000000000004e-66

   1. Initial program 92.9%

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

      1. associate-/l* 85.7%

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

      2. associate-/l* 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in y around 0 54.7%

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

   if 6.0000000000000004e-66 < y < 4.5000000000000002e-27

   1. Initial program 90.5%

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

      1. associate-/l* 90.5%

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

      2. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around inf 81.3%

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

   6. Taylor expanded in a around inf 52.5%

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

   7. Taylor expanded in t around 0 70.2%

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

   8. Taylor expanded in t around 0 69.7%

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

      1. associate-*r/ 69.5%

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

   10. Simplified 69.5%

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

   if 4.5000000000000002e-27 < y < 5e17

   1. Initial program 85.2%

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

      1. associate-/l* 85.0%

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

      2. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in x around inf 62.7%

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

   6. Taylor expanded in a around 0 55.1%

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

   if 5e17 < y < 1.55000000000000009e38

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0 99.8%

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

   6. Taylor expanded in x around 0 85.6%

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

      1. associate-*r/ 85.6%

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

   8. Simplified 85.6%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+84}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot \frac{z}{a}}{t}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+84}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+37}:\\ \;\;\;\;\frac{y \cdot \frac{z}{a}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.4e+84)
   (/ z b)
   (if (<= y 5.2e-78)
     (/ x (+ a 1.0))
     (if (<= y 1.8e-21)
       (/ z b)
       (if (<= y 5.2e+18)
         (+ x (/ (* y z) t))
         (if (<= y 1.45e+37) (/ (* y (/ z a)) t) (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.4e+84) {
		tmp = z / b;
	} else if (y <= 5.2e-78) {
		tmp = x / (a + 1.0);
	} else if (y <= 1.8e-21) {
		tmp = z / b;
	} else if (y <= 5.2e+18) {
		tmp = x + ((y * z) / t);
	} else if (y <= 1.45e+37) {
		tmp = (y * (z / a)) / 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 <= (-4.4d+84)) then
        tmp = z / b
    else if (y <= 5.2d-78) then
        tmp = x / (a + 1.0d0)
    else if (y <= 1.8d-21) then
        tmp = z / b
    else if (y <= 5.2d+18) then
        tmp = x + ((y * z) / t)
    else if (y <= 1.45d+37) then
        tmp = (y * (z / a)) / 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 <= -4.4e+84) {
		tmp = z / b;
	} else if (y <= 5.2e-78) {
		tmp = x / (a + 1.0);
	} else if (y <= 1.8e-21) {
		tmp = z / b;
	} else if (y <= 5.2e+18) {
		tmp = x + ((y * z) / t);
	} else if (y <= 1.45e+37) {
		tmp = (y * (z / a)) / t;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.4e+84:
		tmp = z / b
	elif y <= 5.2e-78:
		tmp = x / (a + 1.0)
	elif y <= 1.8e-21:
		tmp = z / b
	elif y <= 5.2e+18:
		tmp = x + ((y * z) / t)
	elif y <= 1.45e+37:
		tmp = (y * (z / a)) / t
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.4e+84)
		tmp = Float64(z / b);
	elseif (y <= 5.2e-78)
		tmp = Float64(x / Float64(a + 1.0));
	elseif (y <= 1.8e-21)
		tmp = Float64(z / b);
	elseif (y <= 5.2e+18)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (y <= 1.45e+37)
		tmp = Float64(Float64(y * Float64(z / a)) / 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 <= -4.4e+84)
		tmp = z / b;
	elseif (y <= 5.2e-78)
		tmp = x / (a + 1.0);
	elseif (y <= 1.8e-21)
		tmp = z / b;
	elseif (y <= 5.2e+18)
		tmp = x + ((y * z) / t);
	elseif (y <= 1.45e+37)
		tmp = (y * (z / a)) / t;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.4e+84], N[(z / b), $MachinePrecision], If[LessEqual[y, 5.2e-78], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-21], N[(z / b), $MachinePrecision], If[LessEqual[y, 5.2e+18], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+37], N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.3999999999999997e84 or 5.2000000000000002e-78 < y < 1.79999999999999995e-21 or 1.44999999999999989e37 < y

