Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B

Percentage Accurate: 96.5% → 99.6%

Time: 17.8s

Alternatives: 15

Speedup: 1.0×

• 41.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (fma y (- (log z) t) (* a (- (log1p (- z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(fma(y, (log(z) - t), (a * (log1p(-z) - b))));
}

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(fma(y, Float64(log(z) - t), Float64(a * Float64(log1p(Float64(-z)) - b)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(a * N[(N[Log[1 + (-z)], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.4%

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

   1. fma-define 97.4%

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

   2. sub-neg 97.4%

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

   3. log1p-define 99.2%

      \[\leadsto x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)\right)} \]

3. Simplified 99.2%

   \[\leadsto \color{blue}{x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.4%

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

Alternative 3: 87.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-11} \lor \neg \left(y \leq 6.3 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.05e-11) (not (<= y 6.3e-12)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (+ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e-11) || !(y <= 6.3e-12)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((a * -(z + 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 <= (-1.05d-11)) .or. (.not. (y <= 6.3d-12))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((a * -(z + 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 <= -1.05e-11) || !(y <= 6.3e-12)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * -(z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.05e-11) or not (y <= 6.3e-12):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * -(z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.05e-11) || !(y <= 6.3e-12))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-Float64(z + b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.05e-11) || ~((y <= 6.3e-12)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((a * -(z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.05e-11], N[Not[LessEqual[y, 6.3e-12]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-N[(z + b), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0499999999999999e-11 or 6.3000000000000002e-12 < y

   1. Initial program 97.6%

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

   3. Taylor expanded in y around inf 87.3%

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

   if -1.0499999999999999e-11 < y < 6.3000000000000002e-12

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0 87.8%

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

      1. sub-neg 87.8%

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

      2. log1p-define 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in z around 0 91.3%

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

      1. +-commutative 91.3%

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

      2. associate-*r* 91.3%

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

      3. associate-*r* 91.3%

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

      4. distribute-lft-out 91.3%

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

      5. mul-1-neg 91.3%

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

   8. Simplified 91.3%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-11} \lor \neg \left(y \leq 6.3 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+136} \lor \neg \left(y \leq 2.6 \cdot 10^{+25}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.3e+136) (not (<= y 2.6e+25)))
   (* x (pow z y))
   (* x (exp (* a (- (+ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.3e+136) || !(y <= 2.6e+25)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp((a * -(z + 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 <= (-4.3d+136)) .or. (.not. (y <= 2.6d+25))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp((a * -(z + 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 <= -4.3e+136) || !(y <= 2.6e+25)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((a * -(z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.3e+136) or not (y <= 2.6e+25):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((a * -(z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.3e+136) || !(y <= 2.6e+25))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-Float64(z + b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.3e+136) || ~((y <= 2.6e+25)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((a * -(z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.3e+136], N[Not[LessEqual[y, 2.6e+25]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-N[(z + b), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2999999999999999e136 or 2.5999999999999998e25 < y

   1. Initial program 97.5%

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

   3. Taylor expanded in y around inf 92.7%

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

   4. Taylor expanded in t around 0 72.0%

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

   if -4.2999999999999999e136 < y < 2.5999999999999998e25

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 79.8%

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

      1. sub-neg 79.8%

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

      2. log1p-define 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in z around 0 83.5%

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

      1. +-commutative 83.5%

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

      2. associate-*r* 83.5%

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

      3. associate-*r* 83.5%

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

      4. distribute-lft-out 83.5%

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

      5. mul-1-neg 83.5%

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

   8. Simplified 83.5%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+136} \lor \neg \left(y \leq 2.6 \cdot 10^{+25}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+136} \lor \neg \left(y \leq 1.1 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.4e+136) (not (<= y 1.1e-8)))
   (* x (pow z y))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.4e+136) || !(y <= 1.1e-8)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp((a * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.4d+136)) .or. (.not. (y <= 1.1d-8))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp((a * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.4e+136) || !(y <= 1.1e-8)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.4e+136) or not (y <= 1.1e-8):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.4e+136) || !(y <= 1.1e-8))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.4e+136) || ~((y <= 1.1e-8)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.4e+136], N[Not[LessEqual[y, 1.1e-8]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999999e136 or 1.0999999999999999e-8 < y

