Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A

Percentage Accurate: 98.6% → 98.6%

Time: 23.5s

Alternatives: 22

Speedup: 1.0×

• 47.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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 * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

Alternative 2: 80.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{z}^{y}}{y} \cdot x\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1550000:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (pow z y) y) x)))
   (if (<= y -1.4e+124)
     t_1
     (if (<= y 1550000.0) (* x (/ (pow a (+ t -1.0)) (* y (exp b)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(z, y) / y) * x;
	double tmp;
	if (y <= -1.4e+124) {
		tmp = t_1;
	} else if (y <= 1550000.0) {
		tmp = x * (pow(a, (t + -1.0)) / (y * exp(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 = ((z ** y) / y) * x
    if (y <= (-1.4d+124)) then
        tmp = t_1
    else if (y <= 1550000.0d0) then
        tmp = x * ((a ** (t + (-1.0d0))) / (y * exp(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 = (Math.pow(z, y) / y) * x;
	double tmp;
	if (y <= -1.4e+124) {
		tmp = t_1;
	} else if (y <= 1550000.0) {
		tmp = x * (Math.pow(a, (t + -1.0)) / (y * Math.exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(z, y) / y) * x
	tmp = 0
	if y <= -1.4e+124:
		tmp = t_1
	elif y <= 1550000.0:
		tmp = x * (math.pow(a, (t + -1.0)) / (y * math.exp(b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((z ^ y) / y) * x)
	tmp = 0.0
	if (y <= -1.4e+124)
		tmp = t_1;
	elseif (y <= 1550000.0)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / Float64(y * exp(b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z ^ y) / y) * x;
	tmp = 0.0;
	if (y <= -1.4e+124)
		tmp = t_1;
	elseif (y <= 1550000.0)
		tmp = x * ((a ^ (t + -1.0)) / (y * exp(b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -1.4e+124], t$95$1, If[LessEqual[y, 1550000.0], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e124 or 1.55e6 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.4e124 < y < 1.55e6

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 3: 58.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(\left(b \cdot b\right) \cdot \left(b \cdot -0.16666666666666666\right)\right)}{y}\\ t_2 := \frac{x}{y \cdot e^{b}}\\ t_3 := b \cdot \left(-1 + b \cdot 0.5\right)\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-132}:\\ \;\;\;\;\frac{x}{\left(b + 1\right) \cdot \left(a \cdot y\right) + b \cdot \left(\left(y \cdot b\right) \cdot \left(a \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}\\ \mathbf{elif}\;b \leq -9.4 \cdot 10^{-286}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-184}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 400:\\ \;\;\;\;\frac{\frac{x \cdot \left(\left(t\_3 \cdot t\_3 + -1\right) \cdot \frac{x}{y}\right)}{y}}{x \cdot \left(-1 + t\_3\right)} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (* (* b b) (* b -0.16666666666666666))) y))
        (t_2 (/ x (* y (exp b))))
        (t_3 (* b (+ -1.0 (* b 0.5)))))
   (if (<= b -1.6e+19)
     t_2
     (if (<= b -2.4e-132)
       (/
        x
        (+
         (* (+ b 1.0) (* a y))
         (* b (* (* y b) (* a (+ 0.5 (* b 0.16666666666666666)))))))
       (if (<= b -9.4e-286)
         t_1
         (if (<= b 1.3e-184)
           (/ x (* a y))
           (if (<= b 7.4e-121)
             t_1
             (if (<= b 400.0)
               (*
                (/
                 (/ (* x (* (+ (* t_3 t_3) -1.0) (/ x y))) y)
                 (* x (+ -1.0 t_3)))
                y)
               t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	double t_2 = x / (y * exp(b));
	double t_3 = b * (-1.0 + (b * 0.5));
	double tmp;
	if (b <= -1.6e+19) {
		tmp = t_2;
	} else if (b <= -2.4e-132) {
		tmp = x / (((b + 1.0) * (a * y)) + (b * ((y * b) * (a * (0.5 + (b * 0.16666666666666666))))));
	} else if (b <= -9.4e-286) {
		tmp = t_1;
	} else if (b <= 1.3e-184) {
		tmp = x / (a * y);
	} else if (b <= 7.4e-121) {
		tmp = t_1;
	} else if (b <= 400.0) {
		tmp = (((x * (((t_3 * t_3) + -1.0) * (x / y))) / y) / (x * (-1.0 + t_3))) * y;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = (x * ((b * b) * (b * (-0.16666666666666666d0)))) / y
    t_2 = x / (y * exp(b))
    t_3 = b * ((-1.0d0) + (b * 0.5d0))
    if (b <= (-1.6d+19)) then
        tmp = t_2
    else if (b <= (-2.4d-132)) then
        tmp = x / (((b + 1.0d0) * (a * y)) + (b * ((y * b) * (a * (0.5d0 + (b * 0.16666666666666666d0))))))
    else if (b <= (-9.4d-286)) then
        tmp = t_1
    else if (b <= 1.3d-184) then
        tmp = x / (a * y)
    else if (b <= 7.4d-121) then
        tmp = t_1
    else if (b <= 400.0d0) then
        tmp = (((x * (((t_3 * t_3) + (-1.0d0)) * (x / y))) / y) / (x * ((-1.0d0) + t_3))) * y
    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 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	double t_2 = x / (y * Math.exp(b));
	double t_3 = b * (-1.0 + (b * 0.5));
	double tmp;
	if (b <= -1.6e+19) {
		tmp = t_2;
	} else if (b <= -2.4e-132) {
		tmp = x / (((b + 1.0) * (a * y)) + (b * ((y * b) * (a * (0.5 + (b * 0.16666666666666666))))));
	} else if (b <= -9.4e-286) {
		tmp = t_1;
	} else if (b <= 1.3e-184) {
		tmp = x / (a * y);
	} else if (b <= 7.4e-121) {
		tmp = t_1;
	} else if (b <= 400.0) {
		tmp = (((x * (((t_3 * t_3) + -1.0) * (x / y))) / y) / (x * (-1.0 + t_3))) * y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y
	t_2 = x / (y * math.exp(b))
	t_3 = b * (-1.0 + (b * 0.5))
	tmp = 0
	if b <= -1.6e+19:
		tmp = t_2
	elif b <= -2.4e-132:
		tmp = x / (((b + 1.0) * (a * y)) + (b * ((y * b) * (a * (0.5 + (b * 0.16666666666666666))))))
	elif b <= -9.4e-286:
		tmp = t_1
	elif b <= 1.3e-184:
		tmp = x / (a * y)
	elif b <= 7.4e-121:
		tmp = t_1
	elif b <= 400.0:
		tmp = (((x * (((t_3 * t_3) + -1.0) * (x / y))) / y) / (x * (-1.0 + t_3))) * y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(Float64(b * b) * Float64(b * -0.16666666666666666))) / y)
	t_2 = Float64(x / Float64(y * exp(b)))
	t_3 = Float64(b * Float64(-1.0 + Float64(b * 0.5)))
	tmp = 0.0
	if (b <= -1.6e+19)
		tmp = t_2;
	elseif (b <= -2.4e-132)
		tmp = Float64(x / Float64(Float64(Float64(b + 1.0) * Float64(a * y)) + Float64(b * Float64(Float64(y * b) * Float64(a * Float64(0.5 + Float64(b * 0.16666666666666666)))))));
	elseif (b <= -9.4e-286)
		tmp = t_1;
	elseif (b <= 1.3e-184)
		tmp = Float64(x / Float64(a * y));
	elseif (b <= 7.4e-121)
		tmp = t_1;
	elseif (b <= 400.0)
		tmp = Float64(Float64(Float64(Float64(x * Float64(Float64(Float64(t_3 * t_3) + -1.0) * Float64(x / y))) / y) / Float64(x * Float64(-1.0 + t_3))) * y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	t_2 = x / (y * exp(b));
	t_3 = b * (-1.0 + (b * 0.5));
	tmp = 0.0;
	if (b <= -1.6e+19)
		tmp = t_2;
	elseif (b <= -2.4e-132)
		tmp = x / (((b + 1.0) * (a * y)) + (b * ((y * b) * (a * (0.5 + (b * 0.16666666666666666))))));
	elseif (b <= -9.4e-286)
		tmp = t_1;
	elseif (b <= 1.3e-184)
		tmp = x / (a * y);
	elseif (b <= 7.4e-121)
		tmp = t_1;
	elseif (b <= 400.0)
		tmp = (((x * (((t_3 * t_3) + -1.0) * (x / y))) / y) / (x * (-1.0 + t_3))) * y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[(b * b), $MachinePrecision] * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.6e+19], t$95$2, If[LessEqual[b, -2.4e-132], N[(x / N[(N[(N[(b + 1.0), $MachinePrecision] * N[(a * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(y * b), $MachinePrecision] * N[(a * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.4e-286], t$95$1, If[LessEqual[b, 1.3e-184], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.4e-121], t$95$1, If[LessEqual[b, 400.0], N[(N[(N[(N[(x * N[(N[(N[(t$95$3 * t$95$3), $MachinePrecision] + -1.0), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / N[(x * N[(-1.0 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.6e19 or 400 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.6e19 < b < -2.40000000000000015e-132

