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

Percentage Accurate: 98.4% → 98.4%

Time: 19.1s

Alternatives: 24

Speedup: 1.0×

• 47.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Final simplification 98.0%

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

Alternative 2: 66.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-43} \lor \neg \left(y \leq 1.3 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\log x + \log a \cdot \left(t + -1\right)\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2e-43) (not (<= y 1.3e+65)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (/ (exp (- (+ (log x) (* (log a) (+ t -1.0))) b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2e-43) || !(y <= 1.3e+65)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = exp(((log(x) + (log(a) * (t + -1.0))) - b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2d-43)) .or. (.not. (y <= 1.3d+65))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = exp(((log(x) + (log(a) * (t + (-1.0d0)))) - b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2e-43) || !(y <= 1.3e+65)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = Math.exp(((Math.log(x) + (Math.log(a) * (t + -1.0))) - b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2e-43) or not (y <= 1.3e+65):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = math.exp(((math.log(x) + (math.log(a) * (t + -1.0))) - b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2e-43) || !(y <= 1.3e+65))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(exp(Float64(Float64(log(x) + Float64(log(a) * Float64(t + -1.0))) - b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2e-43) || ~((y <= 1.3e+65)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = exp(((log(x) + (log(a) * (t + -1.0))) - b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2e-43], N[Not[LessEqual[y, 1.3e+65]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[Exp[N[(N[(N[Log[x], $MachinePrecision] + N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000015e-43 or 1.30000000000000001e65 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. mul-1-neg 92.0%

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

      3. unsub-neg 92.0%

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

   5. Simplified 92.0%

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

   if -2.00000000000000015e-43 < y < 1.30000000000000001e65

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-exp-log 65.0%

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

      2. *-commutative 65.0%

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

      3. associate--l+ 65.0%

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

      4. sub-neg 65.0%

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

      5. metadata-eval 65.0%

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

      6. fma-undefine 65.0%

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

      7. log-prod 47.0%

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

   4. Applied egg-rr 47.6%

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

   5. Taylor expanded in y around 0 47.6%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-43} \lor \neg \left(y \leq 1.3 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\log x + \log a \cdot \left(t + -1\right)\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+50} \lor \neg \left(y \leq 5 \cdot 10^{+209}\right):\\ \;\;\;\;\frac{e^{y \cdot \log z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\log x + \log a \cdot \left(t + -1\right)\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.1e+50) (not (<= y 5e+209)))
   (/ (exp (* y (log z))) y)
   (/ (exp (- (+ (log x) (* (log a) (+ t -1.0))) b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.1e+50) || !(y <= 5e+209)) {
		tmp = exp((y * log(z))) / y;
	} else {
		tmp = exp(((log(x) + (log(a) * (t + -1.0))) - b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.1d+50)) .or. (.not. (y <= 5d+209))) then
        tmp = exp((y * log(z))) / y
    else
        tmp = exp(((log(x) + (log(a) * (t + (-1.0d0)))) - b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.1e+50) || !(y <= 5e+209)) {
		tmp = Math.exp((y * Math.log(z))) / y;
	} else {
		tmp = Math.exp(((Math.log(x) + (Math.log(a) * (t + -1.0))) - b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.1e+50) or not (y <= 5e+209):
		tmp = math.exp((y * math.log(z))) / y
	else:
		tmp = math.exp(((math.log(x) + (math.log(a) * (t + -1.0))) - b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.1e+50) || !(y <= 5e+209))
		tmp = Float64(exp(Float64(y * log(z))) / y);
	else
		tmp = Float64(exp(Float64(Float64(log(x) + Float64(log(a) * Float64(t + -1.0))) - b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.1e+50) || ~((y <= 5e+209)))
		tmp = exp((y * log(z))) / y;
	else
		tmp = exp(((log(x) + (log(a) * (t + -1.0))) - b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.1e+50], N[Not[LessEqual[y, 5e+209]], $MachinePrecision]], N[(N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision], N[(N[Exp[N[(N[(N[Log[x], $MachinePrecision] + N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1e50 or 4.99999999999999964e209 < 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. Step-by-step derivation

      1. add-exp-log 74.3%

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

      2. *-commutative 74.3%

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

      3. associate--l+ 74.3%

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

      4. sub-neg 74.3%

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

      5. metadata-eval 74.3%

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

      6. fma-undefine 74.3%

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

      7. log-prod 51.4%

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

   4. Applied egg-rr 51.4%

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

   5. Taylor expanded in y around inf 63.7%

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

   if -2.1e50 < y < 4.99999999999999964e209

   1. Initial program 97.2%

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

      1. add-exp-log 62.7%

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

      2. *-commutative 62.7%

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

      3. associate--l+ 62.7%

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

      4. sub-neg 62.7%

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

      5. metadata-eval 62.7%

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

      6. fma-undefine 62.7%

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

      7. log-prod 45.6%

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

   4. Applied egg-rr 46.0%

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

   5. Taylor expanded in y around 0 45.5%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+50} \lor \neg \left(y \leq 5 \cdot 10^{+209}\right):\\ \;\;\;\;\frac{e^{y \cdot \log z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\left(\log x + \log a \cdot \left(t + -1\right)\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+50} \lor \neg \left(y \leq 4 \cdot 10^{+209}\right):\\ \;\;\;\;\frac{e^{y \cdot \log z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.2e+50) (not (<= y 4e+209)))
   (/ (exp (* y (log z))) y)
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+50) || !(y <= 4e+209)) {
		tmp = exp((y * log(z))) / y;
	} else {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.2d+50)) .or. (.not. (y <= 4d+209))) then
        tmp = exp((y * log(z))) / y
    else
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+50) || !(y <= 4e+209)) {
		tmp = Math.exp((y * Math.log(z))) / y;
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.2e+50) or not (y <= 4e+209):
		tmp = math.exp((y * math.log(z))) / y
	else:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.2e+50) || !(y <= 4e+209))
		tmp = Float64(exp(Float64(y * log(z))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.2e+50) || ~((y <= 4e+209)))
		tmp = exp((y * log(z))) / y;
	else
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.2e+50], N[Not[LessEqual[y, 4e+209]], $MachinePrecision]], N[(N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999983e50 or 4.0000000000000003e209 < 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. Step-by-step derivation

