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

Percentage Accurate: 98.4% → 98.5%

Time: 33.8s

Alternatives: 23

Speedup: 1.0×

• 48.1% 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: 98.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. associate-/l* 98.3%

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

   2. fma-def 98.3%

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

   3. sub-neg 98.3%

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

   4. metadata-eval 98.3%

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

3. Simplified 98.3%

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

5. Final simplification 98.3%

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

Alternative 2: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+94} \lor \neg \left(t + -1 \leq 20000\right):\\ \;\;\;\;\frac{x}{\frac{y}{e^{\log a \cdot \left(t + -1\right) - b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -1e+94) (not (<= (+ t -1.0) 20000.0)))
   (/ x (/ y (exp (- (* (log a) (+ t -1.0)) b))))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+94) || !((t + -1.0) <= 20000.0)) {
		tmp = x / (y / exp(((log(a) * (t + -1.0)) - b)));
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-1d+94)) .or. (.not. ((t + (-1.0d0)) <= 20000.0d0))) then
        tmp = x / (y / exp(((log(a) * (t + (-1.0d0))) - b)))
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+94) || !((t + -1.0) <= 20000.0)) {
		tmp = x / (y / Math.exp(((Math.log(a) * (t + -1.0)) - b)));
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -1e+94) or not ((t + -1.0) <= 20000.0):
		tmp = x / (y / math.exp(((math.log(a) * (t + -1.0)) - b)))
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -1e+94) || !(Float64(t + -1.0) <= 20000.0))
		tmp = Float64(x / Float64(y / exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -1e+94) || ~(((t + -1.0) <= 20000.0)))
		tmp = x / (y / exp(((log(a) * (t + -1.0)) - b)));
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -1e+94], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 20000.0]], $MachinePrecision]], N[(x / N[(y / N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -1e94 or 2e4 < (-.f64 t 1)

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 93.1%

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

   if -1e94 < (-.f64 t 1) < 2e4

   1. Initial program 96.2%

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

   3. Taylor expanded in t around 0 95.5%

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

      1. +-commutative 95.5%

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

      2. mul-1-neg 95.5%

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

      3. unsub-neg 95.5%

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

   5. Simplified 95.5%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+94} \lor \neg \left(t + -1 \leq 20000\right):\\ \;\;\;\;\frac{x}{\frac{y}{e^{\log a \cdot \left(t + -1\right) - b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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 97.9%

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

3. Final simplification 97.9%

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

Alternative 4: 87.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+111} \lor \neg \left(y \leq 1.1 \cdot 10^{+69} \lor \neg \left(y \leq 9 \cdot 10^{+224}\right) \land y \leq 1.25 \cdot 10^{+267}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{e^{\log a \cdot \left(t + -1\right) - b}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.6e+111)
         (not (or (<= y 1.1e+69) (and (not (<= y 9e+224)) (<= y 1.25e+267)))))
   (/ (* x (/ (pow z y) a)) y)
   (/ x (/ y (exp (- (* (log a) (+ t -1.0)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.6e+111) || !((y <= 1.1e+69) || (!(y <= 9e+224) && (y <= 1.25e+267)))) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = x / (y / exp(((log(a) * (t + -1.0)) - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.6d+111)) .or. (.not. (y <= 1.1d+69) .or. (.not. (y <= 9d+224)) .and. (y <= 1.25d+267))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = x / (y / exp(((log(a) * (t + (-1.0d0))) - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.6e+111) || !((y <= 1.1e+69) || (!(y <= 9e+224) && (y <= 1.25e+267)))) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = x / (y / Math.exp(((Math.log(a) * (t + -1.0)) - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.6e+111) or not ((y <= 1.1e+69) or (not (y <= 9e+224) and (y <= 1.25e+267))):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = x / (y / math.exp(((math.log(a) * (t + -1.0)) - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.6e+111) || !((y <= 1.1e+69) || (!(y <= 9e+224) && (y <= 1.25e+267))))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(x / Float64(y / exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.6e+111) || ~(((y <= 1.1e+69) || (~((y <= 9e+224)) && (y <= 1.25e+267)))))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = x / (y / exp(((log(a) * (t + -1.0)) - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.6e+111], N[Not[Or[LessEqual[y, 1.1e+69], And[N[Not[LessEqual[y, 9e+224]], $MachinePrecision], LessEqual[y, 1.25e+267]]]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y / N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6000000000000002e111 or 1.1000000000000001e69 < y < 8.9999999999999995e224 or 1.25e267 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 94.9%

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

      1. +-commutative 94.9%

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

      2. mul-1-neg 94.9%

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

      3. unsub-neg 94.9%

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

   5. Simplified 94.9%

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

   6. Taylor expanded in b around 0 89.8%

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

      1. div-exp 89.8%

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

      2. *-commutative 89.8%

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

      3. exp-to-pow 89.8%

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

      4. rem-exp-log 89.8%

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

   8. Simplified 89.8%

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

   if -3.6000000000000002e111 < y < 1.1000000000000001e69 or 8.9999999999999995e224 < y < 1.25e267

   1. Initial program 97.0%

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

      1. associate-/l* 97.5%

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

      2. fma-def 97.5%

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

      3. sub-neg 97.5%

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

      4. metadata-eval 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around 0 94.0%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+111} \lor \neg \left(y \leq 1.1 \cdot 10^{+69} \lor \neg \left(y \leq 9 \cdot 10^{+224}\right) \land y \leq 1.25 \cdot 10^{+267}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{e^{\log a \cdot \left(t + -1\right) - b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{t}}{a}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{t_1}{e^{b}}}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+224} \lor \neg \left(y \leq 1.25 \cdot 10^{+267}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{t_1}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (pow a t) a)) (t_2 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -3.3e+111)
     t_2
     (if (<= y 5.4e+64)
       (/ x (/ y (/ t_1 (exp b))))
       (if (or (<= y 9e+224) (not (<= y 1.25e+267))) t_2 (/ x (/ y t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, t) / a;
	double t_2 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -3.3e+111) {
		tmp = t_2;
	} else if (y <= 5.4e+64) {
		tmp = x / (y / (t_1 / exp(b)));
	} else if ((y <= 9e+224) || !(y <= 1.25e+267)) {
		tmp = t_2;
	} else {
		tmp = x / (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a ** t) / a
    t_2 = (x * ((z ** y) / a)) / y
    if (y <= (-3.3d+111)) then
        tmp = t_2
    else if (y <= 5.4d+64) then
        tmp = x / (y / (t_1 / exp(b)))
    else if ((y <= 9d+224) .or. (.not. (y <= 1.25d+267))) then
        tmp = t_2
    else
        tmp = x / (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, t) / a;
	double t_2 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -3.3e+111) {
		tmp = t_2;
	} else if (y <= 5.4e+64) {
		tmp = x / (y / (t_1 / Math.exp(b)));
	} else if ((y <= 9e+224) || !(y <= 1.25e+267)) {
		tmp = t_2;
	} else {
		tmp = x / (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, t) / a
	t_2 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -3.3e+111:
		tmp = t_2
	elif y <= 5.4e+64:
		tmp = x / (y / (t_1 / math.exp(b)))
	elif (y <= 9e+224) or not (y <= 1.25e+267):
		tmp = t_2
	else:
		tmp = x / (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64((a ^ t) / a)
	t_2 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -3.3e+111)
		tmp = t_2;
	elseif (y <= 5.4e+64)
		tmp = Float64(x / Float64(y / Float64(t_1 / exp(b))));
	elseif ((y <= 9e+224) || !(y <= 1.25e+267))
		tmp = t_2;
	else
		tmp = Float64(x / Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a ^ t) / a;
	t_2 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -3.3e+111)
		tmp = t_2;
	elseif (y <= 5.4e+64)
		tmp = x / (y / (t_1 / exp(b)));
	elseif ((y <= 9e+224) || ~((y <= 1.25e+267)))
		tmp = t_2;
	else
		tmp = x / (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -3.3e+111], t$95$2, If[LessEqual[y, 5.4e+64], N[(x / N[(y / N[(t$95$1 / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 9e+224], N[Not[LessEqual[y, 1.25e+267]], $MachinePrecision]], t$95$2, N[(x / N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3000000000000001e111 or 5.3999999999999999e64 < y < 8.9999999999999995e224 or 1.25e267 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 94.9%

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

      1. +-commutative 94.9%

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

      2. mul-1-neg 94.9%

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

      3. unsub-neg 94.9%

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

   5. Simplified 94.9%

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

   6. Taylor expanded in b around 0 89.8%

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

      1. div-exp 89.8%

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

      2. *-commutative 89.8%

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

      3. exp-to-pow 89.8%

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

      4. rem-exp-log 89.8%

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

   8. Simplified 89.8%

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

   if -3.3000000000000001e111 < y < 5.3999999999999999e64

   1. Initial program 96.8%

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

      1. associate-/l* 97.3%

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

      2. fma-def 97.3%

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

      3. sub-neg 97.3%

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

      4. metadata-eval 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in y around 0 93.5%

