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

Percentage Accurate: 98.4% → 98.4%

Time: 27.3s

Alternatives: 17

Speedup: 1.0×

• 20.9% 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: 98.4% 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: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + (log(a) * (t + -1.0))) - 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)) + (log(a) * (t + (-1.0d0)))) - 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)) + (Math.log(a) * (t + -1.0))) - b))) / y;
}

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + (log(a) * (t + -1.0))) - 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[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

2. Final simplification 99.2%

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

Alternative 2: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+27} \lor \neg \left(y \leq 10^{+45}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.35e+27) (not (<= y 1e+45)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e+27) || !(y <= 1e+45)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.35d+27)) .or. (.not. (y <= 1d+45))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e+27) || !(y <= 1e+45)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.35e+27) or not (y <= 1e+45):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.35e+27) || !(y <= 1e+45))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.35e+27) || ~((y <= 1e+45)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.35e+27], N[Not[LessEqual[y, 1e+45]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3499999999999999e27 or 9.9999999999999993e44 < 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. Taylor expanded in t around 0 91.7%

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

      1. +-commutative 91.7%

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

      2. mul-1-neg 91.7%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 91.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 91.7%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   if -1.3499999999999999e27 < y < 9.9999999999999993e44

   1. Initial program 98.5%

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

      1. associate-/l* 97.8%

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

      2. fma-def 97.8%

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

      3. sub-neg 97.8%

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

      4. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around 0 96.9%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+27} \lor \neg \left(y \leq 10^{+45}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]

Alternative 3: 77.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ t_2 := \frac{{z}^{y}}{a \cdot e^{b}} \cdot \frac{x}{y}\\ t_3 := {a}^{\left(t + -1\right)}\\ t_4 := \frac{x}{\frac{y}{t_3}}\\ t_5 := y \cdot e^{b}\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+31}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{a \cdot t_5}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{y} \cdot t_3\\ \mathbf{elif}\;t \leq 2.12 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{t_5}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (/ y (/ (pow z y) a))))
        (t_2 (* (/ (pow z y) (* a (exp b))) (/ x y)))
        (t_3 (pow a (+ t -1.0)))
        (t_4 (/ x (/ y t_3)))
        (t_5 (* y (exp b))))
   (if (<= t -3.9e+31)
     t_4
     (if (<= t -7.8e-177)
       t_2
       (if (<= t -2e-299)
         t_1
         (if (<= t 4.6e-127)
           t_2
           (if (<= t 1.3e-47)
             t_1
             (if (<= t 6.5e+43)
               (/ x (* a t_5))
               (if (<= t 3.3e+66)
                 (* (/ x y) t_3)
                 (if (<= t 2.12e+89)
                   (* (/ x a) (/ (pow z y) t_5))
                   t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / (pow(z, y) / a));
	double t_2 = (pow(z, y) / (a * exp(b))) * (x / y);
	double t_3 = pow(a, (t + -1.0));
	double t_4 = x / (y / t_3);
	double t_5 = y * exp(b);
	double tmp;
	if (t <= -3.9e+31) {
		tmp = t_4;
	} else if (t <= -7.8e-177) {
		tmp = t_2;
	} else if (t <= -2e-299) {
		tmp = t_1;
	} else if (t <= 4.6e-127) {
		tmp = t_2;
	} else if (t <= 1.3e-47) {
		tmp = t_1;
	} else if (t <= 6.5e+43) {
		tmp = x / (a * t_5);
	} else if (t <= 3.3e+66) {
		tmp = (x / y) * t_3;
	} else if (t <= 2.12e+89) {
		tmp = (x / a) * (pow(z, y) / t_5);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = x / (y / ((z ** y) / a))
    t_2 = ((z ** y) / (a * exp(b))) * (x / y)
    t_3 = a ** (t + (-1.0d0))
    t_4 = x / (y / t_3)
    t_5 = y * exp(b)
    if (t <= (-3.9d+31)) then
        tmp = t_4
    else if (t <= (-7.8d-177)) then
        tmp = t_2
    else if (t <= (-2d-299)) then
        tmp = t_1
    else if (t <= 4.6d-127) then
        tmp = t_2
    else if (t <= 1.3d-47) then
        tmp = t_1
    else if (t <= 6.5d+43) then
        tmp = x / (a * t_5)
    else if (t <= 3.3d+66) then
        tmp = (x / y) * t_3
    else if (t <= 2.12d+89) then
        tmp = (x / a) * ((z ** y) / t_5)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / (Math.pow(z, y) / a));
	double t_2 = (Math.pow(z, y) / (a * Math.exp(b))) * (x / y);
	double t_3 = Math.pow(a, (t + -1.0));
	double t_4 = x / (y / t_3);
	double t_5 = y * Math.exp(b);
	double tmp;
	if (t <= -3.9e+31) {
		tmp = t_4;
	} else if (t <= -7.8e-177) {
		tmp = t_2;
	} else if (t <= -2e-299) {
		tmp = t_1;
	} else if (t <= 4.6e-127) {
		tmp = t_2;
	} else if (t <= 1.3e-47) {
		tmp = t_1;
	} else if (t <= 6.5e+43) {
		tmp = x / (a * t_5);
	} else if (t <= 3.3e+66) {
		tmp = (x / y) * t_3;
	} else if (t <= 2.12e+89) {
		tmp = (x / a) * (Math.pow(z, y) / t_5);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y / (math.pow(z, y) / a))
	t_2 = (math.pow(z, y) / (a * math.exp(b))) * (x / y)
	t_3 = math.pow(a, (t + -1.0))
	t_4 = x / (y / t_3)
	t_5 = y * math.exp(b)
	tmp = 0
	if t <= -3.9e+31:
		tmp = t_4
	elif t <= -7.8e-177:
		tmp = t_2
	elif t <= -2e-299:
		tmp = t_1
	elif t <= 4.6e-127:
		tmp = t_2
	elif t <= 1.3e-47:
		tmp = t_1
	elif t <= 6.5e+43:
		tmp = x / (a * t_5)
	elif t <= 3.3e+66:
		tmp = (x / y) * t_3
	elif t <= 2.12e+89:
		tmp = (x / a) * (math.pow(z, y) / t_5)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y / Float64((z ^ y) / a)))
	t_2 = Float64(Float64((z ^ y) / Float64(a * exp(b))) * Float64(x / y))
	t_3 = a ^ Float64(t + -1.0)
	t_4 = Float64(x / Float64(y / t_3))
	t_5 = Float64(y * exp(b))
	tmp = 0.0
	if (t <= -3.9e+31)
		tmp = t_4;
	elseif (t <= -7.8e-177)
		tmp = t_2;
	elseif (t <= -2e-299)
		tmp = t_1;
	elseif (t <= 4.6e-127)
		tmp = t_2;
	elseif (t <= 1.3e-47)
		tmp = t_1;
	elseif (t <= 6.5e+43)
		tmp = Float64(x / Float64(a * t_5));
	elseif (t <= 3.3e+66)
		tmp = Float64(Float64(x / y) * t_3);
	elseif (t <= 2.12e+89)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / t_5));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y / ((z ^ y) / a));
	t_2 = ((z ^ y) / (a * exp(b))) * (x / y);
	t_3 = a ^ (t + -1.0);
	t_4 = x / (y / t_3);
	t_5 = y * exp(b);
	tmp = 0.0;
	if (t <= -3.9e+31)
		tmp = t_4;
	elseif (t <= -7.8e-177)
		tmp = t_2;
	elseif (t <= -2e-299)
		tmp = t_1;
	elseif (t <= 4.6e-127)
		tmp = t_2;
	elseif (t <= 1.3e-47)
		tmp = t_1;
	elseif (t <= 6.5e+43)
		tmp = x / (a * t_5);
	elseif (t <= 3.3e+66)
		tmp = (x / y) * t_3;
	elseif (t <= 2.12e+89)
		tmp = (x / a) * ((z ^ y) / t_5);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y / N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Power[z, y], $MachinePrecision] / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(x / N[(y / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+31], t$95$4, If[LessEqual[t, -7.8e-177], t$95$2, If[LessEqual[t, -2e-299], t$95$1, If[LessEqual[t, 4.6e-127], t$95$2, If[LessEqual[t, 1.3e-47], t$95$1, If[LessEqual[t, 6.5e+43], N[(x / N[(a * t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+66], N[(N[(x / y), $MachinePrecision] * t$95$3), $MachinePrecision], If[LessEqual[t, 2.12e+89], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.89999999999999999e31 or 2.11999999999999995e89 < 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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 91.3%