   1. Initial program 57.3%

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

      1. associate-/l* 61.0%

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

      2. associate-/l* 66.5%

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

   3. Simplified 66.5%

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

   5. Taylor expanded in y around inf 59.4%

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

   if -4.3999999999999997e84 < y < 5.2000000000000002e-78

   1. Initial program 93.4%

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

      1. associate-/l* 86.0%

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

      2. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in y around 0 56.1%

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

   if 1.79999999999999995e-21 < y < 5.2e18

   1. Initial program 82.5%

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

      1. associate-/l* 82.4%

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

      2. associate-/l* 73.6%

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

   3. Simplified 73.6%

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

   5. Taylor expanded in b around 0 64.8%

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

   6. Taylor expanded in a around 0 55.9%

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

   if 5.2e18 < y < 1.44999999999999989e37

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.3%

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

   6. Taylor expanded in a around inf 72.0%

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

   7. Taylor expanded in t around 0 71.5%

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

   8. Taylor expanded in t around 0 71.5%

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

      1. associate-*r/ 72.0%

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

   10. Simplified 72.0%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+84}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+37}:\\ \;\;\;\;\frac{y \cdot \frac{z}{a}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \frac{z}{a}}{t}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+84}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y (/ z a)) t)))
   (if (<= y -4.4e+84)
     (/ z b)
     (if (<= y 6e-66)
       (/ x (+ a 1.0))
       (if (<= y 5.3e-27)
         t_1
         (if (<= y 6.5e+18)
           (/ x (+ 1.0 (/ (* y b) t)))
           (if (<= y 1.55e+38) t_1 (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * (z / a)) / t;
	double tmp;
	if (y <= -4.4e+84) {
		tmp = z / b;
	} else if (y <= 6e-66) {
		tmp = x / (a + 1.0);
	} else if (y <= 5.3e-27) {
		tmp = t_1;
	} else if (y <= 6.5e+18) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (y <= 1.55e+38) {
		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 = (y * (z / a)) / t
    if (y <= (-4.4d+84)) then
        tmp = z / b
    else if (y <= 6d-66) then
        tmp = x / (a + 1.0d0)
    else if (y <= 5.3d-27) then
        tmp = t_1
    else if (y <= 6.5d+18) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (y <= 1.55d+38) 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 = (y * (z / a)) / t;
	double tmp;
	if (y <= -4.4e+84) {
		tmp = z / b;
	} else if (y <= 6e-66) {
		tmp = x / (a + 1.0);
	} else if (y <= 5.3e-27) {
		tmp = t_1;
	} else if (y <= 6.5e+18) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (y <= 1.55e+38) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * (z / a)) / t
	tmp = 0
	if y <= -4.4e+84:
		tmp = z / b
	elif y <= 6e-66:
		tmp = x / (a + 1.0)
	elif y <= 5.3e-27:
		tmp = t_1
	elif y <= 6.5e+18:
		tmp = x / (1.0 + ((y * b) / t))
	elif y <= 1.55e+38:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(z / a)) / t)
	tmp = 0.0
	if (y <= -4.4e+84)
		tmp = Float64(z / b);
	elseif (y <= 6e-66)
		tmp = Float64(x / Float64(a + 1.0));
	elseif (y <= 5.3e-27)
		tmp = t_1;
	elseif (y <= 6.5e+18)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (y <= 1.55e+38)
		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 = (y * (z / a)) / t;
	tmp = 0.0;
	if (y <= -4.4e+84)
		tmp = z / b;
	elseif (y <= 6e-66)
		tmp = x / (a + 1.0);
	elseif (y <= 5.3e-27)
		tmp = t_1;
	elseif (y <= 6.5e+18)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (y <= 1.55e+38)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[y, -4.4e+84], N[(z / b), $MachinePrecision], If[LessEqual[y, 6e-66], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.3e-27], t$95$1, If[LessEqual[y, 6.5e+18], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+38], t$95$1, N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.3999999999999997e84 or 1.55000000000000009e38 < y

   1. Initial program 51.8%

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

      1. associate-/l* 56.2%

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

      2. associate-/l* 63.8%

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

   3. Simplified 63.8%

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

   5. Taylor expanded in y around inf 61.9%

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

   if -4.3999999999999997e84 < y < 6.0000000000000004e-66

   1. Initial program 92.9%

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

      1. associate-/l* 85.7%

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

      2. associate-/l* 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in y around 0 54.7%

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

   if 6.0000000000000004e-66 < y < 5.30000000000000006e-27 or 6.5e18 < y < 1.55000000000000009e38