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf 91.6%

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

   4. Taylor expanded in t around 0 68.6%

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

   if -4.3999999999999999e136 < y < 1.0999999999999999e-8

   1. Initial program 97.7%

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

   3. Taylor expanded in b around inf 83.1%

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

      1. mul-1-neg 83.1%

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

      2. distribute-rgt-neg-out 83.1%

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

   5. Simplified 83.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+136} \lor \neg \left(y \leq 1.1 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-15} \lor \neg \left(y \leq 2.2 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(\frac{1 - a \cdot b}{z} - a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9e-15) (not (<= y 2.2e-34)))
   (* x (pow z y))
   (* x (* z (- (/ (- 1.0 (* a b)) z) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e-15) || !(y <= 2.2e-34)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * (z * (((1.0 - (a * b)) / z) - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9d-15)) .or. (.not. (y <= 2.2d-34))) then
        tmp = x * (z ** y)
    else
        tmp = x * (z * (((1.0d0 - (a * b)) / z) - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e-15) || !(y <= 2.2e-34)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * (z * (((1.0 - (a * b)) / z) - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9e-15) or not (y <= 2.2e-34):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * (z * (((1.0 - (a * b)) / z) - a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9e-15) || !(y <= 2.2e-34))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * Float64(z * Float64(Float64(Float64(1.0 - Float64(a * b)) / z) - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9e-15) || ~((y <= 2.2e-34)))
		tmp = x * (z ^ y);
	else
		tmp = x * (z * (((1.0 - (a * b)) / z) - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9e-15], N[Not[LessEqual[y, 2.2e-34]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[(z * N[(N[(N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.9999999999999995e-15 or 2.1999999999999999e-34 < y

   1. Initial program 97.0%

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

   3. Taylor expanded in y around inf 84.4%

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

   4. Taylor expanded in t around 0 62.9%

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

   if -8.9999999999999995e-15 < y < 2.1999999999999999e-34

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0 88.0%

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

      1. sub-neg 88.0%

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

      2. log1p-define 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in z around 0 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-*r* 90.9%

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

      3. associate-*r* 90.9%

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

      4. distribute-lft-out 90.9%

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

      5. mul-1-neg 90.9%

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

   8. Simplified 90.9%

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

   9. Taylor expanded in a around 0 49.9%

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

       1. associate-*r* 49.9%

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

       2. mul-1-neg 49.9%

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

   11. Simplified 49.9%

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

   12. Taylor expanded in z around inf 55.1%

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

       1. +-commutative 55.1%

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

       2. mul-1-neg 55.1%

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

       3. unsub-neg 55.1%

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

       4. +-commutative 55.1%

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

       5. mul-1-neg 55.1%

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

       6. unsub-neg 55.1%

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

       7. div-sub 55.1%

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

   14. Simplified 55.1%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-15} \lor \neg \left(y \leq 2.2 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(\frac{1 - a \cdot b}{z} - a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.4% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(z \cdot \left(\frac{1 - a \cdot b}{z} - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.1e+33)
   (* t (- (/ x t) (* x y)))
   (if (<= y 1.32e+16)
     (* x (* z (- (/ (- 1.0 (* a b)) z) a)))
     (* a (* x (- z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.1e+33) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 1.32e+16) {
		tmp = x * (z * (((1.0 - (a * b)) / z) - a));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.1d+33)) then
        tmp = t * ((x / t) - (x * y))
    else if (y <= 1.32d+16) then
        tmp = x * (z * (((1.0d0 - (a * b)) / z) - a))
    else
        tmp = a * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.1e+33) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 1.32e+16) {
		tmp = x * (z * (((1.0 - (a * b)) / z) - a));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.1e+33:
		tmp = t * ((x / t) - (x * y))
	elif y <= 1.32e+16:
		tmp = x * (z * (((1.0 - (a * b)) / z) - a))
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.1e+33)
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	elseif (y <= 1.32e+16)
		tmp = Float64(x * Float64(z * Float64(Float64(Float64(1.0 - Float64(a * b)) / z) - a)));
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.1e+33)
		tmp = t * ((x / t) - (x * y));
	elseif (y <= 1.32e+16)
		tmp = x * (z * (((1.0 - (a * b)) / z) - a));
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.1e+33], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.32e+16], N[(x * N[(z * N[(N[(N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.09999999999999995e33

