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

Percentage Accurate: 98.4% → 98.4%

Time: 42.5s

Alternatives: 27

Speedup: 1.0×

• 46.5% 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 98.3%

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

3. Final simplification 98.3%

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

Alternative 2: 91.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+69} \lor \neg \left(y \leq 2 \cdot 10^{+121}\right):\\ \;\;\;\;x \cdot \frac{e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.4e+69) (not (<= y 2e+121)))
   (* 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 <= -6.4e+69) || !(y <= 2e+121)) {
		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 <= (-6.4d+69)) .or. (.not. (y <= 2d+121))) 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 <= -6.4e+69) || !(y <= 2e+121)) {
		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 <= -6.4e+69) or not (y <= 2e+121):
		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 <= -6.4e+69) || !(y <= 2e+121))
		tmp = Float64(x * Float64(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 <= -6.4e+69) || ~((y <= 2e+121)))
		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, -6.4e+69], N[Not[LessEqual[y, 2e+121]], $MachinePrecision]], N[(x * N[(N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] / y), $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 < -6.3999999999999997e69 or 2.00000000000000007e121 < 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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. associate-/l* 85.5%

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

      3. associate--l+ 85.5%

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

      4. fma-define 85.5%

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

      5. sub-neg 85.5%

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

      6. metadata-eval 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in t around 0 96.1%

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

      1. associate-/l* 96.1%

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

      2. +-commutative 96.1%

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

      3. mul-1-neg 96.1%

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

      4. unsub-neg 96.1%

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

   7. Simplified 96.1%

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

   if -6.3999999999999997e69 < y < 2.00000000000000007e121

   1. Initial program 97.5%

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

      1. *-commutative 97.5%

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

      2. associate-/l* 86.2%

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

      3. associate--l+ 86.2%

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

      4. fma-define 86.2%

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

      5. sub-neg 86.2%

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

      6. metadata-eval 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in y around 0 95.1%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+69} \lor \neg \left(y \leq 2 \cdot 10^{+121}\right):\\ \;\;\;\;x \cdot \frac{e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+16}:\\ \;\;\;\;e^{y \cdot \log z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-143}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow a (+ t -1.0)) (exp b)) y))))
   (if (<= y -7.5e+16)
     (* (exp (* y (log z))) (/ x y))
     (if (<= y 6e-209)
       t_1
       (if (<= y 2.3e-143)
         (/ (* x (/ 1.0 (* a (exp b)))) y)
         (if (<= y 1.15e+142) t_1 (* (/ x a) (/ (pow z y) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((pow(a, (t + -1.0)) / exp(b)) / y);
	double tmp;
	if (y <= -7.5e+16) {
		tmp = exp((y * log(z))) * (x / y);
	} else if (y <= 6e-209) {
		tmp = t_1;
	} else if (y <= 2.3e-143) {
		tmp = (x * (1.0 / (a * exp(b)))) / y;
	} else if (y <= 1.15e+142) {
		tmp = t_1;
	} else {
		tmp = (x / a) * (pow(z, y) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (((a ** (t + (-1.0d0))) / exp(b)) / y)
    if (y <= (-7.5d+16)) then
        tmp = exp((y * log(z))) * (x / y)
    else if (y <= 6d-209) then
        tmp = t_1
    else if (y <= 2.3d-143) then
        tmp = (x * (1.0d0 / (a * exp(b)))) / y
    else if (y <= 1.15d+142) then
        tmp = t_1
    else
        tmp = (x / a) * ((z ** y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((Math.pow(a, (t + -1.0)) / Math.exp(b)) / y);
	double tmp;
	if (y <= -7.5e+16) {
		tmp = Math.exp((y * Math.log(z))) * (x / y);
	} else if (y <= 6e-209) {
		tmp = t_1;
	} else if (y <= 2.3e-143) {
		tmp = (x * (1.0 / (a * Math.exp(b)))) / y;
	} else if (y <= 1.15e+142) {
		tmp = t_1;
	} else {
		tmp = (x / a) * (Math.pow(z, y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((math.pow(a, (t + -1.0)) / math.exp(b)) / y)
	tmp = 0
	if y <= -7.5e+16:
		tmp = math.exp((y * math.log(z))) * (x / y)
	elif y <= 6e-209:
		tmp = t_1
	elif y <= 2.3e-143:
		tmp = (x * (1.0 / (a * math.exp(b)))) / y
	elif y <= 1.15e+142:
		tmp = t_1
	else:
		tmp = (x / a) * (math.pow(z, y) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((a ^ Float64(t + -1.0)) / exp(b)) / y))
	tmp = 0.0
	if (y <= -7.5e+16)
		tmp = Float64(exp(Float64(y * log(z))) * Float64(x / y));
	elseif (y <= 6e-209)
		tmp = t_1;
	elseif (y <= 2.3e-143)
		tmp = Float64(Float64(x * Float64(1.0 / Float64(a * exp(b)))) / y);
	elseif (y <= 1.15e+142)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (((a ^ (t + -1.0)) / exp(b)) / y);
	tmp = 0.0;
	if (y <= -7.5e+16)
		tmp = exp((y * log(z))) * (x / y);
	elseif (y <= 6e-209)
		tmp = t_1;
	elseif (y <= 2.3e-143)
		tmp = (x * (1.0 / (a * exp(b)))) / y;
	elseif (y <= 1.15e+142)
		tmp = t_1;
	else
		tmp = (x / a) * ((z ^ y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+16], N[(N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-209], t$95$1, If[LessEqual[y, 2.3e-143], N[(N[(x * N[(1.0 / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.15e+142], t$95$1, N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.5e16

   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. *-commutative 100.0%

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

      2. associate-/l* 87.5%

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

      3. associate--l+ 87.5%

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

      4. fma-define 87.5%

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

      5. sub-neg 87.5%

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

      6. metadata-eval 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around inf 73.1%

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

   if -7.5e16 < y < 5.9999999999999997e-209 or 2.30000000000000011e-143 < y < 1.15000000000000001e142

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-/l* 86.4%

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

      3. associate--l+ 86.4%

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

      4. fma-define 86.4%

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

      5. sub-neg 86.4%

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

      6. metadata-eval 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in y around 0 95.3%

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

      1. associate-/l* 95.2%

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

      2. div-exp 83.3%

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

      3. exp-to-pow 84.0%

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

      4. sub-neg 84.0%

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

      5. metadata-eval 84.0%

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

   7. Simplified 84.0%

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

   if 5.9999999999999997e-209 < y < 2.30000000000000011e-143

   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. Step-by-step derivation

      1. *-commutative 98.6%

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

      2. associate-/l* 81.0%

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

      3. associate--l+ 81.0%

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

      4. fma-define 81.0%

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

      5. sub-neg 81.0%

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

      6. metadata-eval 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in y around 0 98.6%

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

   6. Taylor expanded in t around 0 64.0%

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

      1. *-commutative 64.0%

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

      2. exp-diff 64.0%

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

      3. mul-1-neg 64.0%

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

      4. log-rec 64.0%

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

      5. rem-exp-log 65.3%

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

      6. associate-/l/ 65.3%

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

      7. *-commutative 65.3%

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

   8. Simplified 65.3%

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

   if 1.15000000000000001e142 < y

   1. Initial program 100.0%

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

   4. Applied egg-rr 59.4%

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

   5. Taylor expanded in t around 0 68.8%

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

   6. Taylor expanded in b around 0 87.5%

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

      1. times-frac 93.8%

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

   8. Simplified 93.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+16}:\\ \;\;\;\;e^{y \cdot \log z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-143}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+223} \lor \neg \left(y \leq 1.4 \cdot 10^{+144}\right):\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.2e+223) (not (<= y 1.4e+144)))
   (* (/ x a) (/ (pow z y) 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 <= -4.2e+223) || !(y <= 1.4e+144)) {
		tmp = (x / a) * (pow(z, y) / 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 <= (-4.2d+223)) .or. (.not. (y <= 1.4d+144))) then
        tmp = (x / a) * ((z ** y) / 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 <= -4.2e+223) || !(y <= 1.4e+144)) {
		tmp = (x / a) * (Math.pow(z, y) / 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 <= -4.2e+223) or not (y <= 1.4e+144):
		tmp = (x / a) * (math.pow(z, y) / 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 <= -4.2e+223) || !(y <= 1.4e+144))
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / 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 <= -4.2e+223) || ~((y <= 1.4e+144)))
		tmp = (x / a) * ((z ^ y) / 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, -4.2e+223], N[Not[LessEqual[y, 1.4e+144]], $MachinePrecision]], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $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 < -4.19999999999999981e223 or 1.40000000000000003e144 < y

   1. Initial program 100.0%

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

   4. Applied egg-rr 51.2%

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

   5. Taylor expanded in t around 0 61.0%

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

   6. Taylor expanded in b around 0 80.5%

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

      1. times-frac 95.2%

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

   8. Simplified 95.2%

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

   if -4.19999999999999981e223 < y < 1.40000000000000003e144

   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. Step-by-step derivation

      1. *-commutative 97.9%

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

      2. associate-/l* 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. associate--l+ 85.7%

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

      4. fma-define 85.7%

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

      5. sub-neg 85.7%

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

      6. metadata-eval 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in y around 0 92.3%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+223} \lor \neg \left(y \leq 1.4 \cdot 10^{+144}\right):\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-134}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a (+ t -1.0)) y))))
   (if (<= t -9e+70)
     t_1
     (if (<= t 1.08e-134)
       (* x (/ (pow z y) (* a (* y (exp b)))))
       (if (<= t 2e+33) (/ (* x (/ 1.0 (* 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 * (pow(a, (t + -1.0)) / y);
	double tmp;
	if (t <= -9e+70) {
		tmp = t_1;
	} else if (t <= 1.08e-134) {
		tmp = x * (pow(z, y) / (a * (y * exp(b))));
	} else if (t <= 2e+33) {
		tmp = (x * (1.0 / (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 * ((a ** (t + (-1.0d0))) / y)
    if (t <= (-9d+70)) then
        tmp = t_1
    else if (t <= 1.08d-134) then
        tmp = x * ((z ** y) / (a * (y * exp(b))))
    else if (t <= 2d+33) then
        tmp = (x * (1.0d0 / (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 * (Math.pow(a, (t + -1.0)) / y);
	double tmp;
	if (t <= -9e+70) {
		tmp = t_1;
	} else if (t <= 1.08e-134) {
		tmp = x * (Math.pow(z, y) / (a * (y * Math.exp(b))));
	} else if (t <= 2e+33) {
		tmp = (x * (1.0 / (a * Math.exp(b)))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(a, (t + -1.0)) / y)
	tmp = 0
	if t <= -9e+70:
		tmp = t_1
	elif t <= 1.08e-134:
		tmp = x * (math.pow(z, y) / (a * (y * math.exp(b))))
	elif t <= 2e+33:
		tmp = (x * (1.0 / (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((a ^ Float64(t + -1.0)) / y))
	tmp = 0.0
	if (t <= -9e+70)
		tmp = t_1;
	elseif (t <= 1.08e-134)
		tmp = Float64(x * Float64((z ^ y) / Float64(a * Float64(y * exp(b)))));
	elseif (t <= 2e+33)
		tmp = Float64(Float64(x * Float64(1.0 / 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 * ((a ^ (t + -1.0)) / y);
	tmp = 0.0;
	if (t <= -9e+70)
		tmp = t_1;
	elseif (t <= 1.08e-134)
		tmp = x * ((z ^ y) / (a * (y * exp(b))));
	elseif (t <= 2e+33)
		tmp = (x * (1.0 / (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[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+70], t$95$1, If[LessEqual[t, 1.08e-134], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+33], N[(N[(x * N[(1.0 / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.9999999999999999e70 or 1.9999999999999999e33 < 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. *-commutative 100.0%