   1. Initial program 94.3%

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

      1. associate-/l* 94.3%

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

      2. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around inf 88.7%

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

   6. Taylor expanded in a around inf 60.5%

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

   7. Taylor expanded in t around 0 70.7%

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

   8. Taylor expanded in t around 0 70.4%

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

      1. associate-*r/ 70.5%

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

   10. Simplified 70.5%

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

   if 5.30000000000000006e-27 < y < 6.5e18

   1. Initial program 85.2%

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

      1. associate-/l* 85.0%

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

      2. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in x around inf 62.7%

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

   6. Taylor expanded in a around 0 55.1%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+84}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot \frac{z}{a}}{t}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;\frac{y \cdot \frac{z}{a}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{if}\;y \leq -9 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 0.00069:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b)))
   (if (<= y -9e-104)
     t_1
     (if (<= y 1.9e-79)
       (/ x (+ a 1.0))
       (if (<= y 0.00069)
         t_1
         (if (<= y 1.55e+38)
           (/ (* y (/ z t)) (+ a 1.0))
           (+ (/ z b) (* t (/ (/ x b) y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double tmp;
	if (y <= -9e-104) {
		tmp = t_1;
	} else if (y <= 1.9e-79) {
		tmp = x / (a + 1.0);
	} else if (y <= 0.00069) {
		tmp = t_1;
	} else if (y <= 1.55e+38) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else {
		tmp = (z / b) + (t * ((x / b) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + ((x * t) / y)) / b
    if (y <= (-9d-104)) then
        tmp = t_1
    else if (y <= 1.9d-79) then
        tmp = x / (a + 1.0d0)
    else if (y <= 0.00069d0) then
        tmp = t_1
    else if (y <= 1.55d+38) then
        tmp = (y * (z / t)) / (a + 1.0d0)
    else
        tmp = (z / b) + (t * ((x / b) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double tmp;
	if (y <= -9e-104) {
		tmp = t_1;
	} else if (y <= 1.9e-79) {
		tmp = x / (a + 1.0);
	} else if (y <= 0.00069) {
		tmp = t_1;
	} else if (y <= 1.55e+38) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else {
		tmp = (z / b) + (t * ((x / b) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	tmp = 0
	if y <= -9e-104:
		tmp = t_1
	elif y <= 1.9e-79:
		tmp = x / (a + 1.0)
	elif y <= 0.00069:
		tmp = t_1
	elif y <= 1.55e+38:
		tmp = (y * (z / t)) / (a + 1.0)
	else:
		tmp = (z / b) + (t * ((x / b) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	tmp = 0.0
	if (y <= -9e-104)
		tmp = t_1;
	elseif (y <= 1.9e-79)
		tmp = Float64(x / Float64(a + 1.0));
	elseif (y <= 0.00069)
		tmp = t_1;
	elseif (y <= 1.55e+38)
		tmp = Float64(Float64(y * Float64(z / t)) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((x * t) / y)) / b;
	tmp = 0.0;
	if (y <= -9e-104)
		tmp = t_1;
	elseif (y <= 1.9e-79)
		tmp = x / (a + 1.0);
	elseif (y <= 0.00069)
		tmp = t_1;
	elseif (y <= 1.55e+38)
		tmp = (y * (z / t)) / (a + 1.0);
	else
		tmp = (z / b) + (t * ((x / b) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -9e-104], t$95$1, If[LessEqual[y, 1.9e-79], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00069], t$95$1, If[LessEqual[y, 1.55e+38], N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.9999999999999995e-104 or 1.9000000000000001e-79 < y < 6.89999999999999967e-4

   1. Initial program 70.4%

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

      1. associate-/l* 72.3%

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

      2. associate-/l* 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in b around inf 38.8%

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

   6. Taylor expanded in y around inf 47.4%

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

   7. Taylor expanded in b around 0 57.0%

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

   if -8.9999999999999995e-104 < y < 1.9000000000000001e-79

   1. Initial program 96.8%

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

      1. associate-/l* 86.9%

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

      2. associate-/l* 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in y around 0 66.6%

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

   if 6.89999999999999967e-4 < y < 1.55000000000000009e38

   1. Initial program 99.9%

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

      1. associate-/l* 99.7%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in b around 0 99.9%

