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

Percentage Accurate: 96.5% → 99.6%

Time: 24.2s

Alternatives: 15

Speedup: 0.8×

• 20.8% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.2%

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

   1. +-commutative 94.2%

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

   2. fma-def 94.6%

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

   3. sub-neg 94.6%

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

   4. log1p-def 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 96.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+268}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5e+268)
   (* x (exp (* a (- (- b) z))))
   (* 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) {
	double tmp;
	if (a <= -5e+268) {
		tmp = x * exp((a * (-b - z)));
	} else {
		tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - 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 (a <= (-5d+268)) then
        tmp = x * exp((a * (-b - z)))
    else
        tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - 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 (a <= -5e+268) {
		tmp = x * Math.exp((a * (-b - z)));
	} else {
		tmp = x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5e+268:
		tmp = x * math.exp((a * (-b - z)))
	else:
		tmp = x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5e+268)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-b) - z))));
	else
		tmp = Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5e+268)
		tmp = x * exp((a * (-b - z)));
	else
		tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5e+268], N[(x * N[Exp[N[(a * N[((-b) - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 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. Split input into 2 regimes

2. if a < -5.0000000000000002e268

   1. Initial program 17.7%

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

   2. Taylor expanded in y around 0 34.4%

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

      1. sub-neg 34.4%

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

      2. neg-mul-1 34.4%

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

      3. log1p-def 100.0%

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

      4. neg-mul-1 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r* 100.0%

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

      3. associate-*r* 100.0%

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

      4. distribute-lft-out 100.0%

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

      5. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

   if -5.0000000000000002e268 < a

   1. Initial program 96.0%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+268}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\\ \end{array} \]

Alternative 3: 86.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+18} \lor \neg \left(y \leq 4.5\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.45e+18) (not (<= y 4.5)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (- b) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e+18) || !(y <= 4.5)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((a * (-b - 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 <= (-1.45d+18)) .or. (.not. (y <= 4.5d0))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((a * (-b - 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 <= -1.45e+18) || !(y <= 4.5)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * (-b - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.45e+18) or not (y <= 4.5):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * (-b - z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.45e+18) || !(y <= 4.5))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-b) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.45e+18) || ~((y <= 4.5)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((a * (-b - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.45e+18], N[Not[LessEqual[y, 4.5]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[((-b) - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e18 or 4.5 < y

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 87.3%

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

   if -1.45e18 < y < 4.5

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 77.6%

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

      1. sub-neg 77.6%

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

      2. neg-mul-1 77.6%

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

      3. log1p-def 86.1%

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

      4. neg-mul-1 86.1%

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

   4. Simplified 86.1%

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

   5. Taylor expanded in z around 0 86.1%

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

      1. +-commutative 86.1%

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

      2. associate-*r* 86.1%

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

      3. associate-*r* 86.1%

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

      4. distribute-lft-out 86.1%

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

      5. neg-mul-1 86.1%

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

   7. Simplified 86.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+18} \lor \neg \left(y \leq 4.5\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \end{array} \]

Alternative 4: 72.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+15} \lor \neg \left(a \leq 1.1 \cdot 10^{-105}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.9e+15) (not (<= a 1.1e-105)))
   (* x (exp (* a (- (- b) z))))
   (* x (exp (* y (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.9e+15) || !(a <= 1.1e-105)) {
		tmp = x * exp((a * (-b - z)));
	} else {
		tmp = x * exp((y * -t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.9d+15)) .or. (.not. (a <= 1.1d-105))) then
        tmp = x * exp((a * (-b - z)))
    else
        tmp = x * exp((y * -t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.9e+15) || !(a <= 1.1e-105)) {
		tmp = x * Math.exp((a * (-b - z)));
	} else {
		tmp = x * Math.exp((y * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.9e+15) or not (a <= 1.1e-105):
		tmp = x * math.exp((a * (-b - z)))
	else:
		tmp = x * math.exp((y * -t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.9e+15) || !(a <= 1.1e-105))
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-b) - z))));
	else
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.9e+15) || ~((a <= 1.1e-105)))
		tmp = x * exp((a * (-b - z)));
	else
		tmp = x * exp((y * -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.9e+15], N[Not[LessEqual[a, 1.1e-105]], $MachinePrecision]], N[(x * N[Exp[N[(a * N[((-b) - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9e15 or 1.10000000000000002e-105 < a