      1. add-exp-log 74.3%

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

      2. *-commutative 74.3%

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

      3. associate--l+ 74.3%

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

      4. sub-neg 74.3%

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

      5. metadata-eval 74.3%

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

      6. fma-undefine 74.3%

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

      7. log-prod 51.4%

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

   4. Applied egg-rr 51.4%

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

   5. Taylor expanded in y around inf 63.7%

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

   if -3.19999999999999983e50 < y < 4.0000000000000003e209

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

      2. associate-/l* 88.3%

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

      3. associate--l+ 88.3%

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

      4. fma-define 88.3%

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

      5. sub-neg 88.3%

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

      6. metadata-eval 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in y around 0 90.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+50} \lor \neg \left(y \leq 4 \cdot 10^{+209}\right):\\ \;\;\;\;\frac{e^{y \cdot \log z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+27} \lor \neg \left(b \leq 5 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y} \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8.5e+27) (not (<= b 5e+57)))
   (/ (exp (- b)) y)
   (* x (/ (* (pow z y) (pow a (+ t -1.0))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.5e+27) || !(b <= 5e+57)) {
		tmp = exp(-b) / y;
	} else {
		tmp = x * ((pow(z, y) * pow(a, (t + -1.0))) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-8.5d+27)) .or. (.not. (b <= 5d+57))) then
        tmp = exp(-b) / y
    else
        tmp = x * (((z ** y) * (a ** (t + (-1.0d0)))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.5e+27) || !(b <= 5e+57)) {
		tmp = Math.exp(-b) / y;
	} else {
		tmp = x * ((Math.pow(z, y) * Math.pow(a, (t + -1.0))) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -8.5e+27) or not (b <= 5e+57):
		tmp = math.exp(-b) / y
	else:
		tmp = x * ((math.pow(z, y) * math.pow(a, (t + -1.0))) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -8.5e+27) || !(b <= 5e+57))
		tmp = Float64(exp(Float64(-b)) / y);
	else
		tmp = Float64(x * Float64(Float64((z ^ y) * (a ^ Float64(t + -1.0))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -8.5e+27) || ~((b <= 5e+57)))
		tmp = exp(-b) / y;
	else
		tmp = x * (((z ^ y) * (a ^ (t + -1.0))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -8.5e+27], N[Not[LessEqual[b, 5e+57]], $MachinePrecision]], N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.5e27 or 4.99999999999999972e57 < b

   1. Initial program 100.0%

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

      1. add-exp-log 74.0%

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

      2. *-commutative 74.0%

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

      3. associate--l+ 74.0%

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

      4. sub-neg 74.0%

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

      5. metadata-eval 74.0%

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

      6. fma-undefine 74.0%

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

      7. log-prod 50.0%

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

   4. Applied egg-rr 50.0%

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

   5. Taylor expanded in b around inf 61.8%

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

      1. neg-mul-1 61.8%

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

   7. Simplified 61.8%

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

   if -8.5e27 < b < 4.99999999999999972e57

   1. Initial program 96.7%

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

      1. associate-/l* 97.2%

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

      2. associate--l+ 97.2%

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

      3. exp-sum 82.7%

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

      4. associate-/l* 79.4%

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

      5. *-commutative 79.4%

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

      6. exp-to-pow 79.4%

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

      7. exp-diff 77.5%

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

      8. *-commutative 77.5%

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

      9. exp-to-pow 78.8%

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

      10. sub-neg 78.8%

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

      11. metadata-eval 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in b around 0 83.0%

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

      1. *-commutative 83.0%

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

      2. exp-to-pow 84.2%

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

      3. sub-neg 84.2%

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

      4. metadata-eval 84.2%

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

   7. Simplified 84.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+27} \lor \neg \left(b \leq 5 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y} \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -880000 \lor \neg \left(y \leq 1.4 \cdot 10^{+145}\right):\\ \;\;\;\;\frac{e^{y \cdot \log z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -880000.0) (not (<= y 1.4e+145)))
   (/ (exp (* y (log z))) y)
   (/ (/ (* x (pow a (+ t -1.0))) (exp b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -880000.0) || !(y <= 1.4e+145)) {
		tmp = exp((y * log(z))) / y;
	} else {
		tmp = ((x * pow(a, (t + -1.0))) / exp(b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-880000.0d0)) .or. (.not. (y <= 1.4d+145))) then
        tmp = exp((y * log(z))) / y
    else
        tmp = ((x * (a ** (t + (-1.0d0)))) / exp(b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -880000.0) || !(y <= 1.4e+145)) {
		tmp = Math.exp((y * Math.log(z))) / y;
	} else {
		tmp = ((x * Math.pow(a, (t + -1.0))) / Math.exp(b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -880000.0) or not (y <= 1.4e+145):
		tmp = math.exp((y * math.log(z))) / y
	else:
		tmp = ((x * math.pow(a, (t + -1.0))) / math.exp(b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -880000.0) || !(y <= 1.4e+145))
		tmp = Float64(exp(Float64(y * log(z))) / y);
	else
		tmp = Float64(Float64(Float64(x * (a ^ Float64(t + -1.0))) / exp(b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -880000.0) || ~((y <= 1.4e+145)))
		tmp = exp((y * log(z))) / y;
	else
		tmp = ((x * (a ^ (t + -1.0))) / exp(b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -880000.0], N[Not[LessEqual[y, 1.4e+145]], $MachinePrecision]], N[(N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8e5 or 1.3999999999999999e145 < 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. Step-by-step derivation