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

      2. associate-/l* 81.4%

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

      3. associate--l+ 81.4%

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

      4. fma-define 81.4%

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

      5. sub-neg 81.4%

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

      6. metadata-eval 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in y around 0 90.4%

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

      1. associate-/l* 90.4%

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

      2. div-exp 63.0%

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

      3. exp-to-pow 63.0%

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

      4. sub-neg 63.0%

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

      5. metadata-eval 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in b around 0 78.2%

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

      1. exp-to-pow 78.2%

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

      2. sub-neg 78.2%

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

      3. metadata-eval 78.2%

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

   10. Simplified 78.2%

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

   if -8.9999999999999999e70 < t < 1.07999999999999999e-134

   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* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 88.1%

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

      4. associate-/l* 87.1%

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

      5. *-commutative 87.1%

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

      6. exp-to-pow 87.1%

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

      7. exp-diff 87.1%

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

      8. *-commutative 87.1%

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

      9. exp-to-pow 88.1%

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

      10. sub-neg 88.1%

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

      11. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in t around 0 89.2%

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

   if 1.07999999999999999e-134 < t < 1.9999999999999999e33

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

      2. associate-/l* 86.3%

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

      3. associate--l+ 86.3%

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

      4. fma-define 86.3%

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

      5. sub-neg 86.3%

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

      6. metadata-eval 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in y around 0 81.6%

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

   6. Taylor expanded in t around 0 76.9%

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

      1. *-commutative 76.9%

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

      2. exp-diff 77.0%

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

      3. mul-1-neg 77.0%

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

      4. log-rec 77.0%

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

      5. rem-exp-log 78.5%

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

      6. associate-/l/ 78.5%

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

      7. *-commutative 78.5%

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

   8. Simplified 78.5%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-134}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot e^{b}}\\ \mathbf{if}\;b \leq -9.8 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y (exp b)))))
   (if (<= b -9.8e+39)
     t_1
     (if (<= b 3.4e-271)
       (* b (- (/ x (* y (* a b))) (/ x (* y a))))
       (if (<= b 7.5e-8) (/ x (* a (+ y (* b (+ y (* 0.5 (* y b))))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * exp(b));
	double tmp;
	if (b <= -9.8e+39) {
		tmp = t_1;
	} else if (b <= 3.4e-271) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else if (b <= 7.5e-8) {
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y * exp(b))
    if (b <= (-9.8d+39)) then
        tmp = t_1
    else if (b <= 3.4d-271) then
        tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
    else if (b <= 7.5d-8) then
        tmp = x / (a * (y + (b * (y + (0.5d0 * (y * b))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * Math.exp(b));
	double tmp;
	if (b <= -9.8e+39) {
		tmp = t_1;
	} else if (b <= 3.4e-271) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else if (b <= 7.5e-8) {
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * math.exp(b))
	tmp = 0
	if b <= -9.8e+39:
		tmp = t_1
	elif b <= 3.4e-271:
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
	elif b <= 7.5e-8:
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * exp(b)))
	tmp = 0.0
	if (b <= -9.8e+39)
		tmp = t_1;
	elseif (b <= 3.4e-271)
		tmp = Float64(b * Float64(Float64(x / Float64(y * Float64(a * b))) - Float64(x / Float64(y * a))));
	elseif (b <= 7.5e-8)
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(0.5 * Float64(y * b)))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * exp(b));
	tmp = 0.0;
	if (b <= -9.8e+39)
		tmp = t_1;
	elseif (b <= 3.4e-271)
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	elseif (b <= 7.5e-8)
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.8e+39], t$95$1, If[LessEqual[b, 3.4e-271], N[(b * N[(N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e-8], N[(x / N[(a * N[(y + N[(b * N[(y + N[(0.5 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.79999999999999974e39 or 7.4999999999999997e-8 < b

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 85.5%

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

      3. associate--l+ 85.5%

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

      4. fma-define 85.5%

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

      5. sub-neg 85.5%

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

      6. metadata-eval 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in b around inf 69.7%

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

      1. neg-mul-1 69.7%

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

   7. Simplified 69.7%

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

      1. exp-neg 69.7%

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

      2. frac-times 82.0%

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

      3. *-un-lft-identity 82.0%

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

      4. *-commutative 82.0%

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

   9. Applied egg-rr 82.0%

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

   if -9.79999999999999974e39 < b < 3.4000000000000001e-271

   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. Step-by-step derivation

      1. *-commutative 97.9%

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

      2. associate-/l* 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. associate--l+ 87.6%

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

      4. fma-define 87.6%

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

      5. sub-neg 87.6%

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

      6. metadata-eval 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in y around 0 75.4%

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

   6. Taylor expanded in t around 0 34.2%

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

      1. *-commutative 34.2%

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

      2. exp-diff 34.2%

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

      3. mul-1-neg 34.2%

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

      4. log-rec 34.2%

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

      5. rem-exp-log 34.9%

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

      6. associate-/l/ 34.9%

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

      7. *-commutative 34.9%

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

   8. Simplified 34.9%

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

   9. Taylor expanded in b around 0 35.0%

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

       1. +-commutative 35.0%

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

       2. mul-1-neg 35.0%

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

       3. unsub-neg 35.0%

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

       4. associate-/l* 35.0%

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

   11. Simplified 35.0%

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

   12. Taylor expanded in b around inf 44.3%

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

       1. mul-1-neg 44.3%

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

       2. +-commutative 44.3%

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

       3. unsub-neg 44.3%

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

       4. *-commutative 44.3%

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

       5. *-commutative 44.3%

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

       6. associate-*l* 45.5%

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

       7. *-commutative 45.5%

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

       8. *-commutative 45.5%

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

   14. Simplified 45.5%

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

   if 3.4000000000000001e-271 < b < 7.4999999999999997e-8

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-/l* 84.7%

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

      3. associate--l+ 84.7%

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

      4. fma-define 84.7%

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

      5. sub-neg 84.7%

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

      6. metadata-eval 84.7%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in y around 0 74.5%

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

      1. associate-/l* 74.3%

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

      2. div-exp 74.4%

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

      3. exp-to-pow 76.1%

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

      4. sub-neg 76.1%

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

      5. metadata-eval 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in t around 0 43.9%

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

   9. Taylor expanded in b around 0 43.9%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + 0.5 \cdot \left(b \cdot y\right)\right)\right)}} \]
   10. Step-by-step derivation

       1. *-commutative 43.9%

          \[\leadsto \frac{x}{a \cdot \left(y + b \cdot \left(y + 0.5 \cdot \color{blue}{\left(y \cdot b\right)}\right)\right)} \]

   11. Simplified 43.9%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot e^{b}\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+87}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (exp b))))
   (if (<= b -1.45e+87)
     (/ x t_1)
     (if (<= b 8e-20) (* x (/ (pow a (+ t -1.0)) y)) (/ x (* a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * exp(b);
	double tmp;
	if (b <= -1.45e+87) {
		tmp = x / t_1;
	} else if (b <= 8e-20) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else {
		tmp = x / (a * 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 = y * exp(b)
    if (b <= (-1.45d+87)) then
        tmp = x / t_1
    else if (b <= 8d-20) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else
        tmp = x / (a * 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 = y * Math.exp(b);
	double tmp;
	if (b <= -1.45e+87) {
		tmp = x / t_1;
	} else if (b <= 8e-20) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else {
		tmp = x / (a * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * math.exp(b)
	tmp = 0
	if b <= -1.45e+87:
		tmp = x / t_1
	elif b <= 8e-20:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	else:
		tmp = x / (a * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * exp(b))
	tmp = 0.0
	if (b <= -1.45e+87)
		tmp = Float64(x / t_1);
	elseif (b <= 8e-20)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	else
		tmp = Float64(x / Float64(a * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * exp(b);
	tmp = 0.0;
	if (b <= -1.45e+87)
		tmp = x / t_1;
	elseif (b <= 8e-20)
		tmp = x * ((a ^ (t + -1.0)) / y);
	else
		tmp = x / (a * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+87], N[(x / t$95$1), $MachinePrecision], If[LessEqual[b, 8e-20], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4499999999999999e87

   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. *-commutative 100.0%

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

      2. associate-/l* 96.6%

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

      3. associate--l+ 96.6%

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

      4. fma-define 96.6%

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

      5. sub-neg 96.6%

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

      6. metadata-eval 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in b around inf 82.9%

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

      1. neg-mul-1 82.9%

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

   7. Simplified 82.9%

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

      1. exp-neg 82.9%

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

      2. frac-times 84.7%

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

      3. *-un-lft-identity 84.7%

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

      4. *-commutative 84.7%

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

   9. Applied egg-rr 84.7%

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

   if -1.4499999999999999e87 < b < 7.99999999999999956e-20

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

      2. associate-/l* 86.9%

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

      3. associate--l+ 86.9%

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

      4. fma-define 86.9%

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

      5. sub-neg 86.9%

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

      6. metadata-eval 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in y around 0 75.5%

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

      1. associate-/l* 74.8%

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

      2. div-exp 70.9%

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

      3. exp-to-pow 71.8%

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

      4. sub-neg 71.8%

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

      5. metadata-eval 71.8%

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

   7. Simplified 71.8%

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

   8. Taylor expanded in b around 0 72.6%

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

      1. exp-to-pow 73.6%

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

      2. sub-neg 73.6%

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

      3. metadata-eval 73.6%

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

   10. Simplified 73.6%

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

   if 7.99999999999999956e-20 < b

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 75.9%

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

      3. associate--l+ 75.9%

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

      4. fma-define 75.9%

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

      5. sub-neg 75.9%

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

      6. metadata-eval 75.9%

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

   3. Simplified 75.9%

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

   5. Taylor expanded in y around 0 88.8%

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

      1. associate-/l* 88.8%

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

      2. div-exp 64.8%

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

      3. exp-to-pow 64.9%

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

      4. sub-neg 64.9%

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

      5. metadata-eval 64.9%

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

   7. Simplified 64.9%

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

   8. Taylor expanded in t around 0 83.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+87}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot e^{b}\\ \mathbf{if}\;b \leq -3.9 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-20}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (exp b))))
   (if (<= b -3.9e+86)
     (/ x t_1)
     (if (<= b 8e-20) (/ (* x (pow a (+ t -1.0))) y) (/ x (* a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * exp(b);
	double tmp;
	if (b <= -3.9e+86) {
		tmp = x / t_1;
	} else if (b <= 8e-20) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else {
		tmp = x / (a * 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 = y * exp(b)
    if (b <= (-3.9d+86)) then
        tmp = x / t_1
    else if (b <= 8d-20) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else
        tmp = x / (a * 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 = y * Math.exp(b);
	double tmp;
	if (b <= -3.9e+86) {
		tmp = x / t_1;
	} else if (b <= 8e-20) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else {
		tmp = x / (a * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * math.exp(b)
	tmp = 0
	if b <= -3.9e+86:
		tmp = x / t_1
	elif b <= 8e-20:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	else:
		tmp = x / (a * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * exp(b))
	tmp = 0.0
	if (b <= -3.9e+86)
		tmp = Float64(x / t_1);
	elseif (b <= 8e-20)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	else
		tmp = Float64(x / Float64(a * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * exp(b);
	tmp = 0.0;
	if (b <= -3.9e+86)
		tmp = x / t_1;
	elseif (b <= 8e-20)
		tmp = (x * (a ^ (t + -1.0))) / y;
	else
		tmp = x / (a * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.9e+86], N[(x / t$95$1), $MachinePrecision], If[LessEqual[b, 8e-20], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.9000000000000002e86

   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. *-commutative 100.0%

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

      2. associate-/l* 96.6%

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

      3. associate--l+ 96.6%

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

      4. fma-define 96.6%

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

      5. sub-neg 96.6%

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

      6. metadata-eval 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in b around inf 82.9%

