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

Percentage Accurate: 75.9% → 91.0%

Time: 18.0s

Alternatives: 15

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: 75.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := 1 + \left(a + y \cdot \frac{b}{t}\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{t\_2} + \frac{y}{t \cdot t\_2}\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \left(\frac{x}{b} - z \cdot \frac{1 + a}{b \cdot b}\right)}{y}\\ \mathbf{elif}\;t\_1 \leq 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (+ 1.0 (+ a (* y (/ b t))))))
   (if (<= t_1 (- INFINITY))
     (* z (+ (/ (/ x z) t_2) (/ y (* t t_2))))
     (if (<= t_1 -2e-275)
       t_1
       (if (<= t_1 0.0)
         (+ (/ z b) (/ (* t (- (/ x b) (* z (/ (+ 1.0 a) (* b b))))) y))
         (if (<= t_1 1e+301) t_1 (+ (/ z b) (/ (* x (/ t y)) b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = 1.0 + (a + (y * (b / t)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z * (((x / z) / t_2) + (y / (t * t_2)));
	} else if (t_1 <= -2e-275) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + ((t * ((x / b) - (z * ((1.0 + a) / (b * b))))) / y);
	} else if (t_1 <= 1e+301) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((x * (t / y)) / b);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = 1.0 + (a + (y * (b / t)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (((x / z) / t_2) + (y / (t * t_2)));
	} else if (t_1 <= -2e-275) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + ((t * ((x / b) - (z * ((1.0 + a) / (b * b))))) / y);
	} else if (t_1 <= 1e+301) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((x * (t / y)) / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	t_2 = 1.0 + (a + (y * (b / t)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z * (((x / z) / t_2) + (y / (t * t_2)))
	elif t_1 <= -2e-275:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (z / b) + ((t * ((x / b) - (z * ((1.0 + a) / (b * b))))) / y)
	elif t_1 <= 1e+301:
		tmp = t_1
	else:
		tmp = (z / b) + ((x * (t / y)) / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(Float64(x / z) / t_2) + Float64(y / Float64(t * t_2))));
	elseif (t_1 <= -2e-275)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(Float64(x / b) - Float64(z * Float64(Float64(1.0 + a) / Float64(b * b))))) / y));
	elseif (t_1 <= 1e+301)
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / y)) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	t_2 = 1.0 + (a + (y * (b / t)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z * (((x / z) / t_2) + (y / (t * t_2)));
	elseif (t_1 <= -2e-275)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (z / b) + ((t * ((x / b) - (z * ((1.0 + a) / (b * b))))) / y);
	elseif (t_1 <= 1e+301)
		tmp = t_1;
	else
		tmp = (z / b) + ((x * (t / y)) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(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]}, Block[{t$95$2 = N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(N[(N[(x / z), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(y / N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-275], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(N[(x / b), $MachinePrecision] - N[(z * N[(N[(1.0 + a), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+301], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $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))) < -inf.0

   1. Initial program 24.6%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999987e-275 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.00000000000000005e301

   1. Initial program 99.7%

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

   if -1.99999999999999987e-275 < (/.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 42.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.00000000000000005e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 18.2%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 2: 90.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{t \cdot \left(1 + \left(a + \frac{y}{\frac{t}{b}}\right)\right)}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \left(\frac{x}{b} - z \cdot \frac{1 + a}{b \cdot b}\right)}{y}\\ \mathbf{elif}\;t\_1 \leq 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (* z (/ y (* t (+ 1.0 (+ a (/ y (/ t b)))))))
     (if (<= t_1 -2e-275)
       t_1
       (if (<= t_1 0.0)
         (+ (/ z b) (/ (* t (- (/ x b) (* z (/ (+ 1.0 a) (* b b))))) y))
         (if (<= t_1 1e+301) t_1 (+ (/ z b) (/ (* x (/ t y)) b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z * (y / (t * (1.0 + (a + (y / (t / b))))));
	} else if (t_1 <= -2e-275) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + ((t * ((x / b) - (z * ((1.0 + a) / (b * b))))) / y);
	} else if (t_1 <= 1e+301) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((x * (t / y)) / b);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (y / (t * (1.0 + (a + (y / (t / b))))));
	} else if (t_1 <= -2e-275) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + ((t * ((x / b) - (z * ((1.0 + a) / (b * b))))) / y);
	} else if (t_1 <= 1e+301) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((x * (t / y)) / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z * (y / (t * (1.0 + (a + (y / (t / b))))))
	elif t_1 <= -2e-275:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (z / b) + ((t * ((x / b) - (z * ((1.0 + a) / (b * b))))) / y)
	elif t_1 <= 1e+301:
		tmp = t_1
	else:
		tmp = (z / b) + ((x * (t / y)) / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z * Float64(y / Float64(t * Float64(1.0 + Float64(a + Float64(y / Float64(t / b)))))));
	elseif (t_1 <= -2e-275)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(Float64(x / b) - Float64(z * Float64(Float64(1.0 + a) / Float64(b * b))))) / y));
	elseif (t_1 <= 1e+301)
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / y)) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z * (y / (t * (1.0 + (a + (y / (t / b))))));
	elseif (t_1 <= -2e-275)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (z / b) + ((t * ((x / b) - (z * ((1.0 + a) / (b * b))))) / y);
	elseif (t_1 <= 1e+301)
		tmp = t_1;
	else
		tmp = (z / b) + ((x * (t / y)) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(y / N[(t * N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-275], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(N[(x / b), $MachinePrecision] - N[(z * N[(N[(1.0 + a), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+301], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $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))) < -inf.0