      1. add-exp-log 73.4%

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

      2. *-commutative 73.4%

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

      3. associate--l+ 73.4%

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

      4. sub-neg 73.4%

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

      5. metadata-eval 73.4%

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

      6. fma-undefine 73.4%

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

      7. log-prod 50.0%

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

   4. Applied egg-rr 50.0%

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

   5. Taylor expanded in y around inf 63.0%

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

   if -8.8e5 < y < 1.3999999999999999e145

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0 91.0%

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

      1. div-exp 79.9%

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

      2. associate-/l* 78.7%

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

      3. exp-to-pow 79.8%

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

      4. sub-neg 79.8%

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

      5. metadata-eval 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -880000 \lor \neg \left(y \leq 1.4 \cdot 10^{+145}\right):\\ \;\;\;\;\frac{e^{y \cdot \log z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1020000 \lor \neg \left(y \leq 8.5 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{e^{y \cdot \log z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{t}}{a}}{e^{b}} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1020000.0) (not (<= y 8.5e+134)))
   (/ (exp (* y (log z))) y)
   (* (/ (/ (pow a t) a) (exp b)) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1020000.0) || !(y <= 8.5e+134)) {
		tmp = exp((y * log(z))) / y;
	} else {
		tmp = ((pow(a, t) / a) / exp(b)) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1020000.0d0)) .or. (.not. (y <= 8.5d+134))) then
        tmp = exp((y * log(z))) / y
    else
        tmp = (((a ** t) / a) / exp(b)) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1020000.0) || !(y <= 8.5e+134)) {
		tmp = Math.exp((y * Math.log(z))) / y;
	} else {
		tmp = ((Math.pow(a, t) / a) / Math.exp(b)) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1020000.0) or not (y <= 8.5e+134):
		tmp = math.exp((y * math.log(z))) / y
	else:
		tmp = ((math.pow(a, t) / a) / math.exp(b)) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1020000.0) || !(y <= 8.5e+134))
		tmp = Float64(exp(Float64(y * log(z))) / y);
	else
		tmp = Float64(Float64(Float64((a ^ t) / a) / exp(b)) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1020000.0) || ~((y <= 8.5e+134)))
		tmp = exp((y * log(z))) / y;
	else
		tmp = (((a ^ t) / a) / exp(b)) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1020000.0], N[Not[LessEqual[y, 8.5e+134]], $MachinePrecision]], N[(N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e6 or 8.50000000000000024e134 < 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. Step-by-step derivation

      1. add-exp-log 72.6%

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

      2. *-commutative 72.6%

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

      3. associate--l+ 72.6%

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

      4. sub-neg 72.6%

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

      5. metadata-eval 72.6%

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

      6. fma-undefine 72.6%

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

      7. log-prod 49.5%

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

   4. Applied egg-rr 49.5%

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

   5. Taylor expanded in y around inf 62.4%

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

   if -1.02e6 < y < 8.50000000000000024e134

   1. Initial program 96.9%

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

      1. *-commutative 96.9%

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

      2. associate-/l* 89.3%

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

      3. associate--l+ 89.3%

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

      4. fma-define 89.3%

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

      5. sub-neg 89.3%

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

      6. metadata-eval 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in y around 0 84.1%

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

      1. div-exp 76.0%

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

      2. exp-to-pow 77.1%

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

      3. sub-neg 77.1%

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

      4. metadata-eval 77.1%

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

   7. Simplified 77.1%

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

      1. unpow-prod-up 77.3%

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

      2. unpow-1 77.3%

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

   9. Applied egg-rr 77.3%

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

       1. associate-*r/ 77.3%

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

       2. *-rgt-identity 77.3%

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

   11. Simplified 77.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1020000 \lor \neg \left(y \leq 8.5 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{e^{y \cdot \log z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{t}}{a}}{e^{b}} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t + -1\right)}\\ \mathbf{if}\;t \leq -23:\\ \;\;\;\;x \cdot \frac{t\_1}{y}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-11}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{t\_1}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (+ t -1.0))))
   (if (<= t -23.0)
     (* x (/ t_1 y))
     (if (<= t 1.35e-11)
       (/ (* x (pow z y)) (* a (* y (exp b))))
       (/ 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 + -1.0));
	double tmp;
	if (t <= -23.0) {
		tmp = x * (t_1 / y);
	} else if (t <= 1.35e-11) {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	} 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) :: tmp
    t_1 = a ** (t + (-1.0d0))
    if (t <= (-23.0d0)) then
        tmp = x * (t_1 / y)
    else if (t <= 1.35d-11) then
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    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 + -1.0));
	double tmp;
	if (t <= -23.0) {
		tmp = x * (t_1 / y);
	} else if (t <= 1.35e-11) {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	} else {
		tmp = x / (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t + -1.0))
	tmp = 0
	if t <= -23.0:
		tmp = x * (t_1 / y)
	elif t <= 1.35e-11:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	else:
		tmp = x / (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t + -1.0)
	tmp = 0.0
	if (t <= -23.0)
		tmp = Float64(x * Float64(t_1 / y));
	elseif (t <= 1.35e-11)
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	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 + -1.0);
	tmp = 0.0;
	if (t <= -23.0)
		tmp = x * (t_1 / y);
	elseif (t <= 1.35e-11)
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	else
		tmp = x / (y / t_1);
	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]}, If[LessEqual[t, -23.0], N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-11], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -23

   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. Step-by-step derivation

      1. add-exp-log 75.0%

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

      2. *-commutative 75.0%

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

      3. associate--l+ 75.0%

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

      4. sub-neg 75.0%

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

      5. metadata-eval 75.0%

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

      6. fma-undefine 75.0%

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

      7. log-prod 54.4%

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

   4. Applied egg-rr 54.4%

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

   5. Taylor expanded in y around 0 51.5%

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

   6. Taylor expanded in b around 0 48.6%

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

      1. exp-sum 48.6%

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

      2. rem-exp-log 84.1%

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

      3. associate-/l* 84.1%

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

      4. exp-to-pow 84.1%

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

      5. sub-neg 84.1%

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

      6. metadata-eval 84.1%

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

      7. +-commutative 84.1%

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

   8. Simplified 84.1%

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

   if -23 < t < 1.35000000000000002e-11

   1. Initial program 96.9%

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

      1. associate-/l* 97.0%

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

      2. associate--l+ 97.0%

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

      3. exp-sum 86.0%

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

      4. associate-/l* 82.0%

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

      5. *-commutative 82.0%

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

      6. exp-to-pow 82.0%

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

      7. exp-diff 82.0%

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

      8. *-commutative 82.0%

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

      9. exp-to-pow 83.5%

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

      10. sub-neg 83.5%

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

      11. metadata-eval 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in t around 0 83.5%