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

      1. neg-mul-1 82.9%

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

   7. Simplified 82.9%

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

      1. exp-neg 82.9%

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

      2. frac-times 84.7%

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

      3. *-un-lft-identity 84.7%

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

      4. *-commutative 84.7%

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

   9. Applied egg-rr 84.7%

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

   if -3.9000000000000002e86 < b < 7.99999999999999956e-20

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

      2. associate-/l* 86.9%

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

      3. associate--l+ 86.9%

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

      4. fma-define 86.9%

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

      5. sub-neg 86.9%

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

      6. metadata-eval 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in y around 0 75.5%

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

   6. Taylor expanded in b around 0 72.6%

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

      1. exp-to-pow 73.6%

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

      2. sub-neg 73.6%

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

      3. metadata-eval 73.6%

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

      4. +-commutative 73.6%

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

   8. Simplified 73.6%

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

   if 7.99999999999999956e-20 < b

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 75.9%

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

      3. associate--l+ 75.9%

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

      4. fma-define 75.9%

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

      5. sub-neg 75.9%

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

      6. metadata-eval 75.9%

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

   3. Simplified 75.9%

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

   5. Taylor expanded in y around 0 88.8%

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

      1. associate-/l* 88.8%

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

      2. div-exp 64.8%

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

      3. exp-to-pow 64.9%

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

      4. sub-neg 64.9%

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

      5. metadata-eval 64.9%

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

   7. Simplified 64.9%

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

   8. Taylor expanded in t around 0 83.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-20}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot e^{b}\\ \mathbf{if}\;b \leq -9.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (exp b))))
   (if (<= b -9.8e+39)
     (/ x t_1)
     (if (<= b 6.5e-274)
       (* b (- (/ x (* y (* a b))) (/ x (* y a))))
       (/ x (* a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * exp(b);
	double tmp;
	if (b <= -9.8e+39) {
		tmp = x / t_1;
	} else if (b <= 6.5e-274) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * 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 = y * exp(b)
    if (b <= (-9.8d+39)) then
        tmp = x / t_1
    else if (b <= 6.5d-274) then
        tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
    else
        tmp = x / (a * 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 = y * Math.exp(b);
	double tmp;
	if (b <= -9.8e+39) {
		tmp = x / t_1;
	} else if (b <= 6.5e-274) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * math.exp(b)
	tmp = 0
	if b <= -9.8e+39:
		tmp = x / t_1
	elif b <= 6.5e-274:
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
	else:
		tmp = x / (a * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * exp(b))
	tmp = 0.0
	if (b <= -9.8e+39)
		tmp = Float64(x / t_1);
	elseif (b <= 6.5e-274)
		tmp = Float64(b * Float64(Float64(x / Float64(y * Float64(a * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(x / Float64(a * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * exp(b);
	tmp = 0.0;
	if (b <= -9.8e+39)
		tmp = x / t_1;
	elseif (b <= 6.5e-274)
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	else
		tmp = x / (a * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.8e+39], N[(x / t$95$1), $MachinePrecision], If[LessEqual[b, 6.5e-274], N[(b * N[(N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.79999999999999974e39

   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. *-commutative 100.0%

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

      2. associate-/l* 96.9%

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

      3. associate--l+ 96.9%

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

      4. fma-define 96.9%

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

      5. sub-neg 96.9%

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

      6. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in b around inf 79.9%

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

      1. neg-mul-1 79.9%

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

   7. Simplified 79.9%

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

      1. exp-neg 79.9%

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

      2. frac-times 81.5%

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

      3. *-un-lft-identity 81.5%

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

      4. *-commutative 81.5%

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

   9. Applied egg-rr 81.5%

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

   if -9.79999999999999974e39 < b < 6.49999999999999959e-274

   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. Step-by-step derivation

      1. *-commutative 97.9%

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

      2. associate-/l* 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. associate--l+ 87.6%

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

      4. fma-define 87.6%

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

      5. sub-neg 87.6%

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

      6. metadata-eval 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in y around 0 75.4%

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

   6. Taylor expanded in t around 0 34.2%

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

      1. *-commutative 34.2%

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

      2. exp-diff 34.2%

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

      3. mul-1-neg 34.2%

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

      4. log-rec 34.2%

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

      5. rem-exp-log 34.9%

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

      6. associate-/l/ 34.9%

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

      7. *-commutative 34.9%

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

   8. Simplified 34.9%

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

   9. Taylor expanded in b around 0 35.0%

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

       1. +-commutative 35.0%

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

       2. mul-1-neg 35.0%

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

       3. unsub-neg 35.0%

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

       4. associate-/l* 35.0%

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

   11. Simplified 35.0%

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

   12. Taylor expanded in b around inf 44.3%

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

       1. mul-1-neg 44.3%

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

       2. +-commutative 44.3%

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

       3. unsub-neg 44.3%

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

       4. *-commutative 44.3%

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

       5. *-commutative 44.3%

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

       6. associate-*l* 45.5%

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

       7. *-commutative 45.5%

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

       8. *-commutative 45.5%

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

   14. Simplified 45.5%

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

   if 6.49999999999999959e-274 < b

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 78.7%

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

      3. associate--l+ 78.7%

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

      4. fma-define 78.7%

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

      5. sub-neg 78.7%

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

      6. metadata-eval 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around 0 83.6%

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

      1. associate-/l* 83.5%

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

      2. div-exp 68.3%

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

      3. exp-to-pow 69.0%

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

      4. sub-neg 69.0%

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

      5. metadata-eval 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in t around 0 66.9%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.6% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{x \cdot b}{y}\right) - \frac{x}{y}\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a + b \cdot \left(a + b \cdot \left(\left(a \cdot b\right) \cdot 0.16666666666666666 + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.8e+143)
   (+ (/ x y) (* b (- (* b (* -0.16666666666666666 (/ (* x b) y))) (/ x y))))
   (if (<= b 7.8e-274)
     (* b (- (/ x (* y (* a b))) (/ x (* y a))))
     (/
      (*
       x
       (/
        1.0
        (+ a (* b (+ a (* b (+ (* (* a b) 0.16666666666666666) (* a 0.5))))))))
      y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.8e+143) {
		tmp = (x / y) + (b * ((b * (-0.16666666666666666 * ((x * b) / y))) - (x / y)));
	} else if (b <= 7.8e-274) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = (x * (1.0 / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))))) / 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 <= (-5.8d+143)) then
        tmp = (x / y) + (b * ((b * ((-0.16666666666666666d0) * ((x * b) / y))) - (x / y)))
    else if (b <= 7.8d-274) then
        tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
    else
        tmp = (x * (1.0d0 / (a + (b * (a + (b * (((a * b) * 0.16666666666666666d0) + (a * 0.5d0)))))))) / 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 <= -5.8e+143) {
		tmp = (x / y) + (b * ((b * (-0.16666666666666666 * ((x * b) / y))) - (x / y)));
	} else if (b <= 7.8e-274) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = (x * (1.0 / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.8e+143:
		tmp = (x / y) + (b * ((b * (-0.16666666666666666 * ((x * b) / y))) - (x / y)))
	elif b <= 7.8e-274:
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
	else:
		tmp = (x * (1.0 / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.8e+143)
		tmp = Float64(Float64(x / y) + Float64(b * Float64(Float64(b * Float64(-0.16666666666666666 * Float64(Float64(x * b) / y))) - Float64(x / y))));
	elseif (b <= 7.8e-274)
		tmp = Float64(b * Float64(Float64(x / Float64(y * Float64(a * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(Float64(x * Float64(1.0 / Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(Float64(a * b) * 0.16666666666666666) + Float64(a * 0.5)))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.8e+143)
		tmp = (x / y) + (b * ((b * (-0.16666666666666666 * ((x * b) / y))) - (x / y)));
	elseif (b <= 7.8e-274)
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	else
		tmp = (x * (1.0 / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.8e+143], N[(N[(x / y), $MachinePrecision] + N[(b * N[(N[(b * N[(-0.16666666666666666 * N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e-274], N[(b * N[(N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(1.0 / N[(a + N[(b * N[(a + N[(b * N[(N[(N[(a * b), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.7999999999999996e143

   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. *-commutative 100.0%

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

      2. associate-/l* 95.0%

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

      3. associate--l+ 95.0%

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

      4. fma-define 95.0%

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

      5. sub-neg 95.0%

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

      6. metadata-eval 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in b around inf 85.2%

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

      1. neg-mul-1 85.2%

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

   7. Simplified 85.2%

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

   8. Taylor expanded in b around 0 85.3%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in b around inf 85.3%

      \[\leadsto b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \color{blue}{\left(-0.16666666666666666 \cdot \frac{b \cdot x}{y}\right)}\right) + \frac{x}{y} \]

   if -5.7999999999999996e143 < b < 7.79999999999999971e-274

   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. Step-by-step derivation

      1. *-commutative 98.3%

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

      2. associate-/l* 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. associate--l+ 90.5%

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

      4. fma-define 90.5%

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

      5. sub-neg 90.5%

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

      6. metadata-eval 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in y around 0 78.2%

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

   6. Taylor expanded in t around 0 42.8%

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

      1. *-commutative 42.8%

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

      2. exp-diff 42.8%

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

      3. mul-1-neg 42.8%

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

      4. log-rec 42.8%

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

      5. rem-exp-log 43.3%

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

      6. associate-/l/ 43.3%

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

      7. *-commutative 43.3%

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

   8. Simplified 43.3%

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

   9. Taylor expanded in b around 0 33.2%

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

       1. +-commutative 33.2%

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

       2. mul-1-neg 33.2%

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

       3. unsub-neg 33.2%

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

       4. associate-/l* 33.2%

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

   11. Simplified 33.2%

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

   12. Taylor expanded in b around inf 41.3%

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

       1. mul-1-neg 41.3%

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

       2. +-commutative 41.3%

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

       3. unsub-neg 41.3%

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

       4. *-commutative 41.3%

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

       5. *-commutative 41.3%

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

       6. associate-*l* 42.2%

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

       7. *-commutative 42.2%

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

       8. *-commutative 42.2%

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

   14. Simplified 42.2%

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

   if 7.79999999999999971e-274 < b

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 78.7%

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

      3. associate--l+ 78.7%

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

      4. fma-define 78.7%

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

      5. sub-neg 78.7%

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

      6. metadata-eval 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around 0 83.6%