   1. Initial program 24.6%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999987e-275 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.00000000000000005e301

   1. Initial program 99.7%

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

   if -1.99999999999999987e-275 < (/.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 42.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.00000000000000005e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 18.2%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 90.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot \frac{t}{y}}{b}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{t \cdot \left(1 + \left(a + \frac{y}{\frac{t}{b}}\right)\right)}\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+301}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* x (/ t y)) b)))
        (t_2 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_2 (- INFINITY))
     (* z (/ y (* t (+ 1.0 (+ a (/ y (/ t b)))))))
     (if (<= t_2 -2e-275)
       t_2
       (if (<= t_2 0.0) t_1 (if (<= t_2 1e+301) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / y)) / b);
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * (y / (t * (1.0 + (a + (y / (t / b))))));
	} else if (t_2 <= -2e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+301) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / y)) / b);
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (y / (t * (1.0 + (a + (y / (t / b))))));
	} else if (t_2 <= -2e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+301) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((x * (t / y)) / b)
	t_2 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * (y / (t * (1.0 + (a + (y / (t / b))))))
	elif t_2 <= -2e-275:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 1e+301:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / y)) / b))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(y / Float64(t * Float64(1.0 + Float64(a + Float64(y / Float64(t / b)))))));
	elseif (t_2 <= -2e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 1e+301)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((x * (t / y)) / b);
	t_2 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * (y / (t * (1.0 + (a + (y / (t / b))))));
	elseif (t_2 <= -2e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 1e+301)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(y / N[(t * N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-275], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 1e+301], t$95$2, t$95$1]]]]]]

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))) < -inf.0

   1. Initial program 24.6%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.99999999999999987e-275 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.00000000000000005e301

   1. Initial program 99.7%

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

   if -1.99999999999999987e-275 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -0.0 or 1.00000000000000005e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 30.2%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 54.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + a}\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-227}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{a + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-31}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 a))))
   (if (<= t -1.02e-19)
     t_1
     (if (<= t 5e-227)
       (/ z b)
       (if (<= t 1.25e-181)
         t_1
         (if (<= t 4.5e-84)
           (/ z b)
           (if (<= t 1.35e-71)
             (/ x (+ a (/ (* y b) t)))
             (if (<= t 1.55e-31) (/ z b) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + a);
	double tmp;
	if (t <= -1.02e-19) {
		tmp = t_1;
	} else if (t <= 5e-227) {
		tmp = z / b;
	} else if (t <= 1.25e-181) {
		tmp = t_1;
	} else if (t <= 4.5e-84) {
		tmp = z / b;
	} else if (t <= 1.35e-71) {
		tmp = x / (a + ((y * b) / t));
	} else if (t <= 1.55e-31) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 + a)
    if (t <= (-1.02d-19)) then
        tmp = t_1
    else if (t <= 5d-227) then
        tmp = z / b
    else if (t <= 1.25d-181) then
        tmp = t_1
    else if (t <= 4.5d-84) then
        tmp = z / b
    else if (t <= 1.35d-71) then
        tmp = x / (a + ((y * b) / t))
    else if (t <= 1.55d-31) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + a);
	double tmp;
	if (t <= -1.02e-19) {
		tmp = t_1;
	} else if (t <= 5e-227) {
		tmp = z / b;
	} else if (t <= 1.25e-181) {
		tmp = t_1;
	} else if (t <= 4.5e-84) {
		tmp = z / b;
	} else if (t <= 1.35e-71) {
		tmp = x / (a + ((y * b) / t));
	} else if (t <= 1.55e-31) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + a)
	tmp = 0
	if t <= -1.02e-19:
		tmp = t_1
	elif t <= 5e-227:
		tmp = z / b
	elif t <= 1.25e-181:
		tmp = t_1
	elif t <= 4.5e-84:
		tmp = z / b
	elif t <= 1.35e-71:
		tmp = x / (a + ((y * b) / t))
	elif t <= 1.55e-31:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + a))
	tmp = 0.0
	if (t <= -1.02e-19)
		tmp = t_1;
	elseif (t <= 5e-227)
		tmp = Float64(z / b);
	elseif (t <= 1.25e-181)
		tmp = t_1;
	elseif (t <= 4.5e-84)
		tmp = Float64(z / b);
	elseif (t <= 1.35e-71)
		tmp = Float64(x / Float64(a + Float64(Float64(y * b) / t)));
	elseif (t <= 1.55e-31)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + a);
	tmp = 0.0;
	if (t <= -1.02e-19)
		tmp = t_1;
	elseif (t <= 5e-227)
		tmp = z / b;
	elseif (t <= 1.25e-181)
		tmp = t_1;
	elseif (t <= 4.5e-84)
		tmp = z / b;
	elseif (t <= 1.35e-71)
		tmp = x / (a + ((y * b) / t));
	elseif (t <= 1.55e-31)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.02e-19], t$95$1, If[LessEqual[t, 5e-227], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.25e-181], t$95$1, If[LessEqual[t, 4.5e-84], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.35e-71], N[(x / N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e-31], N[(z / b), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02000000000000004e-19 or 4.99999999999999961e-227 < t < 1.25e-181 or 1.55e-31 < t