   1. Initial program 90.7%

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

   2. Taylor expanded in y around 0 67.8%

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

      1. sub-neg 67.8%

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

      2. neg-mul-1 67.8%

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

      3. log1p-def 79.9%

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

      4. neg-mul-1 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in z around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-*r* 79.9%

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

      3. associate-*r* 79.9%

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

      4. distribute-lft-out 79.9%

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

      5. neg-mul-1 79.9%

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

   7. Simplified 79.9%

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

   if -1.9e15 < a < 1.10000000000000002e-105

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.0%

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

      1. mul-1-neg 76.0%

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

      2. distribute-rgt-neg-out 76.0%

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

   4. Simplified 76.0%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+15} \lor \neg \left(a \leq 1.1 \cdot 10^{-105}\right):\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-b\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 5: 73.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+24} \lor \neg \left(y \leq 0.7\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2e+24) (not (<= y 0.7)))
   (* 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 <= -2e+24) || !(y <= 0.7)) {
		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 <= (-2d+24)) .or. (.not. (y <= 0.7d0))) 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 <= -2e+24) || !(y <= 0.7)) {
		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 <= -2e+24) or not (y <= 0.7):
		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 <= -2e+24) || !(y <= 0.7))
		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 <= -2e+24) || ~((y <= 0.7)))
		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, -2e+24], N[Not[LessEqual[y, 0.7]], $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 < -2e24 or 0.69999999999999996 < y

   1. Initial program 95.6%

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

   2. Taylor expanded in y around inf 86.9%

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

   3. Taylor expanded in t around 0 69.5%

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

   if -2e24 < y < 0.69999999999999996

   1. Initial program 93.0%

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

   2. Taylor expanded in b around inf 74.7%

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

      1. associate-*r* 74.7%

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

      2. *-commutative 74.7%

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

      3. neg-mul-1 74.7%

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

   4. Simplified 74.7%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+24} \lor \neg \left(y \leq 0.7\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 6: 72.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+47} \lor \neg \left(t \leq 1.45 \cdot 10^{-74}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9.4e+47) (not (<= t 1.45e-74)))
   (* x (exp (* y (- t))))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9.4e+47) || !(t <= 1.45e-74)) {
		tmp = x * exp((y * -t));
	} 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 ((t <= (-9.4d+47)) .or. (.not. (t <= 1.45d-74))) then
        tmp = x * exp((y * -t))
    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 ((t <= -9.4e+47) || !(t <= 1.45e-74)) {
		tmp = x * Math.exp((y * -t));
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9.4e+47) or not (t <= 1.45e-74):
		tmp = x * math.exp((y * -t))
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9.4e+47) || !(t <= 1.45e-74))
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	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 ((t <= -9.4e+47) || ~((t <= 1.45e-74)))
		tmp = x * exp((y * -t));
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9.4e+47], N[Not[LessEqual[t, 1.45e-74]], $MachinePrecision]], N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.39999999999999928e47 or 1.45e-74 < t

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. distribute-rgt-neg-out 76.2%

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

   4. Simplified 76.2%

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

   if -9.39999999999999928e47 < t < 1.45e-74

   1. Initial program 93.7%

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

   2. Taylor expanded in b around inf 70.8%

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

      1. associate-*r* 70.8%

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

      2. *-commutative 70.8%

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

      3. neg-mul-1 70.8%

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

   4. Simplified 70.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+47} \lor \neg \left(t \leq 1.45 \cdot 10^{-74}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 7: 55.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-67} \lor \neg \left(y \leq 3.05 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot \left(z + b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.2e-67) (not (<= y 3.05e-15)))
   (* x (pow z y))
   (- x (* a (* x (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.2e-67) || !(y <= 3.05e-15)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x - (a * (x * (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 <= (-8.2d-67)) .or. (.not. (y <= 3.05d-15))) then
        tmp = x * (z ** y)
    else
        tmp = x - (a * (x * (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 <= -8.2e-67) || !(y <= 3.05e-15)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x - (a * (x * (z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.2e-67) or not (y <= 3.05e-15):
		tmp = x * math.pow(z, y)
	else:
		tmp = x - (a * (x * (z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.2e-67) || !(y <= 3.05e-15))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x - Float64(a * Float64(x * Float64(z + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.2e-67) || ~((y <= 3.05e-15)))
		tmp = x * (z ^ y);
	else
		tmp = x - (a * (x * (z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.2e-67], N[Not[LessEqual[y, 3.05e-15]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(x * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999994e-67 or 3.04999999999999986e-15 < y