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -2.40000000000000015e-132 < b < -9.399999999999999e-286 or 1.29999999999999989e-184 < b < 7.4000000000000004e-121

   1. Initial program 97.1%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -9.399999999999999e-286 < b < 1.29999999999999989e-184

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 7.4000000000000004e-121 < b < 400

   1. Initial program 99.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 63.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{z}^{y}}{y} \cdot x\\ t_2 := \frac{{a}^{t}}{y} \cdot x\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-131}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (pow z y) y) x)) (t_2 (* (/ (pow a t) y) x)))
   (if (<= t -9.2e+75)
     t_2
     (if (<= t -1.12e-17)
       t_1
       (if (<= t 7.2e-131)
         (/
          x
          (*
           a
           (*
            y
            (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))))
         (if (<= t 1.1e+44) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(z, y) / y) * x;
	double t_2 = (pow(a, t) / y) * x;
	double tmp;
	if (t <= -9.2e+75) {
		tmp = t_2;
	} else if (t <= -1.12e-17) {
		tmp = t_1;
	} else if (t <= 7.2e-131) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	} else if (t <= 1.1e+44) {
		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 ** y) / y) * x
    t_2 = ((a ** t) / y) * x
    if (t <= (-9.2d+75)) then
        tmp = t_2
    else if (t <= (-1.12d-17)) then
        tmp = t_1
    else if (t <= 7.2d-131) then
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0))))))))
    else if (t <= 1.1d+44) 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 = (Math.pow(z, y) / y) * x;
	double t_2 = (Math.pow(a, t) / y) * x;
	double tmp;
	if (t <= -9.2e+75) {
		tmp = t_2;
	} else if (t <= -1.12e-17) {
		tmp = t_1;
	} else if (t <= 7.2e-131) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	} else if (t <= 1.1e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(z, y) / y) * x
	t_2 = (math.pow(a, t) / y) * x
	tmp = 0
	if t <= -9.2e+75:
		tmp = t_2
	elif t <= -1.12e-17:
		tmp = t_1
	elif t <= 7.2e-131:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))))
	elif t <= 1.1e+44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((z ^ y) / y) * x)
	t_2 = Float64(Float64((a ^ t) / y) * x)
	tmp = 0.0
	if (t <= -9.2e+75)
		tmp = t_2;
	elseif (t <= -1.12e-17)
		tmp = t_1;
	elseif (t <= 7.2e-131)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	elseif (t <= 1.1e+44)
		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 ^ y) / y) * x;
	t_2 = ((a ^ t) / y) * x;
	tmp = 0.0;
	if (t <= -9.2e+75)
		tmp = t_2;
	elseif (t <= -1.12e-17)
		tmp = t_1;
	elseif (t <= 7.2e-131)
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	elseif (t <= 1.1e+44)
		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[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -9.2e+75], t$95$2, If[LessEqual[t, -1.12e-17], t$95$1, If[LessEqual[t, 7.2e-131], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+44], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.1999999999999994e75 or 1.09999999999999998e44 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -9.1999999999999994e75 < t < -1.12000000000000005e-17 or 7.1999999999999999e-131 < t < 1.09999999999999998e44

   1. Initial program 99.4%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.12000000000000005e-17 < t < 7.1999999999999999e-131

   1. Initial program 95.5%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

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

Alternative 5: 73.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{t}}{y} \cdot x\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+31}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (pow a t) y) x)))
   (if (<= t -1.85e+74)
     t_1
     (if (<= t -2.9e+31)
       (* (/ (pow z y) y) x)
       (if (<= t 2.6e+91) (/ x (* a (* y (exp b)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(a, t) / y) * x;
	double tmp;
	if (t <= -1.85e+74) {
		tmp = t_1;
	} else if (t <= -2.9e+31) {
		tmp = (pow(z, y) / y) * x;
	} else if (t <= 2.6e+91) {
		tmp = x / (a * (y * exp(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 = ((a ** t) / y) * x
    if (t <= (-1.85d+74)) then
        tmp = t_1
    else if (t <= (-2.9d+31)) then
        tmp = ((z ** y) / y) * x
    else if (t <= 2.6d+91) then
        tmp = x / (a * (y * exp(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 = (Math.pow(a, t) / y) * x;
	double tmp;
	if (t <= -1.85e+74) {
		tmp = t_1;
	} else if (t <= -2.9e+31) {
		tmp = (Math.pow(z, y) / y) * x;
	} else if (t <= 2.6e+91) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(a, t) / y) * x
	tmp = 0
	if t <= -1.85e+74:
		tmp = t_1
	elif t <= -2.9e+31:
		tmp = (math.pow(z, y) / y) * x
	elif t <= 2.6e+91:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((a ^ t) / y) * x)
	tmp = 0.0
	if (t <= -1.85e+74)
		tmp = t_1;
	elseif (t <= -2.9e+31)
		tmp = Float64(Float64((z ^ y) / y) * x);
	elseif (t <= 2.6e+91)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a ^ t) / y) * x;
	tmp = 0.0;
	if (t <= -1.85e+74)
		tmp = t_1;
	elseif (t <= -2.9e+31)
		tmp = ((z ^ y) / y) * x;
	elseif (t <= 2.6e+91)
		tmp = x / (a * (y * exp(b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -1.85e+74], t$95$1, If[LessEqual[t, -2.9e+31], N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 2.6e+91], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8500000000000001e74 or 2.6e91 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.8500000000000001e74 < t < -2.9e31