   1. Initial program 80.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.02000000000000004e-19 < t < 4.99999999999999961e-227 or 1.25e-181 < t < 4.50000000000000016e-84 or 1.3500000000000001e-71 < t < 1.55e-31

   1. Initial program 68.2%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 4.50000000000000016e-84 < t < 1.3500000000000001e-71

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 81.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot \frac{t}{y}}{b}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+52}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+223}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* x (/ t y)) b))))
   (if (<= y -1.1e+78)
     t_1
     (if (<= y 2e+52)
       (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (* b (/ y t))))
       (if (<= y 2.15e+223)
         (/ (+ x (* z (/ y t))) (+ (+ a 1.0) (/ (* y b) t)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / y)) / b);
	double tmp;
	if (y <= -1.1e+78) {
		tmp = t_1;
	} else if (y <= 2e+52) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	} else if (y <= 2.15e+223) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((x * (t / y)) / b)
    if (y <= (-1.1d+78)) then
        tmp = t_1
    else if (y <= 2d+52) then
        tmp = (x + ((y * z) / t)) / ((a + 1.0d0) + (b * (y / t)))
    else if (y <= 2.15d+223) then
        tmp = (x + (z * (y / t))) / ((a + 1.0d0) + ((y * b) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / y)) / b);
	double tmp;
	if (y <= -1.1e+78) {
		tmp = t_1;
	} else if (y <= 2e+52) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	} else if (y <= 2.15e+223) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((x * (t / y)) / b)
	tmp = 0
	if y <= -1.1e+78:
		tmp = t_1
	elif y <= 2e+52:
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)))
	elif y <= 2.15e+223:
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / y)) / b))
	tmp = 0.0
	if (y <= -1.1e+78)
		tmp = t_1;
	elseif (y <= 2e+52)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	elseif (y <= 2.15e+223)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((x * (t / y)) / b);
	tmp = 0.0;
	if (y <= -1.1e+78)
		tmp = t_1;
	elseif (y <= 2e+52)
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	elseif (y <= 2.15e+223)
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+78], t$95$1, If[LessEqual[y, 2e+52], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+223], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.10000000000000007e78 or 2.15e223 < y