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 82.8%

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

   3. Taylor expanded in t around 0 62.1%

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

   if -8.1999999999999994e-67 < y < 3.04999999999999986e-15

   1. Initial program 92.4%

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

   2. Taylor expanded in y around 0 79.3%

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

      1. sub-neg 79.3%

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

      2. neg-mul-1 79.3%

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

      3. log1p-def 87.7%

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

      4. neg-mul-1 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in z around 0 87.7%

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

      1. +-commutative 87.7%

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

      2. associate-*r* 87.7%

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

      3. associate-*r* 87.7%

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

      4. distribute-lft-out 87.7%

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

      5. neg-mul-1 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in a around 0 41.6%

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

      1. +-commutative 41.6%

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

      2. mul-1-neg 41.6%

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

      3. unsub-neg 41.6%

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

   10. Simplified 41.6%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-67} \lor \neg \left(y \leq 3.05 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot \left(z + b\right)\right)\\ \end{array} \]

Alternative 8: 25.9% accurate, 22.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00034:\\ \;\;\;\;\left(-b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-292} \lor \neg \left(y \leq 2.2 \cdot 10^{-17}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -0.00034)
   (* (- b) (* x a))
   (if (<= y -1.1e-220)
     x
     (if (or (<= y -7.2e-292) (not (<= y 2.2e-17))) (* a (* x (- z))) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -0.00034) {
		tmp = -b * (x * a);
	} else if (y <= -1.1e-220) {
		tmp = x;
	} else if ((y <= -7.2e-292) || !(y <= 2.2e-17)) {
		tmp = a * (x * -z);
	} 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 <= (-0.00034d0)) then
        tmp = -b * (x * a)
    else if (y <= (-1.1d-220)) then
        tmp = x
    else if ((y <= (-7.2d-292)) .or. (.not. (y <= 2.2d-17))) then
        tmp = a * (x * -z)
    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 <= -0.00034) {
		tmp = -b * (x * a);
	} else if (y <= -1.1e-220) {
		tmp = x;
	} else if ((y <= -7.2e-292) || !(y <= 2.2e-17)) {
		tmp = a * (x * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -0.00034:
		tmp = -b * (x * a)
	elif y <= -1.1e-220:
		tmp = x
	elif (y <= -7.2e-292) or not (y <= 2.2e-17):
		tmp = a * (x * -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -0.00034)
		tmp = Float64(Float64(-b) * Float64(x * a));
	elseif (y <= -1.1e-220)
		tmp = x;
	elseif ((y <= -7.2e-292) || !(y <= 2.2e-17))
		tmp = Float64(a * Float64(x * Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -0.00034)
		tmp = -b * (x * a);
	elseif (y <= -1.1e-220)
		tmp = x;
	elseif ((y <= -7.2e-292) || ~((y <= 2.2e-17)))
		tmp = a * (x * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -0.00034], N[((-b) * N[(x * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e-220], x, If[Or[LessEqual[y, -7.2e-292], N[Not[LessEqual[y, 2.2e-17]], $MachinePrecision]], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4e-4

   1. Initial program 98.2%

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

   2. Taylor expanded in b around inf 43.8%

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

      1. associate-*r* 43.8%

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

      2. *-commutative 43.8%

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

      3. neg-mul-1 43.8%

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

   4. Simplified 43.8%

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

   5. Taylor expanded in b around 0 10.4%

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

      1. +-commutative 10.4%

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

      2. mul-1-neg 10.4%

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

      3. unsub-neg 10.4%

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

      4. associate-*r* 17.2%

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

      5. *-commutative 17.2%

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

   7. Simplified 17.2%

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

   8. Taylor expanded in a around inf 13.2%

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

      1. mul-1-neg 13.2%

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

      2. *-commutative 13.2%

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

      3. associate-*r* 18.3%

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

      4. distribute-rgt-neg-in 18.3%

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

      5. *-commutative 18.3%

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

   10. Simplified 18.3%

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

   if -3.4e-4 < y < -1.09999999999999993e-220 or -7.2000000000000004e-292 < y < 2.2e-17