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -2.9e31 < t < 2.6e91

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

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

Alternative 6: 74.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{z}^{y}}{y} \cdot x\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (pow z y) y) x)))
   (if (<= y -3.8e+42)
     t_1
     (if (<= y 2.25e-14) (* x (/ (pow a (+ t -1.0)) y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(z, y) / y) * x;
	double tmp;
	if (y <= -3.8e+42) {
		tmp = t_1;
	} else if (y <= 2.25e-14) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} 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 ** y) / y) * x
    if (y <= (-3.8d+42)) then
        tmp = t_1
    else if (y <= 2.25d-14) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    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 = (Math.pow(z, y) / y) * x;
	double tmp;
	if (y <= -3.8e+42) {
		tmp = t_1;
	} else if (y <= 2.25e-14) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(z, y) / y) * x
	tmp = 0
	if y <= -3.8e+42:
		tmp = t_1
	elif y <= 2.25e-14:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((z ^ y) / y) * x)
	tmp = 0.0
	if (y <= -3.8e+42)
		tmp = t_1;
	elseif (y <= 2.25e-14)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z ^ y) / y) * x;
	tmp = 0.0;
	if (y <= -3.8e+42)
		tmp = t_1;
	elseif (y <= 2.25e-14)
		tmp = x * ((a ^ (t + -1.0)) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -3.8e+42], t$95$1, If[LessEqual[y, 2.25e-14], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999998e42 or 2.2499999999999999e-14 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -3.7999999999999998e42 < y < 2.2499999999999999e-14

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

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

Alternative 7: 63.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{t}}{y} \cdot x\\ \mathbf{if}\;t \leq -130000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (pow a t) y) x)))
   (if (<= t -130000000000.0)
     t_1
     (if (<= t 2.3)
       (/
        x
        (*
         a
         (* y (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(a, t) / y) * x;
	double tmp;
	if (t <= -130000000000.0) {
		tmp = t_1;
	} else if (t <= 2.3) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	} 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 = ((a ** t) / y) * x
    if (t <= (-130000000000.0d0)) then
        tmp = t_1
    else if (t <= 2.3d0) then
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0))))))))
    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 = (Math.pow(a, t) / y) * x;
	double tmp;
	if (t <= -130000000000.0) {
		tmp = t_1;
	} else if (t <= 2.3) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(a, t) / y) * x
	tmp = 0
	if t <= -130000000000.0:
		tmp = t_1
	elif t <= 2.3:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((a ^ t) / y) * x)
	tmp = 0.0
	if (t <= -130000000000.0)
		tmp = t_1;
	elseif (t <= 2.3)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a ^ t) / y) * x;
	tmp = 0.0;
	if (t <= -130000000000.0)
		tmp = t_1;
	elseif (t <= 2.3)
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -130000000000.0], t$95$1, If[LessEqual[t, 2.3], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e11 or 2.2999999999999998 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.3e11 < t < 2.2999999999999998

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

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

Alternative 8: 53.4% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(\left(b \cdot b\right) \cdot \left(b \cdot -0.16666666666666666\right)\right)}{y}\\ t_2 := \frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+53}:\\ \;\;\;\;\frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y} \cdot x\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.42 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-181}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+99}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (* (* b b) (* b -0.16666666666666666))) y))
        (t_2 (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5)))))))))
   (if (<= b -1.1e+53)
     (*
      (/ (+ 1.0 (* b (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666)))))) y)
      x)
     (if (<= b -3.7e-135)
       t_2
       (if (<= b -1.42e-282)
         t_1
         (if (<= b 5e-181)
           (/ x (* a y))
           (if (<= b 3.2e-115)
             t_1
             (if (<= b 4.2e+99)
               t_2
               (/
                x
                (*
                 y
                 (+
                  1.0
                  (*
                   b
                   (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	double t_2 = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	double tmp;
	if (b <= -1.1e+53) {
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x;
	} else if (b <= -3.7e-135) {
		tmp = t_2;
	} else if (b <= -1.42e-282) {
		tmp = t_1;
	} else if (b <= 5e-181) {
		tmp = x / (a * y);
	} else if (b <= 3.2e-115) {
		tmp = t_1;
	} else if (b <= 4.2e+99) {
		tmp = t_2;
	} else {
		tmp = x / (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((b * b) * (b * (-0.16666666666666666d0)))) / y
    t_2 = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))))
    if (b <= (-1.1d+53)) then
        tmp = ((1.0d0 + (b * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0))))))) / y) * x
    else if (b <= (-3.7d-135)) then
        tmp = t_2
    else if (b <= (-1.42d-282)) then
        tmp = t_1
    else if (b <= 5d-181) then
        tmp = x / (a * y)
    else if (b <= 3.2d-115) then
        tmp = t_1
    else if (b <= 4.2d+99) then
        tmp = t_2
    else
        tmp = x / (y * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0)))))))
    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 * ((b * b) * (b * -0.16666666666666666))) / y;
	double t_2 = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	double tmp;
	if (b <= -1.1e+53) {
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x;
	} else if (b <= -3.7e-135) {
		tmp = t_2;
	} else if (b <= -1.42e-282) {
		tmp = t_1;
	} else if (b <= 5e-181) {
		tmp = x / (a * y);
	} else if (b <= 3.2e-115) {
		tmp = t_1;
	} else if (b <= 4.2e+99) {
		tmp = t_2;
	} else {
		tmp = x / (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y
	t_2 = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	tmp = 0
	if b <= -1.1e+53:
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x
	elif b <= -3.7e-135:
		tmp = t_2
	elif b <= -1.42e-282:
		tmp = t_1
	elif b <= 5e-181:
		tmp = x / (a * y)
	elif b <= 3.2e-115:
		tmp = t_1
	elif b <= 4.2e+99:
		tmp = t_2
	else:
		tmp = x / (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(Float64(b * b) * Float64(b * -0.16666666666666666))) / y)
	t_2 = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))))
	tmp = 0.0
	if (b <= -1.1e+53)
		tmp = Float64(Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666)))))) / y) * x);
	elseif (b <= -3.7e-135)
		tmp = t_2;
	elseif (b <= -1.42e-282)
		tmp = t_1;
	elseif (b <= 5e-181)
		tmp = Float64(x / Float64(a * y));
	elseif (b <= 3.2e-115)
		tmp = t_1;
	elseif (b <= 4.2e+99)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	t_2 = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	tmp = 0.0;
	if (b <= -1.1e+53)
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x;
	elseif (b <= -3.7e-135)
		tmp = t_2;
	elseif (b <= -1.42e-282)
		tmp = t_1;
	elseif (b <= 5e-181)
		tmp = x / (a * y);
	elseif (b <= 3.2e-115)
		tmp = t_1;
	elseif (b <= 4.2e+99)
		tmp = t_2;
	else
		tmp = x / (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[(b * b), $MachinePrecision] * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.1e+53], N[(N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, -3.7e-135], t$95$2, If[LessEqual[b, -1.42e-282], t$95$1, If[LessEqual[b, 5e-181], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e-115], t$95$1, If[LessEqual[b, 4.2e+99], t$95$2, N[(x / N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.09999999999999999e53

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]

   if -1.09999999999999999e53 < b < -3.6999999999999997e-135 or 3.2e-115 < b < 4.2000000000000002e99