   1. Initial program 45.2%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.10000000000000007e78 < y < 2e52

   1. Initial program 91.1%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if 2e52 < y < 2.15e223

   1. Initial program 55.8%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 66.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot \frac{t}{y}}{b}\\ \mathbf{if}\;b \leq -5.6 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{1 + a}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+95}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* x (/ t y)) b))))
   (if (<= b -5.6e+87)
     t_1
     (if (<= b 2.6e-19)
       (/ (+ x (/ y (/ t z))) (+ 1.0 a))
       (if (<= b 4.8e+34)
         t_1
         (if (<= b 1.4e+95) (/ (+ x (/ (* y z) t)) (+ 1.0 a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / y)) / b);
	double tmp;
	if (b <= -5.6e+87) {
		tmp = t_1;
	} else if (b <= 2.6e-19) {
		tmp = (x + (y / (t / z))) / (1.0 + a);
	} else if (b <= 4.8e+34) {
		tmp = t_1;
	} else if (b <= 1.4e+95) {
		tmp = (x + ((y * z) / t)) / (1.0 + a);
	} 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 = (z / b) + ((x * (t / y)) / b)
    if (b <= (-5.6d+87)) then
        tmp = t_1
    else if (b <= 2.6d-19) then
        tmp = (x + (y / (t / z))) / (1.0d0 + a)
    else if (b <= 4.8d+34) then
        tmp = t_1
    else if (b <= 1.4d+95) then
        tmp = (x + ((y * z) / t)) / (1.0d0 + a)
    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 = (z / b) + ((x * (t / y)) / b);
	double tmp;
	if (b <= -5.6e+87) {
		tmp = t_1;
	} else if (b <= 2.6e-19) {
		tmp = (x + (y / (t / z))) / (1.0 + a);
	} else if (b <= 4.8e+34) {
		tmp = t_1;
	} else if (b <= 1.4e+95) {
		tmp = (x + ((y * z) / t)) / (1.0 + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((x * (t / y)) / b)
	tmp = 0
	if b <= -5.6e+87:
		tmp = t_1
	elif b <= 2.6e-19:
		tmp = (x + (y / (t / z))) / (1.0 + a)
	elif b <= 4.8e+34:
		tmp = t_1
	elif b <= 1.4e+95:
		tmp = (x + ((y * z) / t)) / (1.0 + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / y)) / b))
	tmp = 0.0
	if (b <= -5.6e+87)
		tmp = t_1;
	elseif (b <= 2.6e-19)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(1.0 + a));
	elseif (b <= 4.8e+34)
		tmp = t_1;
	elseif (b <= 1.4e+95)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(1.0 + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((x * (t / y)) / b);
	tmp = 0.0;
	if (b <= -5.6e+87)
		tmp = t_1;
	elseif (b <= 2.6e-19)
		tmp = (x + (y / (t / z))) / (1.0 + a);
	elseif (b <= 4.8e+34)
		tmp = t_1;
	elseif (b <= 1.4e+95)
		tmp = (x + ((y * z) / t)) / (1.0 + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.6e+87], t$95$1, If[LessEqual[b, 2.6e-19], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e+34], t$95$1, If[LessEqual[b, 1.4e+95], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.6000000000000003e87 or 2.60000000000000013e-19 < b < 4.79999999999999974e34 or 1.3999999999999999e95 < b

   1. Initial program 56.3%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -5.6000000000000003e87 < b < 2.60000000000000013e-19

   1. Initial program 86.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 4.79999999999999974e34 < b < 1.3999999999999999e95

   1. Initial program 89.7%

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

   3. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot \frac{t}{y}}{b}\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-19}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{1 + a}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* x (/ t y)) b))))
   (if (<= b -3.6e+93)
     t_1
     (if (<= b 1.9e-19)
       (/ (+ x (/ y (/ t z))) (+ 1.0 a))
       (if (<= b 4.8e+32) t_1 (if (<= b 1.05e+94) (/ x (+ 1.0 a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / y)) / b);
	double tmp;
	if (b <= -3.6e+93) {
		tmp = t_1;
	} else if (b <= 1.9e-19) {
		tmp = (x + (y / (t / z))) / (1.0 + a);
	} else if (b <= 4.8e+32) {
		tmp = t_1;
	} else if (b <= 1.05e+94) {
		tmp = x / (1.0 + a);
	} 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 = (z / b) + ((x * (t / y)) / b)
    if (b <= (-3.6d+93)) then
        tmp = t_1
    else if (b <= 1.9d-19) then
        tmp = (x + (y / (t / z))) / (1.0d0 + a)
    else if (b <= 4.8d+32) then
        tmp = t_1
    else if (b <= 1.05d+94) then
        tmp = x / (1.0d0 + a)
    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 = (z / b) + ((x * (t / y)) / b);
	double tmp;
	if (b <= -3.6e+93) {
		tmp = t_1;
	} else if (b <= 1.9e-19) {
		tmp = (x + (y / (t / z))) / (1.0 + a);
	} else if (b <= 4.8e+32) {
		tmp = t_1;
	} else if (b <= 1.05e+94) {
		tmp = x / (1.0 + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((x * (t / y)) / b)
	tmp = 0
	if b <= -3.6e+93:
		tmp = t_1
	elif b <= 1.9e-19:
		tmp = (x + (y / (t / z))) / (1.0 + a)
	elif b <= 4.8e+32:
		tmp = t_1
	elif b <= 1.05e+94:
		tmp = x / (1.0 + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / y)) / b))
	tmp = 0.0
	if (b <= -3.6e+93)
		tmp = t_1;
	elseif (b <= 1.9e-19)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(1.0 + a));
	elseif (b <= 4.8e+32)
		tmp = t_1;
	elseif (b <= 1.05e+94)
		tmp = Float64(x / Float64(1.0 + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((x * (t / y)) / b);
	tmp = 0.0;
	if (b <= -3.6e+93)
		tmp = t_1;
	elseif (b <= 1.9e-19)
		tmp = (x + (y / (t / z))) / (1.0 + a);
	elseif (b <= 4.8e+32)
		tmp = t_1;
	elseif (b <= 1.05e+94)
		tmp = x / (1.0 + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.6e+93], t$95$1, If[LessEqual[b, 1.9e-19], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e+32], t$95$1, If[LessEqual[b, 1.05e+94], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.5999999999999999e93 or 1.9e-19 < b < 4.79999999999999983e32 or 1.04999999999999995e94 < b