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

   if 1.35000000000000002e-11 < t

   1. Initial program 98.0%

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

      1. *-commutative 98.0%

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

      2. associate-/l* 84.6%

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

      3. associate--l+ 84.6%

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

      4. fma-define 84.6%

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

      5. sub-neg 84.6%

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

      6. metadata-eval 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in y around 0 66.8%

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

      1. div-exp 57.0%

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

      2. exp-to-pow 57.2%

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

      3. sub-neg 57.2%

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

      4. metadata-eval 57.2%

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

   7. Simplified 57.2%

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

   8. Taylor expanded in b around 0 57.3%

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

      1. +-commutative 57.3%

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

   10. Simplified 57.3%

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

       1. clear-num 57.3%

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

       2. frac-times 63.9%

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

       3. *-un-lft-identity 63.9%

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

       4. +-commutative 63.9%

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

   12. Applied egg-rr 63.9%

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

       1. *-commutative 63.9%

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

       2. associate-*r/ 63.9%

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

       3. +-commutative 63.9%

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

   14. Simplified 63.9%

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

   15. Taylor expanded in b around 0 70.3%

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

       1. exp-to-pow 70.5%

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

       2. sub-neg 70.5%

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

       3. metadata-eval 70.5%

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

       4. +-commutative 70.5%

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

   17. Simplified 70.5%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -23:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-11}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \lor \neg \left(y \leq 1.2 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{e^{y \cdot \log z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.6) (not (<= y 1.2e+54)))
   (/ (exp (* y (log z))) y)
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.6) || !(y <= 1.2e+54)) {
		tmp = exp((y * log(z))) / y;
	} 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 ((y <= (-5.6d0)) .or. (.not. (y <= 1.2d+54))) then
        tmp = exp((y * log(z))) / y
    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 ((y <= -5.6) || !(y <= 1.2e+54)) {
		tmp = Math.exp((y * Math.log(z))) / y;
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.6) or not (y <= 1.2e+54):
		tmp = math.exp((y * math.log(z))) / y
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.6) || !(y <= 1.2e+54))
		tmp = Float64(exp(Float64(y * log(z))) / y);
	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 ((y <= -5.6) || ~((y <= 1.2e+54)))
		tmp = exp((y * log(z))) / y;
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.6], N[Not[LessEqual[y, 1.2e+54]], $MachinePrecision]], N[(N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5999999999999996 or 1.19999999999999999e54 < 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. Step-by-step derivation

      1. add-exp-log 70.6%

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

      2. *-commutative 70.6%

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

      3. associate--l+ 70.6%

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

      4. sub-neg 70.6%

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

      5. metadata-eval 70.6%

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

      6. fma-undefine 70.6%

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

      7. log-prod 48.7%

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

   4. Applied egg-rr 48.7%

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

   5. Taylor expanded in y around inf 57.4%

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

   if -5.5999999999999996 < y < 1.19999999999999999e54

   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. *-commutative 96.3%

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

      2. associate-/l* 88.2%

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

      3. associate--l+ 88.2%

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

      4. fma-define 88.2%

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

      5. sub-neg 88.2%

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

      6. metadata-eval 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in y around 0 85.5%

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

      1. div-exp 76.0%

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

      2. exp-to-pow 77.3%

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

      3. sub-neg 77.3%

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

      4. metadata-eval 77.3%

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

   7. Simplified 77.3%

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

   8. Taylor expanded in t around 0 76.4%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \lor \neg \left(y \leq 1.2 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{e^{y \cdot \log z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.034 \lor \neg \left(b \leq 5.8 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot \left(1 + b\right)}{{a}^{\left(t + -1\right)}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -0.034) (not (<= b 5.8e+62)))
   (/ x (* y (exp b)))
   (/ x (/ (* y (+ 1.0 b)) (pow a (+ t -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.034) || !(b <= 5.8e+62)) {
		tmp = x / (y * exp(b));
	} else {
		tmp = x / ((y * (1.0 + b)) / pow(a, (t + -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 <= (-0.034d0)) .or. (.not. (b <= 5.8d+62))) then
        tmp = x / (y * exp(b))
    else
        tmp = x / ((y * (1.0d0 + b)) / (a ** (t + (-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 <= -0.034) || !(b <= 5.8e+62)) {
		tmp = x / (y * Math.exp(b));
	} else {
		tmp = x / ((y * (1.0 + b)) / Math.pow(a, (t + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -0.034) or not (b <= 5.8e+62):
		tmp = x / (y * math.exp(b))
	else:
		tmp = x / ((y * (1.0 + b)) / math.pow(a, (t + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -0.034) || !(b <= 5.8e+62))
		tmp = Float64(x / Float64(y * exp(b)));
	else
		tmp = Float64(x / Float64(Float64(y * Float64(1.0 + b)) / (a ^ Float64(t + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -0.034) || ~((b <= 5.8e+62)))
		tmp = x / (y * exp(b));
	else
		tmp = x / ((y * (1.0 + b)) / (a ^ (t + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -0.034], N[Not[LessEqual[b, 5.8e+62]], $MachinePrecision]], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision] / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.034000000000000002 or 5.79999999999999968e62 < b

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 84.0%

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

      3. associate--l+ 84.0%

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

      4. fma-define 84.0%

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

      5. sub-neg 84.0%

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

      6. metadata-eval 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in b around inf 71.0%

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

      1. neg-mul-1 71.0%

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

   7. Simplified 71.0%

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

      1. exp-neg 71.0%

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

      2. frac-times 84.2%

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

      3. *-un-lft-identity 84.2%

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

   9. Applied egg-rr 84.2%

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

   if -0.034000000000000002 < b < 5.79999999999999968e62

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

      2. associate-/l* 87.8%

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

      3. associate--l+ 87.8%

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

      4. fma-define 87.8%

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

      5. sub-neg 87.8%

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

      6. metadata-eval 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in y around 0 68.1%

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

      1. div-exp 65.4%

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

      2. exp-to-pow 66.6%

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

      3. sub-neg 66.6%

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

      4. metadata-eval 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in b around 0 68.7%