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

   5. Taylor expanded in b around 0 88.4%

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

      1. associate-/l* 88.4%

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

      2. exp-to-pow 88.4%

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

      3. sub-neg 88.4%

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

      4. metadata-eval 88.4%

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

      5. +-commutative 88.4%

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

   7. Simplified 88.4%

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

   if -3.89999999999999999e31 < t < -7.80000000000000028e-177 or -1.99999999999999998e-299 < t < 4.60000000000000038e-127

   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. Step-by-step derivation

      1. associate-*l/ 94.1%

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

      2. *-commutative 94.1%

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

      3. exp-diff 83.7%

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

      4. exp-sum 82.4%

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

      5. *-commutative 82.4%

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

      6. exp-to-pow 82.4%

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

      7. *-commutative 82.4%

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

      8. exp-to-pow 82.9%

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

      9. sub-neg 82.9%

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

      10. metadata-eval 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in t around 0 84.9%

      \[\leadsto \color{blue}{\frac{{z}^{y}}{a \cdot e^{b}}} \cdot \frac{x}{y} \]

   if -7.80000000000000028e-177 < t < -1.99999999999999998e-299 or 4.60000000000000038e-127 < t < 1.3e-47

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0 98.5%

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

      1. +-commutative 98.5%

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

      2. mul-1-neg 98.5%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 98.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 98.5%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in b around 0 82.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z - \log a}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 82.6%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{y \cdot \log z - \log a}}}} \]

      2. div-exp 82.8%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}} \]

      3. *-commutative 82.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}} \]

      4. exp-to-pow 82.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}} \]

      5. rem-exp-log 83.8%

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

   7. Simplified 83.8%

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

   if 1.3e-47 < t < 6.4999999999999998e43

   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. Step-by-step derivation

      1. associate-*l/ 84.6%

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

      2. *-commutative 84.6%

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

      3. exp-diff 61.5%

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

      4. exp-sum 50.0%

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

      5. *-commutative 50.0%

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

      6. exp-to-pow 50.0%

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

      7. *-commutative 50.0%

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

      8. exp-to-pow 50.0%

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

      9. sub-neg 50.0%

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

      10. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in t around 0 76.9%

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

      1. times-frac 69.2%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 69.2%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 77.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   if 6.4999999999999998e43 < t < 3.3000000000000001e66

   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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 82.1%

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

   5. Taylor expanded in b around 0 73.2%

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

      1. associate-/l* 73.2%

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

      2. exp-to-pow 73.2%

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

      3. sub-neg 73.2%

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

      4. metadata-eval 73.2%

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

      5. +-commutative 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in x around 0 73.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y}} \]
   9. Step-by-step derivation

      1. *-commutative 73.2%

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

      2. exp-to-pow 73.2%

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

      3. sub-neg 73.2%

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

      4. metadata-eval 73.2%

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

      5. associate-*r/ 73.2%

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

   10. Simplified 73.2%

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

   if 3.3000000000000001e66 < t < 2.11999999999999995e89

   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. Step-by-step derivation

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

      3. exp-diff 70.0%

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

      4. exp-sum 30.0%

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

      5. *-commutative 30.0%

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

      6. exp-to-pow 30.0%

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

      7. *-commutative 30.0%

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

      8. exp-to-pow 30.0%

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

      9. sub-neg 30.0%

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

      10. metadata-eval 30.0%

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

   3. Simplified 30.0%

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

   4. Taylor expanded in t around 0 80.2%

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

      1. times-frac 90.2%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 90.2%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-177}:\\ \;\;\;\;\frac{{z}^{y}}{a \cdot e^{b}} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-299}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-127}:\\ \;\;\;\;\frac{{z}^{y}}{a \cdot e^{b}} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{y} \cdot {a}^{\left(t + -1\right)}\\ \mathbf{elif}\;t \leq 2.12 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \end{array} \]

Alternative 4: 76.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ t_2 := y \cdot e^{b}\\ t_3 := \frac{x}{a} \cdot \frac{{z}^{y}}{t_2}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-106}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-112}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{a \cdot t_2}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+88}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (/ y (pow a (+ t -1.0)))))
        (t_2 (* y (exp b)))
        (t_3 (* (/ x a) (/ (pow z y) t_2))))
   (if (<= t -5e+30)
     t_1
     (if (<= t -1.4e-106)
       t_3
       (if (<= t -2.4e-301)
         (/ x (/ y (/ (pow z y) a)))
         (if (<= t 1.05e-112)
           t_3
           (if (<= t 7.8e+52) (/ x (* a t_2)) (if (<= t 9e+88) t_3 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / pow(a, (t + -1.0)));
	double t_2 = y * exp(b);
	double t_3 = (x / a) * (pow(z, y) / t_2);
	double tmp;
	if (t <= -5e+30) {
		tmp = t_1;
	} else if (t <= -1.4e-106) {
		tmp = t_3;
	} else if (t <= -2.4e-301) {
		tmp = x / (y / (pow(z, y) / a));
	} else if (t <= 1.05e-112) {
		tmp = t_3;
	} else if (t <= 7.8e+52) {
		tmp = x / (a * t_2);
	} else if (t <= 9e+88) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = x / (y / (a ** (t + (-1.0d0))))
    t_2 = y * exp(b)
    t_3 = (x / a) * ((z ** y) / t_2)
    if (t <= (-5d+30)) then
        tmp = t_1
    else if (t <= (-1.4d-106)) then
        tmp = t_3
    else if (t <= (-2.4d-301)) then
        tmp = x / (y / ((z ** y) / a))
    else if (t <= 1.05d-112) then
        tmp = t_3
    else if (t <= 7.8d+52) then
        tmp = x / (a * t_2)
    else if (t <= 9d+88) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / Math.pow(a, (t + -1.0)));
	double t_2 = y * Math.exp(b);
	double t_3 = (x / a) * (Math.pow(z, y) / t_2);
	double tmp;
	if (t <= -5e+30) {
		tmp = t_1;
	} else if (t <= -1.4e-106) {
		tmp = t_3;
	} else if (t <= -2.4e-301) {
		tmp = x / (y / (Math.pow(z, y) / a));
	} else if (t <= 1.05e-112) {
		tmp = t_3;
	} else if (t <= 7.8e+52) {
		tmp = x / (a * t_2);
	} else if (t <= 9e+88) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y / math.pow(a, (t + -1.0)))
	t_2 = y * math.exp(b)
	t_3 = (x / a) * (math.pow(z, y) / t_2)
	tmp = 0
	if t <= -5e+30:
		tmp = t_1
	elif t <= -1.4e-106:
		tmp = t_3
	elif t <= -2.4e-301:
		tmp = x / (y / (math.pow(z, y) / a))
	elif t <= 1.05e-112:
		tmp = t_3
	elif t <= 7.8e+52:
		tmp = x / (a * t_2)
	elif t <= 9e+88:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y / (a ^ Float64(t + -1.0))))
	t_2 = Float64(y * exp(b))
	t_3 = Float64(Float64(x / a) * Float64((z ^ y) / t_2))
	tmp = 0.0
	if (t <= -5e+30)
		tmp = t_1;
	elseif (t <= -1.4e-106)
		tmp = t_3;
	elseif (t <= -2.4e-301)
		tmp = Float64(x / Float64(y / Float64((z ^ y) / a)));
	elseif (t <= 1.05e-112)
		tmp = t_3;
	elseif (t <= 7.8e+52)
		tmp = Float64(x / Float64(a * t_2));
	elseif (t <= 9e+88)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y / (a ^ (t + -1.0)));
	t_2 = y * exp(b);
	t_3 = (x / a) * ((z ^ y) / t_2);
	tmp = 0.0;
	if (t <= -5e+30)
		tmp = t_1;
	elseif (t <= -1.4e-106)
		tmp = t_3;
	elseif (t <= -2.4e-301)
		tmp = x / (y / ((z ^ y) / a));
	elseif (t <= 1.05e-112)
		tmp = t_3;
	elseif (t <= 7.8e+52)
		tmp = x / (a * t_2);
	elseif (t <= 9e+88)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+30], t$95$1, If[LessEqual[t, -1.4e-106], t$95$3, If[LessEqual[t, -2.4e-301], N[(x / N[(y / N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-112], t$95$3, If[LessEqual[t, 7.8e+52], N[(x / N[(a * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+88], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.9999999999999998e30 or 9e88 < 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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 91.3%