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

   6. Taylor expanded in t around 0 64.6%

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

      1. *-commutative 64.6%

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

      2. exp-diff 64.6%

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

      3. mul-1-neg 64.6%

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

      4. log-rec 64.6%

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

      5. rem-exp-log 65.3%

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

      6. associate-/l/ 65.3%

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

      7. *-commutative 65.3%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in b around 0 61.0%

      \[\leadsto \frac{\frac{1}{\color{blue}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + 0.5 \cdot a\right)\right)}} \cdot x}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{x \cdot b}{y}\right) - \frac{x}{y}\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a + b \cdot \left(a + b \cdot \left(\left(a \cdot b\right) \cdot 0.16666666666666666 + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.3% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{b}{y} + 0.5 \cdot \frac{1}{y}\right) + \frac{-1}{y}\right)\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a + b \cdot \left(a + b \cdot \left(\left(a \cdot b\right) \cdot 0.16666666666666666 + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.45e+40)
   (*
    x
    (+
     (/ 1.0 y)
     (*
      b
      (+
       (* b (+ (* -0.16666666666666666 (/ b y)) (* 0.5 (/ 1.0 y))))
       (/ -1.0 y)))))
   (if (<= b 7.6e-273)
     (* b (- (/ x (* y (* a b))) (/ x (* y a))))
     (/
      (*
       x
       (/
        1.0
        (+ a (* b (+ a (* b (+ (* (* a b) 0.16666666666666666) (* a 0.5))))))))
      y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.45e+40) {
		tmp = x * ((1.0 / y) + (b * ((b * ((-0.16666666666666666 * (b / y)) + (0.5 * (1.0 / y)))) + (-1.0 / y))));
	} else if (b <= 7.6e-273) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = (x * (1.0 / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))))) / 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 <= (-1.45d+40)) then
        tmp = x * ((1.0d0 / y) + (b * ((b * (((-0.16666666666666666d0) * (b / y)) + (0.5d0 * (1.0d0 / y)))) + ((-1.0d0) / y))))
    else if (b <= 7.6d-273) then
        tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
    else
        tmp = (x * (1.0d0 / (a + (b * (a + (b * (((a * b) * 0.16666666666666666d0) + (a * 0.5d0)))))))) / 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 <= -1.45e+40) {
		tmp = x * ((1.0 / y) + (b * ((b * ((-0.16666666666666666 * (b / y)) + (0.5 * (1.0 / y)))) + (-1.0 / y))));
	} else if (b <= 7.6e-273) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = (x * (1.0 / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.45e+40:
		tmp = x * ((1.0 / y) + (b * ((b * ((-0.16666666666666666 * (b / y)) + (0.5 * (1.0 / y)))) + (-1.0 / y))))
	elif b <= 7.6e-273:
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
	else:
		tmp = (x * (1.0 / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.45e+40)
		tmp = Float64(x * Float64(Float64(1.0 / y) + Float64(b * Float64(Float64(b * Float64(Float64(-0.16666666666666666 * Float64(b / y)) + Float64(0.5 * Float64(1.0 / y)))) + Float64(-1.0 / y)))));
	elseif (b <= 7.6e-273)
		tmp = Float64(b * Float64(Float64(x / Float64(y * Float64(a * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(Float64(x * Float64(1.0 / Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(Float64(a * b) * 0.16666666666666666) + Float64(a * 0.5)))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.45e+40)
		tmp = x * ((1.0 / y) + (b * ((b * ((-0.16666666666666666 * (b / y)) + (0.5 * (1.0 / y)))) + (-1.0 / y))));
	elseif (b <= 7.6e-273)
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	else
		tmp = (x * (1.0 / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.45e+40], N[(x * N[(N[(1.0 / y), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(-0.16666666666666666 * N[(b / y), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.6e-273], N[(b * N[(N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(1.0 / N[(a + N[(b * N[(a + N[(b * N[(N[(N[(a * b), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.45000000000000009e40

   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. *-commutative 100.0%

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

      2. associate-/l* 96.9%

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

      3. associate--l+ 96.9%

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

      4. fma-define 96.9%

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

      5. sub-neg 96.9%

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

      6. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in b around inf 79.9%

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

      1. neg-mul-1 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in b around 0 63.9%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in x around 0 75.6%

      \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{b}{y} + 0.5 \cdot \frac{1}{y}\right) - \frac{1}{y}\right) + \frac{1}{y}\right)} \]

   if -1.45000000000000009e40 < b < 7.6000000000000007e-273

   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. Step-by-step derivation

      1. *-commutative 97.9%

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

      2. associate-/l* 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. associate--l+ 87.6%

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

      4. fma-define 87.6%

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

      5. sub-neg 87.6%

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

      6. metadata-eval 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in y around 0 75.4%

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

   6. Taylor expanded in t around 0 34.2%

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

      1. *-commutative 34.2%

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

      2. exp-diff 34.2%

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

      3. mul-1-neg 34.2%

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

      4. log-rec 34.2%

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

      5. rem-exp-log 34.9%

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

      6. associate-/l/ 34.9%

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

      7. *-commutative 34.9%

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

   8. Simplified 34.9%

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

   9. Taylor expanded in b around 0 35.0%

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

       1. +-commutative 35.0%

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

       2. mul-1-neg 35.0%

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

       3. unsub-neg 35.0%

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

       4. associate-/l* 35.0%

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

   11. Simplified 35.0%

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

   12. Taylor expanded in b around inf 44.3%

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

       1. mul-1-neg 44.3%

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

       2. +-commutative 44.3%

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

       3. unsub-neg 44.3%

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

       4. *-commutative 44.3%

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

       5. *-commutative 44.3%

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

       6. associate-*l* 45.5%

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

       7. *-commutative 45.5%

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

       8. *-commutative 45.5%

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

   14. Simplified 45.5%

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

   if 7.6000000000000007e-273 < b

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 78.7%

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

      3. associate--l+ 78.7%

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

      4. fma-define 78.7%

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

      5. sub-neg 78.7%

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

      6. metadata-eval 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around 0 83.6%

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

   6. Taylor expanded in t around 0 64.6%

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

      1. *-commutative 64.6%

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

      2. exp-diff 64.6%

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

      3. mul-1-neg 64.6%

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

      4. log-rec 64.6%

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

      5. rem-exp-log 65.3%

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

      6. associate-/l/ 65.3%

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

      7. *-commutative 65.3%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in b around 0 61.0%

      \[\leadsto \frac{\frac{1}{\color{blue}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + 0.5 \cdot a\right)\right)}} \cdot x}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{b}{y} + 0.5 \cdot \frac{1}{y}\right) + \frac{-1}{y}\right)\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a + b \cdot \left(a + b \cdot \left(\left(a \cdot b\right) \cdot 0.16666666666666666 + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.4% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{x \cdot b}{y}\right) - \frac{x}{y}\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.15e+143)
   (+ (/ x y) (* b (- (* b (* -0.16666666666666666 (/ (* x b) y))) (/ x y))))
   (if (<= b 6.5e-274)
     (* b (- (/ x (* y (* a b))) (/ x (* y a))))
     (/
      x
      (*
       a
       (+
        y
        (* b (+ y (* b (+ (* 0.16666666666666666 (* y b)) (* y 0.5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.15e+143) {
		tmp = (x / y) + (b * ((b * (-0.16666666666666666 * ((x * b) / y))) - (x / y)));
	} else if (b <= 6.5e-274) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.15d+143)) then
        tmp = (x / y) + (b * ((b * ((-0.16666666666666666d0) * ((x * b) / y))) - (x / y)))
    else if (b <= 6.5d-274) then
        tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
    else
        tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666d0 * (y * b)) + (y * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.15e+143) {
		tmp = (x / y) + (b * ((b * (-0.16666666666666666 * ((x * b) / y))) - (x / y)));
	} else if (b <= 6.5e-274) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.15e+143:
		tmp = (x / y) + (b * ((b * (-0.16666666666666666 * ((x * b) / y))) - (x / y)))
	elif b <= 6.5e-274:
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
	else:
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.15e+143)
		tmp = Float64(Float64(x / y) + Float64(b * Float64(Float64(b * Float64(-0.16666666666666666 * Float64(Float64(x * b) / y))) - Float64(x / y))));
	elseif (b <= 6.5e-274)
		tmp = Float64(b * Float64(Float64(x / Float64(y * Float64(a * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(0.16666666666666666 * Float64(y * b)) + Float64(y * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.15e+143)
		tmp = (x / y) + (b * ((b * (-0.16666666666666666 * ((x * b) / y))) - (x / y)));
	elseif (b <= 6.5e-274)
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	else
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.15e+143], N[(N[(x / y), $MachinePrecision] + N[(b * N[(N[(b * N[(-0.16666666666666666 * N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e-274], N[(b * N[(N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(N[(0.16666666666666666 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.15000000000000001e143

   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. *-commutative 100.0%

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

      2. associate-/l* 95.0%

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

      3. associate--l+ 95.0%

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

      4. fma-define 95.0%

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

      5. sub-neg 95.0%

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

      6. metadata-eval 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in b around inf 85.2%

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

      1. neg-mul-1 85.2%

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

   7. Simplified 85.2%

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

   8. Taylor expanded in b around 0 85.3%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in b around inf 85.3%

      \[\leadsto b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \color{blue}{\left(-0.16666666666666666 \cdot \frac{b \cdot x}{y}\right)}\right) + \frac{x}{y} \]

   if -2.15000000000000001e143 < b < 6.49999999999999959e-274

   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. Step-by-step derivation

      1. *-commutative 98.3%

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

      2. associate-/l* 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. associate--l+ 90.5%

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

      4. fma-define 90.5%

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

      5. sub-neg 90.5%

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

      6. metadata-eval 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in y around 0 78.2%

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

   6. Taylor expanded in t around 0 42.8%

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

      1. *-commutative 42.8%

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

      2. exp-diff 42.8%

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

      3. mul-1-neg 42.8%

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

      4. log-rec 42.8%

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

      5. rem-exp-log 43.3%

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

      6. associate-/l/ 43.3%

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

      7. *-commutative 43.3%

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

   8. Simplified 43.3%

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

   9. Taylor expanded in b around 0 33.2%

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

       1. +-commutative 33.2%

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

       2. mul-1-neg 33.2%

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

       3. unsub-neg 33.2%

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

       4. associate-/l* 33.2%

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

   11. Simplified 33.2%

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

   12. Taylor expanded in b around inf 41.3%

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

       1. mul-1-neg 41.3%

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

       2. +-commutative 41.3%

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

       3. unsub-neg 41.3%

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

       4. *-commutative 41.3%

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

       5. *-commutative 41.3%

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

       6. associate-*l* 42.2%

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

       7. *-commutative 42.2%

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

       8. *-commutative 42.2%

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

   14. Simplified 42.2%

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

   if 6.49999999999999959e-274 < b

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 78.7%

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

      3. associate--l+ 78.7%

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

      4. fma-define 78.7%

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

      5. sub-neg 78.7%

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

      6. metadata-eval 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around 0 83.6%

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

      1. associate-/l* 83.5%

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

      2. div-exp 68.3%

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

      3. exp-to-pow 69.0%

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

      4. sub-neg 69.0%

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

      5. metadata-eval 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in t around 0 66.9%

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

   9. Taylor expanded in b around 0 59.2%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot y\right) + 0.5 \cdot y\right)\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{x \cdot b}{y}\right) - \frac{x}{y}\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.9% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(\frac{x}{y} \cdot \left(-1 + b \cdot 0.5\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a + b \cdot \left(a + \left(a \cdot b\right) \cdot 0.5\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4e+119)
   (+ (/ x y) (* b (* (/ x y) (+ -1.0 (* b 0.5)))))
   (if (<= b 1.2e-273)
     (* b (- (/ x (* y (* a b))) (/ x (* y a))))
     (/ (* x (/ 1.0 (+ a (* b (+ a (* (* a b) 0.5)))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4e+119) {
		tmp = (x / y) + (b * ((x / y) * (-1.0 + (b * 0.5))));
	} else if (b <= 1.2e-273) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = (x * (1.0 / (a + (b * (a + ((a * b) * 0.5)))))) / 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 <= (-4d+119)) then
        tmp = (x / y) + (b * ((x / y) * ((-1.0d0) + (b * 0.5d0))))
    else if (b <= 1.2d-273) then
        tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
    else
        tmp = (x * (1.0d0 / (a + (b * (a + ((a * b) * 0.5d0)))))) / 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 <= -4e+119) {
		tmp = (x / y) + (b * ((x / y) * (-1.0 + (b * 0.5))));
	} else if (b <= 1.2e-273) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = (x * (1.0 / (a + (b * (a + ((a * b) * 0.5)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4e+119:
		tmp = (x / y) + (b * ((x / y) * (-1.0 + (b * 0.5))))
	elif b <= 1.2e-273:
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
	else:
		tmp = (x * (1.0 / (a + (b * (a + ((a * b) * 0.5)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4e+119)
		tmp = Float64(Float64(x / y) + Float64(b * Float64(Float64(x / y) * Float64(-1.0 + Float64(b * 0.5)))));
	elseif (b <= 1.2e-273)
		tmp = Float64(b * Float64(Float64(x / Float64(y * Float64(a * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(Float64(x * Float64(1.0 / Float64(a + Float64(b * Float64(a + Float64(Float64(a * b) * 0.5)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4e+119)
		tmp = (x / y) + (b * ((x / y) * (-1.0 + (b * 0.5))));
	elseif (b <= 1.2e-273)
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	else
		tmp = (x * (1.0 / (a + (b * (a + ((a * b) * 0.5)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4e+119], N[(N[(x / y), $MachinePrecision] + N[(b * N[(N[(x / y), $MachinePrecision] * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e-273], N[(b * N[(N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(1.0 / N[(a + N[(b * N[(a + N[(N[(a * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.99999999999999978e119