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -3.6999999999999997e-135 < b < -1.42e-282 or 5.0000000000000001e-181 < b < 3.2e-115

   1. Initial program 97.2%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -1.42e-282 < b < 5.0000000000000001e-181

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 4.2000000000000002e99 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 9: 54.0% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot y}\\ t_2 := \frac{x \cdot \left(\left(b \cdot b\right) \cdot \left(b \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{if}\;b \leq -2 \cdot 10^{+71}:\\ \;\;\;\;\frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y} \cdot x\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-150}:\\ \;\;\;\;t\_1 + b \cdot \left(b \cdot \left(\frac{0.5 \cdot \frac{x}{y}}{a} - b \cdot \frac{0.16666666666666666 \cdot \frac{x}{y}}{a}\right) - t\_1\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-287}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-115}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a y)))
        (t_2 (/ (* x (* (* b b) (* b -0.16666666666666666))) y)))
   (if (<= b -2e+71)
     (*
      (/ (+ 1.0 (* b (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666)))))) y)
      x)
     (if (<= b -4.6e-150)
       (+
        t_1
        (*
         b
         (-
          (*
           b
           (-
            (/ (* 0.5 (/ x y)) a)
            (* b (/ (* 0.16666666666666666 (/ x y)) a))))
          t_1)))
       (if (<= b -2.8e-287)
         t_2
         (if (<= b 1.7e-187)
           t_1
           (if (<= b 1.75e-115)
             t_2
             (/
              x
              (*
               a
               (*
                y
                (+
                 1.0
                 (*
                  b
                  (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * y);
	double t_2 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	double tmp;
	if (b <= -2e+71) {
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x;
	} else if (b <= -4.6e-150) {
		tmp = t_1 + (b * ((b * (((0.5 * (x / y)) / a) - (b * ((0.16666666666666666 * (x / y)) / a)))) - t_1));
	} else if (b <= -2.8e-287) {
		tmp = t_2;
	} else if (b <= 1.7e-187) {
		tmp = t_1;
	} else if (b <= 1.75e-115) {
		tmp = t_2;
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (a * y)
    t_2 = (x * ((b * b) * (b * (-0.16666666666666666d0)))) / y
    if (b <= (-2d+71)) then
        tmp = ((1.0d0 + (b * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0))))))) / y) * x
    else if (b <= (-4.6d-150)) then
        tmp = t_1 + (b * ((b * (((0.5d0 * (x / y)) / a) - (b * ((0.16666666666666666d0 * (x / y)) / a)))) - t_1))
    else if (b <= (-2.8d-287)) then
        tmp = t_2
    else if (b <= 1.7d-187) then
        tmp = t_1
    else if (b <= 1.75d-115) then
        tmp = t_2
    else
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * y);
	double t_2 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	double tmp;
	if (b <= -2e+71) {
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x;
	} else if (b <= -4.6e-150) {
		tmp = t_1 + (b * ((b * (((0.5 * (x / y)) / a) - (b * ((0.16666666666666666 * (x / y)) / a)))) - t_1));
	} else if (b <= -2.8e-287) {
		tmp = t_2;
	} else if (b <= 1.7e-187) {
		tmp = t_1;
	} else if (b <= 1.75e-115) {
		tmp = t_2;
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * y)
	t_2 = (x * ((b * b) * (b * -0.16666666666666666))) / y
	tmp = 0
	if b <= -2e+71:
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x
	elif b <= -4.6e-150:
		tmp = t_1 + (b * ((b * (((0.5 * (x / y)) / a) - (b * ((0.16666666666666666 * (x / y)) / a)))) - t_1))
	elif b <= -2.8e-287:
		tmp = t_2
	elif b <= 1.7e-187:
		tmp = t_1
	elif b <= 1.75e-115:
		tmp = t_2
	else:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * y))
	t_2 = Float64(Float64(x * Float64(Float64(b * b) * Float64(b * -0.16666666666666666))) / y)
	tmp = 0.0
	if (b <= -2e+71)
		tmp = Float64(Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666)))))) / y) * x);
	elseif (b <= -4.6e-150)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(b * Float64(Float64(Float64(0.5 * Float64(x / y)) / a) - Float64(b * Float64(Float64(0.16666666666666666 * Float64(x / y)) / a)))) - t_1)));
	elseif (b <= -2.8e-287)
		tmp = t_2;
	elseif (b <= 1.7e-187)
		tmp = t_1;
	elseif (b <= 1.75e-115)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * y);
	t_2 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	tmp = 0.0;
	if (b <= -2e+71)
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x;
	elseif (b <= -4.6e-150)
		tmp = t_1 + (b * ((b * (((0.5 * (x / y)) / a) - (b * ((0.16666666666666666 * (x / y)) / a)))) - t_1));
	elseif (b <= -2.8e-287)
		tmp = t_2;
	elseif (b <= 1.7e-187)
		tmp = t_1;
	elseif (b <= 1.75e-115)
		tmp = t_2;
	else
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(b * b), $MachinePrecision] * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -2e+71], N[(N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, -4.6e-150], N[(t$95$1 + N[(b * N[(N[(b * N[(N[(N[(0.5 * N[(x / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] - N[(b * N[(N[(0.16666666666666666 * N[(x / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e-287], t$95$2, If[LessEqual[b, 1.7e-187], t$95$1, If[LessEqual[b, 1.75e-115], t$95$2, N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.0000000000000001e71

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]

   if -2.0000000000000001e71 < b < -4.60000000000000006e-150

   1. Initial program 94.7%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -4.60000000000000006e-150 < b < -2.8000000000000002e-287 or 1.7000000000000001e-187 < b < 1.7500000000000001e-115

   1. Initial program 97.2%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -2.8000000000000002e-287 < b < 1.7000000000000001e-187

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 1.7500000000000001e-115 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 10: 53.8% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(\left(b \cdot b\right) \cdot \left(b \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{if}\;b \leq -1.02 \cdot 10^{+55}:\\ \;\;\;\;\frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y} \cdot x\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-131}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-286}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-182}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (* (* b b) (* b -0.16666666666666666))) y)))
   (if (<= b -1.02e+55)
     (*
      (/ (+ 1.0 (* b (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666)))))) y)
      x)
     (if (<= b -3.6e-131)
       (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5)))))))
       (if (<= b -4.7e-286)
         t_1
         (if (<= b 5.4e-182)
           (/ x (* a y))
           (if (<= b 1.45e-115)
             t_1
             (/
              x
              (*
               a
               (*
                y
                (+
                 1.0
                 (*
                  b
                  (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	double tmp;
	if (b <= -1.02e+55) {
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x;
	} else if (b <= -3.6e-131) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	} else if (b <= -4.7e-286) {
		tmp = t_1;
	} else if (b <= 5.4e-182) {
		tmp = x / (a * y);
	} else if (b <= 1.45e-115) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	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 * ((b * b) * (b * (-0.16666666666666666d0)))) / y
    if (b <= (-1.02d+55)) then
        tmp = ((1.0d0 + (b * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0))))))) / y) * x
    else if (b <= (-3.6d-131)) then
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))))
    else if (b <= (-4.7d-286)) then
        tmp = t_1
    else if (b <= 5.4d-182) then
        tmp = x / (a * y)
    else if (b <= 1.45d-115) then
        tmp = t_1
    else
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0))))))))
    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 * ((b * b) * (b * -0.16666666666666666))) / y;
	double tmp;
	if (b <= -1.02e+55) {
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x;
	} else if (b <= -3.6e-131) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	} else if (b <= -4.7e-286) {
		tmp = t_1;
	} else if (b <= 5.4e-182) {
		tmp = x / (a * y);
	} else if (b <= 1.45e-115) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y
	tmp = 0
	if b <= -1.02e+55:
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x
	elif b <= -3.6e-131:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	elif b <= -4.7e-286:
		tmp = t_1
	elif b <= 5.4e-182:
		tmp = x / (a * y)
	elif b <= 1.45e-115:
		tmp = t_1
	else:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(Float64(b * b) * Float64(b * -0.16666666666666666))) / y)
	tmp = 0.0
	if (b <= -1.02e+55)
		tmp = Float64(Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666)))))) / y) * x);
	elseif (b <= -3.6e-131)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))));
	elseif (b <= -4.7e-286)
		tmp = t_1;
	elseif (b <= 5.4e-182)
		tmp = Float64(x / Float64(a * y));
	elseif (b <= 1.45e-115)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	tmp = 0.0;
	if (b <= -1.02e+55)
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x;
	elseif (b <= -3.6e-131)
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	elseif (b <= -4.7e-286)
		tmp = t_1;
	elseif (b <= 5.4e-182)
		tmp = x / (a * y);
	elseif (b <= 1.45e-115)
		tmp = t_1;
	else
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[(b * b), $MachinePrecision] * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.02e+55], N[(N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, -3.6e-131], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.7e-286], t$95$1, If[LessEqual[b, 5.4e-182], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e-115], t$95$1, N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.02000000000000002e55