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

      1. +-commutative 68.7%

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

   10. Simplified 68.7%

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

       1. clear-num 68.7%

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

       2. frac-times 73.3%

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

       3. *-un-lft-identity 73.3%

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

       4. +-commutative 73.3%

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

   12. Applied egg-rr 73.3%

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

       1. *-commutative 73.3%

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

       2. associate-*r/ 73.3%

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

       3. +-commutative 73.3%

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

   14. Simplified 73.3%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.034 \lor \neg \left(b \leq 5.8 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot \left(1 + b\right)}{{a}^{\left(t + -1\right)}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.034 \lor \neg \left(b \leq 1.6 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -0.034) (not (<= b 1.6e+62)))
   (/ x (* y (exp b)))
   (* x (/ (pow a (+ t -1.0)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.034) || !(b <= 1.6e+62)) {
		tmp = x / (y * exp(b));
	} else {
		tmp = x * (pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-0.034d0)) .or. (.not. (b <= 1.6d+62))) then
        tmp = x / (y * exp(b))
    else
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.034) || !(b <= 1.6e+62)) {
		tmp = x / (y * Math.exp(b));
	} else {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -0.034) or not (b <= 1.6e+62):
		tmp = x / (y * math.exp(b))
	else:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -0.034) || !(b <= 1.6e+62))
		tmp = Float64(x / Float64(y * exp(b)));
	else
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -0.034) || ~((b <= 1.6e+62)))
		tmp = x / (y * exp(b));
	else
		tmp = x * ((a ^ (t + -1.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -0.034], N[Not[LessEqual[b, 1.6e+62]], $MachinePrecision]], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.034000000000000002 or 1.59999999999999992e62 < b

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 84.0%

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

      3. associate--l+ 84.0%

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

      4. fma-define 84.0%

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

      5. sub-neg 84.0%

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

      6. metadata-eval 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in b around inf 71.0%

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

      1. neg-mul-1 71.0%

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

   7. Simplified 71.0%

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

      1. exp-neg 71.0%

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

      2. frac-times 84.2%

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

      3. *-un-lft-identity 84.2%

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

   9. Applied egg-rr 84.2%

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

   if -0.034000000000000002 < b < 1.59999999999999992e62

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-exp-log 61.4%

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

      2. *-commutative 61.4%

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

      3. associate--l+ 61.4%

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

      4. sub-neg 61.4%

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

      5. metadata-eval 61.4%

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

      6. fma-undefine 61.4%

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

      7. log-prod 46.0%

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

   4. Applied egg-rr 46.5%

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

   5. Taylor expanded in y around 0 35.5%

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

   6. Taylor expanded in b around 0 34.3%

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

      1. exp-sum 34.3%

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

      2. rem-exp-log 70.1%

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

      3. associate-/l* 72.0%

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

      4. exp-to-pow 73.2%

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

      5. sub-neg 73.2%

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

      6. metadata-eval 73.2%

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

      7. +-commutative 73.2%

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

   8. Simplified 73.2%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.034 \lor \neg \left(b \leq 1.6 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.034 \lor \neg \left(b \leq 205\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -0.034) (not (<= b 205.0)))
   (/ x (* y (exp b)))
   (/ x (* a (* y (+ 1.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.034) || !(b <= 205.0)) {
		tmp = x / (y * exp(b));
	} else {
		tmp = x / (a * (y * (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 ((b <= (-0.034d0)) .or. (.not. (b <= 205.0d0))) then
        tmp = x / (y * exp(b))
    else
        tmp = x / (a * (y * (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 ((b <= -0.034) || !(b <= 205.0)) {
		tmp = x / (y * Math.exp(b));
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -0.034) or not (b <= 205.0):
		tmp = x / (y * math.exp(b))
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -0.034) || !(b <= 205.0))
		tmp = Float64(x / Float64(y * exp(b)));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -0.034) || ~((b <= 205.0)))
		tmp = x / (y * exp(b));
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -0.034], N[Not[LessEqual[b, 205.0]], $MachinePrecision]], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.034000000000000002 or 205 < 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. *-commutative 99.2%

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

      2. associate-/l* 83.8%

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

      3. associate--l+ 83.8%

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

      4. fma-define 83.8%

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

      5. sub-neg 83.8%

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

      6. metadata-eval 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in b around inf 67.0%

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

      1. neg-mul-1 67.0%

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

   7. Simplified 67.0%

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

      1. exp-neg 67.0%

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

      2. frac-times 79.0%

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

      3. *-un-lft-identity 79.0%

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

   9. Applied egg-rr 79.0%

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

   if -0.034000000000000002 < b < 205

   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. *-commutative 97.0%

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

      2. associate-/l* 88.3%

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

      3. associate--l+ 88.3%

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

      4. fma-define 88.3%

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

      5. sub-neg 88.3%

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

      6. metadata-eval 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in y around 0 68.4%

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

      1. div-exp 68.4%

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

      2. exp-to-pow 69.7%

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

      3. sub-neg 69.7%

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

      4. metadata-eval 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in b around 0 69.7%

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

      1. +-commutative 69.7%

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

   10. Simplified 69.7%

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

   11. Taylor expanded in t around 0 46.9%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.034 \lor \neg \left(b \leq 205\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.034 \lor \neg \left(b \leq 440\right):\\ \;\;\;\;\frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -0.034) (not (<= b 440.0)))
   (/ (exp (- b)) y)
   (/ x (* a (* y (+ 1.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.034) || !(b <= 440.0)) {
		tmp = exp(-b) / y;
	} else {
		tmp = x / (a * (y * (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 ((b <= (-0.034d0)) .or. (.not. (b <= 440.0d0))) then
        tmp = exp(-b) / y
    else
        tmp = x / (a * (y * (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 ((b <= -0.034) || !(b <= 440.0)) {
		tmp = Math.exp(-b) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -0.034) or not (b <= 440.0):
		tmp = math.exp(-b) / y
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -0.034) || !(b <= 440.0))
		tmp = Float64(exp(Float64(-b)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -0.034) || ~((b <= 440.0)))
		tmp = exp(-b) / y;
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -0.034], N[Not[LessEqual[b, 440.0]], $MachinePrecision]], N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.034000000000000002 or 440 < 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. Add Preprocessing
   3. Step-by-step derivation