   1. Initial program 56.3%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -3.5999999999999999e93 < b < 1.9e-19

   1. Initial program 86.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 4.79999999999999983e32 < b < 1.04999999999999995e94

   1. Initial program 89.7%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 64.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot \frac{t}{y}}{b}\\ t_2 := \frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-195}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* x (/ t y)) b)))
        (t_2 (/ x (+ 1.0 (+ a (* y (/ b t)))))))
   (if (<= t -2e-21)
     t_2
     (if (<= t 4.5e-231)
       t_1
       (if (<= t 2.9e-195)
         (/ (+ x (/ (* y z) t)) a)
         (if (<= t 1.02e-30) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / y)) / b);
	double t_2 = x / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -2e-21) {
		tmp = t_2;
	} else if (t <= 4.5e-231) {
		tmp = t_1;
	} else if (t <= 2.9e-195) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 1.02e-30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z / b) + ((x * (t / y)) / b)
    t_2 = x / (1.0d0 + (a + (y * (b / t))))
    if (t <= (-2d-21)) then
        tmp = t_2
    else if (t <= 4.5d-231) then
        tmp = t_1
    else if (t <= 2.9d-195) then
        tmp = (x + ((y * z) / t)) / a
    else if (t <= 1.02d-30) then
        tmp = t_1
    else
        tmp = t_2
    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 / b) + ((x * (t / y)) / b);
	double t_2 = x / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -2e-21) {
		tmp = t_2;
	} else if (t <= 4.5e-231) {
		tmp = t_1;
	} else if (t <= 2.9e-195) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 1.02e-30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((x * (t / y)) / b)
	t_2 = x / (1.0 + (a + (y * (b / t))))
	tmp = 0
	if t <= -2e-21:
		tmp = t_2
	elif t <= 4.5e-231:
		tmp = t_1
	elif t <= 2.9e-195:
		tmp = (x + ((y * z) / t)) / a
	elif t <= 1.02e-30:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / y)) / b))
	t_2 = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))))
	tmp = 0.0
	if (t <= -2e-21)
		tmp = t_2;
	elseif (t <= 4.5e-231)
		tmp = t_1;
	elseif (t <= 2.9e-195)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	elseif (t <= 1.02e-30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((x * (t / y)) / b);
	t_2 = x / (1.0 + (a + (y * (b / t))));
	tmp = 0.0;
	if (t <= -2e-21)
		tmp = t_2;
	elseif (t <= 4.5e-231)
		tmp = t_1;
	elseif (t <= 2.9e-195)
		tmp = (x + ((y * z) / t)) / a;
	elseif (t <= 1.02e-30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e-21], t$95$2, If[LessEqual[t, 4.5e-231], t$95$1, If[LessEqual[t, 2.9e-195], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 1.02e-30], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.99999999999999982e-21 or 1.0199999999999999e-30 < t

   1. Initial program 80.1%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.99999999999999982e-21 < t < 4.4999999999999998e-231 or 2.9000000000000002e-195 < t < 1.0199999999999999e-30

   1. Initial program 69.3%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 4.4999999999999998e-231 < t < 2.9000000000000002e-195