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]

   if -1.02000000000000002e55 < b < -3.5999999999999999e-131

   1. Initial program 94.4%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -3.5999999999999999e-131 < b < -4.7e-286 or 5.39999999999999999e-182 < b < 1.4499999999999999e-115

   1. Initial program 97.2%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -4.7e-286 < b < 5.39999999999999999e-182

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 1.4499999999999999e-115 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 11: 51.5% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(\left(b \cdot b\right) \cdot \left(b \cdot -0.16666666666666666\right)\right)}{y}\\ t_2 := \frac{x}{a \cdot y}\\ \mathbf{if}\;b \leq -3.55 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-129}:\\ \;\;\;\;\left(\left(0 - b\right) + 1\right) \cdot t\_2\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (* (* b b) (* b -0.16666666666666666))) y))
        (t_2 (/ x (* a y))))
   (if (<= b -3.55e+53)
     t_1
     (if (<= b -2e-129)
       (* (+ (- 0.0 b) 1.0) t_2)
       (if (<= b -1.55e-283)
         t_1
         (if (<= b 5.4e-186)
           t_2
           (if (<= b 1.25e-115)
             t_1
             (if (<= b 2.3e+56)
               t_2
               (/ x (* y (+ 1.0 (* b (+ 1.0 (* b 0.5))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	double t_2 = x / (a * y);
	double tmp;
	if (b <= -3.55e+53) {
		tmp = t_1;
	} else if (b <= -2e-129) {
		tmp = ((0.0 - b) + 1.0) * t_2;
	} else if (b <= -1.55e-283) {
		tmp = t_1;
	} else if (b <= 5.4e-186) {
		tmp = t_2;
	} else if (b <= 1.25e-115) {
		tmp = t_1;
	} else if (b <= 2.3e+56) {
		tmp = t_2;
	} else {
		tmp = x / (y * (1.0 + (b * (1.0 + (b * 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((b * b) * (b * (-0.16666666666666666d0)))) / y
    t_2 = x / (a * y)
    if (b <= (-3.55d+53)) then
        tmp = t_1
    else if (b <= (-2d-129)) then
        tmp = ((0.0d0 - b) + 1.0d0) * t_2
    else if (b <= (-1.55d-283)) then
        tmp = t_1
    else if (b <= 5.4d-186) then
        tmp = t_2
    else if (b <= 1.25d-115) then
        tmp = t_1
    else if (b <= 2.3d+56) then
        tmp = t_2
    else
        tmp = x / (y * (1.0d0 + (b * (1.0d0 + (b * 0.5d0)))))
    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 * ((b * b) * (b * -0.16666666666666666))) / y;
	double t_2 = x / (a * y);
	double tmp;
	if (b <= -3.55e+53) {
		tmp = t_1;
	} else if (b <= -2e-129) {
		tmp = ((0.0 - b) + 1.0) * t_2;
	} else if (b <= -1.55e-283) {
		tmp = t_1;
	} else if (b <= 5.4e-186) {
		tmp = t_2;
	} else if (b <= 1.25e-115) {
		tmp = t_1;
	} else if (b <= 2.3e+56) {
		tmp = t_2;
	} else {
		tmp = x / (y * (1.0 + (b * (1.0 + (b * 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y
	t_2 = x / (a * y)
	tmp = 0
	if b <= -3.55e+53:
		tmp = t_1
	elif b <= -2e-129:
		tmp = ((0.0 - b) + 1.0) * t_2
	elif b <= -1.55e-283:
		tmp = t_1
	elif b <= 5.4e-186:
		tmp = t_2
	elif b <= 1.25e-115:
		tmp = t_1
	elif b <= 2.3e+56:
		tmp = t_2
	else:
		tmp = x / (y * (1.0 + (b * (1.0 + (b * 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(Float64(b * b) * Float64(b * -0.16666666666666666))) / y)
	t_2 = Float64(x / Float64(a * y))
	tmp = 0.0
	if (b <= -3.55e+53)
		tmp = t_1;
	elseif (b <= -2e-129)
		tmp = Float64(Float64(Float64(0.0 - b) + 1.0) * t_2);
	elseif (b <= -1.55e-283)
		tmp = t_1;
	elseif (b <= 5.4e-186)
		tmp = t_2;
	elseif (b <= 1.25e-115)
		tmp = t_1;
	elseif (b <= 2.3e+56)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	t_2 = x / (a * y);
	tmp = 0.0;
	if (b <= -3.55e+53)
		tmp = t_1;
	elseif (b <= -2e-129)
		tmp = ((0.0 - b) + 1.0) * t_2;
	elseif (b <= -1.55e-283)
		tmp = t_1;
	elseif (b <= 5.4e-186)
		tmp = t_2;
	elseif (b <= 1.25e-115)
		tmp = t_1;
	elseif (b <= 2.3e+56)
		tmp = t_2;
	else
		tmp = x / (y * (1.0 + (b * (1.0 + (b * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[(b * b), $MachinePrecision] * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.55e+53], t$95$1, If[LessEqual[b, -2e-129], N[(N[(N[(0.0 - b), $MachinePrecision] + 1.0), $MachinePrecision] * t$95$2), $MachinePrecision], If[LessEqual[b, -1.55e-283], t$95$1, If[LessEqual[b, 5.4e-186], t$95$2, If[LessEqual[b, 1.25e-115], t$95$1, If[LessEqual[b, 2.3e+56], t$95$2, N[(x / N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.54999999999999987e53 or -1.9999999999999999e-129 < b < -1.55000000000000002e-283 or 5.3999999999999998e-186 < b < 1.2500000000000001e-115

   1. Initial program 98.6%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -3.54999999999999987e53 < b < -1.9999999999999999e-129