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

      1. div-exp 86.3%

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

      2. exp-to-pow 87.1%

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

      3. sub-neg 87.1%

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

      4. metadata-eval 87.1%

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

   7. Simplified 87.1%

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

      1. unpow-prod-up 87.1%

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

      2. *-un-lft-identity 87.1%

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

      3. times-frac 87.1%

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

      4. unpow-1 87.1%

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

   9. Applied egg-rr 87.1%

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

       1. /-rgt-identity 87.1%

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

       2. associate-*r/ 87.1%

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

       3. associate-*r/ 87.1%

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

       4. *-rgt-identity 87.1%

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

   11. Simplified 87.1%

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

   if 8.9999999999999995e224 < y < 1.25e267

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. div-exp 78.6%

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

      2. exp-to-pow 78.6%

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

      3. sub-neg 78.6%

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

      4. metadata-eval 78.6%

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

   7. Simplified 78.6%

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

      1. unpow-prod-up 78.6%

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

      2. *-un-lft-identity 78.6%

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

      3. times-frac 78.6%

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

      4. unpow-1 78.6%

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

   9. Applied egg-rr 78.6%

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

       1. /-rgt-identity 78.6%

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

       2. associate-*r/ 78.6%

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

       3. associate-*r/ 78.6%

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

       4. *-rgt-identity 78.6%

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

   11. Simplified 78.6%

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

   12. Taylor expanded in b around 0 79.3%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+111}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{\frac{{a}^{t}}{a}}{e^{b}}}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+224} \lor \neg \left(y \leq 1.25 \cdot 10^{+267}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot e^{b}\\ \mathbf{if}\;b \leq -140000000:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+98}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (exp b))))
   (if (<= b -140000000.0)
     (/ x t_1)
     (if (<= b 9.8e-112)
       (/ x (/ y (/ (pow a t) a)))
       (if (<= b 3.7e+98) (/ (* x (/ (pow z y) a)) 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 <= -140000000.0) {
		tmp = x / t_1;
	} else if (b <= 9.8e-112) {
		tmp = x / (y / (pow(a, t) / a));
	} else if (b <= 3.7e+98) {
		tmp = (x * (pow(z, y) / a)) / 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 <= (-140000000.0d0)) then
        tmp = x / t_1
    else if (b <= 9.8d-112) then
        tmp = x / (y / ((a ** t) / a))
    else if (b <= 3.7d+98) then
        tmp = (x * ((z ** y) / a)) / 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 <= -140000000.0) {
		tmp = x / t_1;
	} else if (b <= 9.8e-112) {
		tmp = x / (y / (Math.pow(a, t) / a));
	} else if (b <= 3.7e+98) {
		tmp = (x * (Math.pow(z, y) / a)) / 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 <= -140000000.0:
		tmp = x / t_1
	elif b <= 9.8e-112:
		tmp = x / (y / (math.pow(a, t) / a))
	elif b <= 3.7e+98:
		tmp = (x * (math.pow(z, y) / a)) / 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 <= -140000000.0)
		tmp = Float64(x / t_1);
	elseif (b <= 9.8e-112)
		tmp = Float64(x / Float64(y / Float64((a ^ t) / a)));
	elseif (b <= 3.7e+98)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / 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 <= -140000000.0)
		tmp = x / t_1;
	elseif (b <= 9.8e-112)
		tmp = x / (y / ((a ^ t) / a));
	elseif (b <= 3.7e+98)
		tmp = (x * ((z ^ y) / a)) / 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, -140000000.0], N[(x / t$95$1), $MachinePrecision], If[LessEqual[b, 9.8e-112], N[(x / N[(y / N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e+98], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.4e8

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf 86.8%

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

      1. neg-mul-1 86.8%

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

   7. Simplified 86.8%

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

      1. expm1-log1p-u 86.8%

         \[\leadsto \frac{x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{e^{-b}}\right)\right)}} \]

      2. expm1-udef 39.0%

         \[\leadsto \frac{x}{\color{blue}{e^{\mathsf{log1p}\left(\frac{y}{e^{-b}}\right)} - 1}} \]

      3. div-inv 39.0%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(\color{blue}{y \cdot \frac{1}{e^{-b}}}\right)} - 1} \]

      4. rec-exp 39.0%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot \color{blue}{e^{-\left(-b\right)}}\right)} - 1} \]

      5. add-sqr-sqrt 39.0%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{\sqrt{-b} \cdot \sqrt{-b}}}\right)} - 1} \]

      6. sqrt-unprod 39.0%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}}}\right)} - 1} \]

      7. sqr-neg 39.0%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\sqrt{\color{blue}{b \cdot b}}}\right)} - 1} \]

      8. sqrt-prod 0.0%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{\sqrt{b} \cdot \sqrt{b}}}\right)} - 1} \]

      9. add-sqr-sqrt 3.6%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{b}}\right)} - 1} \]

      10. add-sqr-sqrt 3.6%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{\sqrt{-b} \cdot \sqrt{-b}}}\right)} - 1} \]

      11. sqrt-unprod 3.6%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}}}\right)} - 1} \]

      12. sqr-neg 3.6%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\sqrt{\color{blue}{b \cdot b}}}\right)} - 1} \]

      13. sqrt-prod 0.0%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{\sqrt{b} \cdot \sqrt{b}}}\right)} - 1} \]

      14. add-sqr-sqrt 39.0%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{b}}\right)} - 1} \]

   9. Applied egg-rr 39.0%

      \[\leadsto \frac{x}{\color{blue}{e^{\mathsf{log1p}\left(y \cdot e^{b}\right)} - 1}} \]
   10. Step-by-step derivation

       1. expm1-def 86.8%

          \[\leadsto \frac{x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot e^{b}\right)\right)}} \]

       2. expm1-log1p 86.8%

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

   11. Simplified 86.8%

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

   if -1.4e8 < b < 9.7999999999999996e-112

   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. associate-/l* 96.6%

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

      2. fma-def 96.6%

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

      3. sub-neg 96.6%

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

      4. metadata-eval 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in y around 0 77.0%

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

      1. div-exp 76.2%

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

      2. exp-to-pow 77.1%

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

      3. sub-neg 77.1%

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

      4. metadata-eval 77.1%

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

   7. Simplified 77.1%

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

      1. unpow-prod-up 77.2%

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

      2. *-un-lft-identity 77.2%

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

      3. times-frac 77.2%

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

      4. unpow-1 77.2%

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

   9. Applied egg-rr 77.2%

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

       1. /-rgt-identity 77.2%

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

       2. associate-*r/ 77.2%

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

       3. associate-*r/ 77.2%

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

       4. *-rgt-identity 77.2%

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

   11. Simplified 77.2%

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

   12. Taylor expanded in b around 0 78.8%

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

   if 9.7999999999999996e-112 < b < 3.6999999999999999e98

   1. Initial program 95.7%

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

   3. Taylor expanded in t around 0 81.9%

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

      1. +-commutative 81.9%

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

      2. mul-1-neg 81.9%

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

      3. unsub-neg 81.9%

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

   5. Simplified 81.9%

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

   6. Taylor expanded in b around 0 71.4%

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

      1. div-exp 71.4%

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

      2. *-commutative 71.4%

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

      3. exp-to-pow 71.4%

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

      4. rem-exp-log 72.1%

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

   8. Simplified 72.1%

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

   if 3.6999999999999999e98 < 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. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 92.4%

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

      1. div-exp 77.0%

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

      2. exp-to-pow 77.0%

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

      3. sub-neg 77.0%

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

      4. metadata-eval 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in t around 0 84.9%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -140000000:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+98}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot e^{b}\\ \mathbf{if}\;b \leq -190000000:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (exp b))))
   (if (<= b -190000000.0)
     (/ x t_1)
     (if (<= b 4.4e+80) (/ x (/ y (/ (pow a t) 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 <= -190000000.0) {
		tmp = x / t_1;
	} else if (b <= 4.4e+80) {
		tmp = x / (y / (pow(a, t) / 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 <= (-190000000.0d0)) then
        tmp = x / t_1
    else if (b <= 4.4d+80) then
        tmp = x / (y / ((a ** t) / 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 <= -190000000.0) {
		tmp = x / t_1;
	} else if (b <= 4.4e+80) {
		tmp = x / (y / (Math.pow(a, t) / 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 <= -190000000.0:
		tmp = x / t_1
	elif b <= 4.4e+80:
		tmp = x / (y / (math.pow(a, t) / 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 <= -190000000.0)
		tmp = Float64(x / t_1);
	elseif (b <= 4.4e+80)
		tmp = Float64(x / Float64(y / Float64((a ^ t) / 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 <= -190000000.0)
		tmp = x / t_1;
	elseif (b <= 4.4e+80)
		tmp = x / (y / ((a ^ t) / 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, -190000000.0], N[(x / t$95$1), $MachinePrecision], If[LessEqual[b, 4.4e+80], N[(x / N[(y / N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9e8

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf 86.8%

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

      1. neg-mul-1 86.8%

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

   7. Simplified 86.8%

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

      1. expm1-log1p-u 86.8%

         \[\leadsto \frac{x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{e^{-b}}\right)\right)}} \]

      2. expm1-udef 39.0%

         \[\leadsto \frac{x}{\color{blue}{e^{\mathsf{log1p}\left(\frac{y}{e^{-b}}\right)} - 1}} \]