      1. add-exp-log 71.8%

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

      2. *-commutative 71.8%

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

      3. associate--l+ 71.8%

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

      4. sub-neg 71.8%

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

      5. metadata-eval 71.8%

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

      6. fma-undefine 71.8%

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

      7. log-prod 50.5%

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

   4. Applied egg-rr 51.1%

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

   5. Taylor expanded in b around inf 57.6%

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

      1. neg-mul-1 57.6%

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

   7. Simplified 57.6%

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

   if -0.034000000000000002 < b < 440

   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. *-commutative 97.0%

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

      2. associate-/l* 88.3%

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

      3. associate--l+ 88.3%

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

      4. fma-define 88.3%

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

      5. sub-neg 88.3%

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

      6. metadata-eval 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in y around 0 68.4%

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

      1. div-exp 68.4%

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

      2. exp-to-pow 69.7%

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

      3. sub-neg 69.7%

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

      4. metadata-eval 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in b around 0 69.7%

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

      1. +-commutative 69.7%

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

   10. Simplified 69.7%

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

   11. Taylor expanded in t around 0 46.9%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.034 \lor \neg \left(b \leq 440\right):\\ \;\;\;\;\frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \frac{x}{a \cdot \left(y \cdot e^{b}\right)} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. *-commutative 98.0%

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

   2. associate-/l* 86.2%

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

   3. associate--l+ 86.2%

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

   4. fma-define 86.2%

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

   5. sub-neg 86.2%

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

   6. metadata-eval 86.2%

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

3. Simplified 86.2%

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

5. Taylor expanded in y around 0 70.8%

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

   1. div-exp 62.6%

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

   2. exp-to-pow 63.3%

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

   3. sub-neg 63.3%

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

   4. metadata-eval 63.3%

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

7. Simplified 63.3%

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

8. Taylor expanded in t around 0 61.6%

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

Alternative 15: 37.1% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.034:\\ \;\;\;\;\frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.034)
   (/ (+ 1.0 (* b (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666)))))) y)
   (/ x (* a (* y (+ 1.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.034) {
		tmp = (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y;
	} else {
		tmp = x / (a * (y * (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 (b <= (-0.034d0)) then
        tmp = (1.0d0 + (b * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0))))))) / y
    else
        tmp = x / (a * (y * (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 (b <= -0.034) {
		tmp = (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.034:
		tmp = (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.034)
		tmp = Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666)))))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.034)
		tmp = (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666)))))) / y;
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.034], N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.034000000000000002

   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. Step-by-step derivation

      1. add-exp-log 58.3%

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

      2. *-commutative 58.3%

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

      3. associate--l+ 58.3%

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

      4. sub-neg 58.3%

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

      5. metadata-eval 58.3%

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

      6. fma-undefine 58.3%

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

      7. log-prod 51.7%

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

   4. Applied egg-rr 51.7%

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

   5. Taylor expanded in b around inf 40.3%

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

      1. neg-mul-1 40.3%

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

   7. Simplified 40.3%

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

   8. Taylor expanded in b around 0 37.3%

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

   if -0.034000000000000002 < b

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-/l* 85.6%

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

      3. associate--l+ 85.6%

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

      4. fma-define 85.6%

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

      5. sub-neg 85.6%

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

      6. metadata-eval 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in y around 0 69.5%

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

      1. div-exp 63.9%

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

      2. exp-to-pow 64.8%

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

      3. sub-neg 64.8%

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

      4. metadata-eval 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in b around 0 65.1%

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

      1. +-commutative 65.1%

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

   10. Simplified 65.1%

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

   11. Taylor expanded in t around 0 45.6%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.034:\\ \;\;\;\;\frac{1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.0% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.034:\\ \;\;\;\;\frac{1 + b \cdot \left(-1 + b \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.034)
   (/ (+ 1.0 (* b (+ -1.0 (* b 0.5)))) y)
   (/ x (* a (* y (+ 1.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.034) {
		tmp = (1.0 + (b * (-1.0 + (b * 0.5)))) / y;
	} else {
		tmp = x / (a * (y * (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 (b <= (-0.034d0)) then
        tmp = (1.0d0 + (b * ((-1.0d0) + (b * 0.5d0)))) / y
    else
        tmp = x / (a * (y * (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 (b <= -0.034) {
		tmp = (1.0 + (b * (-1.0 + (b * 0.5)))) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.034:
		tmp = (1.0 + (b * (-1.0 + (b * 0.5)))) / y
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.034)
		tmp = Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * 0.5)))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.034)
		tmp = (1.0 + (b * (-1.0 + (b * 0.5)))) / y;
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.034], N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.034000000000000002

   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. Step-by-step derivation

      1. add-exp-log 58.3%

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

      2. *-commutative 58.3%

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

      3. associate--l+ 58.3%

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

      4. sub-neg 58.3%

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

      5. metadata-eval 58.3%

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

      6. fma-undefine 58.3%

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

      7. log-prod 51.7%

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

   4. Applied egg-rr 51.7%

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

   5. Taylor expanded in b around inf 40.3%

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

      1. neg-mul-1 40.3%

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

   7. Simplified 40.3%

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

   8. Taylor expanded in b around 0 32.6%

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

   if -0.034000000000000002 < b

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-/l* 85.6%

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

      3. associate--l+ 85.6%

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

      4. fma-define 85.6%

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

      5. sub-neg 85.6%

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

      6. metadata-eval 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in y around 0 69.5%

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

      1. div-exp 63.9%

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

      2. exp-to-pow 64.8%

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

      3. sub-neg 64.8%

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

      4. metadata-eval 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in b around 0 65.1%