   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. *-commutative 100.0%

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

      2. associate-/l* 95.5%

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

      3. associate--l+ 95.5%

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

      4. fma-define 95.5%

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

      5. sub-neg 95.5%

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

      6. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in b around inf 82.0%

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

      1. neg-mul-1 82.0%

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

   7. Simplified 82.0%

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

   8. Taylor expanded in b around 0 78.2%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in b around 0 69.4%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + 0.5 \cdot \frac{b \cdot x}{y}\right)} + \frac{x}{y} \]
   10. Step-by-step derivation

       1. mul-1-neg 69.4%

          \[\leadsto b \cdot \left(\color{blue}{\left(-\frac{x}{y}\right)} + 0.5 \cdot \frac{b \cdot x}{y}\right) + \frac{x}{y} \]

       2. +-commutative 69.4%

          \[\leadsto b \cdot \color{blue}{\left(0.5 \cdot \frac{b \cdot x}{y} + \left(-\frac{x}{y}\right)\right)} + \frac{x}{y} \]

       3. associate-*r/ 73.8%

          \[\leadsto b \cdot \left(0.5 \cdot \color{blue}{\left(b \cdot \frac{x}{y}\right)} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       4. *-commutative 73.8%

          \[\leadsto b \cdot \left(0.5 \cdot \color{blue}{\left(\frac{x}{y} \cdot b\right)} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       5. associate-*l* 73.8%

          \[\leadsto b \cdot \left(\color{blue}{\left(0.5 \cdot \frac{x}{y}\right) \cdot b} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       6. *-commutative 73.8%

          \[\leadsto b \cdot \left(\color{blue}{b \cdot \left(0.5 \cdot \frac{x}{y}\right)} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       7. associate-*r* 73.8%

          \[\leadsto b \cdot \left(\color{blue}{\left(b \cdot 0.5\right) \cdot \frac{x}{y}} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       8. mul-1-neg 73.8%

          \[\leadsto b \cdot \left(\left(b \cdot 0.5\right) \cdot \frac{x}{y} + \color{blue}{-1 \cdot \frac{x}{y}}\right) + \frac{x}{y} \]

       9. distribute-rgt-out 73.8%

          \[\leadsto b \cdot \color{blue}{\left(\frac{x}{y} \cdot \left(b \cdot 0.5 + -1\right)\right)} + \frac{x}{y} \]

   11. Simplified 73.8%

       \[\leadsto \color{blue}{b \cdot \left(\frac{x}{y} \cdot \left(b \cdot 0.5 + -1\right)\right)} + \frac{x}{y} \]

   if -3.99999999999999978e119 < b < 1.19999999999999991e-273

   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. Step-by-step derivation

      1. *-commutative 98.3%

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

      2. associate-/l* 90.1%

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

      3. associate--l+ 90.1%

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

      4. fma-define 90.1%

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

      5. sub-neg 90.1%

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

      6. metadata-eval 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around 0 78.3%

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

   6. Taylor expanded in t around 0 42.4%

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

      1. *-commutative 42.4%

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

      2. exp-diff 42.4%

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

      3. mul-1-neg 42.4%

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

      4. log-rec 42.4%

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

      5. rem-exp-log 43.0%

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

      6. associate-/l/ 43.0%

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

      7. *-commutative 43.0%

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

   8. Simplified 43.0%

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

   9. Taylor expanded in b around 0 34.4%

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

       1. +-commutative 34.4%

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

       2. mul-1-neg 34.4%

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

       3. unsub-neg 34.4%

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

       4. associate-/l* 34.4%

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

   11. Simplified 34.4%

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

   12. Taylor expanded in b around inf 41.9%

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

       1. mul-1-neg 41.9%

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

       2. +-commutative 41.9%

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

       3. unsub-neg 41.9%

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

       4. *-commutative 41.9%

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

       5. *-commutative 41.9%

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

       6. associate-*l* 42.9%

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

       7. *-commutative 42.9%

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

       8. *-commutative 42.9%

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

   14. Simplified 42.9%

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

   if 1.19999999999999991e-273 < b

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 78.7%

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

      3. associate--l+ 78.7%

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

      4. fma-define 78.7%

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

      5. sub-neg 78.7%

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

      6. metadata-eval 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around 0 83.6%

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

   6. Taylor expanded in t around 0 64.6%

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

      1. *-commutative 64.6%

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

      2. exp-diff 64.6%

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

      3. mul-1-neg 64.6%

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

      4. log-rec 64.6%

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

      5. rem-exp-log 65.3%

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

      6. associate-/l/ 65.3%

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

      7. *-commutative 65.3%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in b around 0 53.3%

      \[\leadsto \frac{\frac{1}{\color{blue}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}} \cdot x}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(\frac{x}{y} \cdot \left(-1 + b \cdot 0.5\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a + b \cdot \left(a + \left(a \cdot b\right) \cdot 0.5\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.5% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{x \cdot b}{y}\right) - \frac{x}{y}\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a + b \cdot \left(a + \left(a \cdot b\right) \cdot 0.5\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.15e+143)
   (+ (/ x y) (* b (- (* b (* -0.16666666666666666 (/ (* x b) y))) (/ x y))))
   (if (<= b 1.4e-273)
     (* b (- (/ x (* y (* a b))) (/ x (* y a))))
     (/ (* x (/ 1.0 (+ a (* b (+ a (* (* a b) 0.5)))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.15e+143) {
		tmp = (x / y) + (b * ((b * (-0.16666666666666666 * ((x * b) / y))) - (x / y)));
	} else if (b <= 1.4e-273) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = (x * (1.0 / (a + (b * (a + ((a * b) * 0.5)))))) / 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 <= (-2.15d+143)) then
        tmp = (x / y) + (b * ((b * ((-0.16666666666666666d0) * ((x * b) / y))) - (x / y)))
    else if (b <= 1.4d-273) then
        tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
    else
        tmp = (x * (1.0d0 / (a + (b * (a + ((a * b) * 0.5d0)))))) / 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 <= -2.15e+143) {
		tmp = (x / y) + (b * ((b * (-0.16666666666666666 * ((x * b) / y))) - (x / y)));
	} else if (b <= 1.4e-273) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = (x * (1.0 / (a + (b * (a + ((a * b) * 0.5)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.15e+143:
		tmp = (x / y) + (b * ((b * (-0.16666666666666666 * ((x * b) / y))) - (x / y)))
	elif b <= 1.4e-273:
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
	else:
		tmp = (x * (1.0 / (a + (b * (a + ((a * b) * 0.5)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.15e+143)
		tmp = Float64(Float64(x / y) + Float64(b * Float64(Float64(b * Float64(-0.16666666666666666 * Float64(Float64(x * b) / y))) - Float64(x / y))));
	elseif (b <= 1.4e-273)
		tmp = Float64(b * Float64(Float64(x / Float64(y * Float64(a * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(Float64(x * Float64(1.0 / Float64(a + Float64(b * Float64(a + Float64(Float64(a * b) * 0.5)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.15e+143)
		tmp = (x / y) + (b * ((b * (-0.16666666666666666 * ((x * b) / y))) - (x / y)));
	elseif (b <= 1.4e-273)
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	else
		tmp = (x * (1.0 / (a + (b * (a + ((a * b) * 0.5)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.15e+143], N[(N[(x / y), $MachinePrecision] + N[(b * N[(N[(b * N[(-0.16666666666666666 * N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-273], N[(b * N[(N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(1.0 / N[(a + N[(b * N[(a + N[(N[(a * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.15000000000000001e143

   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. *-commutative 100.0%

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

      2. associate-/l* 95.0%

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

      3. associate--l+ 95.0%

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

      4. fma-define 95.0%

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

      5. sub-neg 95.0%

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

      6. metadata-eval 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in b around inf 85.2%

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

      1. neg-mul-1 85.2%

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

   7. Simplified 85.2%

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

   8. Taylor expanded in b around 0 85.3%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in b around inf 85.3%

      \[\leadsto b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \color{blue}{\left(-0.16666666666666666 \cdot \frac{b \cdot x}{y}\right)}\right) + \frac{x}{y} \]

   if -2.15000000000000001e143 < b < 1.39999999999999993e-273

   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. Step-by-step derivation

      1. *-commutative 98.3%

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

      2. associate-/l* 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. associate--l+ 90.5%

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

      4. fma-define 90.5%

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

      5. sub-neg 90.5%

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

      6. metadata-eval 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in y around 0 78.2%

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

   6. Taylor expanded in t around 0 42.8%

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

      1. *-commutative 42.8%

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

      2. exp-diff 42.8%

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

      3. mul-1-neg 42.8%

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

      4. log-rec 42.8%

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

      5. rem-exp-log 43.3%

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

      6. associate-/l/ 43.3%

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

      7. *-commutative 43.3%

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

   8. Simplified 43.3%

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

   9. Taylor expanded in b around 0 33.2%

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

       1. +-commutative 33.2%

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

       2. mul-1-neg 33.2%

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

       3. unsub-neg 33.2%

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

       4. associate-/l* 33.2%

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

   11. Simplified 33.2%

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

   12. Taylor expanded in b around inf 41.3%

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

       1. mul-1-neg 41.3%

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

       2. +-commutative 41.3%

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

       3. unsub-neg 41.3%

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

       4. *-commutative 41.3%

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

       5. *-commutative 41.3%

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

       6. associate-*l* 42.2%

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

       7. *-commutative 42.2%

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

       8. *-commutative 42.2%

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

   14. Simplified 42.2%

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

   if 1.39999999999999993e-273 < b

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 78.7%

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

      3. associate--l+ 78.7%

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

      4. fma-define 78.7%

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

      5. sub-neg 78.7%

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

      6. metadata-eval 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around 0 83.6%

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

   6. Taylor expanded in t around 0 64.6%

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

      1. *-commutative 64.6%

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

      2. exp-diff 64.6%

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

      3. mul-1-neg 64.6%

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

      4. log-rec 64.6%

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

      5. rem-exp-log 65.3%

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

      6. associate-/l/ 65.3%

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

      7. *-commutative 65.3%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in b around 0 53.3%

      \[\leadsto \frac{\frac{1}{\color{blue}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}} \cdot x}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{x \cdot b}{y}\right) - \frac{x}{y}\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a + b \cdot \left(a + \left(a \cdot b\right) \cdot 0.5\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.4% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(\frac{x}{y} \cdot \left(-1 + b \cdot 0.5\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.5e+117)
   (+ (/ x y) (* b (* (/ x y) (+ -1.0 (* b 0.5)))))
   (if (<= b 1.12e-271)
     (* b (- (/ x (* y (* a b))) (/ x (* y a))))
     (/ x (* a (+ y (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.5e+117) {
		tmp = (x / y) + (b * ((x / y) * (-1.0 + (b * 0.5))));
	} else if (b <= 1.12e-271) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.5d+117)) then
        tmp = (x / y) + (b * ((x / y) * ((-1.0d0) + (b * 0.5d0))))
    else if (b <= 1.12d-271) then
        tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.5e+117) {
		tmp = (x / y) + (b * ((x / y) * (-1.0 + (b * 0.5))));
	} else if (b <= 1.12e-271) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.5e+117:
		tmp = (x / y) + (b * ((x / y) * (-1.0 + (b * 0.5))))
	elif b <= 1.12e-271:
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.5e+117)
		tmp = Float64(Float64(x / y) + Float64(b * Float64(Float64(x / y) * Float64(-1.0 + Float64(b * 0.5)))));
	elseif (b <= 1.12e-271)
		tmp = Float64(b * Float64(Float64(x / Float64(y * Float64(a * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.5e+117)
		tmp = (x / y) + (b * ((x / y) * (-1.0 + (b * 0.5))));
	elseif (b <= 1.12e-271)
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.5e+117], N[(N[(x / y), $MachinePrecision] + N[(b * N[(N[(x / y), $MachinePrecision] * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.12e-271], N[(b * N[(N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.5e117