      3. div-inv 39.0%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(\color{blue}{y \cdot \frac{1}{e^{-b}}}\right)} - 1} \]

      4. rec-exp 39.0%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot \color{blue}{e^{-\left(-b\right)}}\right)} - 1} \]

      5. add-sqr-sqrt 39.0%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{\sqrt{-b} \cdot \sqrt{-b}}}\right)} - 1} \]

      6. sqrt-unprod 39.0%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}}}\right)} - 1} \]

      7. sqr-neg 39.0%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\sqrt{\color{blue}{b \cdot b}}}\right)} - 1} \]

      8. sqrt-prod 0.0%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{\sqrt{b} \cdot \sqrt{b}}}\right)} - 1} \]

      9. add-sqr-sqrt 3.6%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{b}}\right)} - 1} \]

      10. add-sqr-sqrt 3.6%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{\sqrt{-b} \cdot \sqrt{-b}}}\right)} - 1} \]

      11. sqrt-unprod 3.6%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}}}\right)} - 1} \]

      12. sqr-neg 3.6%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\sqrt{\color{blue}{b \cdot b}}}\right)} - 1} \]

      13. sqrt-prod 0.0%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{\sqrt{b} \cdot \sqrt{b}}}\right)} - 1} \]

      14. add-sqr-sqrt 39.0%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{b}}\right)} - 1} \]

   9. Applied egg-rr 39.0%

      \[\leadsto \frac{x}{\color{blue}{e^{\mathsf{log1p}\left(y \cdot e^{b}\right)} - 1}} \]
   10. Step-by-step derivation

       1. expm1-def 86.8%

          \[\leadsto \frac{x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot e^{b}\right)\right)}} \]

       2. expm1-log1p 86.8%

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

   11. Simplified 86.8%

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

   if -1.9e8 < b < 4.40000000000000005e80

   1. Initial program 96.3%

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

      1. associate-/l* 96.9%

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

      2. fma-def 96.9%

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

      3. sub-neg 96.9%

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

      4. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around 0 73.2%

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

      1. div-exp 70.5%

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

      2. exp-to-pow 71.4%

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

      3. sub-neg 71.4%

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

      4. metadata-eval 71.4%

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

   7. Simplified 71.4%

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

      1. unpow-prod-up 71.5%

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

      2. *-un-lft-identity 71.5%

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

      3. times-frac 71.5%

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

      4. unpow-1 71.5%

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

   9. Applied egg-rr 71.5%

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

       1. /-rgt-identity 71.5%

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

       2. associate-*r/ 71.5%

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

       3. associate-*r/ 71.5%

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

       4. *-rgt-identity 71.5%

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

   11. Simplified 71.5%

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

   12. Taylor expanded in b around 0 72.9%

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

   if 4.40000000000000005e80 < 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. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 90.8%

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

      1. div-exp 76.9%

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

      2. exp-to-pow 76.9%

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

      3. sub-neg 76.9%

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

      4. metadata-eval 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in t around 0 84.0%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -190000000:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+35} \lor \neg \left(t \leq 0.0085\right):\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.1e+35) (not (<= t 0.0085)))
   (/ x (/ y (pow a t)))
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.1e+35) || !(t <= 0.0085)) {
		tmp = x / (y / pow(a, t));
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3.1d+35)) .or. (.not. (t <= 0.0085d0))) then
        tmp = x / (y / (a ** t))
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.1e+35) || !(t <= 0.0085)) {
		tmp = x / (y / Math.pow(a, t));
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.1e+35) or not (t <= 0.0085):
		tmp = x / (y / math.pow(a, t))
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.1e+35) || !(t <= 0.0085))
		tmp = Float64(x / Float64(y / (a ^ t)));
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.1e+35) || ~((t <= 0.0085)))
		tmp = x / (y / (a ^ t));
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.1e+35], N[Not[LessEqual[t, 0.0085]], $MachinePrecision]], N[(x / N[(y / N[Power[a, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.09999999999999987e35 or 0.0085000000000000006 < t

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 81.4%

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

      1. *-commutative 81.4%

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

   7. Simplified 81.4%

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

   8. Taylor expanded in y around 0 81.4%

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

   if -3.09999999999999987e35 < t < 0.0085000000000000006

   1. Initial program 95.7%

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

      1. associate-/l* 96.4%

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

      2. fma-def 96.4%

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

      3. sub-neg 96.4%

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

      4. metadata-eval 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in y around 0 71.6%

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

      1. div-exp 70.9%

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

      2. exp-to-pow 71.9%

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

      3. sub-neg 71.9%

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

      4. metadata-eval 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in t around 0 72.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+35} \lor \neg \left(t \leq 0.0085\right):\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -235000000 \lor \neg \left(b \leq 1.3 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{t}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -235000000.0) (not (<= b 1.3e+80)))
   (/ x (* y (exp b)))
   (/ x (/ y (pow a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -235000000.0) || !(b <= 1.3e+80)) {
		tmp = x / (y * exp(b));
	} else {
		tmp = x / (y / pow(a, t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-235000000.0d0)) .or. (.not. (b <= 1.3d+80))) then
        tmp = x / (y * exp(b))
    else
        tmp = x / (y / (a ** t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -235000000.0) || !(b <= 1.3e+80)) {
		tmp = x / (y * Math.exp(b));
	} else {
		tmp = x / (y / Math.pow(a, t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -235000000.0) or not (b <= 1.3e+80):
		tmp = x / (y * math.exp(b))
	else:
		tmp = x / (y / math.pow(a, t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -235000000.0) || !(b <= 1.3e+80))
		tmp = Float64(x / Float64(y * exp(b)));
	else
		tmp = Float64(x / Float64(y / (a ^ t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -235000000.0) || ~((b <= 1.3e+80)))
		tmp = x / (y * exp(b));
	else
		tmp = x / (y / (a ^ t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -235000000.0], N[Not[LessEqual[b, 1.3e+80]], $MachinePrecision]], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y / N[Power[a, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.35e8 or 1.29999999999999991e80 < 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. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf 85.7%

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

      1. neg-mul-1 85.7%

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

   7. Simplified 85.7%

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

      1. expm1-log1p-u 70.2%

         \[\leadsto \frac{x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{e^{-b}}\right)\right)}} \]

      2. expm1-udef 41.1%

         \[\leadsto \frac{x}{\color{blue}{e^{\mathsf{log1p}\left(\frac{y}{e^{-b}}\right)} - 1}} \]

      3. div-inv 41.1%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(\color{blue}{y \cdot \frac{1}{e^{-b}}}\right)} - 1} \]

      4. rec-exp 41.1%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot \color{blue}{e^{-\left(-b\right)}}\right)} - 1} \]

      5. add-sqr-sqrt 23.8%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{\sqrt{-b} \cdot \sqrt{-b}}}\right)} - 1} \]

      6. sqrt-unprod 28.8%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}}}\right)} - 1} \]

      7. sqr-neg 28.8%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\sqrt{\color{blue}{b \cdot b}}}\right)} - 1} \]

      8. sqrt-prod 5.1%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{\sqrt{b} \cdot \sqrt{b}}}\right)} - 1} \]

      9. add-sqr-sqrt 7.2%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{b}}\right)} - 1} \]

      10. add-sqr-sqrt 2.2%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{\sqrt{-b} \cdot \sqrt{-b}}}\right)} - 1} \]

      11. sqrt-unprod 19.5%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}}}\right)} - 1} \]

      12. sqr-neg 19.5%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\sqrt{\color{blue}{b \cdot b}}}\right)} - 1} \]

      13. sqrt-prod 17.3%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{\sqrt{b} \cdot \sqrt{b}}}\right)} - 1} \]

      14. add-sqr-sqrt 41.1%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{b}}\right)} - 1} \]

   9. Applied egg-rr 41.1%

      \[\leadsto \frac{x}{\color{blue}{e^{\mathsf{log1p}\left(y \cdot e^{b}\right)} - 1}} \]
   10. Step-by-step derivation

       1. expm1-def 70.2%

          \[\leadsto \frac{x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot e^{b}\right)\right)}} \]

       2. expm1-log1p 85.7%

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

   11. Simplified 85.7%

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

   if -2.35e8 < b < 1.29999999999999991e80

   1. Initial program 96.3%

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

      1. associate-/l* 96.9%

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

      2. fma-def 96.9%

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

      3. sub-neg 96.9%

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

      4. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in t around inf 58.0%

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

      1. *-commutative 58.0%

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

   7. Simplified 58.0%

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

   8. Taylor expanded in y around 0 58.0%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -235000000 \lor \neg \left(b \leq 1.3 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{t}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -16500000000000 \lor \neg \left(b \leq 3.1\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -16500000000000.0) (not (<= b 3.1)))
   (/ x (* y (exp b)))
   (* x (/ 1.0 (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -16500000000000.0) || !(b <= 3.1)) {
		tmp = x / (y * exp(b));
	} 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 <= (-16500000000000.0d0)) .or. (.not. (b <= 3.1d0))) then
        tmp = x / (y * exp(b))
    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 <= -16500000000000.0) || !(b <= 3.1)) {
		tmp = x / (y * Math.exp(b));
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -16500000000000.0) or not (b <= 3.1):
		tmp = x / (y * math.exp(b))
	else:
		tmp = x * (1.0 / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -16500000000000.0) || !(b <= 3.1))
		tmp = Float64(x / Float64(y * exp(b)));
	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 <= -16500000000000.0) || ~((b <= 3.1)))
		tmp = x / (y * exp(b));
	else
		tmp = x * (1.0 / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -16500000000000.0], N[Not[LessEqual[b, 3.1]], $MachinePrecision]], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.65e13 or 3.10000000000000009 < b