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

      1. +-commutative 65.1%

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

   10. Simplified 65.1%

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

   11. Taylor expanded in t around 0 45.6%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.034:\\ \;\;\;\;\frac{1 + b \cdot \left(-1 + b \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.8% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.034:\\ \;\;\;\;\frac{x}{y} \cdot \left(1 + b \cdot \left(b \cdot 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.034)
   (* (/ x y) (+ 1.0 (* b (* b 0.5))))
   (/ x (* a (* y (+ 1.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.034) {
		tmp = (x / y) * (1.0 + (b * (b * 0.5)));
	} else {
		tmp = x / (a * (y * (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 (b <= (-0.034d0)) then
        tmp = (x / y) * (1.0d0 + (b * (b * 0.5d0)))
    else
        tmp = x / (a * (y * (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 (b <= -0.034) {
		tmp = (x / y) * (1.0 + (b * (b * 0.5)));
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.034:
		tmp = (x / y) * (1.0 + (b * (b * 0.5)))
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.034)
		tmp = Float64(Float64(x / y) * Float64(1.0 + Float64(b * Float64(b * 0.5))));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.034)
		tmp = (x / y) * (1.0 + (b * (b * 0.5)));
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.034], N[(N[(x / y), $MachinePrecision] * N[(1.0 + N[(b * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.034000000000000002

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 88.3%

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

      3. associate--l+ 88.3%

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

      4. fma-define 88.3%

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

      5. sub-neg 88.3%

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

      6. metadata-eval 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in b around inf 71.9%

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

      1. neg-mul-1 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in b around 0 46.7%

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

   9. Taylor expanded in b around inf 46.7%

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

       1. *-commutative 46.7%

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

   11. Simplified 46.7%

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

   if -0.034000000000000002 < b

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-/l* 85.6%

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

      3. associate--l+ 85.6%

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

      4. fma-define 85.6%

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

      5. sub-neg 85.6%

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

      6. metadata-eval 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in y around 0 69.5%

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

      1. div-exp 63.9%

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

      2. exp-to-pow 64.8%

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

      3. sub-neg 64.8%

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

      4. metadata-eval 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in b around 0 65.1%

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

      1. +-commutative 65.1%

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

   10. Simplified 65.1%

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

   11. Taylor expanded in t around 0 45.6%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.034:\\ \;\;\;\;\frac{x}{y} \cdot \left(1 + b \cdot \left(b \cdot 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.7% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.034:\\ \;\;\;\;\frac{x}{y} - x \cdot \frac{b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.034) (- (/ x y) (* x (/ b y))) (/ x (* a (* y (+ 1.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.034) {
		tmp = (x / y) - (x * (b / y));
	} else {
		tmp = x / (a * (y * (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 (b <= (-0.034d0)) then
        tmp = (x / y) - (x * (b / y))
    else
        tmp = x / (a * (y * (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 (b <= -0.034) {
		tmp = (x / y) - (x * (b / y));
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.034:
		tmp = (x / y) - (x * (b / y))
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.034)
		tmp = Float64(Float64(x / y) - Float64(x * Float64(b / y)));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.034)
		tmp = (x / y) - (x * (b / y));
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.034], N[(N[(x / y), $MachinePrecision] - N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.034000000000000002

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 88.3%

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

      3. associate--l+ 88.3%

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

      4. fma-define 88.3%

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

      5. sub-neg 88.3%

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

      6. metadata-eval 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in b around inf 71.9%

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

      1. neg-mul-1 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in b around 0 45.6%

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

   9. Taylor expanded in b around 0 34.3%

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

       1. +-commutative 34.3%

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

       2. mul-1-neg 34.3%

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

       3. associate-*r/ 34.2%

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

       4. unsub-neg 34.2%

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

       5. *-commutative 34.2%

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

       6. associate-*l/ 34.3%

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

       7. associate-*r/ 39.0%

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

   11. Simplified 39.0%

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

   if -0.034000000000000002 < b

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-/l* 85.6%

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

      3. associate--l+ 85.6%

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

      4. fma-define 85.6%

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

      5. sub-neg 85.6%

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

      6. metadata-eval 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in y around 0 69.5%

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

      1. div-exp 63.9%

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

      2. exp-to-pow 64.8%

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

      3. sub-neg 64.8%

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

      4. metadata-eval 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in b around 0 65.1%

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

      1. +-commutative 65.1%

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

   10. Simplified 65.1%

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

   11. Taylor expanded in t around 0 45.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 21.6% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.0021:\\ \;\;\;\;\frac{x}{y} - x \cdot \frac{b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + b}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.0021) (- (/ x y) (* x (/ b y))) (/ (+ 1.0 b) (/ y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.0021) {
		tmp = (x / y) - (x * (b / y));
	} else {
		tmp = (1.0 + b) / (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 (b <= (-0.0021d0)) then
        tmp = (x / y) - (x * (b / y))
    else
        tmp = (1.0d0 + b) / (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 (b <= -0.0021) {
		tmp = (x / y) - (x * (b / y));
	} else {
		tmp = (1.0 + b) / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.0021:
		tmp = (x / y) - (x * (b / y))
	else:
		tmp = (1.0 + b) / (y / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.0021)
		tmp = Float64(Float64(x / y) - Float64(x * Float64(b / y)));
	else
		tmp = Float64(Float64(1.0 + b) / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.0021)
		tmp = (x / y) - (x * (b / y));
	else
		tmp = (1.0 + b) / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.0021], N[(N[(x / y), $MachinePrecision] - N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + b), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.00209999999999999987

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 88.7%

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

      3. associate--l+ 88.7%

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

      4. fma-define 88.7%

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

      5. sub-neg 88.7%

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

      6. metadata-eval 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in b around inf 71.2%

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

      1. neg-mul-1 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in b around 0 45.8%

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

   9. Taylor expanded in b around 0 34.8%

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

       1. +-commutative 34.8%

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

       2. mul-1-neg 34.8%

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

       3. associate-*r/ 34.8%

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

       4. unsub-neg 34.8%

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

       5. *-commutative 34.8%

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

       6. associate-*l/ 34.8%

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

       7. associate-*r/ 39.4%

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

   11. Simplified 39.4%

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

   if -0.00209999999999999987 < b

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-/l* 85.4%

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

      3. associate--l+ 85.4%

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

      4. fma-define 85.4%

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

      5. sub-neg 85.4%

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

      6. metadata-eval 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in b around inf 30.3%