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

   6. Taylor expanded in x around 0 64.5%

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

      1. associate-*r/ 64.3%

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

   8. Simplified 64.3%

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

   if 1.55000000000000009e38 < y

   1. Initial program 57.7%

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

      1. associate-/l* 59.6%

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

      2. associate-/l* 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in b around inf 39.2%

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

   6. Taylor expanded in y around inf 44.7%

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

   7. Taylor expanded in y around inf 63.2%

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

      1. associate-/l* 65.1%

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

      2. associate-/r* 68.0%

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

   9. Simplified 68.0%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-104}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 0.00069:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 0.00048 \lor \neg \left(y \leq 2.5 \cdot 10^{+41}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b)))
   (if (<= y -5.8e-106)
     t_1
     (if (<= y 5.9e-81)
       (/ x (+ a 1.0))
       (if (or (<= y 0.00048) (not (<= y 2.5e+41)))
         t_1
         (/ (* y (/ z t)) (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double tmp;
	if (y <= -5.8e-106) {
		tmp = t_1;
	} else if (y <= 5.9e-81) {
		tmp = x / (a + 1.0);
	} else if ((y <= 0.00048) || !(y <= 2.5e+41)) {
		tmp = t_1;
	} else {
		tmp = (y * (z / t)) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + ((x * t) / y)) / b
    if (y <= (-5.8d-106)) then
        tmp = t_1
    else if (y <= 5.9d-81) then
        tmp = x / (a + 1.0d0)
    else if ((y <= 0.00048d0) .or. (.not. (y <= 2.5d+41))) then
        tmp = t_1
    else
        tmp = (y * (z / t)) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double tmp;
	if (y <= -5.8e-106) {
		tmp = t_1;
	} else if (y <= 5.9e-81) {
		tmp = x / (a + 1.0);
	} else if ((y <= 0.00048) || !(y <= 2.5e+41)) {
		tmp = t_1;
	} else {
		tmp = (y * (z / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	tmp = 0
	if y <= -5.8e-106:
		tmp = t_1
	elif y <= 5.9e-81:
		tmp = x / (a + 1.0)
	elif (y <= 0.00048) or not (y <= 2.5e+41):
		tmp = t_1
	else:
		tmp = (y * (z / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	tmp = 0.0
	if (y <= -5.8e-106)
		tmp = t_1;
	elseif (y <= 5.9e-81)
		tmp = Float64(x / Float64(a + 1.0));
	elseif ((y <= 0.00048) || !(y <= 2.5e+41))
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(z / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((x * t) / y)) / b;
	tmp = 0.0;
	if (y <= -5.8e-106)
		tmp = t_1;
	elseif (y <= 5.9e-81)
		tmp = x / (a + 1.0);
	elseif ((y <= 0.00048) || ~((y <= 2.5e+41)))
		tmp = t_1;
	else
		tmp = (y * (z / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -5.8e-106], t$95$1, If[LessEqual[y, 5.9e-81], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 0.00048], N[Not[LessEqual[y, 2.5e+41]], $MachinePrecision]], t$95$1, N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8000000000000001e-106 or 5.90000000000000024e-81 < y < 4.80000000000000012e-4 or 2.50000000000000011e41 < y

   1. Initial program 66.0%

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

      1. associate-/l* 67.9%

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

      2. associate-/l* 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in b around inf 39.0%

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

   6. Taylor expanded in y around inf 46.5%

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

   7. Taylor expanded in b around 0 59.9%

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

   if -5.8000000000000001e-106 < y < 5.90000000000000024e-81

   1. Initial program 96.8%

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

      1. associate-/l* 86.9%

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

      2. associate-/l* 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in y around 0 66.6%

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

   if 4.80000000000000012e-4 < y < 2.50000000000000011e41

   1. Initial program 99.9%

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

      1. associate-/l* 99.7%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in b around 0 99.9%