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

      2. fma-def 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around inf 80.8%

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

      1. neg-mul-1 80.8%

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

   7. Simplified 80.8%

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

      1. expm1-log1p-u 66.3%

         \[\leadsto \frac{x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{e^{-b}}\right)\right)}} \]

      2. expm1-udef 39.2%

         \[\leadsto \frac{x}{\color{blue}{e^{\mathsf{log1p}\left(\frac{y}{e^{-b}}\right)} - 1}} \]

      3. div-inv 39.2%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(\color{blue}{y \cdot \frac{1}{e^{-b}}}\right)} - 1} \]

      4. rec-exp 39.2%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot \color{blue}{e^{-\left(-b\right)}}\right)} - 1} \]

      5. add-sqr-sqrt 21.3%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{\sqrt{-b} \cdot \sqrt{-b}}}\right)} - 1} \]

      6. sqrt-unprod 28.6%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}}}\right)} - 1} \]

      7. sqr-neg 28.6%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\sqrt{\color{blue}{b \cdot b}}}\right)} - 1} \]

      8. sqrt-prod 7.3%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{\sqrt{b} \cdot \sqrt{b}}}\right)} - 1} \]

      9. add-sqr-sqrt 8.5%

         \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{-\color{blue}{b}}\right)} - 1} \]

      10. add-sqr-sqrt 1.2%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{\sqrt{-b} \cdot \sqrt{-b}}}\right)} - 1} \]

      11. sqrt-unprod 19.1%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}}}\right)} - 1} \]

      12. sqr-neg 19.1%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\sqrt{\color{blue}{b \cdot b}}}\right)} - 1} \]

      13. sqrt-prod 17.9%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{\sqrt{b} \cdot \sqrt{b}}}\right)} - 1} \]

      14. add-sqr-sqrt 39.2%

          \[\leadsto \frac{x}{e^{\mathsf{log1p}\left(y \cdot e^{\color{blue}{b}}\right)} - 1} \]

   9. Applied egg-rr 39.2%

      \[\leadsto \frac{x}{\color{blue}{e^{\mathsf{log1p}\left(y \cdot e^{b}\right)} - 1}} \]
   10. Step-by-step derivation

       1. expm1-def 66.3%

          \[\leadsto \frac{x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot e^{b}\right)\right)}} \]

       2. expm1-log1p 80.8%

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

   11. Simplified 80.8%

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

   if -1.65e13 < b < 3.10000000000000009

   1. Initial program 96.8%

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

      1. associate-/l* 96.9%

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

      2. fma-def 96.9%

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

      3. sub-neg 96.9%

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

      4. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around 0 74.6%

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

      1. div-exp 73.8%

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

      2. exp-to-pow 74.8%

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

      3. sub-neg 74.8%

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

      4. metadata-eval 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in t around 0 41.3%

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

   9. Taylor expanded in b around 0 42.7%

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

       1. *-commutative 42.7%

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

   11. Simplified 42.7%

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

       1. div-inv 42.7%

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

   13. Applied egg-rr 42.7%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -16500000000000 \lor \neg \left(b \leq 3.1\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.6% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+184}:\\ \;\;\;\;\frac{x}{y} - \frac{x \cdot b}{y}\\ \mathbf{elif}\;b \leq -1 \cdot 10^{+118}:\\ \;\;\;\;\frac{-b}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -130000000:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(b + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.8e+184)
   (- (/ x y) (/ (* x b) y))
   (if (<= b -1e+118)
     (/ (- b) (* a (/ y x)))
     (if (<= b -130000000.0)
       (* (/ x y) (/ (- b) a))
       (if (<= b -2.9e-128)
         (/ (/ x a) y)
         (if (<= b 4.2e+105) (* x (/ 1.0 (* y a))) (/ x (* y (+ b 1.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e+184) {
		tmp = (x / y) - ((x * b) / y);
	} else if (b <= -1e+118) {
		tmp = -b / (a * (y / x));
	} else if (b <= -130000000.0) {
		tmp = (x / y) * (-b / a);
	} else if (b <= -2.9e-128) {
		tmp = (x / a) / y;
	} else if (b <= 4.2e+105) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * (b + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.8d+184)) then
        tmp = (x / y) - ((x * b) / y)
    else if (b <= (-1d+118)) then
        tmp = -b / (a * (y / x))
    else if (b <= (-130000000.0d0)) then
        tmp = (x / y) * (-b / a)
    else if (b <= (-2.9d-128)) then
        tmp = (x / a) / y
    else if (b <= 4.2d+105) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = x / (y * (b + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e+184) {
		tmp = (x / y) - ((x * b) / y);
	} else if (b <= -1e+118) {
		tmp = -b / (a * (y / x));
	} else if (b <= -130000000.0) {
		tmp = (x / y) * (-b / a);
	} else if (b <= -2.9e-128) {
		tmp = (x / a) / y;
	} else if (b <= 4.2e+105) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * (b + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.8e+184:
		tmp = (x / y) - ((x * b) / y)
	elif b <= -1e+118:
		tmp = -b / (a * (y / x))
	elif b <= -130000000.0:
		tmp = (x / y) * (-b / a)
	elif b <= -2.9e-128:
		tmp = (x / a) / y
	elif b <= 4.2e+105:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (y * (b + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.8e+184)
		tmp = Float64(Float64(x / y) - Float64(Float64(x * b) / y));
	elseif (b <= -1e+118)
		tmp = Float64(Float64(-b) / Float64(a * Float64(y / x)));
	elseif (b <= -130000000.0)
		tmp = Float64(Float64(x / y) * Float64(Float64(-b) / a));
	elseif (b <= -2.9e-128)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 4.2e+105)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(x / Float64(y * Float64(b + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.8e+184)
		tmp = (x / y) - ((x * b) / y);
	elseif (b <= -1e+118)
		tmp = -b / (a * (y / x));
	elseif (b <= -130000000.0)
		tmp = (x / y) * (-b / a);
	elseif (b <= -2.9e-128)
		tmp = (x / a) / y;
	elseif (b <= 4.2e+105)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (y * (b + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.8e+184], N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1e+118], N[((-b) / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -130000000.0], N[(N[(x / y), $MachinePrecision] * N[((-b) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.9e-128], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.2e+105], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.79999999999999993e184

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf 96.1%

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

      1. neg-mul-1 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in b around 0 0.8%

      \[\leadsto \frac{x}{\color{blue}{y + \left(-1 \cdot \left({b}^{2} \cdot \left(-1 \cdot y + 0.5 \cdot y\right)\right) + b \cdot y\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 0.8%

         \[\leadsto \frac{x}{y + \color{blue}{\left(b \cdot y + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot y + 0.5 \cdot y\right)\right)\right)}} \]

      2. mul-1-neg 0.8%

         \[\leadsto \frac{x}{y + \left(b \cdot y + \color{blue}{\left(-{b}^{2} \cdot \left(-1 \cdot y + 0.5 \cdot y\right)\right)}\right)} \]

      3. unsub-neg 0.8%

         \[\leadsto \frac{x}{y + \color{blue}{\left(b \cdot y - {b}^{2} \cdot \left(-1 \cdot y + 0.5 \cdot y\right)\right)}} \]

      4. *-commutative 0.8%

         \[\leadsto \frac{x}{y + \left(\color{blue}{y \cdot b} - {b}^{2} \cdot \left(-1 \cdot y + 0.5 \cdot y\right)\right)} \]

      5. distribute-rgt-out 0.8%

         \[\leadsto \frac{x}{y + \left(y \cdot b - {b}^{2} \cdot \color{blue}{\left(y \cdot \left(-1 + 0.5\right)\right)}\right)} \]

      6. metadata-eval 0.8%

         \[\leadsto \frac{x}{y + \left(y \cdot b - {b}^{2} \cdot \left(y \cdot \color{blue}{-0.5}\right)\right)} \]

   10. Simplified 0.8%

       \[\leadsto \frac{x}{\color{blue}{y + \left(y \cdot b - {b}^{2} \cdot \left(y \cdot -0.5\right)\right)}} \]