   1. Initial program 93.7%

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

   2. Taylor expanded in b around inf 75.5%

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

      1. associate-*r* 75.5%

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

      2. *-commutative 75.5%

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

      3. neg-mul-1 75.5%

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

   4. Simplified 75.5%

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

   5. Taylor expanded in b around 0 34.6%

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

   if -1.09999999999999993e-220 < y < -7.2000000000000004e-292 or 2.2e-17 < y

   1. Initial program 92.3%

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

   2. Taylor expanded in y around 0 49.1%

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

      1. sub-neg 49.1%

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

      2. neg-mul-1 49.1%

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

      3. log1p-def 55.7%

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

      4. neg-mul-1 55.7%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in z around 0 55.7%

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

      1. +-commutative 55.7%

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

      2. associate-*r* 55.7%

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

      3. associate-*r* 55.7%

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

      4. distribute-lft-out 55.7%

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

      5. neg-mul-1 55.7%

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

   7. Simplified 55.7%

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

   8. Taylor expanded in a around 0 12.5%

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

      1. +-commutative 12.5%

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

      2. mul-1-neg 12.5%

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

      3. unsub-neg 12.5%

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

   10. Simplified 12.5%

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

   11. Taylor expanded in z around inf 32.3%

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

       1. mul-1-neg 32.3%

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

   13. Simplified 32.3%

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

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00034:\\ \;\;\;\;\left(-b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-220}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-292} \lor \neg \left(y \leq 2.2 \cdot 10^{-17}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 27.2% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00085:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-17}:\\ \;\;\;\;x + b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -0.00085)
   (* x (* a (- b)))
   (if (<= y 8.2e-17) (+ x (* b (* x a))) (* a (* x (- z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -0.00085) {
		tmp = x * (a * -b);
	} else if (y <= 8.2e-17) {
		tmp = x + (b * (x * 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 <= (-0.00085d0)) then
        tmp = x * (a * -b)
    else if (y <= 8.2d-17) then
        tmp = x + (b * (x * 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 <= -0.00085) {
		tmp = x * (a * -b);
	} else if (y <= 8.2e-17) {
		tmp = x + (b * (x * a));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -0.00085:
		tmp = x * (a * -b)
	elif y <= 8.2e-17:
		tmp = x + (b * (x * a))
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -0.00085)
		tmp = Float64(x * Float64(a * Float64(-b)));
	elseif (y <= 8.2e-17)
		tmp = Float64(x + Float64(b * Float64(x * 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 <= -0.00085)
		tmp = x * (a * -b);
	elseif (y <= 8.2e-17)
		tmp = x + (b * (x * a));
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -0.00085], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-17], N[(x + N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.49999999999999953e-4