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

   5. Taylor expanded in b around 0 88.4%

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

      1. associate-/l* 88.4%

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

      2. exp-to-pow 88.4%

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

      3. sub-neg 88.4%

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

      4. metadata-eval 88.4%

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

      5. +-commutative 88.4%

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

   7. Simplified 88.4%

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

   if -4.9999999999999998e30 < t < -1.39999999999999994e-106 or -2.39999999999999991e-301 < t < 1.05e-112 or 7.7999999999999999e52 < t < 9e88

   1. Initial program 98.4%

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

      1. associate-*l/ 90.5%

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

      2. *-commutative 90.5%

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

      3. exp-diff 81.4%

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

      4. exp-sum 74.6%

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

      5. *-commutative 74.6%

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

      6. exp-to-pow 74.6%

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

      7. *-commutative 74.6%

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

      8. exp-to-pow 74.9%

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

      9. sub-neg 74.9%

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

      10. metadata-eval 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in t around 0 83.5%

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

      1. times-frac 82.4%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 82.4%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   if -1.39999999999999994e-106 < t < -2.39999999999999991e-301

   1. Initial program 97.9%

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

   2. Taylor expanded in t around 0 97.9%

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

      1. +-commutative 97.9%

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

      2. mul-1-neg 97.9%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 97.9%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 97.9%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in b around 0 79.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z - \log a}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 76.6%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{y \cdot \log z - \log a}}}} \]

      2. div-exp 76.8%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}} \]

      3. *-commutative 76.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}} \]

      4. exp-to-pow 76.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}} \]

      5. rem-exp-log 78.2%

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

   7. Simplified 78.2%

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

   if 1.05e-112 < t < 7.7999999999999999e52

   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. Step-by-step derivation

      1. associate-*l/ 85.7%

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

      2. *-commutative 85.7%

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

      3. exp-diff 57.1%

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

      4. exp-sum 48.6%

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

      5. *-commutative 48.6%

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

      6. exp-to-pow 48.6%

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

      7. *-commutative 48.6%

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

      8. exp-to-pow 48.6%

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

      9. sub-neg 48.6%

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

      10. metadata-eval 48.6%

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

   3. Simplified 48.6%

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

   4. Taylor expanded in t around 0 68.7%

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

      1. times-frac 60.1%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 60.1%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 72.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \end{array} \]

Alternative 5: 89.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+130} \lor \neg \left(y \leq 2.3 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4e+130) (not (<= y 2.3e+44)))
   (/ x (/ y (/ (pow z y) a)))
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4e+130) || !(y <= 2.3e+44)) {
		tmp = x / (y / (pow(z, y) / a));
	} else {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4d+130)) .or. (.not. (y <= 2.3d+44))) then
        tmp = x / (y / ((z ** y) / a))
    else
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4e+130) || !(y <= 2.3e+44)) {
		tmp = x / (y / (Math.pow(z, y) / a));
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4e+130) or not (y <= 2.3e+44):
		tmp = x / (y / (math.pow(z, y) / a))
	else:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4e+130) || !(y <= 2.3e+44))
		tmp = Float64(x / Float64(y / Float64((z ^ y) / a)));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4e+130) || ~((y <= 2.3e+44)))
		tmp = x / (y / ((z ^ y) / a));
	else
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4e+130], N[Not[LessEqual[y, 2.3e+44]], $MachinePrecision]], N[(x / N[(y / N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0000000000000002e130 or 2.30000000000000004e44 < 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. Taylor expanded in t around 0 92.7%

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

      1. +-commutative 92.7%

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

      2. mul-1-neg 92.7%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 92.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 92.7%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in b around 0 85.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z - \log a}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 85.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{y \cdot \log z - \log a}}}} \]

      2. div-exp 85.5%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}} \]

      3. *-commutative 85.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}} \]

      4. exp-to-pow 85.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}} \]

      5. rem-exp-log 85.5%

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

   7. Simplified 85.5%

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

   if -4.0000000000000002e130 < y < 2.30000000000000004e44

   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. Step-by-step derivation

      1. associate-/l* 98.1%

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

      2. fma-def 98.1%

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

      3. sub-neg 98.1%

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

      4. metadata-eval 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in y around 0 93.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+130} \lor \neg \left(y \leq 2.3 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]

Alternative 6: 82.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+22} \lor \neg \left(y \leq 1.45 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{a}^{t}}{a}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.2e+22) (not (<= y 1.45e+37)))
   (/ x (/ y (/ (pow z y) a)))
   (/ (* x (/ (/ (pow a t) a) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.2e+22) || !(y <= 1.45e+37)) {
		tmp = x / (y / (pow(z, y) / a));
	} else {
		tmp = (x * ((pow(a, t) / a) / exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-7.2d+22)) .or. (.not. (y <= 1.45d+37))) then
        tmp = x / (y / ((z ** y) / a))
    else
        tmp = (x * (((a ** t) / a) / exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.2e+22) || !(y <= 1.45e+37)) {
		tmp = x / (y / (Math.pow(z, y) / a));
	} else {
		tmp = (x * ((Math.pow(a, t) / a) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.2e+22) or not (y <= 1.45e+37):
		tmp = x / (y / (math.pow(z, y) / a))
	else:
		tmp = (x * ((math.pow(a, t) / a) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.2e+22) || !(y <= 1.45e+37))
		tmp = Float64(x / Float64(y / Float64((z ^ y) / a)));
	else
		tmp = Float64(Float64(x * Float64(Float64((a ^ t) / a) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.2e+22) || ~((y <= 1.45e+37)))
		tmp = x / (y / ((z ^ y) / a));
	else
		tmp = (x * (((a ^ t) / a) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.2e+22], N[Not[LessEqual[y, 1.45e+37]], $MachinePrecision]], N[(x / N[(y / N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2e22 or 1.44999999999999989e37 < 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. Taylor expanded in t around 0 90.5%