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

   6. Taylor expanded in x around 0 64.5%

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

      1. associate-*r/ 64.3%

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

   8. Simplified 64.3%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-106}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 0.00048 \lor \neg \left(y \leq 2.5 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+84}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-21} \lor \neg \left(y \leq 5.7 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.4e+84)
   (/ z b)
   (if (<= y 6.8e-78)
     (/ x (+ a 1.0))
     (if (or (<= y 1.42e-21) (not (<= y 5.7e+35)))
       (/ z b)
       (+ x (/ (* y z) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.4e+84) {
		tmp = z / b;
	} else if (y <= 6.8e-78) {
		tmp = x / (a + 1.0);
	} else if ((y <= 1.42e-21) || !(y <= 5.7e+35)) {
		tmp = z / b;
	} else {
		tmp = x + ((y * z) / 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 <= (-4.4d+84)) then
        tmp = z / b
    else if (y <= 6.8d-78) then
        tmp = x / (a + 1.0d0)
    else if ((y <= 1.42d-21) .or. (.not. (y <= 5.7d+35))) then
        tmp = z / b
    else
        tmp = x + ((y * z) / 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 <= -4.4e+84) {
		tmp = z / b;
	} else if (y <= 6.8e-78) {
		tmp = x / (a + 1.0);
	} else if ((y <= 1.42e-21) || !(y <= 5.7e+35)) {
		tmp = z / b;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.4e+84:
		tmp = z / b
	elif y <= 6.8e-78:
		tmp = x / (a + 1.0)
	elif (y <= 1.42e-21) or not (y <= 5.7e+35):
		tmp = z / b
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.4e+84)
		tmp = Float64(z / b);
	elseif (y <= 6.8e-78)
		tmp = Float64(x / Float64(a + 1.0));
	elseif ((y <= 1.42e-21) || !(y <= 5.7e+35))
		tmp = Float64(z / b);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.4e+84)
		tmp = z / b;
	elseif (y <= 6.8e-78)
		tmp = x / (a + 1.0);
	elseif ((y <= 1.42e-21) || ~((y <= 5.7e+35)))
		tmp = z / b;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.4e+84], N[(z / b), $MachinePrecision], If[LessEqual[y, 6.8e-78], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.42e-21], N[Not[LessEqual[y, 5.7e+35]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3999999999999997e84 or 6.80000000000000023e-78 < y < 1.42e-21 or 5.69999999999999993e35 < y

   1. Initial program 58.1%

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

      1. associate-/l* 61.7%

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

      2. associate-/l* 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in y around inf 58.4%

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

   if -4.3999999999999997e84 < y < 6.80000000000000023e-78

   1. Initial program 93.4%

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

      1. associate-/l* 86.0%

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

      2. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in y around 0 56.1%

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

   if 1.42e-21 < y < 5.69999999999999993e35

   1. Initial program 87.9%

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

      1. associate-/l* 87.8%

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

      2. associate-/l* 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in b around 0 75.7%

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

   6. Taylor expanded in a around 0 51.3%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+84}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-21} \lor \neg \left(y \leq 5.7 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-109} \lor \neg \left(t \leq 2.35 \cdot 10^{-194}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.6e-109) (not (<= t 2.35e-194)))
   (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0)))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.6e-109) || !(t <= 2.35e-194)) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-7.6d-109)) .or. (.not. (t <= 2.35d-194))) then
        tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0d0))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.6e-109) || !(t <= 2.35e-194)) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.6e-109) or not (t <= 2.35e-194):
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7.6e-109) || !(t <= 2.35e-194))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7.6e-109) || ~((t <= 2.35e-194)))
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.6e-109], N[Not[LessEqual[t, 2.35e-194]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.60000000000000003e-109 or 2.3500000000000001e-194 < t

   1. Initial program 85.1%

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

      1. associate-/l* 86.5%

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

      2. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   if -7.60000000000000003e-109 < t < 2.3500000000000001e-194

   1. Initial program 62.0%

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

      1. associate-/l* 50.5%

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

      2. associate-/l* 44.0%

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

   3. Simplified 44.0%

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

   5. Taylor expanded in b around inf 51.9%

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

   6. Taylor expanded in y around inf 67.3%

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

   7. Taylor expanded in b around 0 77.8%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-109} \lor \neg \left(t \leq 2.35 \cdot 10^{-194}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+84} \lor \neg \left(y \leq 1.5 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8e+84) (not (<= y 1.5e+79)))
   (/ (+ z (* t (/ x y))) b)
   (/ (+ x (* z (/ y t))) (+ (/ (* y b) t) (+ a 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8e+84) || !(y <= 1.5e+79)) {
		tmp = (z + (t * (x / y))) / b;
	} else {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8d+84)) .or. (.not. (y <= 1.5d+79))) then
        tmp = (z + (t * (x / y))) / b
    else
        tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8e+84) || !(y <= 1.5e+79)) {
		tmp = (z + (t * (x / y))) / b;
	} else {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8e+84) or not (y <= 1.5e+79):
		tmp = (z + (t * (x / y))) / b
	else:
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8e+84) || !(y <= 1.5e+79))
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8e+84) || ~((y <= 1.5e+79)))
		tmp = (z + (t * (x / y))) / b;
	else
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8e+84], N[Not[LessEqual[y, 1.5e+79]], $MachinePrecision]], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.00000000000000046e84 or 1.49999999999999987e79 < y

