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

Percentage Accurate: 96.4% → 99.4%

Time: 24.2s

Alternatives: 15

Speedup: 1.0×

• 40.8% 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: 96.4% 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: 99.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.5%

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

   1. fma-def 98.7%

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

   2. sub-neg 98.7%

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

   3. log1p-def 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 2: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.5%

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

3. Final simplification 97.5%

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

Alternative 3: 88.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.9 \cdot 10^{-25} \lor \neg \left(y \leq 3.7\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.9e-25) (not (<= y 3.7)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (+ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.9e-25) || !(y <= 3.7)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((a * -(z + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-7.9d-25)) .or. (.not. (y <= 3.7d0))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((a * -(z + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.9e-25) || !(y <= 3.7)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * -(z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.9e-25) or not (y <= 3.7):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * -(z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.9e-25) || !(y <= 3.7))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-Float64(z + b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.9e-25) || ~((y <= 3.7)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((a * -(z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.9e-25], N[Not[LessEqual[y, 3.7]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-N[(z + b), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.8999999999999997e-25 or 3.7000000000000002 < y

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf 91.8%

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

   if -7.8999999999999997e-25 < y < 3.7000000000000002

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 87.2%

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

      1. sub-neg 87.2%

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

      2. neg-mul-1 87.2%

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

      3. log1p-def 88.2%

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

      4. neg-mul-1 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in z around 0 88.2%

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

      1. +-commutative 88.2%

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

      2. associate-*r* 88.2%

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

      3. associate-*r* 88.2%

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

      4. distribute-lft-out 88.2%

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

      5. neg-mul-1 88.2%

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

   8. Simplified 88.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.9 \cdot 10^{-25} \lor \neg \left(y \leq 3.7\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ t_2 := \frac{x}{e^{y \cdot t}}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -15500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 270:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))) (t_2 (/ x (exp (* y t)))))
   (if (<= y -1e+254)
     t_2
     (if (<= y -15500000000000.0)
       t_1
       (if (<= y -2.5e-24)
         t_2
         (if (<= y 270.0) (* x (exp (* a (- (+ z b))))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double t_2 = x / exp((y * t));
	double tmp;
	if (y <= -1e+254) {
		tmp = t_2;
	} else if (y <= -15500000000000.0) {
		tmp = t_1;
	} else if (y <= -2.5e-24) {
		tmp = t_2;
	} else if (y <= 270.0) {
		tmp = x * exp((a * -(z + b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z ** y)
    t_2 = x / exp((y * t))
    if (y <= (-1d+254)) then
        tmp = t_2
    else if (y <= (-15500000000000.0d0)) then
        tmp = t_1
    else if (y <= (-2.5d-24)) then
        tmp = t_2
    else if (y <= 270.0d0) then
        tmp = x * exp((a * -(z + b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double t_2 = x / Math.exp((y * t));
	double tmp;
	if (y <= -1e+254) {
		tmp = t_2;
	} else if (y <= -15500000000000.0) {
		tmp = t_1;
	} else if (y <= -2.5e-24) {
		tmp = t_2;
	} else if (y <= 270.0) {
		tmp = x * Math.exp((a * -(z + b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	t_2 = x / math.exp((y * t))
	tmp = 0
	if y <= -1e+254:
		tmp = t_2
	elif y <= -15500000000000.0:
		tmp = t_1
	elif y <= -2.5e-24:
		tmp = t_2
	elif y <= 270.0:
		tmp = x * math.exp((a * -(z + b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	t_2 = Float64(x / exp(Float64(y * t)))
	tmp = 0.0
	if (y <= -1e+254)
		tmp = t_2;
	elseif (y <= -15500000000000.0)
		tmp = t_1;
	elseif (y <= -2.5e-24)
		tmp = t_2;
	elseif (y <= 270.0)
		tmp = Float64(x * exp(Float64(a * Float64(-Float64(z + b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	t_2 = x / exp((y * t));
	tmp = 0.0;
	if (y <= -1e+254)
		tmp = t_2;
	elseif (y <= -15500000000000.0)
		tmp = t_1;
	elseif (y <= -2.5e-24)
		tmp = t_2;
	elseif (y <= 270.0)
		tmp = x * exp((a * -(z + b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[Exp[N[(y * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+254], t$95$2, If[LessEqual[y, -15500000000000.0], t$95$1, If[LessEqual[y, -2.5e-24], t$95$2, If[LessEqual[y, 270.0], N[(x * N[Exp[N[(a * (-N[(z + b), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.9999999999999994e253 or -1.55e13 < y < -2.4999999999999999e-24