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 57.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot \frac{t}{y}}{b}\\ \mathbf{if}\;y \leq -1.96 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+21}:\\ \;\;\;\;\frac{1}{\frac{1 + a}{x}}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + a\right)}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* x (/ t y)) b))))
   (if (<= y -1.96e+59)
     t_1
     (if (<= y -1.75e+21)
       (/ 1.0 (/ (+ 1.0 a) x))
       (if (<= y -8.2e-25)
         (/ (* y z) (* t (+ 1.0 a)))
         (if (<= y 1.75e-126) (/ x (+ 1.0 a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / y)) / b);
	double tmp;
	if (y <= -1.96e+59) {
		tmp = t_1;
	} else if (y <= -1.75e+21) {
		tmp = 1.0 / ((1.0 + a) / x);
	} else if (y <= -8.2e-25) {
		tmp = (y * z) / (t * (1.0 + a));
	} else if (y <= 1.75e-126) {
		tmp = x / (1.0 + a);
	} 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 = (z / b) + ((x * (t / y)) / b)
    if (y <= (-1.96d+59)) then
        tmp = t_1
    else if (y <= (-1.75d+21)) then
        tmp = 1.0d0 / ((1.0d0 + a) / x)
    else if (y <= (-8.2d-25)) then
        tmp = (y * z) / (t * (1.0d0 + a))
    else if (y <= 1.75d-126) then
        tmp = x / (1.0d0 + a)
    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 = (z / b) + ((x * (t / y)) / b);
	double tmp;
	if (y <= -1.96e+59) {
		tmp = t_1;
	} else if (y <= -1.75e+21) {
		tmp = 1.0 / ((1.0 + a) / x);
	} else if (y <= -8.2e-25) {
		tmp = (y * z) / (t * (1.0 + a));
	} else if (y <= 1.75e-126) {
		tmp = x / (1.0 + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((x * (t / y)) / b)
	tmp = 0
	if y <= -1.96e+59:
		tmp = t_1
	elif y <= -1.75e+21:
		tmp = 1.0 / ((1.0 + a) / x)
	elif y <= -8.2e-25:
		tmp = (y * z) / (t * (1.0 + a))
	elif y <= 1.75e-126:
		tmp = x / (1.0 + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / y)) / b))
	tmp = 0.0
	if (y <= -1.96e+59)
		tmp = t_1;
	elseif (y <= -1.75e+21)
		tmp = Float64(1.0 / Float64(Float64(1.0 + a) / x));
	elseif (y <= -8.2e-25)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + a)));
	elseif (y <= 1.75e-126)
		tmp = Float64(x / Float64(1.0 + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((x * (t / y)) / b);
	tmp = 0.0;
	if (y <= -1.96e+59)
		tmp = t_1;
	elseif (y <= -1.75e+21)
		tmp = 1.0 / ((1.0 + a) / x);
	elseif (y <= -8.2e-25)
		tmp = (y * z) / (t * (1.0 + a));
	elseif (y <= 1.75e-126)
		tmp = x / (1.0 + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.96e+59], t$95$1, If[LessEqual[y, -1.75e+21], N[(1.0 / N[(N[(1.0 + a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.2e-25], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-126], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.96000000000000007e59 or 1.75e-126 < y

   1. Initial program 56.4%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.96000000000000007e59 < y < -1.75e21

   1. Initial program 82.4%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.75e21 < y < -8.19999999999999974e-25

   1. Initial program 78.2%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -8.19999999999999974e-25 < y < 1.75e-126

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 54.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b} \cdot \left(\frac{x}{y} + \frac{z}{t}\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+26}:\\ \;\;\;\;\frac{1}{\frac{1 + a}{x}}\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-24}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + a\right)}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ t b) (+ (/ x y) (/ z t)))))
   (if (<= y -2e+59)
     t_1
     (if (<= y -2.15e+26)
       (/ 1.0 (/ (+ 1.0 a) x))
       (if (<= y -1.26e-24)
         (/ (* y z) (* t (+ 1.0 a)))
         (if (<= y 2.6e+21) (/ x (+ 1.0 a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t / b) * ((x / y) + (z / t));
	double tmp;
	if (y <= -2e+59) {
		tmp = t_1;
	} else if (y <= -2.15e+26) {
		tmp = 1.0 / ((1.0 + a) / x);
	} else if (y <= -1.26e-24) {
		tmp = (y * z) / (t * (1.0 + a));
	} else if (y <= 2.6e+21) {
		tmp = x / (1.0 + a);
	} 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 = (t / b) * ((x / y) + (z / t))
    if (y <= (-2d+59)) then
        tmp = t_1
    else if (y <= (-2.15d+26)) then
        tmp = 1.0d0 / ((1.0d0 + a) / x)
    else if (y <= (-1.26d-24)) then
        tmp = (y * z) / (t * (1.0d0 + a))
    else if (y <= 2.6d+21) then
        tmp = x / (1.0d0 + a)
    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 = (t / b) * ((x / y) + (z / t));
	double tmp;
	if (y <= -2e+59) {
		tmp = t_1;
	} else if (y <= -2.15e+26) {
		tmp = 1.0 / ((1.0 + a) / x);
	} else if (y <= -1.26e-24) {
		tmp = (y * z) / (t * (1.0 + a));
	} else if (y <= 2.6e+21) {
		tmp = x / (1.0 + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t / b) * ((x / y) + (z / t))
	tmp = 0
	if y <= -2e+59:
		tmp = t_1
	elif y <= -2.15e+26:
		tmp = 1.0 / ((1.0 + a) / x)
	elif y <= -1.26e-24:
		tmp = (y * z) / (t * (1.0 + a))
	elif y <= 2.6e+21:
		tmp = x / (1.0 + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t / b) * Float64(Float64(x / y) + Float64(z / t)))
	tmp = 0.0
	if (y <= -2e+59)
		tmp = t_1;
	elseif (y <= -2.15e+26)
		tmp = Float64(1.0 / Float64(Float64(1.0 + a) / x));
	elseif (y <= -1.26e-24)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + a)));
	elseif (y <= 2.6e+21)
		tmp = Float64(x / Float64(1.0 + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t / b) * ((x / y) + (z / t));
	tmp = 0.0;
	if (y <= -2e+59)
		tmp = t_1;
	elseif (y <= -2.15e+26)
		tmp = 1.0 / ((1.0 + a) / x);
	elseif (y <= -1.26e-24)
		tmp = (y * z) / (t * (1.0 + a));
	elseif (y <= 2.6e+21)
		tmp = x / (1.0 + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t / b), $MachinePrecision] * N[(N[(x / y), $MachinePrecision] + N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+59], t$95$1, If[LessEqual[y, -2.15e+26], N[(1.0 / N[(N[(1.0 + a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.26e-24], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+21], N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.99999999999999994e59 or 2.6e21 < y