   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. *-commutative 100.0%

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

      2. associate-/l* 95.5%

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

      3. associate--l+ 95.5%

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

      4. fma-define 95.5%

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

      5. sub-neg 95.5%

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

      6. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in b around inf 82.0%

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

      1. neg-mul-1 82.0%

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

   7. Simplified 82.0%

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

   8. Taylor expanded in b around 0 78.2%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in b around 0 69.4%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + 0.5 \cdot \frac{b \cdot x}{y}\right)} + \frac{x}{y} \]
   10. Step-by-step derivation

       1. mul-1-neg 69.4%

          \[\leadsto b \cdot \left(\color{blue}{\left(-\frac{x}{y}\right)} + 0.5 \cdot \frac{b \cdot x}{y}\right) + \frac{x}{y} \]

       2. +-commutative 69.4%

          \[\leadsto b \cdot \color{blue}{\left(0.5 \cdot \frac{b \cdot x}{y} + \left(-\frac{x}{y}\right)\right)} + \frac{x}{y} \]

       3. associate-*r/ 73.8%

          \[\leadsto b \cdot \left(0.5 \cdot \color{blue}{\left(b \cdot \frac{x}{y}\right)} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       4. *-commutative 73.8%

          \[\leadsto b \cdot \left(0.5 \cdot \color{blue}{\left(\frac{x}{y} \cdot b\right)} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       5. associate-*l* 73.8%

          \[\leadsto b \cdot \left(\color{blue}{\left(0.5 \cdot \frac{x}{y}\right) \cdot b} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       6. *-commutative 73.8%

          \[\leadsto b \cdot \left(\color{blue}{b \cdot \left(0.5 \cdot \frac{x}{y}\right)} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       7. associate-*r* 73.8%

          \[\leadsto b \cdot \left(\color{blue}{\left(b \cdot 0.5\right) \cdot \frac{x}{y}} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       8. mul-1-neg 73.8%

          \[\leadsto b \cdot \left(\left(b \cdot 0.5\right) \cdot \frac{x}{y} + \color{blue}{-1 \cdot \frac{x}{y}}\right) + \frac{x}{y} \]

       9. distribute-rgt-out 73.8%

          \[\leadsto b \cdot \color{blue}{\left(\frac{x}{y} \cdot \left(b \cdot 0.5 + -1\right)\right)} + \frac{x}{y} \]

   11. Simplified 73.8%

       \[\leadsto \color{blue}{b \cdot \left(\frac{x}{y} \cdot \left(b \cdot 0.5 + -1\right)\right)} + \frac{x}{y} \]

   if -7.5e117 < b < 1.11999999999999997e-271

   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. Step-by-step derivation

      1. *-commutative 98.3%

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

      2. associate-/l* 90.1%

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

      3. associate--l+ 90.1%

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

      4. fma-define 90.1%

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

      5. sub-neg 90.1%

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

      6. metadata-eval 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around 0 78.3%

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

   6. Taylor expanded in t around 0 42.4%

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

      1. *-commutative 42.4%

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

      2. exp-diff 42.4%

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

      3. mul-1-neg 42.4%

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

      4. log-rec 42.4%

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

      5. rem-exp-log 43.0%

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

      6. associate-/l/ 43.0%

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

      7. *-commutative 43.0%

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

   8. Simplified 43.0%

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

   9. Taylor expanded in b around 0 34.4%

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

       1. +-commutative 34.4%

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

       2. mul-1-neg 34.4%

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

       3. unsub-neg 34.4%

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

       4. associate-/l* 34.4%

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

   11. Simplified 34.4%

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

   12. Taylor expanded in b around inf 41.9%

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

       1. mul-1-neg 41.9%

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

       2. +-commutative 41.9%

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

       3. unsub-neg 41.9%

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

       4. *-commutative 41.9%

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

       5. *-commutative 41.9%

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

       6. associate-*l* 42.9%

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

       7. *-commutative 42.9%

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

       8. *-commutative 42.9%

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

   14. Simplified 42.9%

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

   if 1.11999999999999997e-271 < b

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 78.7%

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

      3. associate--l+ 78.7%

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

      4. fma-define 78.7%

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

      5. sub-neg 78.7%

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

      6. metadata-eval 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around 0 83.6%

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

      1. associate-/l* 83.5%

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

      2. div-exp 68.3%

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

      3. exp-to-pow 69.0%

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

      4. sub-neg 69.0%

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

      5. metadata-eval 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in t around 0 66.9%

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

   9. Taylor expanded in b around 0 42.7%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(\frac{x}{y} \cdot \left(-1 + b \cdot 0.5\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.8% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{+116}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(\frac{x}{y} \cdot \left(-1 + b \cdot 0.5\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.12e+116)
   (+ (/ x y) (* b (* (/ x y) (+ -1.0 (* b 0.5)))))
   (if (<= b 6.5e-274)
     (* b (- (/ x (* y (* a b))) (/ x (* y a))))
     (/ x (* a (+ y (* b (+ y (* 0.5 (* y b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.12e+116) {
		tmp = (x / y) + (b * ((x / y) * (-1.0 + (b * 0.5))));
	} else if (b <= 6.5e-274) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.12d+116)) then
        tmp = (x / y) + (b * ((x / y) * ((-1.0d0) + (b * 0.5d0))))
    else if (b <= 6.5d-274) then
        tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
    else
        tmp = x / (a * (y + (b * (y + (0.5d0 * (y * b))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.12e+116) {
		tmp = (x / y) + (b * ((x / y) * (-1.0 + (b * 0.5))));
	} else if (b <= 6.5e-274) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.12e+116:
		tmp = (x / y) + (b * ((x / y) * (-1.0 + (b * 0.5))))
	elif b <= 6.5e-274:
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
	else:
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.12e+116)
		tmp = Float64(Float64(x / y) + Float64(b * Float64(Float64(x / y) * Float64(-1.0 + Float64(b * 0.5)))));
	elseif (b <= 6.5e-274)
		tmp = Float64(b * Float64(Float64(x / Float64(y * Float64(a * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(0.5 * Float64(y * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.12e+116)
		tmp = (x / y) + (b * ((x / y) * (-1.0 + (b * 0.5))));
	elseif (b <= 6.5e-274)
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	else
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.12e+116], N[(N[(x / y), $MachinePrecision] + N[(b * N[(N[(x / y), $MachinePrecision] * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e-274], N[(b * N[(N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y + N[(0.5 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.12e116

   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. *-commutative 100.0%

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

      2. associate-/l* 95.5%

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

      3. associate--l+ 95.5%

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

      4. fma-define 95.5%

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

      5. sub-neg 95.5%

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

      6. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in b around inf 82.0%

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

      1. neg-mul-1 82.0%

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

   7. Simplified 82.0%

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

   8. Taylor expanded in b around 0 78.2%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in b around 0 69.4%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + 0.5 \cdot \frac{b \cdot x}{y}\right)} + \frac{x}{y} \]
   10. Step-by-step derivation

       1. mul-1-neg 69.4%

          \[\leadsto b \cdot \left(\color{blue}{\left(-\frac{x}{y}\right)} + 0.5 \cdot \frac{b \cdot x}{y}\right) + \frac{x}{y} \]

       2. +-commutative 69.4%

          \[\leadsto b \cdot \color{blue}{\left(0.5 \cdot \frac{b \cdot x}{y} + \left(-\frac{x}{y}\right)\right)} + \frac{x}{y} \]

       3. associate-*r/ 73.8%

          \[\leadsto b \cdot \left(0.5 \cdot \color{blue}{\left(b \cdot \frac{x}{y}\right)} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       4. *-commutative 73.8%

          \[\leadsto b \cdot \left(0.5 \cdot \color{blue}{\left(\frac{x}{y} \cdot b\right)} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       5. associate-*l* 73.8%

          \[\leadsto b \cdot \left(\color{blue}{\left(0.5 \cdot \frac{x}{y}\right) \cdot b} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       6. *-commutative 73.8%

          \[\leadsto b \cdot \left(\color{blue}{b \cdot \left(0.5 \cdot \frac{x}{y}\right)} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       7. associate-*r* 73.8%

          \[\leadsto b \cdot \left(\color{blue}{\left(b \cdot 0.5\right) \cdot \frac{x}{y}} + \left(-\frac{x}{y}\right)\right) + \frac{x}{y} \]

       8. mul-1-neg 73.8%

          \[\leadsto b \cdot \left(\left(b \cdot 0.5\right) \cdot \frac{x}{y} + \color{blue}{-1 \cdot \frac{x}{y}}\right) + \frac{x}{y} \]

       9. distribute-rgt-out 73.8%

          \[\leadsto b \cdot \color{blue}{\left(\frac{x}{y} \cdot \left(b \cdot 0.5 + -1\right)\right)} + \frac{x}{y} \]

   11. Simplified 73.8%

       \[\leadsto \color{blue}{b \cdot \left(\frac{x}{y} \cdot \left(b \cdot 0.5 + -1\right)\right)} + \frac{x}{y} \]

   if -1.12e116 < b < 6.49999999999999959e-274

   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. Step-by-step derivation

      1. *-commutative 98.3%

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

      2. associate-/l* 90.1%

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

      3. associate--l+ 90.1%

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

      4. fma-define 90.1%

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

      5. sub-neg 90.1%

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

      6. metadata-eval 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around 0 78.3%

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

   6. Taylor expanded in t around 0 42.4%

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

      1. *-commutative 42.4%

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

      2. exp-diff 42.4%

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

      3. mul-1-neg 42.4%

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

      4. log-rec 42.4%

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

      5. rem-exp-log 43.0%

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

      6. associate-/l/ 43.0%

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

      7. *-commutative 43.0%

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

   8. Simplified 43.0%

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

   9. Taylor expanded in b around 0 34.4%

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

       1. +-commutative 34.4%

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

       2. mul-1-neg 34.4%

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

       3. unsub-neg 34.4%

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

       4. associate-/l* 34.4%

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

   11. Simplified 34.4%

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

   12. Taylor expanded in b around inf 41.9%

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

       1. mul-1-neg 41.9%

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

       2. +-commutative 41.9%

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

       3. unsub-neg 41.9%

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

       4. *-commutative 41.9%

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

       5. *-commutative 41.9%

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

       6. associate-*l* 42.9%

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

       7. *-commutative 42.9%

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

       8. *-commutative 42.9%

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

   14. Simplified 42.9%

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

   if 6.49999999999999959e-274 < b

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 78.7%

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

      3. associate--l+ 78.7%

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

      4. fma-define 78.7%

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

      5. sub-neg 78.7%

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

      6. metadata-eval 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around 0 83.6%

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

      1. associate-/l* 83.5%

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

      2. div-exp 68.3%

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

      3. exp-to-pow 69.0%

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

      4. sub-neg 69.0%

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

      5. metadata-eval 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in t around 0 66.9%

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

   9. Taylor expanded in b around 0 51.4%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + 0.5 \cdot \left(b \cdot y\right)\right)\right)}} \]
   10. Step-by-step derivation

       1. *-commutative 51.4%

          \[\leadsto \frac{x}{a \cdot \left(y + b \cdot \left(y + 0.5 \cdot \color{blue}{\left(y \cdot b\right)}\right)\right)} \]