   1. Initial program 48.8%

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

      1. associate-/l* 52.5%

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

      2. associate-/l* 61.0%

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

   3. Simplified 61.0%

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

   5. Taylor expanded in b around inf 35.6%

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

   6. Taylor expanded in y around inf 45.3%

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

   7. Taylor expanded in b around 0 68.8%

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

      1. *-un-lft-identity 68.8%

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

      2. associate-/l* 74.7%

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

   9. Applied egg-rr 74.7%

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

   if -8.00000000000000046e84 < y < 1.49999999999999987e79

   1. Initial program 91.7%

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

      1. *-commutative 69.1%

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

      2. associate-/l* 69.3%

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

   4. Applied egg-rr 92.0%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+84} \lor \neg \left(y \leq 1.5 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+37}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.5e+72)
   (/ (+ z (/ (* x t) y)) b)
   (if (<= y 2.25e+18)
     (/ x (+ 1.0 (+ a (/ (* y b) t))))
     (if (<= y 1.9e+37)
       (/ (* y (/ z t)) (+ a 1.0))
       (+ (/ z b) (* t (/ (/ x b) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.5e+72) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 2.25e+18) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 1.9e+37) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else {
		tmp = (z / b) + (t * ((x / b) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8.5d+72)) then
        tmp = (z + ((x * t) / y)) / b
    else if (y <= 2.25d+18) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (y <= 1.9d+37) then
        tmp = (y * (z / t)) / (a + 1.0d0)
    else
        tmp = (z / b) + (t * ((x / b) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.5e+72) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 2.25e+18) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 1.9e+37) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else {
		tmp = (z / b) + (t * ((x / b) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8.5e+72:
		tmp = (z + ((x * t) / y)) / b
	elif y <= 2.25e+18:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif y <= 1.9e+37:
		tmp = (y * (z / t)) / (a + 1.0)
	else:
		tmp = (z / b) + (t * ((x / b) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8.5e+72)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (y <= 2.25e+18)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (y <= 1.9e+37)
		tmp = Float64(Float64(y * Float64(z / t)) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8.5e+72)
		tmp = (z + ((x * t) / y)) / b;
	elseif (y <= 2.25e+18)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (y <= 1.9e+37)
		tmp = (y * (z / t)) / (a + 1.0);
	else
		tmp = (z / b) + (t * ((x / b) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8.5e+72], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 2.25e+18], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+37], N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.5000000000000004e72

   1. Initial program 45.1%

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

      1. associate-/l* 52.4%

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

      2. associate-/l* 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in b around inf 35.2%

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

   6. Taylor expanded in y around inf 47.8%

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

   7. Taylor expanded in b around 0 70.4%

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

   if -8.5000000000000004e72 < y < 2.25e18

   1. Initial program 92.5%

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

      1. associate-/l* 86.3%

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

      2. associate-/l* 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in x around inf 65.7%

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

   if 2.25e18 < y < 1.89999999999999995e37

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0 99.8%

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

   6. Taylor expanded in x around 0 85.6%

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

      1. associate-*r/ 85.6%

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

   8. Simplified 85.6%

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

   if 1.89999999999999995e37 < y

   1. Initial program 57.7%

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

      1. associate-/l* 59.6%

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

      2. associate-/l* 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in b around inf 39.2%