   1. Initial program 97.8%

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

   3. Taylor expanded in t around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-lft-neg-out 58.8%

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

      3. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in y around 0 15.8%

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

      1. mul-1-neg 15.8%

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

      2. *-commutative 15.8%

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

      3. unsub-neg 15.8%

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

   8. Simplified 15.8%

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

   9. Taylor expanded in t around inf 22.0%

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

       1. neg-mul-1 22.0%

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

       2. +-commutative 22.0%

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

       3. sub-neg 22.0%

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

   11. Simplified 22.0%

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

   if -4.09999999999999995e33 < y < 1.32e16

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 82.2%

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

      1. sub-neg 82.2%

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

      2. log1p-define 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in z around 0 86.4%

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

      1. +-commutative 86.4%

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

      2. associate-*r* 86.4%

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

      3. associate-*r* 86.4%

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

      4. distribute-lft-out 86.4%

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

      5. mul-1-neg 86.4%

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

   8. Simplified 86.4%

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

   9. Taylor expanded in a around 0 45.2%

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

       1. associate-*r* 45.2%

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

       2. mul-1-neg 45.2%

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

   11. Simplified 45.2%

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

   12. Taylor expanded in z around inf 50.5%

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

       1. +-commutative 50.5%

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

       2. mul-1-neg 50.5%

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

       3. unsub-neg 50.5%

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

       4. +-commutative 50.5%

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

       5. mul-1-neg 50.5%

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

       6. unsub-neg 50.5%

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

       7. div-sub 50.5%

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

   14. Simplified 50.5%

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

   if 1.32e16 < y

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 32.9%

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

      1. sub-neg 32.9%

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

      2. log1p-define 32.8%

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

   5. Simplified 32.8%

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

   6. Taylor expanded in z around 0 32.8%

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

      1. +-commutative 32.8%

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

      2. associate-*r* 32.8%

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

      3. associate-*r* 32.8%

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

      4. distribute-lft-out 32.8%

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

      5. mul-1-neg 32.8%

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

   8. Simplified 32.8%

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

   9. Taylor expanded in a around 0 8.1%

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

       1. associate-*r* 8.1%

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

       2. mul-1-neg 8.1%

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

   11. Simplified 8.1%

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

   12. Taylor expanded in z around inf 30.3%

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

       1. associate-*r* 30.3%

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

       2. mul-1-neg 30.3%

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

   14. Simplified 30.3%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(z \cdot \left(\frac{1 - a \cdot b}{z} - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 33.5% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-109}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+17}:\\ \;\;\;\;x - a \cdot \left(x \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4e-109)
   (* t (- (/ x t) (* x y)))
   (if (<= y 1.06e+17) (- x (* a (* x (+ z b)))) (* a (* x (- z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4e-109) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 1.06e+17) {
		tmp = x - (a * (x * (z + b)));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4d-109)) then
        tmp = t * ((x / t) - (x * y))
    else if (y <= 1.06d+17) then
        tmp = x - (a * (x * (z + b)))
    else
        tmp = a * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4e-109) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 1.06e+17) {
		tmp = x - (a * (x * (z + b)));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4e-109:
		tmp = t * ((x / t) - (x * y))
	elif y <= 1.06e+17:
		tmp = x - (a * (x * (z + b)))
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4e-109)
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	elseif (y <= 1.06e+17)
		tmp = Float64(x - Float64(a * Float64(x * Float64(z + b))));
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4e-109)
		tmp = t * ((x / t) - (x * y));
	elseif (y <= 1.06e+17)
		tmp = x - (a * (x * (z + b)));
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4e-109], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e+17], N[(x - N[(a * N[(x * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4e-109

   1. Initial program 98.7%

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

   3. Taylor expanded in t around inf 56.3%

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

      1. mul-1-neg 56.3%

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

      2. distribute-lft-neg-out 56.3%

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

      3. *-commutative 56.3%

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

   5. Simplified 56.3%

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

   6. Taylor expanded in y around 0 25.5%

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

      1. mul-1-neg 25.5%

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

      2. *-commutative 25.5%

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

      3. unsub-neg 25.5%

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

   8. Simplified 25.5%

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

   9. Taylor expanded in t around inf 31.5%

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

       1. neg-mul-1 31.5%

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

       2. +-commutative 31.5%

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

       3. sub-neg 31.5%

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

   11. Simplified 31.5%

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

   if -4e-109 < y < 1.06e17

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 84.8%

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

      1. sub-neg 84.8%

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

      2. log1p-define 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in z around 0 90.2%