   11. Taylor expanded in b around 0 61.3%

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

       1. +-commutative 61.3%

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

       2. mul-1-neg 61.3%

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

       3. unsub-neg 61.3%

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

       4. *-commutative 61.3%

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

   13. Simplified 61.3%

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

   if -4.79999999999999993e184 < b < -9.99999999999999967e117

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 86.6%

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

      1. div-exp 77.5%

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

      2. exp-to-pow 77.5%

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

      3. sub-neg 77.5%

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

      4. metadata-eval 77.5%

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

   7. Simplified 77.5%

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

   8. Taylor expanded in t around 0 86.6%

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

   9. Taylor expanded in b around 0 43.6%

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

       1. +-commutative 43.6%

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

       2. mul-1-neg 43.6%

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

       3. unsub-neg 43.6%

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

       4. associate-/r* 43.6%

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

       5. associate-/r* 43.6%

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

       6. *-commutative 43.6%

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

   11. Simplified 43.6%

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

   12. Taylor expanded in b around inf 43.6%

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

       1. mul-1-neg 43.6%

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

       2. associate-/l* 39.6%

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

       3. *-commutative 39.6%

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

       4. associate-/l* 35.4%

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

       5. associate-/r/ 48.0%

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

   14. Simplified 48.0%

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

   if -9.99999999999999967e117 < b < -1.3e8

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 85.2%

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

      1. div-exp 70.2%

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

      2. exp-to-pow 70.2%

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

      3. sub-neg 70.2%

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

      4. metadata-eval 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in t around 0 75.4%

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

   9. Taylor expanded in b around 0 32.5%

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

       1. +-commutative 32.5%

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

       2. mul-1-neg 32.5%

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

       3. unsub-neg 32.5%

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

       4. associate-/r* 32.5%

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

       5. associate-/r* 37.5%

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

       6. *-commutative 37.5%

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

   11. Simplified 37.5%

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

   12. Taylor expanded in b around inf 32.5%

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

       1. mul-1-neg 32.5%

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

       2. *-commutative 32.5%

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

       3. *-commutative 32.5%

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

       4. times-frac 46.6%

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

       5. distribute-rgt-neg-in 46.6%

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

       6. *-rgt-identity 46.6%

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

       7. associate-*r/ 46.6%

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

       8. rem-exp-log 46.6%

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

       9. log-rec 46.6%

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

       10. distribute-lft-neg-in 46.6%

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

       11. log-rec 46.6%

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

       12. rem-exp-log 46.6%

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

       13. associate-*r/ 46.6%

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

       14. *-rgt-identity 46.6%

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

   14. Simplified 46.6%

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

   if -1.3e8 < b < -2.9e-128

   1. Initial program 99.3%

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

      1. associate-/l* 93.4%

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

      2. fma-def 93.4%

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

      3. sub-neg 93.4%

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

      4. metadata-eval 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in y around 0 69.8%

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

      1. div-exp 66.4%

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

      2. exp-to-pow 66.5%

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

      3. sub-neg 66.5%

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

      4. metadata-eval 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in t around 0 36.7%

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

   9. Taylor expanded in b around 0 43.5%

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

       1. associate-/r* 55.5%

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

   11. Simplified 55.5%

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

   if -2.9e-128 < b < 4.2000000000000002e105

   1. Initial program 95.8%

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

      1. associate-/l* 97.9%

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

      2. fma-def 97.9%

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

      3. sub-neg 97.9%

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

      4. metadata-eval 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in y around 0 74.7%

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

      1. div-exp 72.4%

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

      2. exp-to-pow 73.4%

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

      3. sub-neg 73.4%

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

      4. metadata-eval 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in t around 0 43.2%

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

   9. Taylor expanded in b around 0 38.5%

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

       1. *-commutative 38.5%

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

   11. Simplified 38.5%

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

       1. div-inv 38.5%

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

   13. Applied egg-rr 38.5%

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

   if 4.2000000000000002e105 < 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. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf 83.6%

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

      1. neg-mul-1 83.6%

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

   7. Simplified 83.6%

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

   8. Taylor expanded in b around 0 39.7%

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

      1. distribute-rgt1-in 39.7%

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

   10. Simplified 39.7%

       \[\leadsto \frac{x}{\color{blue}{\left(b + 1\right) \cdot y}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+184}:\\ \;\;\;\;\frac{x}{y} - \frac{x \cdot b}{y}\\ \mathbf{elif}\;b \leq -1 \cdot 10^{+118}:\\ \;\;\;\;\frac{-b}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -130000000:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(b + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.9% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+183}:\\ \;\;\;\;\frac{x}{y} - \frac{x \cdot b}{y}\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{+117}:\\ \;\;\;\;\frac{-b}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -150000000:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{elif}\;b \leq -2.45 \cdot 10^{-129}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.7e+183)
   (- (/ x y) (/ (* x b) y))
   (if (<= b -1.95e+117)
     (/ (- b) (* a (/ y x)))
     (if (<= b -150000000.0)
       (* (/ x y) (/ (- b) a))
       (if (<= b -2.45e-129) (/ (/ 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 <= -2.7e+183) {
		tmp = (x / y) - ((x * b) / y);
	} else if (b <= -1.95e+117) {
		tmp = -b / (a * (y / x));
	} else if (b <= -150000000.0) {
		tmp = (x / y) * (-b / a);
	} else if (b <= -2.45e-129) {
		tmp = (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 <= (-2.7d+183)) then
        tmp = (x / y) - ((x * b) / y)
    else if (b <= (-1.95d+117)) then
        tmp = -b / (a * (y / x))
    else if (b <= (-150000000.0d0)) then
        tmp = (x / y) * (-b / a)
    else if (b <= (-2.45d-129)) then
        tmp = (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 <= -2.7e+183) {
		tmp = (x / y) - ((x * b) / y);
	} else if (b <= -1.95e+117) {
		tmp = -b / (a * (y / x));
	} else if (b <= -150000000.0) {
		tmp = (x / y) * (-b / a);
	} else if (b <= -2.45e-129) {
		tmp = (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 <= -2.7e+183:
		tmp = (x / y) - ((x * b) / y)
	elif b <= -1.95e+117:
		tmp = -b / (a * (y / x))
	elif b <= -150000000.0:
		tmp = (x / y) * (-b / a)
	elif b <= -2.45e-129:
		tmp = (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 <= -2.7e+183)
		tmp = Float64(Float64(x / y) - Float64(Float64(x * b) / y));
	elseif (b <= -1.95e+117)
		tmp = Float64(Float64(-b) / Float64(a * Float64(y / x)));
	elseif (b <= -150000000.0)
		tmp = Float64(Float64(x / y) * Float64(Float64(-b) / a));
	elseif (b <= -2.45e-129)
		tmp = Float64(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 <= -2.7e+183)
		tmp = (x / y) - ((x * b) / y);
	elseif (b <= -1.95e+117)
		tmp = -b / (a * (y / x));
	elseif (b <= -150000000.0)
		tmp = (x / y) * (-b / a);
	elseif (b <= -2.45e-129)
		tmp = (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, -2.7e+183], N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.95e+117], N[((-b) / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -150000000.0], N[(N[(x / y), $MachinePrecision] * N[((-b) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.45e-129], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.69999999999999982e183

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf 96.1%

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

      1. neg-mul-1 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in b around 0 0.8%

      \[\leadsto \frac{x}{\color{blue}{y + \left(-1 \cdot \left({b}^{2} \cdot \left(-1 \cdot y + 0.5 \cdot y\right)\right) + b \cdot y\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 0.8%

         \[\leadsto \frac{x}{y + \color{blue}{\left(b \cdot y + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot y + 0.5 \cdot y\right)\right)\right)}} \]

      2. mul-1-neg 0.8%

         \[\leadsto \frac{x}{y + \left(b \cdot y + \color{blue}{\left(-{b}^{2} \cdot \left(-1 \cdot y + 0.5 \cdot y\right)\right)}\right)} \]

      3. unsub-neg 0.8%

         \[\leadsto \frac{x}{y + \color{blue}{\left(b \cdot y - {b}^{2} \cdot \left(-1 \cdot y + 0.5 \cdot y\right)\right)}} \]

      4. *-commutative 0.8%

         \[\leadsto \frac{x}{y + \left(\color{blue}{y \cdot b} - {b}^{2} \cdot \left(-1 \cdot y + 0.5 \cdot y\right)\right)} \]

      5. distribute-rgt-out 0.8%

         \[\leadsto \frac{x}{y + \left(y \cdot b - {b}^{2} \cdot \color{blue}{\left(y \cdot \left(-1 + 0.5\right)\right)}\right)} \]

      6. metadata-eval 0.8%

         \[\leadsto \frac{x}{y + \left(y \cdot b - {b}^{2} \cdot \left(y \cdot \color{blue}{-0.5}\right)\right)} \]

   10. Simplified 0.8%

       \[\leadsto \frac{x}{\color{blue}{y + \left(y \cdot b - {b}^{2} \cdot \left(y \cdot -0.5\right)\right)}} \]