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

      1. neg-mul-1 30.3%

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

   7. Simplified 30.3%

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

      1. clear-num 30.5%

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

      2. un-div-inv 30.5%

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

      3. add-sqr-sqrt 8.7%

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

      4. sqrt-unprod 17.8%

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

      5. sqr-neg 17.8%

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

      6. sqrt-unprod 9.2%

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

      7. add-sqr-sqrt 17.8%

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

   9. Applied egg-rr 17.8%

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

   10. Taylor expanded in b around 0 16.1%

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

       1. +-commutative 64.7%

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

   12. Simplified 16.1%

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

4. Final simplification 21.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.0021:\\ \;\;\;\;\frac{x}{y} - x \cdot \frac{b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + b}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 15.4% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+23}:\\ \;\;\;\;\frac{1 - b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.45e+23) (/ (- 1.0 b) y) (/ 1.0 (/ y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.45e+23) {
		tmp = (1.0 - b) / y;
	} else {
		tmp = 1.0 / (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 (b <= (-1.45d+23)) then
        tmp = (1.0d0 - b) / y
    else
        tmp = 1.0d0 / (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 (b <= -1.45e+23) {
		tmp = (1.0 - b) / y;
	} else {
		tmp = 1.0 / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.45e+23:
		tmp = (1.0 - b) / y
	else:
		tmp = 1.0 / (y / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.45e+23)
		tmp = Float64(Float64(1.0 - b) / y);
	else
		tmp = Float64(1.0 / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.45e+23)
		tmp = (1.0 - b) / y;
	else
		tmp = 1.0 / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.45e+23], N[(N[(1.0 - b), $MachinePrecision] / y), $MachinePrecision], N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.45000000000000006e23

   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. Step-by-step derivation

      1. add-exp-log 58.6%

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

      2. *-commutative 58.6%

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

      3. associate--l+ 58.6%

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

      4. sub-neg 58.6%

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

      5. metadata-eval 58.6%

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

      6. fma-undefine 58.6%

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

      7. log-prod 51.7%

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

   4. Applied egg-rr 51.7%

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

   5. Taylor expanded in b around inf 41.6%

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

      1. neg-mul-1 41.6%

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

   7. Simplified 41.6%

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

   8. Taylor expanded in b around 0 14.2%

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

      1. neg-mul-1 35.2%

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

      2. unsub-neg 35.2%

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

   10. Simplified 14.2%

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

   if -1.45000000000000006e23 < b

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-/l* 85.7%

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

      3. associate--l+ 85.7%

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

      4. fma-define 85.7%

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

      5. sub-neg 85.7%

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

      6. metadata-eval 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in b around inf 30.7%

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

      1. neg-mul-1 30.7%

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

   7. Simplified 30.7%

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

   8. Taylor expanded in b around 0 15.8%

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

      1. clear-num 16.1%

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

      2. inv-pow 16.1%

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

   10. Applied egg-rr 16.1%

       \[\leadsto \color{blue}{{\left(\frac{y}{x}\right)}^{-1}} \]
   11. Step-by-step derivation

       1. unpow-1 16.1%

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

   12. Simplified 16.1%

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

Alternative 21: 19.0% accurate, 45.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \cdot \left(1 - b\right) \end{array} \]

FPCore

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

C

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

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) * (1.0d0 - b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. *-commutative 98.0%

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

   2. associate-/l* 86.2%

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

   3. associate--l+ 86.2%

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

   4. fma-define 86.2%

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

   5. sub-neg 86.2%

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

   6. metadata-eval 86.2%

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

3. Simplified 86.2%

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

5. Taylor expanded in b around inf 40.2%

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

   1. neg-mul-1 40.2%

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

7. Simplified 40.2%

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

8. Taylor expanded in b around 0 19.6%

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

   1. neg-mul-1 19.6%

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

   2. unsub-neg 19.6%

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

10. Simplified 19.6%

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

11. Final simplification 19.6%

    \[\leadsto \frac{x}{y} \cdot \left(1 - b\right) \]
12. Add Preprocessing

Alternative 22: 16.4% accurate, 63.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. *-commutative 98.0%

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

   2. associate-/l* 86.2%

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

   3. associate--l+ 86.2%

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

   4. fma-define 86.2%

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

   5. sub-neg 86.2%

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

   6. metadata-eval 86.2%

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

3. Simplified 86.2%

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

5. Taylor expanded in b around inf 40.2%

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

   1. neg-mul-1 40.2%

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

7. Simplified 40.2%

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

8. Taylor expanded in b around 0 15.7%

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

   1. clear-num 15.9%

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

   2. inv-pow 15.9%

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

10. Applied egg-rr 15.9%

    \[\leadsto \color{blue}{{\left(\frac{y}{x}\right)}^{-1}} \]
11. Step-by-step derivation

    1. unpow-1 15.9%

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

12. Simplified 15.9%

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]
13. Add Preprocessing

Alternative 23: 16.2% accurate, 105.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. *-commutative 98.0%

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

   2. associate-/l* 86.2%

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

   3. associate--l+ 86.2%

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

   4. fma-define 86.2%

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

   5. sub-neg 86.2%

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

   6. metadata-eval 86.2%

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

3. Simplified 86.2%

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

5. Taylor expanded in b around inf 40.2%

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

   1. neg-mul-1 40.2%

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

7. Simplified 40.2%

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

8. Taylor expanded in b around 0 15.7%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
9. Add Preprocessing

Alternative 24: 3.2% accurate, 105.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / 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 = 1.0d0 / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. add-exp-log 66.1%

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

   2. *-commutative 66.1%

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

   3. associate--l+ 66.1%

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

   4. sub-neg 66.1%

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

   5. metadata-eval 66.1%

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

   6. fma-undefine 66.1%

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

   7. log-prod 47.3%

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

4. Applied egg-rr 47.6%

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

5. Taylor expanded in b around inf 28.1%

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

   1. neg-mul-1 28.1%

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

7. Simplified 28.1%

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

8. Taylor expanded in b around 0 3.1%

   \[\leadsto \color{blue}{\frac{1}{y}} \]
9. Add Preprocessing

Developer Target 1: 72.4% 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 2024135 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8845848504127471/10000000000000000) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 8520312288374073/10000000000) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))))))

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