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

      1. +-commutative 90.2%

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

      2. associate-*r* 90.2%

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

      3. associate-*r* 90.2%

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

      4. distribute-lft-out 90.2%

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

      5. mul-1-neg 90.2%

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

   8. Simplified 90.2%

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

   9. Taylor expanded in a around 0 46.6%

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

       1. mul-1-neg 46.6%

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

       2. unsub-neg 46.6%

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

       3. *-commutative 46.6%

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

   11. Simplified 46.6%

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

   if 1.06e17 < y

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 32.9%

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

      1. sub-neg 32.9%

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

      2. log1p-define 32.8%

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

   5. Simplified 32.8%

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

   6. Taylor expanded in z around 0 32.8%

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

      1. +-commutative 32.8%

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

      2. associate-*r* 32.8%

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

      3. associate-*r* 32.8%

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

      4. distribute-lft-out 32.8%

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

      5. mul-1-neg 32.8%

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

   8. Simplified 32.8%

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

   9. Taylor expanded in a around 0 8.1%

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

       1. associate-*r* 8.1%

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

       2. mul-1-neg 8.1%

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

   11. Simplified 8.1%

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

   12. Taylor expanded in z around inf 30.3%

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

       1. associate-*r* 30.3%

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

       2. mul-1-neg 30.3%

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

   14. Simplified 30.3%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-109}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+17}:\\ \;\;\;\;x - a \cdot \left(x \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 33.3% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+16}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.2e-106)
   (* t (- (/ x t) (* x y)))
   (if (<= y 1.15e+16) (- x (* a (* x b))) (* a (* x (- z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.2e-106) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 1.15e+16) {
		tmp = x - (a * (x * b));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6.2d-106)) then
        tmp = t * ((x / t) - (x * y))
    else if (y <= 1.15d+16) then
        tmp = x - (a * (x * b))
    else
        tmp = a * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.2e-106) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 1.15e+16) {
		tmp = x - (a * (x * b));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.2e-106:
		tmp = t * ((x / t) - (x * y))
	elif y <= 1.15e+16:
		tmp = x - (a * (x * b))
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.2e-106)
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	elseif (y <= 1.15e+16)
		tmp = Float64(x - Float64(a * Float64(x * b)));
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.2e-106)
		tmp = t * ((x / t) - (x * y));
	elseif (y <= 1.15e+16)
		tmp = x - (a * (x * b));
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.2e-106], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+16], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.19999999999999971e-106