   1. Initial program 51.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.99999999999999994e59 < y < -2.1499999999999999e26

   1. Initial program 79.8%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -2.1499999999999999e26 < y < -1.25999999999999992e-24

   1. Initial program 82.2%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.25999999999999992e-24 < y < 2.6e21

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 80.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot \frac{t}{y}}{b}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+222}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* x (/ t y)) b))))
   (if (<= y -1.15e+69)
     t_1
     (if (<= y 2.9e+222)
       (/ (+ x (* z (/ y t))) (+ (+ a 1.0) (/ (* y b) t)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / y)) / b);
	double tmp;
	if (y <= -1.15e+69) {
		tmp = t_1;
	} else if (y <= 2.9e+222) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((x * (t / y)) / b)
    if (y <= (-1.15d+69)) then
        tmp = t_1
    else if (y <= 2.9d+222) then
        tmp = (x + (z * (y / t))) / ((a + 1.0d0) + ((y * b) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / y)) / b);
	double tmp;
	if (y <= -1.15e+69) {
		tmp = t_1;
	} else if (y <= 2.9e+222) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((x * (t / y)) / b)
	tmp = 0
	if y <= -1.15e+69:
		tmp = t_1
	elif y <= 2.9e+222:
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / y)) / b))
	tmp = 0.0
	if (y <= -1.15e+69)
		tmp = t_1;
	elseif (y <= 2.9e+222)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((x * (t / y)) / b);
	tmp = 0.0;
	if (y <= -1.15e+69)
		tmp = t_1;
	elseif (y <= 2.9e+222)
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+69], t$95$1, If[LessEqual[y, 2.9e+222], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15000000000000008e69 or 2.89999999999999981e222 < y

   1. Initial program 45.4%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.15000000000000008e69 < y < 2.89999999999999981e222

   1. Initial program 85.2%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 54.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + a}\\ \mathbf{if}\;t \leq -6.1 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-162}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-31}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 a))))
   (if (<= t -6.1e-21)
     t_1
     (if (<= t 4.5e-231)
       (/ z b)
       (if (<= t 2.4e-162)
         (/ (+ x (/ (* y z) t)) a)
         (if (<= t 2e-31) (/ z b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + a);
	double tmp;
	if (t <= -6.1e-21) {
		tmp = t_1;
	} else if (t <= 4.5e-231) {
		tmp = z / b;
	} else if (t <= 2.4e-162) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 2e-31) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 + a)
    if (t <= (-6.1d-21)) then
        tmp = t_1
    else if (t <= 4.5d-231) then
        tmp = z / b
    else if (t <= 2.4d-162) then
        tmp = (x + ((y * z) / t)) / a
    else if (t <= 2d-31) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + a);
	double tmp;
	if (t <= -6.1e-21) {
		tmp = t_1;
	} else if (t <= 4.5e-231) {
		tmp = z / b;
	} else if (t <= 2.4e-162) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 2e-31) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + a)
	tmp = 0
	if t <= -6.1e-21:
		tmp = t_1
	elif t <= 4.5e-231:
		tmp = z / b
	elif t <= 2.4e-162:
		tmp = (x + ((y * z) / t)) / a
	elif t <= 2e-31:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + a))
	tmp = 0.0
	if (t <= -6.1e-21)
		tmp = t_1;
	elseif (t <= 4.5e-231)
		tmp = Float64(z / b);
	elseif (t <= 2.4e-162)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	elseif (t <= 2e-31)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + a);
	tmp = 0.0;
	if (t <= -6.1e-21)
		tmp = t_1;
	elseif (t <= 4.5e-231)
		tmp = z / b;
	elseif (t <= 2.4e-162)
		tmp = (x + ((y * z) / t)) / a;
	elseif (t <= 2e-31)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.1e-21], t$95$1, If[LessEqual[t, 4.5e-231], N[(z / b), $MachinePrecision], If[LessEqual[t, 2.4e-162], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 2e-31], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.10000000000000013e-21 or 2e-31 < t