   1. Initial program 98.2%

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

   2. Taylor expanded in b around inf 43.8%

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

      1. associate-*r* 43.8%

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

      2. *-commutative 43.8%

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

      3. neg-mul-1 43.8%

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

   4. Simplified 43.8%

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

   5. Taylor expanded in b around 0 10.4%

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

      1. +-commutative 10.4%

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

      2. mul-1-neg 10.4%

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

      3. unsub-neg 10.4%

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

      4. associate-*r* 17.2%

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

      5. *-commutative 17.2%

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

   7. Simplified 17.2%

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

   8. Taylor expanded in a around inf 13.2%

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

      1. mul-1-neg 13.2%

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

      2. distribute-rgt-neg-in 13.2%

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

   10. Simplified 13.2%

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

   11. Taylor expanded in a around 0 13.2%

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

       1. associate-*r* 13.2%

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

       2. associate-*r* 20.1%

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

       3. associate-*r* 20.1%

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

       4. *-commutative 20.1%

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

       5. mul-1-neg 20.1%

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

       6. distribute-rgt-neg-in 20.1%

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

   13. Simplified 20.1%

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

   if -8.49999999999999953e-4 < y < 8.2000000000000001e-17

   1. Initial program 93.1%

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

   2. Taylor expanded in b around inf 75.3%

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

      1. associate-*r* 75.3%

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

      2. *-commutative 75.3%

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

      3. neg-mul-1 75.3%

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

   4. Simplified 75.3%

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

   5. Taylor expanded in b around 0 35.6%

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

      1. +-commutative 35.6%

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

      2. mul-1-neg 35.6%

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

      3. unsub-neg 35.6%

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

      4. associate-*r* 34.8%

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

      5. *-commutative 34.8%

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

   7. Simplified 34.8%

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

      1. sub-neg 34.8%

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

      2. *-commutative 34.8%

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

      3. associate-*r* 35.6%

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

      4. mul-1-neg 35.6%

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

      5. +-commutative 35.6%

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

      6. mul-1-neg 35.6%

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

      7. *-commutative 35.6%

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

      8. distribute-rgt-neg-in 35.6%

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

      9. add-sqr-sqrt 17.2%

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

      10. sqrt-unprod 31.5%

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

      11. sqr-neg 31.5%

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

      12. sqrt-unprod 14.6%

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

      13. add-sqr-sqrt 30.1%

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

      14. associate-*l* 32.1%

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

   9. Applied egg-rr 32.1%

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

   if 8.2000000000000001e-17 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 39.5%

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

      1. sub-neg 39.5%

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

      2. neg-mul-1 39.5%

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

      3. log1p-def 45.0%

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

      4. neg-mul-1 45.0%

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

   4. Simplified 45.0%

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

   5. Taylor expanded in z around 0 45.0%

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

      1. +-commutative 45.0%

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

      2. associate-*r* 45.0%

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

      3. associate-*r* 45.0%

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

      4. distribute-lft-out 45.0%

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

      5. neg-mul-1 45.0%

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

   7. Simplified 45.0%

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

   8. Taylor expanded in a around 0 10.2%

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

      1. +-commutative 10.2%

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

      2. mul-1-neg 10.2%

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

      3. unsub-neg 10.2%

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

   10. Simplified 10.2%

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

   11. Taylor expanded in z around inf 33.3%

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

       1. mul-1-neg 33.3%

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

   13. Simplified 33.3%

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

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00085:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-17}:\\ \;\;\;\;x + b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 10: 28.5% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.17:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-16}:\\ \;\;\;\;x - a \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -0.17)
   (* x (* a (- b)))
   (if (<= y 4.1e-16) (- x (* a (* x z))) (* a (* x (- z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -0.17) {
		tmp = x * (a * -b);
	} else if (y <= 4.1e-16) {
		tmp = x - (a * (x * z));
	} 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 <= (-0.17d0)) then
        tmp = x * (a * -b)
    else if (y <= 4.1d-16) then
        tmp = x - (a * (x * z))
    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 <= -0.17) {
		tmp = x * (a * -b);
	} else if (y <= 4.1e-16) {
		tmp = x - (a * (x * z));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -0.17:
		tmp = x * (a * -b)
	elif y <= 4.1e-16:
		tmp = x - (a * (x * z))
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -0.17)
		tmp = Float64(x * Float64(a * Float64(-b)));
	elseif (y <= 4.1e-16)
		tmp = Float64(x - Float64(a * Float64(x * z)));
	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 <= -0.17)
		tmp = x * (a * -b);
	elseif (y <= 4.1e-16)
		tmp = x - (a * (x * z));
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -0.17], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e-16], N[(x - N[(a * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.170000000000000012