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. sub-neg 99.9%

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

      3. log1p-def 99.9%

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

   3. Simplified 99.9%

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

      1. add-exp-log 58.6%

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

      2. *-commutative 58.6%

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

      3. log-prod 45.0%

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

      4. add-log-exp 45.0%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-unprod 45.0%

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

      7. sqr-neg 45.0%

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

      8. sqrt-unprod 45.0%

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

      9. add-sqr-sqrt 45.0%

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

   6. Applied egg-rr 45.0%

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

   7. Taylor expanded in t around inf 43.8%

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

      1. associate-*r* 43.8%

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

      2. neg-mul-1 43.8%

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

   9. Simplified 43.8%

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

   10. Taylor expanded in t around inf 43.8%

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

       1. mul-1-neg 43.8%

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

       2. sub-neg 43.8%

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

       3. exp-diff 43.8%

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

       4. rem-exp-log 89.5%

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

   12. Simplified 89.5%

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

   if -9.9999999999999994e253 < y < -1.55e13 or 270 < y

   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. Add Preprocessing

   3. Taylor expanded in y around inf 90.2%

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

   4. Taylor expanded in t around 0 69.0%

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

   if -2.4999999999999999e-24 < y < 270

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 87.2%

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

      1. sub-neg 87.2%

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

      2. neg-mul-1 87.2%

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

      3. log1p-def 88.2%

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

      4. neg-mul-1 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in z around 0 88.2%

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

      1. +-commutative 88.2%

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

      2. associate-*r* 88.2%

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

      3. associate-*r* 88.2%

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

      4. distribute-lft-out 88.2%

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

      5. neg-mul-1 88.2%

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

   8. Simplified 88.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+254}:\\ \;\;\;\;\frac{x}{e^{y \cdot t}}\\ \mathbf{elif}\;y \leq -15500000000000:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{e^{y \cdot t}}\\ \mathbf{elif}\;y \leq 270:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ t_2 := \frac{x}{e^{y \cdot t}}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5800000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))) (t_2 (/ x (exp (* y t)))))
   (if (<= y -4.1e+250)
     t_2
     (if (<= y -5800000000000.0)
       t_1
       (if (<= y -2.05e-24) t_2 (if (<= y 4.0) (/ x (exp (* a b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double t_2 = x / exp((y * t));
	double tmp;
	if (y <= -4.1e+250) {
		tmp = t_2;
	} else if (y <= -5800000000000.0) {
		tmp = t_1;
	} else if (y <= -2.05e-24) {
		tmp = t_2;
	} else if (y <= 4.0) {
		tmp = x / exp((a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z ** y)
    t_2 = x / exp((y * t))
    if (y <= (-4.1d+250)) then
        tmp = t_2
    else if (y <= (-5800000000000.0d0)) then
        tmp = t_1
    else if (y <= (-2.05d-24)) then
        tmp = t_2
    else if (y <= 4.0d0) then
        tmp = x / exp((a * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double t_2 = x / Math.exp((y * t));
	double tmp;
	if (y <= -4.1e+250) {
		tmp = t_2;
	} else if (y <= -5800000000000.0) {
		tmp = t_1;
	} else if (y <= -2.05e-24) {
		tmp = t_2;
	} else if (y <= 4.0) {
		tmp = x / Math.exp((a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	t_2 = x / math.exp((y * t))
	tmp = 0
	if y <= -4.1e+250:
		tmp = t_2
	elif y <= -5800000000000.0:
		tmp = t_1
	elif y <= -2.05e-24:
		tmp = t_2
	elif y <= 4.0:
		tmp = x / math.exp((a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	t_2 = Float64(x / exp(Float64(y * t)))
	tmp = 0.0
	if (y <= -4.1e+250)
		tmp = t_2;
	elseif (y <= -5800000000000.0)
		tmp = t_1;
	elseif (y <= -2.05e-24)
		tmp = t_2;
	elseif (y <= 4.0)
		tmp = Float64(x / exp(Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	t_2 = x / exp((y * t));
	tmp = 0.0;
	if (y <= -4.1e+250)
		tmp = t_2;
	elseif (y <= -5800000000000.0)
		tmp = t_1;
	elseif (y <= -2.05e-24)
		tmp = t_2;
	elseif (y <= 4.0)
		tmp = x / exp((a * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[Exp[N[(y * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+250], t$95$2, If[LessEqual[y, -5800000000000.0], t$95$1, If[LessEqual[y, -2.05e-24], t$95$2, If[LessEqual[y, 4.0], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.09999999999999999e250 or -5.8e12 < y < -2.05000000000000007e-24