   1. Initial program 98.7%

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

   3. Taylor expanded in t around inf 56.3%

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

      1. mul-1-neg 56.3%

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

      2. distribute-lft-neg-out 56.3%

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

      3. *-commutative 56.3%

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

   5. Simplified 56.3%

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

   6. Taylor expanded in y around 0 25.5%

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

      1. mul-1-neg 25.5%

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

      2. *-commutative 25.5%

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

      3. unsub-neg 25.5%

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

   8. Simplified 25.5%

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

   9. Taylor expanded in t around inf 31.5%

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

       1. neg-mul-1 31.5%

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

       2. +-commutative 31.5%

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

       3. sub-neg 31.5%

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

   11. Simplified 31.5%

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

   if -6.19999999999999971e-106 < y < 1.15e16

   1. Initial program 97.0%

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

   3. Taylor expanded in b around inf 84.8%

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

      1. mul-1-neg 84.8%

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

      2. distribute-rgt-neg-out 84.8%

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

   5. Simplified 84.8%

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

   6. Taylor expanded in a around 0 46.6%

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

      1. mul-1-neg 46.6%

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

      2. unsub-neg 46.6%

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

      3. *-commutative 46.6%

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

   8. Simplified 46.6%

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

   if 1.15e16 < y

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 32.9%

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

      1. sub-neg 32.9%

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

      2. log1p-define 32.8%

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

   5. Simplified 32.8%

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

   6. Taylor expanded in z around 0 32.8%

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

      1. +-commutative 32.8%

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

      2. associate-*r* 32.8%

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

      3. associate-*r* 32.8%

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

      4. distribute-lft-out 32.8%

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

      5. mul-1-neg 32.8%

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

   8. Simplified 32.8%

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

   9. Taylor expanded in a around 0 8.1%

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

       1. associate-*r* 8.1%

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

       2. mul-1-neg 8.1%

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

   11. Simplified 8.1%

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

   12. Taylor expanded in z around inf 30.3%

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

       1. associate-*r* 30.3%

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

       2. mul-1-neg 30.3%

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

   14. Simplified 30.3%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+16}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.6% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+24}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.05e+24)
   (- x (* t (* x y)))
   (if (<= y 6e+17) (* x (- 1.0 (* a b))) (* a (* x (- z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.05e+24) {
		tmp = x - (t * (x * y));
	} else if (y <= 6e+17) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.05d+24)) then
        tmp = x - (t * (x * y))
    else if (y <= 6d+17) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = a * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.05e+24) {
		tmp = x - (t * (x * y));
	} else if (y <= 6e+17) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.05e+24:
		tmp = x - (t * (x * y))
	elif y <= 6e+17:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.05e+24)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif (y <= 6e+17)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.05e+24)
		tmp = x - (t * (x * y));
	elseif (y <= 6e+17)
		tmp = x * (1.0 - (a * b));
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.05e+24], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+17], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0500000000000001e24

   1. Initial program 97.8%

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

   3. Taylor expanded in t around inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. distribute-lft-neg-out 57.6%

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

      3. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in y around 0 17.6%

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

      1. mul-1-neg 17.6%

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

      2. unsub-neg 17.6%

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

   8. Simplified 17.6%

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

   if -1.0500000000000001e24 < y < 6e17

   1. Initial program 97.6%

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

   3. Taylor expanded in b around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. distribute-rgt-neg-out 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in a around 0 45.4%

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

      1. mul-1-neg 45.4%

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

      2. unsub-neg 45.4%

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

   8. Simplified 45.4%

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

   if 6e17 < y

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 32.9%

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

      1. sub-neg 32.9%

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

      2. log1p-define 32.8%

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

   5. Simplified 32.8%

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

   6. Taylor expanded in z around 0 32.8%

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

      1. +-commutative 32.8%

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

      2. associate-*r* 32.8%

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

      3. associate-*r* 32.8%

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

      4. distribute-lft-out 32.8%

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

      5. mul-1-neg 32.8%

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

   8. Simplified 32.8%

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

   9. Taylor expanded in a around 0 8.1%

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

       1. associate-*r* 8.1%

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

       2. mul-1-neg 8.1%

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

   11. Simplified 8.1%

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

   12. Taylor expanded in z around inf 30.3%

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

       1. associate-*r* 30.3%

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

       2. mul-1-neg 30.3%

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

   14. Simplified 30.3%

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

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+24}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.7% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.8e+23)
   (* t (* x (- y)))
   (if (<= y 4.1e+16) (* x (- 1.0 (* a b))) (* a (* x (- z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.8e+23) {
		tmp = t * (x * -y);
	} else if (y <= 4.1e+16) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * (x * -z);
	}
	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 <= (-3.8d+23)) then
        tmp = t * (x * -y)
    else if (y <= 4.1d+16) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = a * (x * -z)
    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 <= -3.8e+23) {
		tmp = t * (x * -y);
	} else if (y <= 4.1e+16) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.8e+23:
		tmp = t * (x * -y)
	elif y <= 4.1e+16:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.8e+23)
		tmp = Float64(t * Float64(x * Float64(-y)));
	elseif (y <= 4.1e+16)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(a * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.8e+23)
		tmp = t * (x * -y);
	elseif (y <= 4.1e+16)
		tmp = x * (1.0 - (a * b));
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.8e+23], N[(t * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+16], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.79999999999999975e23

   1. Initial program 97.8%

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

   3. Taylor expanded in t around inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. distribute-lft-neg-out 57.6%

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

      3. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in y around 0 15.5%

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

      1. mul-1-neg 15.5%

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

      2. *-commutative 15.5%

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

      3. unsub-neg 15.5%

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

   8. Simplified 15.5%

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

   9. Taylor expanded in y around inf 17.4%

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

   if -3.79999999999999975e23 < y < 4.1e16

   1. Initial program 97.6%

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

   3. Taylor expanded in b around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. distribute-rgt-neg-out 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in a around 0 45.4%