   1. Initial program 98.2%

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

   2. Taylor expanded in b around inf 43.8%

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

      1. associate-*r* 43.8%

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

      2. *-commutative 43.8%

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

      3. neg-mul-1 43.8%

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

   4. Simplified 43.8%

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

   5. Taylor expanded in b around 0 10.4%

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

      1. +-commutative 10.4%

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

      2. mul-1-neg 10.4%

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

      3. unsub-neg 10.4%

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

      4. associate-*r* 17.2%

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

      5. *-commutative 17.2%

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

   7. Simplified 17.2%

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

   8. Taylor expanded in a around inf 13.2%

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

      1. mul-1-neg 13.2%

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

      2. distribute-rgt-neg-in 13.2%

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

   10. Simplified 13.2%

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

   11. Taylor expanded in a around 0 13.2%

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

       1. associate-*r* 13.2%

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

       2. associate-*r* 20.1%

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

       3. associate-*r* 20.1%

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

       4. *-commutative 20.1%

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

       5. mul-1-neg 20.1%

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

       6. distribute-rgt-neg-in 20.1%

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

   13. Simplified 20.1%

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

   if -0.170000000000000012 < y < 4.10000000000000006e-16

   1. Initial program 93.1%

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

   2. Taylor expanded in y around 0 77.5%

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

      1. sub-neg 77.5%

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

      2. neg-mul-1 77.5%

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

      3. log1p-def 85.1%

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

      4. neg-mul-1 85.1%

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

   4. Simplified 85.1%

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

   5. Taylor expanded in z around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-*r* 85.1%

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

      3. associate-*r* 85.1%

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

      4. distribute-lft-out 85.1%

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

      5. neg-mul-1 85.1%

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

   7. Simplified 85.1%

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

   8. Taylor expanded in b around 0 46.3%

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

      1. mul-1-neg 46.3%

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

      2. *-commutative 46.3%

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

      3. distribute-rgt-neg-in 46.3%

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

   10. Simplified 46.3%

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

   11. Taylor expanded in z around 0 34.0%

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

       1. mul-1-neg 34.0%

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

       2. +-commutative 34.0%

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

       3. sub-neg 34.0%

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

   13. Simplified 34.0%

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

   if 4.10000000000000006e-16 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 39.5%

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

      1. sub-neg 39.5%

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

      2. neg-mul-1 39.5%

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

      3. log1p-def 45.0%

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

      4. neg-mul-1 45.0%

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

   4. Simplified 45.0%

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

   5. Taylor expanded in z around 0 45.0%

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

      1. +-commutative 45.0%

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

      2. associate-*r* 45.0%

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

      3. associate-*r* 45.0%

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

      4. distribute-lft-out 45.0%

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

      5. neg-mul-1 45.0%

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

   7. Simplified 45.0%

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

   8. Taylor expanded in a around 0 10.2%

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

      1. +-commutative 10.2%

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

      2. mul-1-neg 10.2%

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

      3. unsub-neg 10.2%

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

   10. Simplified 10.2%

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

   11. Taylor expanded in z around inf 33.3%

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

       1. mul-1-neg 33.3%

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

   13. Simplified 33.3%

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

4. Final simplification 30.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.17:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-16}:\\ \;\;\;\;x - a \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 11: 31.8% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.42 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.42e+80) (* x (- 1.0 (* a (+ z b)))) (* a (* x (- z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.42e+80) {
		tmp = x * (1.0 - (a * (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 <= 1.42d+80) then
        tmp = x * (1.0d0 - (a * (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 <= 1.42e+80) {
		tmp = x * (1.0 - (a * (z + b)));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.42e+80:
		tmp = x * (1.0 - (a * (z + b)))
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.42e+80)
		tmp = Float64(x * Float64(1.0 - Float64(a * 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 <= 1.42e+80)
		tmp = x * (1.0 - (a * (z + b)));
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.42e+80], N[(x * N[(1.0 - N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.4200000000000001e80

   1. Initial program 93.7%

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

   2. Taylor expanded in y around 0 65.1%

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

      1. sub-neg 65.1%

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

      2. neg-mul-1 65.1%

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

      3. log1p-def 74.1%

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

      4. neg-mul-1 74.1%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in z around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. associate-*r* 74.1%

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

      3. associate-*r* 74.1%

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

      4. distribute-lft-out 74.1%

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

      5. neg-mul-1 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in a around 0 30.5%