   1. Initial program 94.4%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -1.55000000000000002e-283 < b < 5.3999999999999998e-186 or 1.2500000000000001e-115 < b < 2.30000000000000015e56

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 2.30000000000000015e56 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

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

Alternative 12: 52.0% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(\left(b \cdot b\right) \cdot \left(b \cdot -0.16666666666666666\right)\right)}{y}\\ t_2 := \frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+56}:\\ \;\;\;\;\frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y} \cdot x\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-138}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.34 \cdot 10^{-182}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (* (* b b) (* b -0.16666666666666666))) y))
        (t_2 (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5)))))))))
   (if (<= b -2.5e+56)
     (*
      (/ (+ 1.0 (* b (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666)))))) y)
      x)
     (if (<= b -1.32e-138)
       t_2
       (if (<= b -4e-283)
         t_1
         (if (<= b 1.34e-182) (/ x (* a y)) (if (<= b 4e-115) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	double t_2 = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	double tmp;
	if (b <= -2.5e+56) {
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x;
	} else if (b <= -1.32e-138) {
		tmp = t_2;
	} else if (b <= -4e-283) {
		tmp = t_1;
	} else if (b <= 1.34e-182) {
		tmp = x / (a * y);
	} else if (b <= 4e-115) {
		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 = (x * ((b * b) * (b * (-0.16666666666666666d0)))) / y
    t_2 = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))))
    if (b <= (-2.5d+56)) then
        tmp = ((1.0d0 + (b * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0))))))) / y) * x
    else if (b <= (-1.32d-138)) then
        tmp = t_2
    else if (b <= (-4d-283)) then
        tmp = t_1
    else if (b <= 1.34d-182) then
        tmp = x / (a * y)
    else if (b <= 4d-115) 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 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	double t_2 = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	double tmp;
	if (b <= -2.5e+56) {
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x;
	} else if (b <= -1.32e-138) {
		tmp = t_2;
	} else if (b <= -4e-283) {
		tmp = t_1;
	} else if (b <= 1.34e-182) {
		tmp = x / (a * y);
	} else if (b <= 4e-115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y
	t_2 = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	tmp = 0
	if b <= -2.5e+56:
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x
	elif b <= -1.32e-138:
		tmp = t_2
	elif b <= -4e-283:
		tmp = t_1
	elif b <= 1.34e-182:
		tmp = x / (a * y)
	elif b <= 4e-115:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(Float64(b * b) * Float64(b * -0.16666666666666666))) / y)
	t_2 = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))))
	tmp = 0.0
	if (b <= -2.5e+56)
		tmp = Float64(Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666)))))) / y) * x);
	elseif (b <= -1.32e-138)
		tmp = t_2;
	elseif (b <= -4e-283)
		tmp = t_1;
	elseif (b <= 1.34e-182)
		tmp = Float64(x / Float64(a * y));
	elseif (b <= 4e-115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	t_2 = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	tmp = 0.0;
	if (b <= -2.5e+56)
		tmp = ((1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y) * x;
	elseif (b <= -1.32e-138)
		tmp = t_2;
	elseif (b <= -4e-283)
		tmp = t_1;
	elseif (b <= 1.34e-182)
		tmp = x / (a * y);
	elseif (b <= 4e-115)
		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[(x * N[(N[(b * b), $MachinePrecision] * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e+56], N[(N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, -1.32e-138], t$95$2, If[LessEqual[b, -4e-283], t$95$1, If[LessEqual[b, 1.34e-182], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e-115], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.50000000000000012e56

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]

   if -2.50000000000000012e56 < b < -1.32e-138 or 4.0000000000000002e-115 < b

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -1.32e-138 < b < -3.99999999999999979e-283 or 1.33999999999999994e-182 < b < 4.0000000000000002e-115

   1. Initial program 97.2%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -3.99999999999999979e-283 < b < 1.33999999999999994e-182

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

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

Alternative 13: 52.1% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ t_2 := \frac{x \cdot \left(\left(b \cdot b\right) \cdot \left(b \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{if}\;b \leq -4.3 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-287}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-181}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-115}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5))))))))
        (t_2 (/ (* x (* (* b b) (* b -0.16666666666666666))) y)))
   (if (<= b -4.3e+56)
     t_2
     (if (<= b -2.05e-151)
       t_1
       (if (<= b -5.2e-287)
         t_2
         (if (<= b 2.4e-181) (/ x (* a y)) (if (<= b 2.5e-115) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	double t_2 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	double tmp;
	if (b <= -4.3e+56) {
		tmp = t_2;
	} else if (b <= -2.05e-151) {
		tmp = t_1;
	} else if (b <= -5.2e-287) {
		tmp = t_2;
	} else if (b <= 2.4e-181) {
		tmp = x / (a * y);
	} else if (b <= 2.5e-115) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))))
    t_2 = (x * ((b * b) * (b * (-0.16666666666666666d0)))) / y
    if (b <= (-4.3d+56)) then
        tmp = t_2
    else if (b <= (-2.05d-151)) then
        tmp = t_1
    else if (b <= (-5.2d-287)) then
        tmp = t_2
    else if (b <= 2.4d-181) then
        tmp = x / (a * y)
    else if (b <= 2.5d-115) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	double t_2 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	double tmp;
	if (b <= -4.3e+56) {
		tmp = t_2;
	} else if (b <= -2.05e-151) {
		tmp = t_1;
	} else if (b <= -5.2e-287) {
		tmp = t_2;
	} else if (b <= 2.4e-181) {
		tmp = x / (a * y);
	} else if (b <= 2.5e-115) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	t_2 = (x * ((b * b) * (b * -0.16666666666666666))) / y
	tmp = 0
	if b <= -4.3e+56:
		tmp = t_2
	elif b <= -2.05e-151:
		tmp = t_1
	elif b <= -5.2e-287:
		tmp = t_2
	elif b <= 2.4e-181:
		tmp = x / (a * y)
	elif b <= 2.5e-115:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))))
	t_2 = Float64(Float64(x * Float64(Float64(b * b) * Float64(b * -0.16666666666666666))) / y)
	tmp = 0.0
	if (b <= -4.3e+56)
		tmp = t_2;
	elseif (b <= -2.05e-151)
		tmp = t_1;
	elseif (b <= -5.2e-287)
		tmp = t_2;
	elseif (b <= 2.4e-181)
		tmp = Float64(x / Float64(a * y));
	elseif (b <= 2.5e-115)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	t_2 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	tmp = 0.0;
	if (b <= -4.3e+56)
		tmp = t_2;
	elseif (b <= -2.05e-151)
		tmp = t_1;
	elseif (b <= -5.2e-287)
		tmp = t_2;
	elseif (b <= 2.4e-181)
		tmp = x / (a * y);
	elseif (b <= 2.5e-115)
		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[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(b * b), $MachinePrecision] * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -4.3e+56], t$95$2, If[LessEqual[b, -2.05e-151], t$95$1, If[LessEqual[b, -5.2e-287], t$95$2, If[LessEqual[b, 2.4e-181], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e-115], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.3000000000000003e56 or -2.0500000000000001e-151 < b < -5.1999999999999999e-287 or 2.4000000000000001e-181 < b < 2.5000000000000001e-115

   1. Initial program 98.6%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -4.3000000000000003e56 < b < -2.0500000000000001e-151 or 2.5000000000000001e-115 < b