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

      1. mul-1-neg 45.4%

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

      2. unsub-neg 45.4%

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

   8. Simplified 45.4%

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

   if 4.1e16 < y

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 32.9%

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

      1. sub-neg 32.9%

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

      2. log1p-define 32.8%

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

   5. Simplified 32.8%

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

   6. Taylor expanded in z around 0 32.8%

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

      1. +-commutative 32.8%

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

      2. associate-*r* 32.8%

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

      3. associate-*r* 32.8%

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

      4. distribute-lft-out 32.8%

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

      5. mul-1-neg 32.8%

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

   8. Simplified 32.8%

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

   9. Taylor expanded in a around 0 8.1%

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

       1. associate-*r* 8.1%

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

       2. mul-1-neg 8.1%

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

   11. Simplified 8.1%

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

   12. Taylor expanded in z around inf 30.3%

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

       1. associate-*r* 30.3%

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

       2. mul-1-neg 30.3%

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

   14. Simplified 30.3%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 24.5% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+121} \lor \neg \left(b \leq 1.35 \cdot 10^{+87}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.5e+121) (not (<= b 1.35e+87))) (* a (* x (- b))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.5e+121) || !(b <= 1.35e+87)) {
		tmp = a * (x * -b);
	} else {
		tmp = 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 <= (-2.5d+121)) .or. (.not. (b <= 1.35d+87))) then
        tmp = a * (x * -b)
    else
        tmp = 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 <= -2.5e+121) || !(b <= 1.35e+87)) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.5e+121) or not (b <= 1.35e+87):
		tmp = a * (x * -b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.5e+121) || !(b <= 1.35e+87))
		tmp = Float64(a * Float64(x * Float64(-b)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.5e+121) || ~((b <= 1.35e+87)))
		tmp = a * (x * -b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.5e+121], N[Not[LessEqual[b, 1.35e+87]], $MachinePrecision]], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -2.50000000000000004e121 or 1.35000000000000003e87 < b

   1. Initial program 98.9%

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

   3. Taylor expanded in b around inf 81.3%

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

      1. mul-1-neg 81.3%

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

      2. distribute-rgt-neg-out 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in a around 0 30.3%

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

      1. mul-1-neg 30.3%

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

      2. unsub-neg 30.3%

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

      3. *-commutative 30.3%

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

   8. Simplified 30.3%

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

   9. Taylor expanded in a around inf 30.3%

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

       1. associate-*r* 30.3%

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

       2. mul-1-neg 30.3%

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

       3. *-commutative 30.3%

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

   11. Simplified 30.3%

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

   if -2.50000000000000004e121 < b < 1.35000000000000003e87

   1. Initial program 96.6%

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

   3. Taylor expanded in y around inf 80.3%

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

   4. Taylor expanded in y around 0 28.8%

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

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+121} \lor \neg \left(b \leq 1.35 \cdot 10^{+87}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.4% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+68} \lor \neg \left(y \leq 6.4\right):\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.6e+68) (not (<= y 6.4))) (* x (* t (- y))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.6e+68) || !(y <= 6.4)) {
		tmp = x * (t * -y);
	} else {
		tmp = 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 ((y <= (-8.6d+68)) .or. (.not. (y <= 6.4d0))) then
        tmp = x * (t * -y)
    else
        tmp = 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 ((y <= -8.6e+68) || !(y <= 6.4)) {
		tmp = x * (t * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.6e+68) or not (y <= 6.4):
		tmp = x * (t * -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.6e+68) || !(y <= 6.4))
		tmp = Float64(x * Float64(t * Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.6e+68) || ~((y <= 6.4)))
		tmp = x * (t * -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.6e+68], N[Not[LessEqual[y, 6.4]], $MachinePrecision]], N[(x * N[(t * (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.6000000000000002e68 or 6.4000000000000004 < y