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

      1. +-commutative 30.5%

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

      2. mul-1-neg 30.5%

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

      3. unsub-neg 30.5%

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

   10. Simplified 30.5%

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

   11. Taylor expanded in x around inf 31.8%

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

   if 1.4200000000000001e80 < y

   1. Initial program 96.0%

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

   2. Taylor expanded in y around 0 38.6%

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

      1. sub-neg 38.6%

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

      2. neg-mul-1 38.6%

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

      3. log1p-def 40.5%

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

      4. neg-mul-1 40.5%

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

   4. Simplified 40.5%

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

   5. Taylor expanded in z around 0 40.5%

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

      1. +-commutative 40.5%

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

      2. associate-*r* 40.5%

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

      3. associate-*r* 40.5%

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

      4. distribute-lft-out 40.5%

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

      5. neg-mul-1 40.5%

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

   7. Simplified 40.5%

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

   8. Taylor expanded in a around 0 5.4%

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

      1. +-commutative 5.4%

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

      2. mul-1-neg 5.4%

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

      3. unsub-neg 5.4%

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

   10. Simplified 5.4%

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

   11. Taylor expanded in z around inf 39.7%

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

       1. mul-1-neg 39.7%

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

   13. Simplified 39.7%

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

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.42 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(1 - a \cdot \left(z + b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 12: 22.7% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-292} \lor \neg \left(y \leq 2.3 \cdot 10^{-16}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.2e-292) (not (<= y 2.3e-16))) (* a (* x (- z))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.2e-292) || !(y <= 2.3e-16)) {
		tmp = a * (x * -z);
	} 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 <= (-7.2d-292)) .or. (.not. (y <= 2.3d-16))) then
        tmp = a * (x * -z)
    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 <= -7.2e-292) || !(y <= 2.3e-16)) {
		tmp = a * (x * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.2e-292) or not (y <= 2.3e-16):
		tmp = a * (x * -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.2e-292) || !(y <= 2.3e-16))
		tmp = Float64(a * Float64(x * Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.2e-292) || ~((y <= 2.3e-16)))
		tmp = a * (x * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.2e-292], N[Not[LessEqual[y, 2.3e-16]], $MachinePrecision]], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.2000000000000004e-292 or 2.2999999999999999e-16 < y

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0 51.1%

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

      1. sub-neg 51.1%

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

      2. neg-mul-1 51.1%

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

      3. log1p-def 58.8%

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

      4. neg-mul-1 58.8%

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

   4. Simplified 58.8%

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

   5. Taylor expanded in z around 0 58.8%

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

      1. +-commutative 58.8%

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

      2. associate-*r* 58.8%

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

      3. associate-*r* 58.8%

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

      4. distribute-lft-out 58.8%

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

      5. neg-mul-1 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in a around 0 16.7%

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

      1. +-commutative 16.7%

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

      2. mul-1-neg 16.7%

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

      3. unsub-neg 16.7%

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

   10. Simplified 16.7%

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

   11. Taylor expanded in z around inf 23.4%

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

       1. mul-1-neg 23.4%

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

   13. Simplified 23.4%

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

   if -7.2000000000000004e-292 < y < 2.2999999999999999e-16

   1. Initial program 92.8%

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

   2. Taylor expanded in b around inf 81.9%

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

      1. associate-*r* 81.9%

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

      2. *-commutative 81.9%

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

      3. neg-mul-1 81.9%

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

   4. Simplified 81.9%

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

   5. Taylor expanded in b around 0 39.2%

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

4. Final simplification 27.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-292} \lor \neg \left(y \leq 2.3 \cdot 10^{-16}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 27.9% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00034:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -0.00034)
   (* x (* a (- b)))
   (if (<= y 6.2e-16) x (* a (* x (- z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -0.00034) {
		tmp = x * (a * -b);
	} else if (y <= 6.2e-16) {
		tmp = x;
	} 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 <= (-0.00034d0)) then
        tmp = x * (a * -b)
    else if (y <= 6.2d-16) then
        tmp = x
    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 <= -0.00034) {
		tmp = x * (a * -b);
	} else if (y <= 6.2e-16) {
		tmp = x;
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -0.00034:
		tmp = x * (a * -b)
	elif y <= 6.2e-16:
		tmp = x
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -0.00034)
		tmp = Float64(x * Float64(a * Float64(-b)));
	elseif (y <= 6.2e-16)
		tmp = x;
	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 <= -0.00034)
		tmp = x * (a * -b);
	elseif (y <= 6.2e-16)
		tmp = x;
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -0.00034], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-16], x, N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4e-4