   1. Initial program 80.1%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.10000000000000013e-21 < t < 4.4999999999999998e-231 or 2.4000000000000002e-162 < t < 2e-31

   1. Initial program 69.3%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 4.4999999999999998e-231 < t < 2.4000000000000002e-162

   1. Initial program 88.1%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 54.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + a}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-227}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-33}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 a))))
   (if (<= t -2.2e-21)
     t_1
     (if (<= t 4.6e-227)
       (/ z b)
       (if (<= t 1.25e-181) t_1 (if (<= t 1.9e-33) (/ z b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + a);
	double tmp;
	if (t <= -2.2e-21) {
		tmp = t_1;
	} else if (t <= 4.6e-227) {
		tmp = z / b;
	} else if (t <= 1.25e-181) {
		tmp = t_1;
	} else if (t <= 1.9e-33) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 + a)
    if (t <= (-2.2d-21)) then
        tmp = t_1
    else if (t <= 4.6d-227) then
        tmp = z / b
    else if (t <= 1.25d-181) then
        tmp = t_1
    else if (t <= 1.9d-33) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + a);
	double tmp;
	if (t <= -2.2e-21) {
		tmp = t_1;
	} else if (t <= 4.6e-227) {
		tmp = z / b;
	} else if (t <= 1.25e-181) {
		tmp = t_1;
	} else if (t <= 1.9e-33) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + a)
	tmp = 0
	if t <= -2.2e-21:
		tmp = t_1
	elif t <= 4.6e-227:
		tmp = z / b
	elif t <= 1.25e-181:
		tmp = t_1
	elif t <= 1.9e-33:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + a))
	tmp = 0.0
	if (t <= -2.2e-21)
		tmp = t_1;
	elseif (t <= 4.6e-227)
		tmp = Float64(z / b);
	elseif (t <= 1.25e-181)
		tmp = t_1;
	elseif (t <= 1.9e-33)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + a);
	tmp = 0.0;
	if (t <= -2.2e-21)
		tmp = t_1;
	elseif (t <= 4.6e-227)
		tmp = z / b;
	elseif (t <= 1.25e-181)
		tmp = t_1;
	elseif (t <= 1.9e-33)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e-21], t$95$1, If[LessEqual[t, 4.6e-227], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.25e-181], t$95$1, If[LessEqual[t, 1.9e-33], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2000000000000001e-21 or 4.60000000000000024e-227 < t < 1.25e-181 or 1.89999999999999997e-33 < t

   1. Initial program 80.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.2000000000000001e-21 < t < 4.60000000000000024e-227 or 1.25e-181 < t < 1.89999999999999997e-33

   1. Initial program 69.8%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 42.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+124}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.9e+124) (/ x a) (if (<= a 5.6e+33) (/ z b) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.9e+124) {
		tmp = x / a;
	} else if (a <= 5.6e+33) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.9d+124)) then
        tmp = x / a
    else if (a <= 5.6d+33) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.9e+124) {
		tmp = x / a;
	} else if (a <= 5.6e+33) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.9e+124:
		tmp = x / a
	elif a <= 5.6e+33:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.9e+124)
		tmp = Float64(x / a);
	elseif (a <= 5.6e+33)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.9e+124)
		tmp = x / a;
	elseif (a <= 5.6e+33)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.9e+124], N[(x / a), $MachinePrecision], If[LessEqual[a, 5.6e+33], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8999999999999999e124 or 5.6000000000000002e33 < a

   1. Initial program 77.6%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1.8999999999999999e124 < a < 5.6000000000000002e33

   1. Initial program 75.1%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 25.8% 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 76.0%

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

3. Taylor expanded in x around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in a around inf 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]
9. 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 2024110 
(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))))