   11. Simplified 51.4%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{+116}:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(\frac{x}{y} \cdot \left(-1 + b \cdot 0.5\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.0% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8.5 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 8.5e-269)
   (* b (- (/ x (* y (* a b))) (/ x (* y a))))
   (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.5e-269) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 8.5d-269) then
        tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.5e-269) {
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 8.5e-269:
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)))
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 8.5e-269)
		tmp = Float64(b * Float64(Float64(x / Float64(y * Float64(a * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 8.5e-269)
		tmp = b * ((x / (y * (a * b))) - (x / (y * a)));
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 8.5e-269], N[(b * N[(N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 8.5e-269

   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. Step-by-step derivation

      1. *-commutative 98.8%

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

      2. associate-/l* 91.7%

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

      3. associate--l+ 91.7%

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

      4. fma-define 91.7%

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

      5. sub-neg 91.7%

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

      6. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in y around 0 83.6%

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

   6. Taylor expanded in t around 0 55.2%

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

      1. *-commutative 55.2%

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

      2. exp-diff 55.2%

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

      3. mul-1-neg 55.2%

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

      4. log-rec 55.2%

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

      5. rem-exp-log 55.6%

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

      6. associate-/l/ 55.6%

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

      7. *-commutative 55.6%

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

   8. Simplified 55.6%

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

   9. Taylor expanded in b around 0 38.3%

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

       1. +-commutative 38.3%

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

       2. mul-1-neg 38.3%

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

       3. unsub-neg 38.3%

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

       4. associate-/l* 36.4%

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

   11. Simplified 36.4%

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

   12. Taylor expanded in b around inf 41.5%

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

       1. mul-1-neg 41.5%

          \[\leadsto b \cdot \left(\color{blue}{\left(-\frac{x}{a \cdot y}\right)} + \frac{x}{a \cdot \left(b \cdot y\right)}\right) \]

       2. +-commutative 41.5%

          \[\leadsto b \cdot \color{blue}{\left(\frac{x}{a \cdot \left(b \cdot y\right)} + \left(-\frac{x}{a \cdot y}\right)\right)} \]

       3. unsub-neg 41.5%

          \[\leadsto b \cdot \color{blue}{\left(\frac{x}{a \cdot \left(b \cdot y\right)} - \frac{x}{a \cdot y}\right)} \]

       4. *-commutative 41.5%

          \[\leadsto b \cdot \left(\frac{x}{\color{blue}{\left(b \cdot y\right) \cdot a}} - \frac{x}{a \cdot y}\right) \]

       5. *-commutative 41.5%

          \[\leadsto b \cdot \left(\frac{x}{\color{blue}{\left(y \cdot b\right)} \cdot a} - \frac{x}{a \cdot y}\right) \]

       6. associate-*l* 42.2%

          \[\leadsto b \cdot \left(\frac{x}{\color{blue}{y \cdot \left(b \cdot a\right)}} - \frac{x}{a \cdot y}\right) \]

       7. *-commutative 42.2%

          \[\leadsto b \cdot \left(\frac{x}{y \cdot \color{blue}{\left(a \cdot b\right)}} - \frac{x}{a \cdot y}\right) \]

       8. *-commutative 42.2%

          \[\leadsto b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{\color{blue}{y \cdot a}}\right) \]

   14. Simplified 42.2%

       \[\leadsto \color{blue}{b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)} \]

   if 8.5e-269 < b

   1. Initial program 97.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 97.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 78.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 78.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 78.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 78.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 78.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 83.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 83.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 68.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 69.0%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 69.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 69.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 69.0%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 66.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 42.7%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 8.5 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(\frac{x}{y \cdot \left(a \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 40.2% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -26000:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-200}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -26000.0)
   (/ (* x (/ b (- a))) y)
   (if (<= b 1.8e-200) (/ (* x (/ 1.0 a)) y) (/ x (* a (+ y (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -26000.0) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= 1.8e-200) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-26000.0d0)) then
        tmp = (x * (b / -a)) / y
    else if (b <= 1.8d-200) then
        tmp = (x * (1.0d0 / a)) / y
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -26000.0) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= 1.8e-200) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -26000.0:
		tmp = (x * (b / -a)) / y
	elif b <= 1.8e-200:
		tmp = (x * (1.0 / a)) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -26000.0)
		tmp = Float64(Float64(x * Float64(b / Float64(-a))) / y);
	elseif (b <= 1.8e-200)
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -26000.0)
		tmp = (x * (b / -a)) / y;
	elseif (b <= 1.8e-200)
		tmp = (x * (1.0 / a)) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -26000.0], N[(N[(x * N[(b / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.8e-200], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -26000

   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. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 95.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 95.8%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 95.8%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 95.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 95.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 95.8%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 93.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 78.1%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 78.1%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 78.1%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 78.1%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 78.1%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 78.1%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 78.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. *-commutative 78.1%

         \[\leadsto \frac{\frac{1}{\color{blue}{a \cdot e^{b}}} \cdot x}{y} \]

   8. Simplified 78.1%

      \[\leadsto \frac{\color{blue}{\frac{1}{a \cdot e^{b}} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 43.5%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 43.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 43.5%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 43.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. associate-/l* 39.5%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   11. Simplified 39.5%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   12. Taylor expanded in b around inf 43.5%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a}}}{y} \]
   13. Step-by-step derivation

       1. associate-*r/ 43.5%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a}}}{y} \]

       2. mul-1-neg 43.5%

          \[\leadsto \frac{\frac{\color{blue}{-b \cdot x}}{a}}{y} \]

       3. *-commutative 43.5%

          \[\leadsto \frac{\frac{-\color{blue}{x \cdot b}}{a}}{y} \]

       4. distribute-rgt-neg-in 43.5%

          \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(-b\right)}}{a}}{y} \]

       5. neg-mul-1 43.5%

          \[\leadsto \frac{\frac{x \cdot \color{blue}{\left(-1 \cdot b\right)}}{a}}{y} \]

       6. associate-*r/ 42.3%

          \[\leadsto \frac{\color{blue}{x \cdot \frac{-1 \cdot b}{a}}}{y} \]

       7. associate-*r/ 42.3%

          \[\leadsto \frac{x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a}\right)}}{y} \]

       8. mul-1-neg 42.3%

          \[\leadsto \frac{x \cdot \color{blue}{\left(-\frac{b}{a}\right)}}{y} \]

       9. distribute-neg-frac2 42.3%

          \[\leadsto \frac{x \cdot \color{blue}{\frac{b}{-a}}}{y} \]

   14. Simplified 42.3%

       \[\leadsto \frac{\color{blue}{x \cdot \frac{b}{-a}}}{y} \]

   if -26000 < b < 1.8000000000000001e-200

   1. Initial program 97.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 97.4%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 88.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 88.6%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.6%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 88.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 88.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 74.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 36.5%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 36.5%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 36.5%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 36.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 36.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 37.7%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 37.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. *-commutative 37.7%

         \[\leadsto \frac{\frac{1}{\color{blue}{a \cdot e^{b}}} \cdot x}{y} \]

   8. Simplified 37.7%

      \[\leadsto \frac{\color{blue}{\frac{1}{a \cdot e^{b}} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 37.7%

      \[\leadsto \frac{\color{blue}{\frac{1}{a}} \cdot x}{y} \]

   if 1.8000000000000001e-200 < b

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 97.8%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 77.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 77.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 77.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 77.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 77.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 77.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 86.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 69.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 69.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 69.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 69.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 69.8%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 69.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 42.7%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -26000:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-200}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 40.3% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -300000000000:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-199}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -300000000000.0)
   (/ (/ (* x b) a) (- y))
   (if (<= b 1.05e-199) (/ (* x (/ 1.0 a)) y) (/ x (* a (+ y (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -300000000000.0) {
		tmp = ((x * b) / a) / -y;
	} else if (b <= 1.05e-199) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-300000000000.0d0)) then
        tmp = ((x * b) / a) / -y
    else if (b <= 1.05d-199) then
        tmp = (x * (1.0d0 / a)) / y
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -300000000000.0) {
		tmp = ((x * b) / a) / -y;
	} else if (b <= 1.05e-199) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -300000000000.0:
		tmp = ((x * b) / a) / -y
	elif b <= 1.05e-199:
		tmp = (x * (1.0 / a)) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -300000000000.0)
		tmp = Float64(Float64(Float64(x * b) / a) / Float64(-y));
	elseif (b <= 1.05e-199)
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -300000000000.0)
		tmp = ((x * b) / a) / -y;
	elseif (b <= 1.05e-199)
		tmp = (x * (1.0 / a)) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -300000000000.0], N[(N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[b, 1.05e-199], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3e11

   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. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 95.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 95.8%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 95.8%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 95.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 95.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 95.8%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 93.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 78.1%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 78.1%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 78.1%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 78.1%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 78.1%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 78.1%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 78.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. *-commutative 78.1%

         \[\leadsto \frac{\frac{1}{\color{blue}{a \cdot e^{b}}} \cdot x}{y} \]

   8. Simplified 78.1%

      \[\leadsto \frac{\color{blue}{\frac{1}{a \cdot e^{b}} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 43.5%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 43.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 43.5%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 43.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. associate-/l* 39.5%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   11. Simplified 39.5%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   12. Taylor expanded in b around inf 43.5%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a}}}{y} \]

   if -3e11 < b < 1.05000000000000001e-199

   1. Initial program 97.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 97.4%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 88.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 88.6%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.6%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 88.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 88.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 74.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 36.5%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 36.5%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 36.5%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 36.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 36.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 37.7%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 37.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. *-commutative 37.7%

         \[\leadsto \frac{\frac{1}{\color{blue}{a \cdot e^{b}}} \cdot x}{y} \]

   8. Simplified 37.7%

      \[\leadsto \frac{\color{blue}{\frac{1}{a \cdot e^{b}} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 37.7%

      \[\leadsto \frac{\color{blue}{\frac{1}{a}} \cdot x}{y} \]

   if 1.05000000000000001e-199 < b

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 97.8%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 77.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 77.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 77.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 77.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 77.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 77.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 86.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 69.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 69.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 69.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 69.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 69.8%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 69.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 42.7%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -300000000000:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-199}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 40.7% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4.5 \cdot 10^{-266}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.5e-266)
   (/ (* b (- (/ x (* a b)) (/ x a))) y)
   (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.5e-266) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 4.5d-266) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.5e-266) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 4.5e-266:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4.5e-266)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 4.5e-266)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 4.5e-266], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.5000000000000003e-266

   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. Step-by-step derivation

      1. *-commutative 98.8%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 91.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 91.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 91.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 91.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 91.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 83.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 55.2%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 55.2%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 55.2%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 55.2%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 55.2%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 55.6%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 55.6%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. *-commutative 55.6%

         \[\leadsto \frac{\frac{1}{\color{blue}{a \cdot e^{b}}} \cdot x}{y} \]

   8. Simplified 55.6%

      \[\leadsto \frac{\color{blue}{\frac{1}{a \cdot e^{b}} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 38.3%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 38.3%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 38.3%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 38.3%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. associate-/l* 36.4%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   11. Simplified 36.4%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   12. Taylor expanded in b around inf 41.6%

       \[\leadsto \frac{\color{blue}{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}}{y} \]

   if 4.5000000000000003e-266 < b

   1. Initial program 97.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 97.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 78.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 78.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 78.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 78.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 78.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 83.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 83.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 68.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 69.0%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 69.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 69.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 69.0%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 66.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 42.7%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.5 \cdot 10^{-266}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 40.2% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3 \cdot 10^{-200}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3e-200)
   (/ (* x (- (/ 1.0 a) (/ b a))) y)
   (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3e-200) {
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3d-200) then
        tmp = (x * ((1.0d0 / a) - (b / a))) / y
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3e-200) {
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3e-200:
		tmp = (x * ((1.0 / a) - (b / a))) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3e-200)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) - Float64(b / a))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3e-200)
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3e-200], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.99999999999999995e-200