   1. Initial program 98.2%

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

   2. Taylor expanded in b around inf 43.8%

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

      1. associate-*r* 43.8%

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

      2. *-commutative 43.8%

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

      3. neg-mul-1 43.8%

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

   4. Simplified 43.8%

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

   5. Taylor expanded in b around 0 10.4%

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

      1. +-commutative 10.4%

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

      2. mul-1-neg 10.4%

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

      3. unsub-neg 10.4%

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

      4. associate-*r* 17.2%

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

      5. *-commutative 17.2%

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

   7. Simplified 17.2%

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

   8. Taylor expanded in a around inf 13.2%

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

      1. mul-1-neg 13.2%

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

      2. distribute-rgt-neg-in 13.2%

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

   10. Simplified 13.2%

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

   11. Taylor expanded in a around 0 13.2%

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

       1. associate-*r* 13.2%

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

       2. associate-*r* 20.1%

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

       3. associate-*r* 20.1%

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

       4. *-commutative 20.1%

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

       5. mul-1-neg 20.1%

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

       6. distribute-rgt-neg-in 20.1%

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

   13. Simplified 20.1%

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

   if -3.4e-4 < y < 6.2000000000000002e-16

   1. Initial program 93.1%

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

   2. Taylor expanded in b around inf 75.3%

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

      1. associate-*r* 75.3%

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

      2. *-commutative 75.3%

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

      3. neg-mul-1 75.3%

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

   4. Simplified 75.3%

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

   5. Taylor expanded in b around 0 30.4%

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

   if 6.2000000000000002e-16 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 39.5%

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

      1. sub-neg 39.5%

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

      2. neg-mul-1 39.5%

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

      3. log1p-def 45.0%

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

      4. neg-mul-1 45.0%

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

   4. Simplified 45.0%

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

   5. Taylor expanded in z around 0 45.0%

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

      1. +-commutative 45.0%

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

      2. associate-*r* 45.0%

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

      3. associate-*r* 45.0%

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

      4. distribute-lft-out 45.0%

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

      5. neg-mul-1 45.0%

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

   7. Simplified 45.0%

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

   8. Taylor expanded in a around 0 10.2%

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

      1. +-commutative 10.2%

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

      2. mul-1-neg 10.2%

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

      3. unsub-neg 10.2%

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

   10. Simplified 10.2%

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

   11. Taylor expanded in z around inf 33.3%

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

       1. mul-1-neg 33.3%

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

   13. Simplified 33.3%

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

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00034:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 14: 32.1% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-15}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.5e-15) (- x (* x (* a b))) (* a (* x (- z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.5e-15) {
		tmp = x - (x * (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 <= 1.5d-15) then
        tmp = x - (x * (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 <= 1.5e-15) {
		tmp = x - (x * (a * b));
	} else {
		tmp = a * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.5e-15:
		tmp = x - (x * (a * b))
	else:
		tmp = a * (x * -z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.5e-15)
		tmp = Float64(x - Float64(x * 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 <= 1.5e-15)
		tmp = x - (x * (a * b));
	else
		tmp = a * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.5e-15], N[(x - N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.5e-15

   1. Initial program 94.6%

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

   2. Taylor expanded in b around inf 66.0%

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

      1. associate-*r* 66.0%

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

      2. *-commutative 66.0%

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

      3. neg-mul-1 66.0%

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

   4. Simplified 66.0%

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

   5. Taylor expanded in b around 0 28.2%

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

      1. +-commutative 28.2%

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

      2. mul-1-neg 28.2%

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

      3. unsub-neg 28.2%

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

      4. associate-*r* 29.6%

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

      5. *-commutative 29.6%

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

   7. Simplified 29.6%

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

   if 1.5e-15 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 39.5%

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

      1. sub-neg 39.5%

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

      2. neg-mul-1 39.5%

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

      3. log1p-def 45.0%

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

      4. neg-mul-1 45.0%

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

   4. Simplified 45.0%

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

   5. Taylor expanded in z around 0 45.0%

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

      1. +-commutative 45.0%

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

      2. associate-*r* 45.0%

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

      3. associate-*r* 45.0%

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

      4. distribute-lft-out 45.0%

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

      5. neg-mul-1 45.0%

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

   7. Simplified 45.0%

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

   8. Taylor expanded in a around 0 10.2%

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

      1. +-commutative 10.2%

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

      2. mul-1-neg 10.2%

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

      3. unsub-neg 10.2%

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

   10. Simplified 10.2%

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

   11. Taylor expanded in z around inf 33.3%

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

       1. mul-1-neg 33.3%

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

   13. Simplified 33.3%

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

4. Final simplification 30.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-15}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 15: 19.1% 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 94.2%

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

2. Taylor expanded in b around inf 58.7%

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

   1. associate-*r* 58.7%

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

   2. *-commutative 58.7%

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

   3. neg-mul-1 58.7%

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

4. Simplified 58.7%

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

5. Taylor expanded in b around 0 17.5%

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

6. Final simplification 17.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(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))))))