   11. Taylor expanded in b around 0 61.3%

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

       1. +-commutative 61.3%

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

       2. mul-1-neg 61.3%

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

       3. unsub-neg 61.3%

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

       4. *-commutative 61.3%

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

   13. Simplified 61.3%

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

   if -2.69999999999999982e183 < b < -1.94999999999999995e117

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 86.6%

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

      1. div-exp 77.5%

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

      2. exp-to-pow 77.5%

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

      3. sub-neg 77.5%

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

      4. metadata-eval 77.5%

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

   7. Simplified 77.5%

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

   8. Taylor expanded in t around 0 86.6%

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

   9. Taylor expanded in b around 0 43.6%

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

       1. +-commutative 43.6%

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

       2. mul-1-neg 43.6%

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

       3. unsub-neg 43.6%

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

       4. associate-/r* 43.6%

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

       5. associate-/r* 43.6%

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

       6. *-commutative 43.6%

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

   11. Simplified 43.6%

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

   12. Taylor expanded in b around inf 43.6%

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

       1. mul-1-neg 43.6%

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

       2. associate-/l* 39.6%

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

       3. *-commutative 39.6%

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

       4. associate-/l* 35.4%

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

       5. associate-/r/ 48.0%

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

   14. Simplified 48.0%

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

   if -1.94999999999999995e117 < b < -1.5e8

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 85.2%

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

      1. div-exp 70.2%

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

      2. exp-to-pow 70.2%

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

      3. sub-neg 70.2%

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

      4. metadata-eval 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in t around 0 75.4%

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

   9. Taylor expanded in b around 0 32.5%

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

       1. +-commutative 32.5%

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

       2. mul-1-neg 32.5%

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

       3. unsub-neg 32.5%

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

       4. associate-/r* 32.5%

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

       5. associate-/r* 37.5%

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

       6. *-commutative 37.5%

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

   11. Simplified 37.5%

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

   12. Taylor expanded in b around inf 32.5%

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

       1. mul-1-neg 32.5%

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

       2. *-commutative 32.5%

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

       3. *-commutative 32.5%

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

       4. times-frac 46.6%

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

       5. distribute-rgt-neg-in 46.6%

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

       6. *-rgt-identity 46.6%

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

       7. associate-*r/ 46.6%

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

       8. rem-exp-log 46.6%

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

       9. log-rec 46.6%

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

       10. distribute-lft-neg-in 46.6%

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

       11. log-rec 46.6%

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

       12. rem-exp-log 46.6%

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

       13. associate-*r/ 46.6%

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

       14. *-rgt-identity 46.6%

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

   14. Simplified 46.6%

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

   if -1.5e8 < b < -2.45000000000000001e-129

   1. Initial program 99.3%

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

      1. associate-/l* 93.4%

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

      2. fma-def 93.4%

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

      3. sub-neg 93.4%

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

      4. metadata-eval 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in y around 0 69.8%

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

      1. div-exp 66.4%

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

      2. exp-to-pow 66.5%

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

      3. sub-neg 66.5%

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

      4. metadata-eval 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in t around 0 36.7%

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

   9. Taylor expanded in b around 0 43.5%

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

       1. associate-/r* 55.5%

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

   11. Simplified 55.5%

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

   if -2.45000000000000001e-129 < b

   1. Initial program 96.8%

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

      1. associate-/l* 98.4%

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

      2. fma-def 98.4%

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

      3. sub-neg 98.4%

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

      4. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in y around 0 78.5%

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

      1. div-exp 73.0%

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

      2. exp-to-pow 73.8%

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

      3. sub-neg 73.8%

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

      4. metadata-eval 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in t around 0 52.3%

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

   9. Taylor expanded in b around 0 39.7%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+183}:\\ \;\;\;\;\frac{x}{y} - \frac{x \cdot b}{y}\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{+117}:\\ \;\;\;\;\frac{-b}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -150000000:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{elif}\;b \leq -2.45 \cdot 10^{-129}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.6% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{if}\;b \leq -190000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(b + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ x y) (/ (- b) a))))
   (if (<= b -190000000.0)
     t_1
     (if (<= b -2.6e-87)
       (/ (/ x a) y)
       (if (<= b -9e-128)
         t_1
         (if (<= b 7.2e+104) (* x (/ 1.0 (* y a))) (/ x (* y (+ b 1.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) * (-b / a);
	double tmp;
	if (b <= -190000000.0) {
		tmp = t_1;
	} else if (b <= -2.6e-87) {
		tmp = (x / a) / y;
	} else if (b <= -9e-128) {
		tmp = t_1;
	} else if (b <= 7.2e+104) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * (b + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) * (-b / a)
    if (b <= (-190000000.0d0)) then
        tmp = t_1
    else if (b <= (-2.6d-87)) then
        tmp = (x / a) / y
    else if (b <= (-9d-128)) then
        tmp = t_1
    else if (b <= 7.2d+104) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = x / (y * (b + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) * (-b / a);
	double tmp;
	if (b <= -190000000.0) {
		tmp = t_1;
	} else if (b <= -2.6e-87) {
		tmp = (x / a) / y;
	} else if (b <= -9e-128) {
		tmp = t_1;
	} else if (b <= 7.2e+104) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * (b + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / y) * (-b / a)
	tmp = 0
	if b <= -190000000.0:
		tmp = t_1
	elif b <= -2.6e-87:
		tmp = (x / a) / y
	elif b <= -9e-128:
		tmp = t_1
	elif b <= 7.2e+104:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (y * (b + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / y) * Float64(Float64(-b) / a))
	tmp = 0.0
	if (b <= -190000000.0)
		tmp = t_1;
	elseif (b <= -2.6e-87)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= -9e-128)
		tmp = t_1;
	elseif (b <= 7.2e+104)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(x / Float64(y * Float64(b + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / y) * (-b / a);
	tmp = 0.0;
	if (b <= -190000000.0)
		tmp = t_1;
	elseif (b <= -2.6e-87)
		tmp = (x / a) / y;
	elseif (b <= -9e-128)
		tmp = t_1;
	elseif (b <= 7.2e+104)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (y * (b + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[((-b) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -190000000.0], t$95$1, If[LessEqual[b, -2.6e-87], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -9e-128], t$95$1, If[LessEqual[b, 7.2e+104], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.9e8 or -2.60000000000000002e-87 < b < -8.9999999999999998e-128

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 85.4%

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

      1. div-exp 70.6%

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

      2. exp-to-pow 70.6%

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

      3. sub-neg 70.6%

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

      4. metadata-eval 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in t around 0 80.2%

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

   9. Taylor expanded in b around 0 39.0%

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

       1. +-commutative 39.0%

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

       2. mul-1-neg 39.0%

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

       3. unsub-neg 39.0%

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

       4. associate-/r* 39.0%

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

       5. associate-/r* 48.0%

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

       6. *-commutative 48.0%

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

   11. Simplified 48.0%

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

   12. Taylor expanded in b around inf 40.3%

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

       1. mul-1-neg 40.3%

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

       2. *-commutative 40.3%

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

       3. *-commutative 40.3%

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

       4. times-frac 45.1%

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

       5. distribute-rgt-neg-in 45.1%

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

       6. *-rgt-identity 45.1%

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

       7. associate-*r/ 45.1%

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

       8. rem-exp-log 45.1%

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

       9. log-rec 45.1%

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

       10. distribute-lft-neg-in 45.1%

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

       11. log-rec 45.1%

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

       12. rem-exp-log 45.1%

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

       13. associate-*r/ 45.1%

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

       14. *-rgt-identity 45.1%

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

   14. Simplified 45.1%

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

   if -1.9e8 < b < -2.60000000000000002e-87

   1. Initial program 99.5%

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

      1. associate-/l* 95.5%

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

      2. fma-def 95.5%

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

      3. sub-neg 95.5%

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

      4. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around 0 86.1%

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

      1. div-exp 81.3%

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

      2. exp-to-pow 81.5%

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

      3. sub-neg 81.5%

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

      4. metadata-eval 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in t around 0 44.6%

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

   9. Taylor expanded in b around 0 54.0%

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

       1. associate-/r* 66.1%

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

   11. Simplified 66.1%

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

   if -8.9999999999999998e-128 < b < 7.20000000000000001e104

   1. Initial program 95.8%

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

      1. associate-/l* 97.2%

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

      2. fma-def 97.2%

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

      3. sub-neg 97.2%

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

      4. metadata-eval 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in y around 0 74.1%

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

      1. div-exp 71.8%

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

      2. exp-to-pow 72.8%

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

      3. sub-neg 72.8%

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

      4. metadata-eval 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in t around 0 42.8%

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

   9. Taylor expanded in b around 0 38.2%

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

       1. *-commutative 38.2%

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

   11. Simplified 38.2%

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

       1. div-inv 38.3%

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

   13. Applied egg-rr 38.3%

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

   if 7.20000000000000001e104 < 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. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf 83.6%

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

      1. neg-mul-1 83.6%

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

   7. Simplified 83.6%

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

   8. Taylor expanded in b around 0 39.7%

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

      1. distribute-rgt1-in 39.7%

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

   10. Simplified 39.7%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -190000000:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-128}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(b + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 40.0% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{-129}:\\ \;\;\;\;\frac{\frac{x}{a}}{y} - \frac{\frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e-129)
   (- (/ (/ x a) y) (/ (/ (* x 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 <= -3.5e-129) {
		tmp = ((x / a) / y) - (((x * 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 <= (-3.5d-129)) then
        tmp = ((x / a) / y) - (((x * 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 <= -3.5e-129) {
		tmp = ((x / a) / y) - (((x * 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 <= -3.5e-129:
		tmp = ((x / a) / y) - (((x * 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 <= -3.5e-129)
		tmp = Float64(Float64(Float64(x / a) / y) - Float64(Float64(Float64(x * 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 <= -3.5e-129)
		tmp = ((x / a) / y) - (((x * 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, -3.5e-129], N[(N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision] - N[(N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision] / y), $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 < -3.4999999999999997e-129