   1. Initial program 97.0%

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

   3. Taylor expanded in t around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. distribute-lft-neg-out 60.0%

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

      3. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in y around 0 17.1%

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

      1. mul-1-neg 17.1%

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

      2. *-commutative 17.1%

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

      3. unsub-neg 17.1%

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

   8. Simplified 17.1%

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

   9. Taylor expanded in y around inf 16.2%

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

       1. associate-*r* 16.2%

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

       2. neg-mul-1 16.2%

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

       3. *-commutative 16.2%

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

       4. associate-*r* 18.1%

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

       5. *-commutative 18.1%

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

       6. neg-mul-1 18.1%

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

       7. associate-*r* 18.1%

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

       8. mul-1-neg 18.1%

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

       9. distribute-rgt-neg-in 18.1%

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

   11. Simplified 18.1%

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

   if -8.6000000000000002e68 < y < 6.4000000000000004

   1. Initial program 97.6%

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

   3. Taylor expanded in y around inf 54.2%

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

   4. Taylor expanded in y around 0 31.7%

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

4. Final simplification 26.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+68} \lor \neg \left(y \leq 6.4\right):\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.4% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.25e+70)
   (* x (* t (- y)))
   (if (<= y 1.12e+16) x (* x (* z (- a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.25e+70) {
		tmp = x * (t * -y);
	} else if (y <= 1.12e+16) {
		tmp = x;
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.25d+70)) then
        tmp = x * (t * -y)
    else if (y <= 1.12d+16) then
        tmp = x
    else
        tmp = x * (z * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.25e+70) {
		tmp = x * (t * -y);
	} else if (y <= 1.12e+16) {
		tmp = x;
	} else {
		tmp = x * (z * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.25e+70:
		tmp = x * (t * -y)
	elif y <= 1.12e+16:
		tmp = x
	else:
		tmp = x * (z * -a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.25e+70)
		tmp = Float64(x * Float64(t * Float64(-y)));
	elseif (y <= 1.12e+16)
		tmp = x;
	else
		tmp = Float64(x * Float64(z * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.25e+70)
		tmp = x * (t * -y);
	elseif (y <= 1.12e+16)
		tmp = x;
	else
		tmp = x * (z * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.25e+70], N[(x * N[(t * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e+16], x, N[(x * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2500000000000001e70

   1. Initial program 97.4%

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

   3. Taylor expanded in t around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. distribute-lft-neg-out 59.9%

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

      3. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in y around 0 17.6%

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

      1. mul-1-neg 17.6%

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

      2. *-commutative 17.6%

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

      3. unsub-neg 17.6%

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

   8. Simplified 17.6%

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

   9. Taylor expanded in y around inf 19.8%

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

       1. associate-*r* 19.8%

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

       2. neg-mul-1 19.8%

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

       3. *-commutative 19.8%

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

       4. associate-*r* 17.4%

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

       5. *-commutative 17.4%

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

       6. neg-mul-1 17.4%

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

       7. associate-*r* 17.4%

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

       8. mul-1-neg 17.4%

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

       9. distribute-rgt-neg-in 17.4%

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

   11. Simplified 17.4%

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

   if -1.2500000000000001e70 < y < 1.12e16

   1. Initial program 97.7%

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

   3. Taylor expanded in y around inf 55.3%

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

   4. Taylor expanded in y around 0 30.6%

      \[\leadsto \color{blue}{x} \]

   if 1.12e16 < y

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 32.9%

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

      1. sub-neg 32.9%

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

      2. log1p-define 32.8%

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

   5. Simplified 32.8%

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

   6. Taylor expanded in z around 0 32.8%

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

      1. +-commutative 32.8%

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

      2. associate-*r* 32.8%

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

      3. associate-*r* 32.8%

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

      4. distribute-lft-out 32.8%

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

      5. mul-1-neg 32.8%

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

   8. Simplified 32.8%

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

   9. Taylor expanded in a around 0 8.1%

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

       1. associate-*r* 8.1%

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

       2. mul-1-neg 8.1%

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

   11. Simplified 8.1%

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

   12. Taylor expanded in z around inf 30.3%

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

       1. mul-1-neg 30.3%

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

       2. associate-*r* 25.1%

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

       3. *-commutative 25.1%

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

       4. associate-*l* 28.6%

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

       5. *-commutative 28.6%

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

       6. distribute-rgt-neg-out 28.6%

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

       7. distribute-rgt-neg-in 28.6%

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

   14. Simplified 28.6%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(-a\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 20.0% accurate, 315.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return 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 = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 97.4%

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

3. Taylor expanded in y around inf 67.1%

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

4. Taylor expanded in y around 0 20.7%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024089 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))