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

      1. +-commutative 90.5%

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

      2. mul-1-neg 90.5%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 90.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 90.5%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in b around 0 81.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z - \log a}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 81.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{y \cdot \log z - \log a}}}} \]

      2. div-exp 81.7%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}} \]

      3. *-commutative 81.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}} \]

      4. exp-to-pow 81.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}} \]

      5. rem-exp-log 81.7%

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

   7. Simplified 81.7%

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

   if -7.2e22 < y < 1.44999999999999989e37

   1. Initial program 98.5%

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

   2. Taylor expanded in y around 0 97.5%

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

      1. div-exp 84.6%

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

      2. exp-to-pow 85.1%

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

      3. sub-neg 85.1%

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

      4. metadata-eval 85.1%

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

   4. Simplified 85.1%

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

      1. unpow-prod-up 85.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{e^{b}}}{y} \]

      2. unpow-1 85.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{e^{b}}}{y} \]

   6. Applied egg-rr 85.2%

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

      1. associate-*r/ 85.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{e^{b}}}{y} \]

      2. *-rgt-identity 85.2%

         \[\leadsto \frac{x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{e^{b}}}{y} \]

   8. Simplified 85.2%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+22} \lor \neg \left(y \leq 1.45 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{a}^{t}}{a}}{e^{b}}}{y}\\ \end{array} \]

Alternative 7: 74.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a \cdot e^{b}}}{y}\\ t_2 := \frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{y} \cdot {a}^{\left(t + -1\right)}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (* a (exp b))) y)) (t_2 (/ x (/ y (/ (pow z y) a)))))
   (if (<= y -2e+87)
     t_2
     (if (<= y 2.5e-60)
       t_1
       (if (<= y 5.5e-12)
         (* (/ x y) (pow a (+ t -1.0)))
         (if (<= y 1.2e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a * exp(b))) / y;
	double t_2 = x / (y / (pow(z, y) / a));
	double tmp;
	if (y <= -2e+87) {
		tmp = t_2;
	} else if (y <= 2.5e-60) {
		tmp = t_1;
	} else if (y <= 5.5e-12) {
		tmp = (x / y) * pow(a, (t + -1.0));
	} else if (y <= 1.2e+37) {
		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 / (a * exp(b))) / y
    t_2 = x / (y / ((z ** y) / a))
    if (y <= (-2d+87)) then
        tmp = t_2
    else if (y <= 2.5d-60) then
        tmp = t_1
    else if (y <= 5.5d-12) then
        tmp = (x / y) * (a ** (t + (-1.0d0)))
    else if (y <= 1.2d+37) 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 / (a * Math.exp(b))) / y;
	double t_2 = x / (y / (Math.pow(z, y) / a));
	double tmp;
	if (y <= -2e+87) {
		tmp = t_2;
	} else if (y <= 2.5e-60) {
		tmp = t_1;
	} else if (y <= 5.5e-12) {
		tmp = (x / y) * Math.pow(a, (t + -1.0));
	} else if (y <= 1.2e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (a * math.exp(b))) / y
	t_2 = x / (y / (math.pow(z, y) / a))
	tmp = 0
	if y <= -2e+87:
		tmp = t_2
	elif y <= 2.5e-60:
		tmp = t_1
	elif y <= 5.5e-12:
		tmp = (x / y) * math.pow(a, (t + -1.0))
	elif y <= 1.2e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(a * exp(b))) / y)
	t_2 = Float64(x / Float64(y / Float64((z ^ y) / a)))
	tmp = 0.0
	if (y <= -2e+87)
		tmp = t_2;
	elseif (y <= 2.5e-60)
		tmp = t_1;
	elseif (y <= 5.5e-12)
		tmp = Float64(Float64(x / y) * (a ^ Float64(t + -1.0)));
	elseif (y <= 1.2e+37)
		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 / (a * exp(b))) / y;
	t_2 = x / (y / ((z ^ y) / a));
	tmp = 0.0;
	if (y <= -2e+87)
		tmp = t_2;
	elseif (y <= 2.5e-60)
		tmp = t_1;
	elseif (y <= 5.5e-12)
		tmp = (x / y) * (a ^ (t + -1.0));
	elseif (y <= 1.2e+37)
		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[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y / N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+87], t$95$2, If[LessEqual[y, 2.5e-60], t$95$1, If[LessEqual[y, 5.5e-12], N[(N[(x / y), $MachinePrecision] * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9999999999999999e87 or 1.2e37 < 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. Taylor expanded in t around 0 89.1%

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

      1. +-commutative 89.1%

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

      2. mul-1-neg 89.1%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 89.1%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 89.1%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in b around 0 82.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z - \log a}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 82.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{y \cdot \log z - \log a}}}} \]

      2. div-exp 82.7%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}} \]

      3. *-commutative 82.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}} \]

      4. exp-to-pow 82.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}} \]

      5. rem-exp-log 82.7%

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

   7. Simplified 82.7%

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

   if -1.9999999999999999e87 < y < 2.5000000000000001e-60 or 5.5000000000000004e-12 < y < 1.2e37

   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. Taylor expanded in y around 0 95.0%

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

      1. div-exp 80.1%

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

      2. exp-to-pow 80.6%

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

      3. sub-neg 80.6%

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

      4. metadata-eval 80.6%

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

   4. Simplified 80.6%

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

   5. Taylor expanded in t around 0 71.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   if 2.5000000000000001e-60 < y < 5.5000000000000004e-12

   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. Step-by-step derivation

      1. associate-/l* 99.0%

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

      2. fma-def 99.0%

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

      3. sub-neg 99.0%

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

      4. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in y around 0 97.6%

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

   5. Taylor expanded in b around 0 97.6%

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

      1. associate-/l* 97.6%

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

      2. exp-to-pow 97.6%

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

      3. sub-neg 97.6%

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

      4. metadata-eval 97.6%

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

      5. +-commutative 97.6%

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

   7. Simplified 97.6%

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

   8. Taylor expanded in x around 0 97.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y}} \]
   9. Step-by-step derivation

      1. *-commutative 97.6%

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

      2. exp-to-pow 97.6%

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

      3. sub-neg 97.6%

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

      4. metadata-eval 97.6%

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

      5. associate-*r/ 97.6%

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

   10. Simplified 97.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{y} \cdot {a}^{\left(t + -1\right)}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ \end{array} \]