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -5.1999999999999999e-287 < b < 2.4000000000000001e-181

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

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

Alternative 14: 46.5% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(\left(b \cdot b\right) \cdot \left(b \cdot -0.16666666666666666\right)\right)}{y}\\ t_2 := \frac{x}{a \cdot y}\\ \mathbf{if}\;b \leq -9.4 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.9 \cdot 10^{-137}:\\ \;\;\;\;\left(\left(0 - b\right) + 1\right) \cdot t\_2\\ \mathbf{elif}\;b \leq -1.82 \cdot 10^{-283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-184}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(b + 1\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (* (* b b) (* b -0.16666666666666666))) y))
        (t_2 (/ x (* a y))))
   (if (<= b -9.4e+55)
     t_1
     (if (<= b -4.9e-137)
       (* (+ (- 0.0 b) 1.0) t_2)
       (if (<= b -1.82e-283)
         t_1
         (if (<= b 1.12e-184)
           t_2
           (if (<= b 2.1e-115) t_1 (/ x (* a (* y (+ b 1.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	double t_2 = x / (a * y);
	double tmp;
	if (b <= -9.4e+55) {
		tmp = t_1;
	} else if (b <= -4.9e-137) {
		tmp = ((0.0 - b) + 1.0) * t_2;
	} else if (b <= -1.82e-283) {
		tmp = t_1;
	} else if (b <= 1.12e-184) {
		tmp = t_2;
	} else if (b <= 2.1e-115) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * (b + 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) :: t_2
    real(8) :: tmp
    t_1 = (x * ((b * b) * (b * (-0.16666666666666666d0)))) / y
    t_2 = x / (a * y)
    if (b <= (-9.4d+55)) then
        tmp = t_1
    else if (b <= (-4.9d-137)) then
        tmp = ((0.0d0 - b) + 1.0d0) * t_2
    else if (b <= (-1.82d-283)) then
        tmp = t_1
    else if (b <= 1.12d-184) then
        tmp = t_2
    else if (b <= 2.1d-115) then
        tmp = t_1
    else
        tmp = x / (a * (y * (b + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	double t_2 = x / (a * y);
	double tmp;
	if (b <= -9.4e+55) {
		tmp = t_1;
	} else if (b <= -4.9e-137) {
		tmp = ((0.0 - b) + 1.0) * t_2;
	} else if (b <= -1.82e-283) {
		tmp = t_1;
	} else if (b <= 1.12e-184) {
		tmp = t_2;
	} else if (b <= 2.1e-115) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * (b + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y
	t_2 = x / (a * y)
	tmp = 0
	if b <= -9.4e+55:
		tmp = t_1
	elif b <= -4.9e-137:
		tmp = ((0.0 - b) + 1.0) * t_2
	elif b <= -1.82e-283:
		tmp = t_1
	elif b <= 1.12e-184:
		tmp = t_2
	elif b <= 2.1e-115:
		tmp = t_1
	else:
		tmp = x / (a * (y * (b + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(Float64(b * b) * Float64(b * -0.16666666666666666))) / y)
	t_2 = Float64(x / Float64(a * y))
	tmp = 0.0
	if (b <= -9.4e+55)
		tmp = t_1;
	elseif (b <= -4.9e-137)
		tmp = Float64(Float64(Float64(0.0 - b) + 1.0) * t_2);
	elseif (b <= -1.82e-283)
		tmp = t_1;
	elseif (b <= 1.12e-184)
		tmp = t_2;
	elseif (b <= 2.1e-115)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(b + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((b * b) * (b * -0.16666666666666666))) / y;
	t_2 = x / (a * y);
	tmp = 0.0;
	if (b <= -9.4e+55)
		tmp = t_1;
	elseif (b <= -4.9e-137)
		tmp = ((0.0 - b) + 1.0) * t_2;
	elseif (b <= -1.82e-283)
		tmp = t_1;
	elseif (b <= 1.12e-184)
		tmp = t_2;
	elseif (b <= 2.1e-115)
		tmp = t_1;
	else
		tmp = x / (a * (y * (b + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[(b * b), $MachinePrecision] * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.4e+55], t$95$1, If[LessEqual[b, -4.9e-137], N[(N[(N[(0.0 - b), $MachinePrecision] + 1.0), $MachinePrecision] * t$95$2), $MachinePrecision], If[LessEqual[b, -1.82e-283], t$95$1, If[LessEqual[b, 1.12e-184], t$95$2, If[LessEqual[b, 2.1e-115], t$95$1, N[(x / N[(a * N[(y * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.4000000000000001e55 or -4.8999999999999996e-137 < b < -1.81999999999999994e-283 or 1.11999999999999997e-184 < b < 2.10000000000000002e-115

   1. Initial program 98.6%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -9.4000000000000001e55 < b < -4.8999999999999996e-137

   1. Initial program 94.4%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -1.81999999999999994e-283 < b < 1.11999999999999997e-184

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 2.10000000000000002e-115 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

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

Alternative 15: 43.0% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot y}\\ t_2 := x \cdot \left(0.5 \cdot \frac{b \cdot b}{y}\right)\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-284}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(b + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a y))) (t_2 (* x (* 0.5 (/ (* b b) y)))))
   (if (<= b -8.5e+55)
     t_2
     (if (<= b -1.1e-134)
       t_1
       (if (<= b -2.25e-284)
         t_2
         (if (<= b 8.8e+67) t_1 (/ x (* y (+ b 1.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * y);
	double t_2 = x * (0.5 * ((b * b) / y));
	double tmp;
	if (b <= -8.5e+55) {
		tmp = t_2;
	} else if (b <= -1.1e-134) {
		tmp = t_1;
	} else if (b <= -2.25e-284) {
		tmp = t_2;
	} else if (b <= 8.8e+67) {
		tmp = t_1;
	} else {
		tmp = x / (y * (b + 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) :: t_2
    real(8) :: tmp
    t_1 = x / (a * y)
    t_2 = x * (0.5d0 * ((b * b) / y))
    if (b <= (-8.5d+55)) then
        tmp = t_2
    else if (b <= (-1.1d-134)) then
        tmp = t_1
    else if (b <= (-2.25d-284)) then
        tmp = t_2
    else if (b <= 8.8d+67) then
        tmp = t_1
    else
        tmp = x / (y * (b + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * y);
	double t_2 = x * (0.5 * ((b * b) / y));
	double tmp;
	if (b <= -8.5e+55) {
		tmp = t_2;
	} else if (b <= -1.1e-134) {
		tmp = t_1;
	} else if (b <= -2.25e-284) {
		tmp = t_2;
	} else if (b <= 8.8e+67) {
		tmp = t_1;
	} else {
		tmp = x / (y * (b + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * y)
	t_2 = x * (0.5 * ((b * b) / y))
	tmp = 0
	if b <= -8.5e+55:
		tmp = t_2
	elif b <= -1.1e-134:
		tmp = t_1
	elif b <= -2.25e-284:
		tmp = t_2
	elif b <= 8.8e+67:
		tmp = t_1
	else:
		tmp = x / (y * (b + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * y))
	t_2 = Float64(x * Float64(0.5 * Float64(Float64(b * b) / y)))
	tmp = 0.0
	if (b <= -8.5e+55)
		tmp = t_2;
	elseif (b <= -1.1e-134)
		tmp = t_1;
	elseif (b <= -2.25e-284)
		tmp = t_2;
	elseif (b <= 8.8e+67)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(y * Float64(b + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * y);
	t_2 = x * (0.5 * ((b * b) / y));
	tmp = 0.0;
	if (b <= -8.5e+55)
		tmp = t_2;
	elseif (b <= -1.1e-134)
		tmp = t_1;
	elseif (b <= -2.25e-284)
		tmp = t_2;
	elseif (b <= 8.8e+67)
		tmp = t_1;
	else
		tmp = x / (y * (b + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(0.5 * N[(N[(b * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.5e+55], t$95$2, If[LessEqual[b, -1.1e-134], t$95$1, If[LessEqual[b, -2.25e-284], t$95$2, If[LessEqual[b, 8.8e+67], t$95$1, N[(x / N[(y * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.50000000000000002e55 or -1.1e-134 < b < -2.25e-284