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

   6. Taylor expanded in y around inf 44.7%

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

   7. Taylor expanded in y around inf 63.2%

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

      1. associate-/l* 65.1%

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

      2. associate-/r* 68.0%

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

   9. Simplified 68.0%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+37}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+84} \lor \neg \left(y \leq 4.3 \cdot 10^{-78} \lor \neg \left(y \leq 1.75 \cdot 10^{-21}\right) \land y \leq 2.6 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.5e+84)
         (not (or (<= y 4.3e-78) (and (not (<= y 1.75e-21)) (<= y 2.6e+36)))))
   (/ z b)
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.5e+84) || !((y <= 4.3e-78) || (!(y <= 1.75e-21) && (y <= 2.6e+36)))) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.5d+84)) .or. (.not. (y <= 4.3d-78) .or. (.not. (y <= 1.75d-21)) .and. (y <= 2.6d+36))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.5e+84) || !((y <= 4.3e-78) || (!(y <= 1.75e-21) && (y <= 2.6e+36)))) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.5e+84) or not ((y <= 4.3e-78) or (not (y <= 1.75e-21) and (y <= 2.6e+36))):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.5e+84) || !((y <= 4.3e-78) || (!(y <= 1.75e-21) && (y <= 2.6e+36))))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.5e+84) || ~(((y <= 4.3e-78) || (~((y <= 1.75e-21)) && (y <= 2.6e+36)))))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.5e+84], N[Not[Or[LessEqual[y, 4.3e-78], And[N[Not[LessEqual[y, 1.75e-21]], $MachinePrecision], LessEqual[y, 2.6e+36]]]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999997e84 or 4.29999999999999994e-78 < y < 1.7500000000000002e-21 or 2.6000000000000001e36 < y

   1. Initial program 57.7%

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

      1. associate-/l* 61.3%

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

      2. associate-/l* 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in y around inf 58.9%

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

   if -4.4999999999999997e84 < y < 4.29999999999999994e-78 or 1.7500000000000002e-21 < y < 2.6000000000000001e36

   1. Initial program 92.8%

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

      1. associate-/l* 86.3%

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

      2. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in y around 0 54.0%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+84} \lor \neg \left(y \leq 4.3 \cdot 10^{-78} \lor \neg \left(y \leq 1.75 \cdot 10^{-21}\right) \land y \leq 2.6 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-97} \lor \neg \left(t \leq 4.7 \cdot 10^{-161}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8.6e-97) (not (<= t 4.7e-161)))
   (/ (+ x (* z (/ y t))) (+ a 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.6e-97) || !(t <= 4.7e-161)) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-8.6d-97)) .or. (.not. (t <= 4.7d-161))) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.6e-97) || !(t <= 4.7e-161)) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -8.6e-97) or not (t <= 4.7e-161):
		tmp = (x + (z * (y / t))) / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -8.6e-97) || !(t <= 4.7e-161))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -8.6e-97) || ~((t <= 4.7e-161)))
		tmp = (x + (z * (y / t))) / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -8.6e-97], N[Not[LessEqual[t, 4.7e-161]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.6e-97 or 4.7000000000000004e-161 < t

   1. Initial program 84.6%

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

      1. associate-/l* 86.2%

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

      2. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in b around 0 70.3%

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

      1. *-commutative 70.3%

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

      2. associate-/l* 72.3%

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

   7. Applied egg-rr 72.3%

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

   if -8.6e-97 < t < 4.7000000000000004e-161

   1. Initial program 66.1%

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

      1. associate-/l* 56.2%

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

      2. associate-/l* 48.4%

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

   3. Simplified 48.4%

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

   5. Taylor expanded in b around inf 53.7%

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

   6. Taylor expanded in y around inf 67.0%

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

   7. Taylor expanded in b around 0 76.1%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-97} \lor \neg \left(t \leq 4.7 \cdot 10^{-161}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-97}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-161}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.35e-97)
   (/ (+ x (* z (/ y t))) (+ a 1.0))
   (if (<= t 1.1e-161)
     (/ (+ z (/ (* x t) y)) b)
     (/ (+ x (* y (/ z t))) (+ a 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.35e-97) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 1.1e-161) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.35d-97)) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else if (t <= 1.1d-161) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.35e-97) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 1.1e-161) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.35e-97:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	elif t <= 1.1e-161:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.35e-97)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	elseif (t <= 1.1e-161)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.35e-97)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	elseif (t <= 1.1e-161)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + (y * (z / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.35e-97], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e-161], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3500000000000001e-97