Alternative 8: 74.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{if}\;t \leq -2.55 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+80}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (/ y (pow a (+ t -1.0))))))
   (if (<= t -2.55e+39)
     t_1
     (if (<= t 1.85e-22)
       (/ x (/ y (/ (pow z y) a)))
       (if (<= t 1.55e+80) (/ (/ x (* a (exp b))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / pow(a, (t + -1.0)));
	double tmp;
	if (t <= -2.55e+39) {
		tmp = t_1;
	} else if (t <= 1.85e-22) {
		tmp = x / (y / (pow(z, y) / a));
	} else if (t <= 1.55e+80) {
		tmp = (x / (a * exp(b))) / 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 = x / (y / (a ** (t + (-1.0d0))))
    if (t <= (-2.55d+39)) then
        tmp = t_1
    else if (t <= 1.85d-22) then
        tmp = x / (y / ((z ** y) / a))
    else if (t <= 1.55d+80) then
        tmp = (x / (a * exp(b))) / 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 = x / (y / Math.pow(a, (t + -1.0)));
	double tmp;
	if (t <= -2.55e+39) {
		tmp = t_1;
	} else if (t <= 1.85e-22) {
		tmp = x / (y / (Math.pow(z, y) / a));
	} else if (t <= 1.55e+80) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y / math.pow(a, (t + -1.0)))
	tmp = 0
	if t <= -2.55e+39:
		tmp = t_1
	elif t <= 1.85e-22:
		tmp = x / (y / (math.pow(z, y) / a))
	elif t <= 1.55e+80:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y / (a ^ Float64(t + -1.0))))
	tmp = 0.0
	if (t <= -2.55e+39)
		tmp = t_1;
	elseif (t <= 1.85e-22)
		tmp = Float64(x / Float64(y / Float64((z ^ y) / a)));
	elseif (t <= 1.55e+80)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y / (a ^ (t + -1.0)));
	tmp = 0.0;
	if (t <= -2.55e+39)
		tmp = t_1;
	elseif (t <= 1.85e-22)
		tmp = x / (y / ((z ^ y) / a));
	elseif (t <= 1.55e+80)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.55e+39], t$95$1, If[LessEqual[t, 1.85e-22], N[(x / N[(y / N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+80], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5499999999999999e39 or 1.54999999999999994e80 < 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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 91.6%

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

   5. Taylor expanded in b around 0 87.8%

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

      1. associate-/l* 87.8%

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

      2. exp-to-pow 87.8%

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

      3. sub-neg 87.8%

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

      4. metadata-eval 87.8%

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

      5. +-commutative 87.8%

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

   7. Simplified 87.8%

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

   if -2.5499999999999999e39 < t < 1.85e-22

   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. Taylor expanded in t around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. mul-1-neg 97.0%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 97.0%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 97.0%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in b around 0 73.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z - \log a}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 73.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{y \cdot \log z - \log a}}}} \]

      2. div-exp 73.1%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}} \]

      3. *-commutative 73.1%

         \[\leadsto \frac{x}{\frac{y}{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}} \]

      4. exp-to-pow 73.1%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}} \]

      5. rem-exp-log 73.7%

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

   7. Simplified 73.7%

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

   if 1.85e-22 < t < 1.54999999999999994e80

   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. Taylor expanded in y around 0 83.1%

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

      1. div-exp 60.3%

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

      2. exp-to-pow 60.3%

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

      3. sub-neg 60.3%

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

      4. metadata-eval 60.3%

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

   4. Simplified 60.3%

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

   5. Taylor expanded in t around 0 69.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{z}^{y}}{a}}}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+80}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \end{array} \]

Alternative 9: 70.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+71} \lor \neg \left(t \leq 4.9 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{x}{y} \cdot {a}^{\left(t + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.8e+71) (not (<= t 4.9e+95)))
   (* (/ x y) (pow a (+ t -1.0)))
   (/ (/ x (* a (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.8e+71) || !(t <= 4.9e+95)) {
		tmp = (x / y) * pow(a, (t + -1.0));
	} else {
		tmp = (x / (a * exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.8d+71)) .or. (.not. (t <= 4.9d+95))) then
        tmp = (x / y) * (a ** (t + (-1.0d0)))
    else
        tmp = (x / (a * exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.8e+71) || !(t <= 4.9e+95)) {
		tmp = (x / y) * Math.pow(a, (t + -1.0));
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.8e+71) or not (t <= 4.9e+95):
		tmp = (x / y) * math.pow(a, (t + -1.0))
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.8e+71) || !(t <= 4.9e+95))
		tmp = Float64(Float64(x / y) * (a ^ Float64(t + -1.0)));
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.8e+71) || ~((t <= 4.9e+95)))
		tmp = (x / y) * (a ^ (t + -1.0));
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.8e+71], N[Not[LessEqual[t, 4.9e+95]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e71 or 4.8999999999999999e95 < 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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 92.5%

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

   5. Taylor expanded in b around 0 89.3%

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

      1. associate-/l* 89.3%

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

      2. exp-to-pow 89.3%

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

      3. sub-neg 89.3%

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

      4. metadata-eval 89.3%

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

      5. +-commutative 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in x around 0 89.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y}} \]
   9. Step-by-step derivation

      1. *-commutative 89.3%

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

      2. exp-to-pow 89.3%

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

      3. sub-neg 89.3%

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

      4. metadata-eval 89.3%

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

      5. associate-*r/ 79.5%

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

   10. Simplified 79.5%

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

   if -1.8e71 < t < 4.8999999999999999e95

   1. Initial program 98.8%

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

   2. Taylor expanded in y around 0 72.4%

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

      1. div-exp 65.1%

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

      2. exp-to-pow 65.5%

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

      3. sub-neg 65.5%

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

      4. metadata-eval 65.5%

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

   4. Simplified 65.5%

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

   5. Taylor expanded in t around 0 65.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+71} \lor \neg \left(t \leq 4.9 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{x}{y} \cdot {a}^{\left(t + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]

Alternative 10: 58.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{-153} \lor \neg \left(b \leq 3.3 \cdot 10^{-256}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot a}{-b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.9e-153) (not (<= b 3.3e-256)))
   (/ x (* a (* y (exp b))))
   (/ x (/ (* y a) (- b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.9e-153) || !(b <= 3.3e-256)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x / ((y * a) / -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.9d-153)) .or. (.not. (b <= 3.3d-256))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x / ((y * a) / -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.9e-153) || !(b <= 3.3e-256)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x / ((y * a) / -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.9e-153) or not (b <= 3.3e-256):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x / ((y * a) / -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.9e-153) || !(b <= 3.3e-256))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x / Float64(Float64(y * a) / Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.9e-153) || ~((b <= 3.3e-256)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x / ((y * a) / -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.9e-153], N[Not[LessEqual[b, 3.3e-256]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y * a), $MachinePrecision] / (-b)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.90000000000000002e-153 or 3.3e-256 < b

   1. Initial program 99.6%

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

      1. associate-*l/ 87.6%

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

      2. *-commutative 87.6%

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

      3. exp-diff 63.7%

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

      4. exp-sum 55.3%

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

      5. *-commutative 55.3%

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

      6. exp-to-pow 55.3%

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

      7. *-commutative 55.3%

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

      8. exp-to-pow 55.6%

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

      9. sub-neg 55.6%

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

      10. metadata-eval 55.6%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in t around 0 60.9%

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

      1. times-frac 59.8%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 59.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 59.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   if -2.90000000000000002e-153 < b < 3.3e-256

   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. Step-by-step derivation

      1. associate-*l/ 92.2%

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

      2. *-commutative 92.2%

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

      3. exp-diff 92.2%

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

      4. exp-sum 75.6%

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

      5. *-commutative 75.6%

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

      6. exp-to-pow 75.6%

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

      7. *-commutative 75.6%

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

      8. exp-to-pow 76.1%

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

      9. sub-neg 76.1%

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

      10. metadata-eval 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in t around 0 65.2%

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

      1. times-frac 55.8%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 55.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 26.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 26.1%