   1. Initial program 98.3%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if -8.50000000000000002e55 < b < -1.1e-134 or -2.25e-284 < b < 8.8e67

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 8.8e67 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

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

Alternative 16: 40.5% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \frac{0.5 \cdot \left(x \cdot b\right)}{y}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(b + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.75e+56)
   (* b (/ (* 0.5 (* x b)) y))
   (if (<= b 3e+57) (/ x (* a y)) (/ x (* y (+ b 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e+56) {
		tmp = b * ((0.5 * (x * b)) / y);
	} else if (b <= 3e+57) {
		tmp = x / (a * y);
	} else {
		tmp = x / (y * (b + 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 (b <= (-1.75d+56)) then
        tmp = b * ((0.5d0 * (x * b)) / y)
    else if (b <= 3d+57) then
        tmp = x / (a * y)
    else
        tmp = x / (y * (b + 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 (b <= -1.75e+56) {
		tmp = b * ((0.5 * (x * b)) / y);
	} else if (b <= 3e+57) {
		tmp = x / (a * y);
	} else {
		tmp = x / (y * (b + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.75e+56:
		tmp = b * ((0.5 * (x * b)) / y)
	elif b <= 3e+57:
		tmp = x / (a * y)
	else:
		tmp = x / (y * (b + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.75e+56)
		tmp = Float64(b * Float64(Float64(0.5 * Float64(x * b)) / y));
	elseif (b <= 3e+57)
		tmp = Float64(x / Float64(a * y));
	else
		tmp = Float64(x / Float64(y * Float64(b + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.75e+56)
		tmp = b * ((0.5 * (x * b)) / y);
	elseif (b <= 3e+57)
		tmp = x / (a * y);
	else
		tmp = x / (y * (b + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.75e+56], N[(b * N[(N[(0.5 * N[(x * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+57], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.75e56

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -1.75e56 < b < 3e57

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 3e57 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

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

Alternative 17: 37.3% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+57}:\\ \;\;\;\;\frac{\left(1 - b\right) \cdot x}{y}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(b + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.25e+57)
   (/ (* (- 1.0 b) x) y)
   (if (<= b 3.5e+63) (/ x (* a y)) (/ x (* y (+ b 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.25e+57) {
		tmp = ((1.0 - b) * x) / y;
	} else if (b <= 3.5e+63) {
		tmp = x / (a * y);
	} else {
		tmp = x / (y * (b + 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 (b <= (-2.25d+57)) then
        tmp = ((1.0d0 - b) * x) / y
    else if (b <= 3.5d+63) then
        tmp = x / (a * y)
    else
        tmp = x / (y * (b + 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 (b <= -2.25e+57) {
		tmp = ((1.0 - b) * x) / y;
	} else if (b <= 3.5e+63) {
		tmp = x / (a * y);
	} else {
		tmp = x / (y * (b + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.25e+57:
		tmp = ((1.0 - b) * x) / y
	elif b <= 3.5e+63:
		tmp = x / (a * y)
	else:
		tmp = x / (y * (b + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.25e+57)
		tmp = Float64(Float64(Float64(1.0 - b) * x) / y);
	elseif (b <= 3.5e+63)
		tmp = Float64(x / Float64(a * y));
	else
		tmp = Float64(x / Float64(y * Float64(b + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.25e+57)
		tmp = ((1.0 - b) * x) / y;
	elseif (b <= 3.5e+63)
		tmp = x / (a * y);
	else
		tmp = x / (y * (b + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.25e+57], N[(N[(N[(1.0 - b), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.5e+63], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.24999999999999998e57

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -2.24999999999999998e57 < b < 3.50000000000000029e63

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 3.50000000000000029e63 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

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

Alternative 18: 44.5% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{b \cdot b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(b + 1\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.8e+19) (* x (* 0.5 (/ (* b b) y))) (/ x (* a (* y (+ b 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.8e+19) {
		tmp = x * (0.5 * ((b * b) / y));
	} else {
		tmp = x / (a * (y * (b + 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 (b <= (-1.8d+19)) then
        tmp = x * (0.5d0 * ((b * b) / y))
    else
        tmp = x / (a * (y * (b + 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 (b <= -1.8e+19) {
		tmp = x * (0.5 * ((b * b) / y));
	} else {
		tmp = x / (a * (y * (b + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.8e+19:
		tmp = x * (0.5 * ((b * b) / y))
	else:
		tmp = x / (a * (y * (b + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.8e+19)
		tmp = Float64(x * Float64(0.5 * Float64(Float64(b * b) / y)));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(b + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.8e+19)
		tmp = x * (0.5 * ((b * b) / y));
	else
		tmp = x / (a * (y * (b + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.8e+19], N[(x * N[(0.5 * N[(N[(b * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8e19

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   12. Taylor expanded in b around inf 0

       \[\leadsto expr\]

   14. Simplified 0

       \[\leadsto expr\]

   if -1.8e19 < b

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

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

Alternative 19: 34.6% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(b + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.5e+59) (/ x (* a y)) (/ x (* y (+ b 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.5e+59) {
		tmp = x / (a * y);
	} else {
		tmp = x / (y * (b + 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 (b <= 2.5d+59) then
        tmp = x / (a * y)
    else
        tmp = x / (y * (b + 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 (b <= 2.5e+59) {
		tmp = x / (a * y);
	} else {
		tmp = x / (y * (b + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.5e+59:
		tmp = x / (a * y)
	else:
		tmp = x / (y * (b + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.5e+59)
		tmp = Float64(x / Float64(a * y));
	else
		tmp = Float64(x / Float64(y * Float64(b + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.5e+59)
		tmp = x / (a * y);
	else
		tmp = x / (y * (b + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.5e+59], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.4999999999999999e59

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 2.4999999999999999e59 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in b around 0 0

      \[\leadsto expr\]

   10. Simplified 0

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

Alternative 20: 31.7% accurate, 63.0× speedup

Math

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

FPCore

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

C

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

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 * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Taylor expanded in y around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in t around 0 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]

9. Taylor expanded in b around 0 0

   \[\leadsto expr\]

11. Simplified 0

    \[\leadsto expr\]
12. Add Preprocessing

Alternative 21: 16.1% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{y}{x}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Taylor expanded in b around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in b around 0 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]

10. Applied egg-rr 0

    \[\leadsto expr\]
11. Add Preprocessing

Alternative 22: 15.9% accurate, 105.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Taylor expanded in b around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in b around 0 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]
9. Add Preprocessing

Developer target: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} 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 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    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 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))