   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. associate-/l* 85.0%

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

      2. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in b around 0 64.4%

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

      1. *-commutative 64.4%

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

      2. associate-/l* 68.0%

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

   7. Applied egg-rr 68.0%

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

   if -2.3500000000000001e-97 < t < 1.10000000000000001e-161

   1. Initial program 66.1%

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

      1. associate-/l* 56.2%

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

      2. associate-/l* 48.4%

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

   3. Simplified 48.4%

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

   5. Taylor expanded in b around inf 53.7%

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

   6. Taylor expanded in y around inf 67.0%

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

   7. Taylor expanded in b around 0 76.1%

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

   if 1.10000000000000001e-161 < t

   1. Initial program 86.3%

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

      1. associate-/l* 87.2%

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

      2. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in b around 0 75.6%

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

      1. associate-*r/ 76.3%

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

      2. *-commutative 76.3%

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

   7. Applied egg-rr 76.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-97}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-161}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-89}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-234}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-100}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.4e-89)
   (/ z b)
   (if (<= y -1.06e-234) (/ x a) (if (<= y 5.2e-100) (- x (* x a)) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.4e-89) {
		tmp = z / b;
	} else if (y <= -1.06e-234) {
		tmp = x / a;
	} else if (y <= 5.2e-100) {
		tmp = x - (x * a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.4d-89)) then
        tmp = z / b
    else if (y <= (-1.06d-234)) then
        tmp = x / a
    else if (y <= 5.2d-100) then
        tmp = x - (x * a)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.4e-89) {
		tmp = z / b;
	} else if (y <= -1.06e-234) {
		tmp = x / a;
	} else if (y <= 5.2e-100) {
		tmp = x - (x * a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.4e-89:
		tmp = z / b
	elif y <= -1.06e-234:
		tmp = x / a
	elif y <= 5.2e-100:
		tmp = x - (x * a)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.4e-89)
		tmp = Float64(z / b);
	elseif (y <= -1.06e-234)
		tmp = Float64(x / a);
	elseif (y <= 5.2e-100)
		tmp = Float64(x - Float64(x * a));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.4e-89)
		tmp = z / b;
	elseif (y <= -1.06e-234)
		tmp = x / a;
	elseif (y <= 5.2e-100)
		tmp = x - (x * a);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.4e-89], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.06e-234], N[(x / a), $MachinePrecision], If[LessEqual[y, 5.2e-100], N[(x - N[(x * a), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000016e-89 or 5.1999999999999997e-100 < y

   1. Initial program 68.7%

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

      1. associate-/l* 70.4%

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

      2. associate-/l* 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in y around inf 46.6%

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

   if -2.40000000000000016e-89 < y < -1.06000000000000004e-234

   1. Initial program 90.8%

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

      1. associate-/l* 89.2%

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

      2. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in x around inf 64.5%

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

   6. Taylor expanded in a around inf 41.3%

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

   if -1.06000000000000004e-234 < y < 5.1999999999999997e-100

   1. Initial program 99.5%

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

      1. associate-/l* 85.4%

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

      2. associate-/l* 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in y around 0 71.4%

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

   6. Taylor expanded in a around 0 41.7%

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

      1. mul-1-neg 41.7%

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

      2. unsub-neg 41.7%

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

   8. Simplified 41.7%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-89}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-234}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-100}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 43.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-86} \lor \neg \left(y \leq 4.1 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.1e-86) (not (<= y 4.1e-78))) (/ z b) (/ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.1e-86) || !(y <= 4.1e-78)) {
		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 ((y <= (-5.1d-86)) .or. (.not. (y <= 4.1d-78))) 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 ((y <= -5.1e-86) || !(y <= 4.1e-78)) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.1e-86) or not (y <= 4.1e-78):
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.1e-86) || !(y <= 4.1e-78))
		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 ((y <= -5.1e-86) || ~((y <= 4.1e-78)))
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.1e-86], N[Not[LessEqual[y, 4.1e-78]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.10000000000000006e-86 or 4.0999999999999998e-78 < y

   1. Initial program 67.9%

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

      1. associate-/l* 69.7%

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

      2. associate-/l* 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in y around inf 47.0%

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

   if -5.10000000000000006e-86 < y < 4.0999999999999998e-78

   1. Initial program 96.8%

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

      1. associate-/l* 87.2%

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

      2. associate-/l* 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in x around inf 73.3%

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

   6. Taylor expanded in a around inf 35.4%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-86} \lor \neg \left(y \leq 4.1 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.3% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.3%

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

   1. associate-/l* 76.0%

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

   2. associate-/l* 76.0%

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

3. Simplified 76.0%

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

5. Taylor expanded in x around inf 50.2%

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

6. Taylor expanded in a around inf 20.7%

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

7. Final simplification 20.7%

   \[\leadsto \frac{x}{a} \]
8. Add Preprocessing

Developer target: 79.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024059 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (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))))