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

      1. +-commutative 26.1%

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

      2. mul-1-neg 26.1%

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

      3. unsub-neg 26.1%

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

      4. times-frac 26.1%

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

   10. Simplified 26.1%

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

   11. Taylor expanded in b around inf 44.6%

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

       1. mul-1-neg 44.6%

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

       2. associate-*r/ 42.1%

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

       3. *-commutative 42.1%

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

       4. distribute-rgt-neg-in 42.1%

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

       5. associate-/r/ 51.1%

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

   13. Simplified 51.1%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{-153} \lor \neg \left(b \leq 3.3 \cdot 10^{-256}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot a}{-b}}\\ \end{array} \]

Alternative 11: 58.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-161} \lor \neg \left(b \leq 3 \cdot 10^{-253}\right):\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot a}{-b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.75e-161) (not (<= b 3e-253)))
   (/ (/ x (* a (exp b))) y)
   (/ x (/ (* y a) (- b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.75e-161) || !(b <= 3e-253)) {
		tmp = (x / (a * exp(b))) / y;
	} else {
		tmp = x / ((y * a) / -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.75d-161)) .or. (.not. (b <= 3d-253))) then
        tmp = (x / (a * exp(b))) / y
    else
        tmp = x / ((y * a) / -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.75e-161) || !(b <= 3e-253)) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = x / ((y * a) / -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.75e-161) or not (b <= 3e-253):
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = x / ((y * a) / -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.75e-161) || !(b <= 3e-253))
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = Float64(x / Float64(Float64(y * a) / Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.75e-161) || ~((b <= 3e-253)))
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = x / ((y * a) / -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.75e-161], N[Not[LessEqual[b, 3e-253]], $MachinePrecision]], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[(y * a), $MachinePrecision] / (-b)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7500000000000001e-161 or 3.0000000000000002e-253 < b

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 82.6%

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

      1. div-exp 66.3%

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

      2. exp-to-pow 66.6%

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

      3. sub-neg 66.6%

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

      4. metadata-eval 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in t around 0 60.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   if -1.7500000000000001e-161 < b < 3.0000000000000002e-253

   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. Step-by-step derivation

      1. associate-*l/ 92.0%

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

      2. *-commutative 92.0%

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

      3. exp-diff 92.0%

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

      4. exp-sum 75.0%

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

      5. *-commutative 75.0%

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

      6. exp-to-pow 75.0%

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

      7. *-commutative 75.0%

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

      8. exp-to-pow 75.5%

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

      9. sub-neg 75.5%

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

      10. metadata-eval 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in t around 0 66.7%

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

      1. times-frac 54.7%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 54.7%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 26.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 26.7%

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

      1. +-commutative 26.7%

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

      2. mul-1-neg 26.7%

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

      3. unsub-neg 26.7%

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

      4. times-frac 26.6%

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

   10. Simplified 26.6%

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

   11. Taylor expanded in b around inf 43.2%

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

       1. mul-1-neg 43.2%

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

       2. associate-*r/ 40.8%

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

       3. *-commutative 40.8%

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

       4. distribute-rgt-neg-in 40.8%

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

       5. associate-/r/ 50.1%

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

   13. Simplified 50.1%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-161} \lor \neg \left(b \leq 3 \cdot 10^{-253}\right):\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot a}{-b}}\\ \end{array} \]

Alternative 12: 34.3% accurate, 22.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -85 \lor \neg \left(b \leq -4.2 \cdot 10^{-159}\right) \land b \leq 1.85 \cdot 10^{-256}:\\ \;\;\;\;\frac{x}{\frac{y \cdot a}{-b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -85.0) (and (not (<= b -4.2e-159)) (<= b 1.85e-256)))
   (/ x (/ (* y a) (- b)))
   (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -85.0) || (!(b <= -4.2e-159) && (b <= 1.85e-256))) {
		tmp = x / ((y * a) / -b);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-85.0d0)) .or. (.not. (b <= (-4.2d-159))) .and. (b <= 1.85d-256)) then
        tmp = x / ((y * a) / -b)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -85.0) || (!(b <= -4.2e-159) && (b <= 1.85e-256))) {
		tmp = x / ((y * a) / -b);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -85.0) or (not (b <= -4.2e-159) and (b <= 1.85e-256)):
		tmp = x / ((y * a) / -b)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -85.0) || (!(b <= -4.2e-159) && (b <= 1.85e-256)))
		tmp = Float64(x / Float64(Float64(y * a) / Float64(-b)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -85.0) || (~((b <= -4.2e-159)) && (b <= 1.85e-256)))
		tmp = x / ((y * a) / -b);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -85.0], And[N[Not[LessEqual[b, -4.2e-159]], $MachinePrecision], LessEqual[b, 1.85e-256]]], N[(x / N[(N[(y * a), $MachinePrecision] / (-b)), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -85 or -4.1999999999999998e-159 < b < 1.85000000000000014e-256

   1. Initial program 98.9%

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

      1. associate-*l/ 94.1%

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

      2. *-commutative 94.1%

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

      3. exp-diff 67.0%

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

      4. exp-sum 56.8%

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

      5. *-commutative 56.8%

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

      6. exp-to-pow 56.8%

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

      7. *-commutative 56.8%

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

      8. exp-to-pow 57.0%

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

      9. sub-neg 57.0%

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

      10. metadata-eval 57.0%

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

   3. Simplified 57.0%

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

   4. Taylor expanded in t around 0 62.1%

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

      1. times-frac 52.8%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 52.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 58.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 32.1%

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

      1. +-commutative 32.1%

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

      2. mul-1-neg 32.1%

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

      3. unsub-neg 32.1%

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

      4. times-frac 31.2%

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

   10. Simplified 31.2%

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

   11. Taylor expanded in b around inf 38.4%

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

       1. mul-1-neg 38.4%

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

       2. associate-*r/ 36.8%

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

       3. *-commutative 36.8%

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

       4. distribute-rgt-neg-in 36.8%

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

       5. associate-/r/ 43.7%

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

   13. Simplified 43.7%

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

   if -85 < b < -4.1999999999999998e-159 or 1.85000000000000014e-256 < b

   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. Taylor expanded in y around 0 80.2%

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

      1. div-exp 68.1%

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

      2. exp-to-pow 68.5%

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

      3. sub-neg 68.5%

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

      4. metadata-eval 68.5%

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

   4. Simplified 68.5%

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

      1. unpow-prod-up 68.6%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{e^{b}}}{y} \]

      2. unpow-1 68.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{e^{b}}}{y} \]

   6. Applied egg-rr 68.6%

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

      1. associate-*r/ 68.6%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{e^{b}}}{y} \]

      2. *-rgt-identity 68.6%

         \[\leadsto \frac{x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{e^{b}}}{y} \]

   8. Simplified 68.6%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t}}{a}}}{e^{b}}}{y} \]

   9. Taylor expanded in t around 0 52.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
   10. Step-by-step derivation

       1. associate-/r* 50.2%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   11. Simplified 50.2%