   1. Initial program 99.8%

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

      1. associate-/l* 98.0%

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

      2. fma-def 98.0%

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

      3. sub-neg 98.0%

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

      4. metadata-eval 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in y around 0 84.7%

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

      1. div-exp 72.2%

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

      2. exp-to-pow 72.3%

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

      3. sub-neg 72.3%

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

      4. metadata-eval 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in t around 0 71.6%

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

   9. Taylor expanded in b around 0 41.8%

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

       1. +-commutative 41.8%

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

       2. mul-1-neg 41.8%

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

       3. unsub-neg 41.8%

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

       4. associate-/r* 42.6%

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

       5. associate-/r* 52.1%

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

       6. *-commutative 52.1%

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

   11. Simplified 52.1%

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

   if -3.4999999999999997e-129 < b

   1. Initial program 96.8%

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

      1. associate-/l* 98.4%

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

      2. fma-def 98.4%

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

      3. sub-neg 98.4%

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

      4. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in y around 0 78.5%

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

      1. div-exp 73.0%

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

      2. exp-to-pow 73.8%

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

      3. sub-neg 73.8%

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

      4. metadata-eval 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in t around 0 52.3%

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

   9. Taylor expanded in b around 0 39.7%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{-129}:\\ \;\;\;\;\frac{\frac{x}{a}}{y} - \frac{\frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.2% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{-128}:\\ \;\;\;\;\frac{-b}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(b + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.9e-128)
   (/ (- b) (* a (/ y x)))
   (if (<= b 8e+104) (* x (/ 1.0 (* y a))) (/ x (* y (+ b 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e-128) {
		tmp = -b / (a * (y / x));
	} else if (b <= 8e+104) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * (b + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.9d-128)) then
        tmp = -b / (a * (y / x))
    else if (b <= 8d+104) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = x / (y * (b + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e-128) {
		tmp = -b / (a * (y / x));
	} else if (b <= 8e+104) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * (b + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.9e-128:
		tmp = -b / (a * (y / x))
	elif b <= 8e+104:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (y * (b + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.9e-128)
		tmp = Float64(Float64(-b) / Float64(a * Float64(y / x)));
	elseif (b <= 8e+104)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(x / Float64(y * Float64(b + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.9e-128)
		tmp = -b / (a * (y / x));
	elseif (b <= 8e+104)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (y * (b + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.9e-128], N[((-b) / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e+104], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.9e-128

   1. Initial program 99.8%

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

      1. associate-/l* 98.0%

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

      2. fma-def 98.0%

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

      3. sub-neg 98.0%

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

      4. metadata-eval 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in y around 0 84.7%

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

      1. div-exp 72.2%

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

      2. exp-to-pow 72.3%

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

      3. sub-neg 72.3%

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

      4. metadata-eval 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in t around 0 71.6%

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

   9. Taylor expanded in b around 0 41.8%

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

       1. +-commutative 41.8%

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

       2. mul-1-neg 41.8%

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

       3. unsub-neg 41.8%

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

       4. associate-/r* 42.6%

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

       5. associate-/r* 52.1%

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

       6. *-commutative 52.1%

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

   11. Simplified 52.1%

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

   12. Taylor expanded in b around inf 41.9%

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

       1. mul-1-neg 41.9%

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

       2. associate-/l* 41.0%

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

       3. *-commutative 41.0%

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

       4. associate-/l* 42.1%

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

       5. associate-/r/ 44.0%

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

   14. Simplified 44.0%

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

   if -2.9e-128 < b < 8e104

   1. Initial program 95.8%

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

      1. associate-/l* 97.9%

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

      2. fma-def 97.9%

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

      3. sub-neg 97.9%

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

      4. metadata-eval 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in y around 0 74.7%

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

      1. div-exp 72.4%

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

      2. exp-to-pow 73.4%

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

      3. sub-neg 73.4%

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

      4. metadata-eval 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in t around 0 43.2%

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

   9. Taylor expanded in b around 0 38.5%

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

       1. *-commutative 38.5%

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

   11. Simplified 38.5%

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

       1. div-inv 38.5%

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

   13. Applied egg-rr 38.5%

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

   if 8e104 < 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. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf 83.6%

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

      1. neg-mul-1 83.6%

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

   7. Simplified 83.6%

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

   8. Taylor expanded in b around 0 39.7%

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

      1. distribute-rgt1-in 39.7%

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

   10. Simplified 39.7%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{-128}:\\ \;\;\;\;\frac{-b}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(b + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.9% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.0024:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.0024)
   (/ x (/ y (- (/ 1.0 a) (/ b 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 <= -0.0024) {
		tmp = x / (y / ((1.0 / a) - (b / 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 <= (-0.0024d0)) then
        tmp = x / (y / ((1.0d0 / a) - (b / 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 <= -0.0024) {
		tmp = x / (y / ((1.0 / a) - (b / a)));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.0024:
		tmp = x / (y / ((1.0 / a) - (b / a)))
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.0024)
		tmp = Float64(x / Float64(y / Float64(Float64(1.0 / a) - Float64(b / 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 <= -0.0024)
		tmp = x / (y / ((1.0 / a) - (b / a)));
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.0024], N[(x / N[(y / N[(N[(1.0 / a), $MachinePrecision] - N[(b / 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 < -0.00239999999999999979

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 90.2%

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

   6. Taylor expanded in t around 0 84.5%

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

      1. associate-/l* 84.5%

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

      2. mul-1-neg 84.5%

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

   8. Simplified 84.5%

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

   9. Taylor expanded in b around 0 53.3%

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

       1. mul-1-neg 53.3%

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

       2. unsub-neg 53.3%

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

       3. log-rec 53.3%

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

       4. rem-exp-log 53.3%

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

       5. log-rec 53.3%

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

       6. rem-exp-log 53.3%

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

       7. associate-*r/ 53.3%

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

       8. *-rgt-identity 53.3%

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

   11. Simplified 53.3%

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

   if -0.00239999999999999979 < b

   1. Initial program 97.1%

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

      1. associate-/l* 97.6%

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

      2. fma-def 97.6%

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

      3. sub-neg 97.6%

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

      4. metadata-eval 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in y around 0 77.4%

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

      1. div-exp 72.6%

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

      2. exp-to-pow 73.3%

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

      3. sub-neg 73.3%

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

      4. metadata-eval 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in t around 0 50.1%

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

   9. Taylor expanded in b around 0 39.3%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.0024:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.7% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x}{\frac{a}{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.65e-128)
   (/ (- (/ x a) (/ x (/ a b))) 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 <= -1.65e-128) {
		tmp = ((x / a) - (x / (a / b))) / 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 <= (-1.65d-128)) then
        tmp = ((x / a) - (x / (a / b))) / 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 <= -1.65e-128) {
		tmp = ((x / a) - (x / (a / b))) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.65e-128:
		tmp = ((x / a) - (x / (a / b))) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.65e-128)
		tmp = Float64(Float64(Float64(x / a) - Float64(x / Float64(a / b))) / 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 <= -1.65e-128)
		tmp = ((x / a) - (x / (a / b))) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.65e-128], N[(N[(N[(x / a), $MachinePrecision] - N[(x / N[(a / b), $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 < -1.65e-128

   1. Initial program 99.8%

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

      1. associate-/l* 98.0%

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

      2. fma-def 98.0%

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

      3. sub-neg 98.0%

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

      4. metadata-eval 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in y around 0 84.7%

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

      1. div-exp 72.2%

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

      2. exp-to-pow 72.3%

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

      3. sub-neg 72.3%

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

      4. metadata-eval 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in t around 0 71.6%

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

   9. Taylor expanded in b around 0 41.8%

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

       1. +-commutative 41.8%

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

       2. mul-1-neg 41.8%

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

       3. unsub-neg 41.8%

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

       4. associate-/r* 42.6%

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

       5. associate-/r* 52.1%

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

       6. *-commutative 52.1%

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

   11. Simplified 52.1%

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

       1. sub-div 52.1%

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

       2. associate-/l* 49.2%

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

   13. Applied egg-rr 49.2%

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

   if -1.65e-128 < b

   1. Initial program 96.8%

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

      1. associate-/l* 98.4%

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

      2. fma-def 98.4%

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

      3. sub-neg 98.4%

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

      4. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in y around 0 78.5%

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

      1. div-exp 73.0%

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

      2. exp-to-pow 73.8%

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

      3. sub-neg 73.8%

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

      4. metadata-eval 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in t around 0 52.3%

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

   9. Taylor expanded in b around 0 39.7%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x}{\frac{a}{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 40.4% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{-130}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.4e-130)
   (/ (- (/ x y) (/ (* x b) 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 <= -6.4e-130) {
		tmp = ((x / y) - ((x * b) / 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 <= (-6.4d-130)) then
        tmp = ((x / y) - ((x * b) / 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 <= -6.4e-130) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.4e-130:
		tmp = ((x / y) - ((x * b) / 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 <= -6.4e-130)
		tmp = Float64(Float64(Float64(x / y) - Float64(Float64(x * b) / 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 <= -6.4e-130)
		tmp = ((x / y) - ((x * b) / 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, -6.4e-130], N[(N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.3999999999999999e-130