   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. Step-by-step derivation

      1. *-commutative 98.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 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. associate--l+ 92.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 92.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 92.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 92.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 83.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 56.0%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 56.0%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 56.0%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 56.0%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 56.0%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 56.6%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 56.6%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. *-commutative 56.6%

         \[\leadsto \frac{\frac{1}{\color{blue}{a \cdot e^{b}}} \cdot x}{y} \]

   8. Simplified 56.6%

      \[\leadsto \frac{\color{blue}{\frac{1}{a \cdot e^{b}} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 39.8%

      \[\leadsto \frac{\color{blue}{\left(-1 \cdot \frac{b}{a} + \frac{1}{a}\right)} \cdot x}{y} \]
   10. Step-by-step derivation

       1. +-commutative 39.8%

          \[\leadsto \frac{\color{blue}{\left(\frac{1}{a} + -1 \cdot \frac{b}{a}\right)} \cdot x}{y} \]

       2. mul-1-neg 39.8%

          \[\leadsto \frac{\left(\frac{1}{a} + \color{blue}{\left(-\frac{b}{a}\right)}\right) \cdot x}{y} \]

       3. unsub-neg 39.8%

          \[\leadsto \frac{\color{blue}{\left(\frac{1}{a} - \frac{b}{a}\right)} \cdot x}{y} \]

   11. Simplified 39.8%

       \[\leadsto \frac{\color{blue}{\left(\frac{1}{a} - \frac{b}{a}\right)} \cdot x}{y} \]

   if 2.99999999999999995e-200 < b

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 97.8%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 77.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 77.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 77.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 77.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 77.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 77.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 86.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 69.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 69.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 69.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 69.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 69.8%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 69.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 42.7%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3 \cdot 10^{-200}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 35.2% accurate, 24.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{b}{-a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.8e+14) (* (/ x y) (/ b (- a))) (* x (/ 1.0 (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.8e+14) {
		tmp = (x / y) * (b / -a);
	} else {
		tmp = x * (1.0 / (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 (b <= (-2.8d+14)) then
        tmp = (x / y) * (b / -a)
    else
        tmp = x * (1.0d0 / (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 (b <= -2.8e+14) {
		tmp = (x / y) * (b / -a);
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.8e+14:
		tmp = (x / y) * (b / -a)
	else:
		tmp = x * (1.0 / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.8e+14)
		tmp = Float64(Float64(x / y) * Float64(b / Float64(-a)));
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.8e+14)
		tmp = (x / y) * (b / -a);
	else
		tmp = x * (1.0 / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.8e+14], N[(N[(x / y), $MachinePrecision] * N[(b / (-a)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.8e14

   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. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 95.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 95.8%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 95.8%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 95.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 95.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 95.8%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 93.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 77.8%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 77.8%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 77.8%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 77.8%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 77.8%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 77.8%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 77.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. *-commutative 77.8%

         \[\leadsto \frac{\frac{1}{\color{blue}{a \cdot e^{b}}} \cdot x}{y} \]

   8. Simplified 77.8%

      \[\leadsto \frac{\color{blue}{\frac{1}{a \cdot e^{b}} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 44.1%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 44.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 44.1%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 44.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. associate-/l* 40.0%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   11. Simplified 40.0%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   12. Taylor expanded in b around inf 41.3%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   13. Step-by-step derivation

       1. mul-1-neg 41.3%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. times-frac 42.7%

          \[\leadsto -\color{blue}{\frac{b}{a} \cdot \frac{x}{y}} \]

   14. Simplified 42.7%

       \[\leadsto \color{blue}{-\frac{b}{a} \cdot \frac{x}{y}} \]

   if -2.8e14 < b

   1. Initial program 97.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 97.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 82.3%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 82.3%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 82.3%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 82.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 82.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 82.3%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 79.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 79.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 70.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 70.9%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 70.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 70.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 70.9%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 52.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.2%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 31.2%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 31.2%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]
   12. Step-by-step derivation

       1. div-inv 31.7%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

   13. Applied egg-rr 31.7%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{b}{-a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 35.9% accurate, 24.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.65e+15) (/ (* x (/ b (- a))) y) (* x (/ 1.0 (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.65e+15) {
		tmp = (x * (b / -a)) / y;
	} else {
		tmp = x * (1.0 / (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 (b <= (-1.65d+15)) then
        tmp = (x * (b / -a)) / y
    else
        tmp = x * (1.0d0 / (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 (b <= -1.65e+15) {
		tmp = (x * (b / -a)) / y;
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.65e+15:
		tmp = (x * (b / -a)) / y
	else:
		tmp = x * (1.0 / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.65e+15)
		tmp = Float64(Float64(x * Float64(b / Float64(-a))) / y);
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.65e+15)
		tmp = (x * (b / -a)) / y;
	else
		tmp = x * (1.0 / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.65e+15], N[(N[(x * N[(b / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.65e15

   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. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 95.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 95.8%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 95.8%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 95.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 95.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 95.8%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 93.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 77.8%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 77.8%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 77.8%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 77.8%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 77.8%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 77.8%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 77.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. *-commutative 77.8%

         \[\leadsto \frac{\frac{1}{\color{blue}{a \cdot e^{b}}} \cdot x}{y} \]

   8. Simplified 77.8%

      \[\leadsto \frac{\color{blue}{\frac{1}{a \cdot e^{b}} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 44.1%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 44.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 44.1%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 44.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. associate-/l* 40.0%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   11. Simplified 40.0%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   12. Taylor expanded in b around inf 44.1%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a}}}{y} \]
   13. Step-by-step derivation

       1. associate-*r/ 44.1%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a}}}{y} \]

       2. mul-1-neg 44.1%

          \[\leadsto \frac{\frac{\color{blue}{-b \cdot x}}{a}}{y} \]

       3. *-commutative 44.1%

          \[\leadsto \frac{\frac{-\color{blue}{x \cdot b}}{a}}{y} \]

       4. distribute-rgt-neg-in 44.1%

          \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(-b\right)}}{a}}{y} \]

       5. neg-mul-1 44.1%

          \[\leadsto \frac{\frac{x \cdot \color{blue}{\left(-1 \cdot b\right)}}{a}}{y} \]

       6. associate-*r/ 42.8%

          \[\leadsto \frac{\color{blue}{x \cdot \frac{-1 \cdot b}{a}}}{y} \]

       7. associate-*r/ 42.8%

          \[\leadsto \frac{x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a}\right)}}{y} \]

       8. mul-1-neg 42.8%

          \[\leadsto \frac{x \cdot \color{blue}{\left(-\frac{b}{a}\right)}}{y} \]

       9. distribute-neg-frac2 42.8%

          \[\leadsto \frac{x \cdot \color{blue}{\frac{b}{-a}}}{y} \]

   14. Simplified 42.8%

       \[\leadsto \frac{\color{blue}{x \cdot \frac{b}{-a}}}{y} \]

   if -1.65e15 < b

   1. Initial program 97.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 97.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 82.3%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 82.3%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 82.3%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 82.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 82.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 82.3%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 79.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 79.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 70.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 70.9%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 70.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 70.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 70.9%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 52.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.2%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 31.2%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 31.2%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]
   12. Step-by-step derivation

       1. div-inv 31.7%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

   13. Applied egg-rr 31.7%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.9% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.05 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.05e-94) (/ (/ x y) a) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.05e-94) {
		tmp = (x / y) / a;
	} else {
		tmp = 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 (b <= 2.05d-94) then
        tmp = (x / y) / a
    else
        tmp = 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 (b <= 2.05e-94) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.05e-94:
		tmp = (x / y) / a
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.05e-94)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.05e-94)
		tmp = (x / y) / a;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.05e-94], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.05e-94

   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. *-commutative 98.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 90.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.4%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.4%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 90.4%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 90.4%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.4%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 80.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 69.8%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 70.5%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 70.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 70.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 70.5%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 52.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.0%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 31.0%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 31.0%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-un-lft-identity 31.0%

          \[\leadsto \color{blue}{1 \cdot \frac{x}{y \cdot a}} \]

       2. associate-/r* 33.8%

          \[\leadsto 1 \cdot \color{blue}{\frac{\frac{x}{y}}{a}} \]

   13. Applied egg-rr 33.8%

       \[\leadsto \color{blue}{1 \cdot \frac{\frac{x}{y}}{a}} \]

   if 2.05e-94 < b

   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. *-commutative 98.7%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 77.2%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 77.2%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 77.2%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 77.2%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 77.2%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 87.0%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 88.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 67.8%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 68.0%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 68.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 68.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 68.0%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 74.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 27.6%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 27.6%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 27.6%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.05 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 31.3% accurate, 45.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{1}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* x (/ 1.0 (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * (1.0 / (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 * (1.0d0 / (y * a))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * (1.0 / (y * a));
}

Python

def code(x, y, z, t, a, b):
	return x * (1.0 / (y * a))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * Float64(1.0 / Float64(y * a)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * (1.0 / (y * a));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. *-commutative 98.3%

      \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

   2. associate-/l* 86.0%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. associate--l+ 86.0%

      \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   4. fma-define 86.0%

      \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   5. sub-neg 86.0%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   6. metadata-eval 86.0%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

3. Simplified 86.0%

   \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 83.6%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
6. Step-by-step derivation

   1. associate-/l* 83.2%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   2. div-exp 69.2%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

   3. exp-to-pow 69.6%

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

   4. sub-neg 69.6%

      \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

   5. metadata-eval 69.6%

      \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

7. Simplified 69.6%

   \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

8. Taylor expanded in t around 0 59.4%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

9. Taylor expanded in b around 0 29.9%

   \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]
10. Step-by-step derivation

    1. *-commutative 29.9%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

11. Simplified 29.9%

    \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]
12. Step-by-step derivation

    1. div-inv 30.3%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

13. Applied egg-rr 30.3%

    \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

14. Final simplification 30.3%

    \[\leadsto x \cdot \frac{1}{y \cdot a} \]
15. Add Preprocessing

Alternative 26: 31.3% 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 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. *-commutative 98.3%

      \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

   2. associate-/l* 86.0%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. associate--l+ 86.0%

      \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   4. fma-define 86.0%

      \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   5. sub-neg 86.0%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   6. metadata-eval 86.0%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

3. Simplified 86.0%

   \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 83.6%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
6. Step-by-step derivation

   1. associate-/l* 83.2%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   2. div-exp 69.2%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

   3. exp-to-pow 69.6%

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

   4. sub-neg 69.6%

      \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

   5. metadata-eval 69.6%

      \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

7. Simplified 69.6%

   \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

8. Taylor expanded in t around 0 59.4%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

9. Taylor expanded in b around 0 29.9%

   \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]
10. Step-by-step derivation

    1. *-commutative 29.9%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

11. Simplified 29.9%

    \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

12. Final simplification 29.9%

    \[\leadsto \frac{x}{y \cdot a} \]
13. Add Preprocessing

Alternative 27: 15.7% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Python

def code(x, y, z, t, a, b):
	return x / y

Julia

function code(x, y, z, t, a, b)
	return Float64(x / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. *-commutative 98.3%

      \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

   2. associate-/l* 86.0%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. associate--l+ 86.0%

      \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   4. fma-define 86.0%

      \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   5. sub-neg 86.0%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   6. metadata-eval 86.0%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

3. Simplified 86.0%

   \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 44.4%

   \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
6. Step-by-step derivation

   1. neg-mul-1 44.4%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

7. Simplified 44.4%

   \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

8. Taylor expanded in b around 0 17.1%

   \[\leadsto \color{blue}{\frac{x}{y}} \]

9. Final simplification 17.1%

   \[\leadsto \frac{x}{y} \]
10. Add Preprocessing

Developer target: 72.1% 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 2024076 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))