       \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   12. Taylor expanded in b around 0 29.4%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -85 \lor \neg \left(b \leq -4.2 \cdot 10^{-159}\right) \land b \leq 1.85 \cdot 10^{-256}:\\ \;\;\;\;\frac{x}{\frac{y \cdot a}{-b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 13: 34.5% accurate, 26.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \frac{1 - b}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-255}:\\ \;\;\;\;\frac{x}{\frac{y \cdot a}{-b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.7e-157)
   (* x (/ (- 1.0 b) (* y a)))
   (if (<= b 3.3e-255) (/ x (/ (* y a) (- b))) (/ (/ x a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e-157) {
		tmp = x * ((1.0 - b) / (y * a));
	} else if (b <= 3.3e-255) {
		tmp = x / ((y * a) / -b);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.7d-157)) then
        tmp = x * ((1.0d0 - b) / (y * a))
    else if (b <= 3.3d-255) then
        tmp = x / ((y * a) / -b)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e-157) {
		tmp = x * ((1.0 - b) / (y * a));
	} else if (b <= 3.3e-255) {
		tmp = x / ((y * a) / -b);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.7e-157:
		tmp = x * ((1.0 - b) / (y * a))
	elif b <= 3.3e-255:
		tmp = x / ((y * a) / -b)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.7e-157)
		tmp = Float64(x * Float64(Float64(1.0 - b) / Float64(y * a)));
	elseif (b <= 3.3e-255)
		tmp = Float64(x / Float64(Float64(y * a) / Float64(-b)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.7e-157)
		tmp = x * ((1.0 - b) / (y * a));
	elseif (b <= 3.3e-255)
		tmp = x / ((y * a) / -b);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.7e-157], N[(x * N[(N[(1.0 - b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e-255], N[(x / N[(N[(y * a), $MachinePrecision] / (-b)), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.6999999999999998e-157

   1. Initial program 99.3%

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

      1. associate-*l/ 90.6%

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

      2. *-commutative 90.6%

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

      3. exp-diff 61.6%

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

      4. exp-sum 51.6%

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

      5. *-commutative 51.6%

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

      6. exp-to-pow 51.6%

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

      7. *-commutative 51.6%

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

      8. exp-to-pow 51.9%

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

      9. sub-neg 51.9%

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

      10. metadata-eval 51.9%

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

   3. Simplified 51.9%

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

   4. Taylor expanded in t around 0 62.7%

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

      1. times-frac 59.6%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 59.6%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 64.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 36.6%

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

      1. +-commutative 36.6%

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

      2. mul-1-neg 36.6%

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

      3. unsub-neg 36.6%

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

      4. times-frac 33.8%

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

   10. Simplified 33.8%

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

   11. Taylor expanded in x around 0 40.2%

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

       1. div-sub 40.2%

          \[\leadsto x \cdot \color{blue}{\frac{1 - b}{a \cdot y}} \]

   13. Simplified 40.2%

       \[\leadsto \color{blue}{x \cdot \frac{1 - b}{a \cdot y}} \]

   if -3.6999999999999998e-157 < b < 3.29999999999999988e-255

   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. Step-by-step derivation

      1. associate-*l/ 92.2%

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

      2. *-commutative 92.2%

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

      3. exp-diff 92.2%

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

      4. exp-sum 75.6%

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

      5. *-commutative 75.6%

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

      6. exp-to-pow 75.6%

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

      7. *-commutative 75.6%

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

      8. exp-to-pow 76.1%

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

      9. sub-neg 76.1%

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

      10. metadata-eval 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in t around 0 65.2%

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

      1. times-frac 55.8%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 55.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 26.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 26.1%

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

      1. +-commutative 26.1%

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

      2. mul-1-neg 26.1%

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

      3. unsub-neg 26.1%

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

      4. times-frac 26.1%

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

   10. Simplified 26.1%

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

   11. Taylor expanded in b around inf 44.6%

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

       1. mul-1-neg 44.6%

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

       2. associate-*r/ 42.1%

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

       3. *-commutative 42.1%

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

       4. distribute-rgt-neg-in 42.1%

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

       5. associate-/r/ 51.1%

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

   13. Simplified 51.1%

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

   if 3.29999999999999988e-255 < b

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 83.6%

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

      1. div-exp 67.8%

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

      2. exp-to-pow 67.9%

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

      3. sub-neg 67.9%

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

      4. metadata-eval 67.9%

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

   4. Simplified 67.9%

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

      1. unpow-prod-up 67.9%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{e^{b}}}{y} \]

      2. unpow-1 67.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{e^{b}}}{y} \]

   6. Applied egg-rr 67.9%

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

      1. associate-*r/ 67.9%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{e^{b}}}{y} \]

      2. *-rgt-identity 67.9%

         \[\leadsto \frac{x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{e^{b}}}{y} \]

   8. Simplified 67.9%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t}}{a}}}{e^{b}}}{y} \]

   9. Taylor expanded in t around 0 55.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
   10. Step-by-step derivation

       1. associate-/r* 52.0%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   11. Simplified 52.0%

       \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   12. Taylor expanded in b around 0 25.5%

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

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \frac{1 - b}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-255}:\\ \;\;\;\;\frac{x}{\frac{y \cdot a}{-b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 14: 34.9% accurate, 26.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-158}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - b\right)}{a}}{y}\\ \mathbf{elif}\;b \leq 1.58 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\frac{y \cdot a}{-b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.3e-158)
   (/ (/ (* x (- 1.0 b)) a) y)
   (if (<= b 1.58e-254) (/ x (/ (* y a) (- b))) (/ (/ x a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.3e-158) {
		tmp = ((x * (1.0 - b)) / a) / y;
	} else if (b <= 1.58e-254) {
		tmp = x / ((y * a) / -b);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.3d-158)) then
        tmp = ((x * (1.0d0 - b)) / a) / y
    else if (b <= 1.58d-254) then
        tmp = x / ((y * a) / -b)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.3e-158) {
		tmp = ((x * (1.0 - b)) / a) / y;
	} else if (b <= 1.58e-254) {
		tmp = x / ((y * a) / -b);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.3e-158:
		tmp = ((x * (1.0 - b)) / a) / y
	elif b <= 1.58e-254:
		tmp = x / ((y * a) / -b)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.3e-158)
		tmp = Float64(Float64(Float64(x * Float64(1.0 - b)) / a) / y);
	elseif (b <= 1.58e-254)
		tmp = Float64(x / Float64(Float64(y * a) / Float64(-b)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.3e-158)
		tmp = ((x * (1.0 - b)) / a) / y;
	elseif (b <= 1.58e-254)
		tmp = x / ((y * a) / -b);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.3e-158], N[(N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.58e-254], N[(x / N[(N[(y * a), $MachinePrecision] / (-b)), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3e-158

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 81.5%

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

      1. div-exp 64.7%

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

      2. exp-to-pow 65.1%

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

      3. sub-neg 65.1%

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

      4. metadata-eval 65.1%

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

   4. Simplified 65.1%

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

      1. unpow-prod-up 65.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{e^{b}}}{y} \]

      2. unpow-1 65.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{e^{b}}}{y} \]

   6. Applied egg-rr 65.2%

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

      1. associate-*r/ 65.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{e^{b}}}{y} \]

      2. *-rgt-identity 65.2%

         \[\leadsto \frac{x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{e^{b}}}{y} \]

   8. Simplified 65.2%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t}}{a}}}{e^{b}}}{y} \]

   9. Taylor expanded in t around 0 66.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
   10. Step-by-step derivation

       1. associate-/r* 59.2%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   11. Simplified 59.2%

       \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   12. Taylor expanded in b around 0 42.1%

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

       1. +-commutative 42.1%

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

       2. mul-1-neg 42.1%

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

       3. sub-neg 42.1%

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

       4. *-commutative 42.1%

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

       5. div-sub 42.1%

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

       6. *-rgt-identity 42.1%

          \[\leadsto \frac{\frac{\color{blue}{x \cdot 1} - x \cdot b}{a}}{y} \]