   1. Initial program 99.8%

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

      1. associate-/l* 98.0%

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

      2. fma-def 98.0%

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

      3. sub-neg 98.0%

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

      4. metadata-eval 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in y around 0 84.7%

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

      1. div-exp 72.2%

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

      2. exp-to-pow 72.3%

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

      3. sub-neg 72.3%

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

      4. metadata-eval 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in t around 0 71.6%

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

   9. Taylor expanded in b around 0 41.8%

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

       1. +-commutative 41.8%

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

       2. mul-1-neg 41.8%

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

       3. unsub-neg 41.8%

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

       4. associate-/r* 42.6%

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

       5. associate-/r* 52.1%

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

       6. *-commutative 52.1%

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

   11. Simplified 52.1%

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

   12. Taylor expanded in a around 0 51.3%

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

   if -6.3999999999999999e-130 < b

   1. Initial program 96.8%

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

      1. associate-/l* 98.4%

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

      2. fma-def 98.4%

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

      3. sub-neg 98.4%

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

      4. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in y around 0 78.5%

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

      1. div-exp 73.0%

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

      2. exp-to-pow 73.8%

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

      3. sub-neg 73.8%

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

      4. metadata-eval 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in t around 0 52.3%

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

   9. Taylor expanded in b around 0 39.7%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{-130}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 31.2% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.3 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.3e-82) (* x (/ 1.0 (* y a))) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.3e-82) {
		tmp = x * (1.0 / (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 (z <= 1.3d-82) then
        tmp = x * (1.0d0 / (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 (z <= 1.3e-82) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.3e-82:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.3e-82)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 1.3e-82)
		tmp = x * (1.0 / (y * a));
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.3e-82], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.3e-82

   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. associate-/l* 99.2%

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

      2. fma-def 99.2%

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

      3. sub-neg 99.2%

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

      4. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0 87.2%

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

      1. div-exp 71.7%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      2. exp-to-pow 72.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      3. sub-neg 72.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      4. metadata-eval 72.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   7. Simplified 72.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   8. Taylor expanded in t around 0 66.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 35.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 35.8%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 35.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. div-inv 35.8%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

   13. Applied egg-rr 35.8%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

   if 1.3e-82 < z

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}} \]

      2. fma-def 97.7%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b}}} \]

      3. sub-neg 97.7%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b}}} \]

      4. metadata-eval 97.7%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b}}} \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.4%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]
   6. Step-by-step derivation

      1. div-exp 73.3%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      2. exp-to-pow 73.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      3. sub-neg 73.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      4. metadata-eval 73.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   7. Simplified 73.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   8. Taylor expanded in t around 0 56.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 31.9%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 31.9%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

   12. Taylor expanded in x around 0 31.9%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   13. Step-by-step derivation

       1. *-commutative 31.9%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

       2. associate-/r* 37.8%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   14. Simplified 37.8%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.3 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.3% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.3 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.3e-82) (* x (/ 1.0 (* y a))) (/ 1.0 (* a (/ y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.3e-82) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	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 (z <= 1.3d-82) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = 1.0d0 / (a * (y / x))
    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 (z <= 1.3e-82) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.3e-82:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = 1.0 / (a * (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.3e-82)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 1.3e-82)
		tmp = x * (1.0 / (y * a));
	else
		tmp = 1.0 / (a * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.3e-82], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.3e-82

   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. associate-/l* 99.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}} \]

      2. fma-def 99.2%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b}}} \]

      3. sub-neg 99.2%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b}}} \]

      4. metadata-eval 99.2%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b}}} \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 87.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]
   6. Step-by-step derivation

      1. div-exp 71.7%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      2. exp-to-pow 72.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      3. sub-neg 72.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      4. metadata-eval 72.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   7. Simplified 72.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   8. Taylor expanded in t around 0 66.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 35.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 35.8%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 35.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. div-inv 35.8%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

   13. Applied egg-rr 35.8%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

   if 1.3e-82 < z

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}} \]

      2. fma-def 97.7%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b}}} \]

      3. sub-neg 97.7%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b}}} \]

      4. metadata-eval 97.7%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b}}} \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.4%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]
   6. Step-by-step derivation

      1. div-exp 73.3%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      2. exp-to-pow 73.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      3. sub-neg 73.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      4. metadata-eval 73.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   7. Simplified 73.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   8. Taylor expanded in t around 0 56.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 31.9%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 31.9%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. clear-num 31.8%

          \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot a}{x}}} \]

       2. inv-pow 31.8%

          \[\leadsto \color{blue}{{\left(\frac{y \cdot a}{x}\right)}^{-1}} \]

   13. Applied egg-rr 31.8%

       \[\leadsto \color{blue}{{\left(\frac{y \cdot a}{x}\right)}^{-1}} \]
   14. Step-by-step derivation

       1. unpow-1 31.8%

          \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot a}{x}}} \]

       2. associate-/l* 33.4%

          \[\leadsto \frac{1}{\color{blue}{\frac{y}{\frac{x}{a}}}} \]

       3. associate-/r/ 37.9%

          \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} \cdot a}} \]

   15. Simplified 37.9%

       \[\leadsto \color{blue}{\frac{1}{\frac{y}{x} \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.3 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.0% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+139}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.35e+139) (/ x y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.35e+139) {
		tmp = x / y;
	} 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 (y <= (-1.35d+139)) then
        tmp = x / y
    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 (y <= -1.35e+139) {
		tmp = x / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.35e+139:
		tmp = x / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.35e+139)
		tmp = Float64(x / y);
	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 (y <= -1.35e+139)
		tmp = x / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.35e+139], N[(x / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3499999999999999e139

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}} \]

      2. fma-def 100.0%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b}}} \]

      3. sub-neg 100.0%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b}}} \]

      4. metadata-eval 100.0%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 49.4%

      \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{-1 \cdot b}}}} \]
   6. Step-by-step derivation

      1. neg-mul-1 49.4%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{-b}}}} \]

   7. Simplified 49.4%

      \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{-b}}}} \]

   8. Taylor expanded in b around 0 41.4%

      \[\leadsto \frac{x}{\color{blue}{y}} \]

   if -1.3499999999999999e139 < y

   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. associate-/l* 98.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}} \]

      2. fma-def 98.0%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b}}} \]

      3. sub-neg 98.0%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b}}} \]

      4. metadata-eval 98.0%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b}}} \]

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]
   6. Step-by-step derivation

      1. div-exp 76.6%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      2. exp-to-pow 77.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      3. sub-neg 77.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      4. metadata-eval 77.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   7. Simplified 77.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   8. Taylor expanded in t around 0 61.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 34.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 34.1%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 34.1%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+139}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.1% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.4e-82) (/ x (* y a)) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.4e-82) {
		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 (z <= 1.4d-82) 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 (z <= 1.4e-82) {
		tmp = x / (y * a);
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.4e-82:
		tmp = x / (y * a)
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.4e-82)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 1.4e-82)
		tmp = x / (y * a);
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.4e-82], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.40000000000000012e-82

   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. associate-/l* 99.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}} \]

      2. fma-def 99.2%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b}}} \]

      3. sub-neg 99.2%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b}}} \]

      4. metadata-eval 99.2%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b}}} \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 87.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]
   6. Step-by-step derivation

      1. div-exp 71.7%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      2. exp-to-pow 72.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      3. sub-neg 72.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      4. metadata-eval 72.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   7. Simplified 72.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   8. Taylor expanded in t around 0 66.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 35.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 35.8%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 35.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

   if 1.40000000000000012e-82 < z

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}} \]

      2. fma-def 97.7%

         \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b}}} \]

      3. sub-neg 97.7%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b}}} \]

      4. metadata-eval 97.7%

         \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b}}} \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.4%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]
   6. Step-by-step derivation

      1. div-exp 73.3%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      2. exp-to-pow 73.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      3. sub-neg 73.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      4. metadata-eval 73.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   7. Simplified 73.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   8. Taylor expanded in t around 0 56.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 31.9%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 31.9%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

   12. Taylor expanded in x around 0 31.9%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   13. Step-by-step derivation

       1. *-commutative 31.9%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

       2. associate-/r* 37.8%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   14. Simplified 37.8%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 16.3% 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 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. associate-/l* 98.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}} \]

   2. fma-def 98.3%

      \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a\right)} - b}}} \]

   3. sub-neg 98.3%

      \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a\right) - b}}} \]

   4. metadata-eval 98.3%

      \[\leadsto \frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a\right) - b}}} \]

3. Simplified 98.3%

   \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a\right) - b}}}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 48.3%

   \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{-1 \cdot b}}}} \]
6. Step-by-step derivation

   1. neg-mul-1 48.3%

      \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{-b}}}} \]

7. Simplified 48.3%

   \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{-b}}}} \]

8. Taylor expanded in b around 0 18.8%

   \[\leadsto \frac{x}{\color{blue}{y}} \]

9. Final simplification 18.8%

   \[\leadsto \frac{x}{y} \]
10. Add Preprocessing

Developer target: 72.0% 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 2024019 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))