       7. distribute-lft-out-- 42.1%

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

   14. Simplified 42.1%

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

   if -1.3e-158 < b < 1.58000000000000002e-254

   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. Step-by-step derivation

      1. associate-*l/ 92.0%

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

      2. *-commutative 92.0%

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

      3. exp-diff 92.0%

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

      4. exp-sum 75.0%

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

      5. *-commutative 75.0%

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

      6. exp-to-pow 75.0%

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

      7. *-commutative 75.0%

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

      8. exp-to-pow 75.5%

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

      9. sub-neg 75.5%

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

      10. metadata-eval 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in t around 0 66.7%

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

      1. times-frac 54.7%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 54.7%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 26.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 26.7%

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

      1. +-commutative 26.7%

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

      2. mul-1-neg 26.7%

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

      3. unsub-neg 26.7%

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

      4. times-frac 26.6%

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

   10. Simplified 26.6%

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

   11. Taylor expanded in b around inf 43.2%

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

       1. mul-1-neg 43.2%

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

       2. associate-*r/ 40.8%

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

       3. *-commutative 40.8%

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

       4. distribute-rgt-neg-in 40.8%

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

       5. associate-/r/ 50.1%

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

   13. Simplified 50.1%

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

   if 1.58000000000000002e-254 < b

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 83.6%

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

      1. div-exp 67.8%

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

      2. exp-to-pow 67.9%

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

      3. sub-neg 67.9%

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

      4. metadata-eval 67.9%

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

   4. Simplified 67.9%

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

      1. unpow-prod-up 67.9%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{e^{b}}}{y} \]

      2. unpow-1 67.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{e^{b}}}{y} \]

   6. Applied egg-rr 67.9%

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

      1. associate-*r/ 67.9%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{e^{b}}}{y} \]

      2. *-rgt-identity 67.9%

         \[\leadsto \frac{x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{e^{b}}}{y} \]

   8. Simplified 67.9%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t}}{a}}}{e^{b}}}{y} \]

   9. Taylor expanded in t around 0 55.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
   10. Step-by-step derivation

       1. associate-/r* 52.0%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   11. Simplified 52.0%

       \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   12. Taylor expanded in b around 0 25.5%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-158}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - b\right)}{a}}{y}\\ \mathbf{elif}\;b \leq 1.58 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\frac{y \cdot a}{-b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 15: 29.5% accurate, 31.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{-x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 4.4e-82) (/ (/ x a) y) (* b (/ (- x) (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 4.4e-82) {
		tmp = (x / a) / y;
	} else {
		tmp = b * (-x / (y * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 4.4d-82) then
        tmp = (x / a) / y
    else
        tmp = b * (-x / (y * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 4.4e-82) {
		tmp = (x / a) / y;
	} else {
		tmp = b * (-x / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 4.4e-82:
		tmp = (x / a) / y
	else:
		tmp = b * (-x / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 4.4e-82)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(b * Float64(Float64(-x) / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 4.4e-82)
		tmp = (x / a) / y;
	else
		tmp = b * (-x / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 4.4e-82], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(b * N[((-x) / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.39999999999999971e-82

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0 76.9%

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

      1. div-exp 68.1%

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

      2. exp-to-pow 68.3%

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

      3. sub-neg 68.3%

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

      4. metadata-eval 68.3%

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

   4. Simplified 68.3%

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

      1. unpow-prod-up 68.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{e^{b}}}{y} \]

      2. unpow-1 68.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{e^{b}}}{y} \]

   6. Applied egg-rr 68.5%

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

      1. associate-*r/ 68.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{e^{b}}}{y} \]

      2. *-rgt-identity 68.5%

         \[\leadsto \frac{x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{e^{b}}}{y} \]

   8. Simplified 68.5%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t}}{a}}}{e^{b}}}{y} \]

   9. Taylor expanded in t around 0 60.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
   10. Step-by-step derivation

       1. associate-/r* 56.3%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   11. Simplified 56.3%

       \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   12. Taylor expanded in b around 0 36.1%

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

   if 4.39999999999999971e-82 < a

   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. Step-by-step derivation

      1. associate-*l/ 87.0%

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

      2. *-commutative 87.0%

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

      3. exp-diff 65.2%

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

      4. exp-sum 57.3%

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

      5. *-commutative 57.3%

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

      6. exp-to-pow 57.3%

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

      7. *-commutative 57.3%

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

      8. exp-to-pow 57.6%

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

      9. sub-neg 57.6%

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

      10. metadata-eval 57.6%

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

   3. Simplified 57.6%

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

   4. Taylor expanded in t around 0 57.5%

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

      1. times-frac 58.6%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 58.6%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 52.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 21.9%

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

      1. +-commutative 21.9%

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

      2. mul-1-neg 21.9%

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

      3. unsub-neg 21.9%

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

      4. times-frac 18.0%

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

   10. Simplified 18.0%

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

   11. Taylor expanded in b around inf 23.7%

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

       1. mul-1-neg 23.7%

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

       2. associate-*r/ 27.2%

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

       3. *-commutative 27.2%

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

       4. distribute-rgt-neg-in 27.2%

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

   13. Simplified 27.2%

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

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{-x}{y \cdot a}\\ \end{array} \]

Alternative 16: 31.4% accurate, 63.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. associate-*l/ 88.3%

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

   2. *-commutative 88.3%

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

   3. exp-diff 68.4%

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

   4. exp-sum 58.7%

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

   5. *-commutative 58.7%

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

   6. exp-to-pow 58.7%

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

   7. *-commutative 58.7%

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

   8. exp-to-pow 58.9%

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

   9. sub-neg 58.9%

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

   10. metadata-eval 58.9%

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

3. Simplified 58.9%

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

4. Taylor expanded in t around 0 61.6%

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

   1. times-frac 59.2%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

6. Simplified 59.2%

   \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

7. Taylor expanded in y around 0 53.6%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

8. Taylor expanded in b around 0 26.0%

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

9. Final simplification 26.0%

   \[\leadsto \frac{x}{y \cdot a} \]

Alternative 17: 31.4% accurate, 63.0× speedup

Math

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

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(Float64(x / 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[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

2. Taylor expanded in y around 0 79.6%

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

   1. div-exp 66.0%

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

   2. exp-to-pow 66.2%

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

   3. sub-neg 66.2%

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

   4. metadata-eval 66.2%

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

4. Simplified 66.2%

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

   1. unpow-prod-up 66.3%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{e^{b}}}{y} \]

   2. unpow-1 66.3%

      \[\leadsto \frac{x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{e^{b}}}{y} \]

6. Applied egg-rr 66.3%

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

   1. associate-*r/ 66.3%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{e^{b}}}{y} \]

   2. *-rgt-identity 66.3%

      \[\leadsto \frac{x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{e^{b}}}{y} \]

8. Simplified 66.3%

   \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{{a}^{t}}{a}}}{e^{b}}}{y} \]

9. Taylor expanded in t around 0 55.1%

   \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
10. Step-by-step derivation

    1. associate-/r* 50.8%

       \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

11. Simplified 50.8%

    \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

12. Taylor expanded in b around 0 27.1%

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

13. Final simplification 27.1%

    \[\leadsto \frac{\frac{x}{a}}{y} \]

Developer target: 72.8% 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 2023310 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (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))