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. sub-neg 99.9%

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

      3. log1p-def 99.9%

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

   3. Simplified 99.9%

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

      1. add-exp-log 58.6%

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

      2. *-commutative 58.6%

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

      3. log-prod 45.0%

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

      4. add-log-exp 45.0%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-unprod 45.0%

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

      7. sqr-neg 45.0%

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

      8. sqrt-unprod 45.0%

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

      9. add-sqr-sqrt 45.0%

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

   6. Applied egg-rr 45.0%

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

   7. Taylor expanded in t around inf 43.8%

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

      1. associate-*r* 43.8%

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

      2. neg-mul-1 43.8%

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

   9. Simplified 43.8%

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

   10. Taylor expanded in t around inf 43.8%

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

       1. mul-1-neg 43.8%

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

       2. sub-neg 43.8%

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

       3. exp-diff 43.8%

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

       4. rem-exp-log 89.5%

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

   12. Simplified 89.5%

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

   if -4.09999999999999999e250 < y < -5.8e12 or 4 < y

   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. Add Preprocessing

   3. Taylor expanded in y around inf 90.2%

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

   4. Taylor expanded in t around 0 69.0%

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

   if -2.05000000000000007e-24 < y < 4

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 87.2%

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

      1. sub-neg 87.2%

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

      2. neg-mul-1 87.2%

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

      3. log1p-def 88.2%

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

      4. neg-mul-1 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in z around 0 87.2%

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

      1. rem-exp-log 39.2%

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

      2. exp-sum 39.2%

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

      3. mul-1-neg 39.2%

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

      4. sub-neg 39.2%

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

      5. exp-diff 39.2%

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

      6. rem-exp-log 87.2%

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

   8. Simplified 87.2%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+250}:\\ \;\;\;\;\frac{x}{e^{y \cdot t}}\\ \mathbf{elif}\;y \leq -5800000000000:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{e^{y \cdot t}}\\ \mathbf{elif}\;y \leq 4:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{a \cdot \left(-b\right)}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-61}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-114} \lor \neg \left(b \leq 1.5 \cdot 10^{-160}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (exp (* a (- b)))))
   (if (<= b -2.5e+39)
     t_1
     (if (<= b -1.55e-61)
       (- x (* t (* x y)))
       (if (or (<= b -3.2e-114) (not (<= b 1.5e-160)))
         t_1
         (- x (* x (* y t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp((a * -b));
	double tmp;
	if (b <= -2.5e+39) {
		tmp = t_1;
	} else if (b <= -1.55e-61) {
		tmp = x - (t * (x * y));
	} else if ((b <= -3.2e-114) || !(b <= 1.5e-160)) {
		tmp = t_1;
	} else {
		tmp = x - (x * (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) :: t_1
    real(8) :: tmp
    t_1 = exp((a * -b))
    if (b <= (-2.5d+39)) then
        tmp = t_1
    else if (b <= (-1.55d-61)) then
        tmp = x - (t * (x * y))
    else if ((b <= (-3.2d-114)) .or. (.not. (b <= 1.5d-160))) then
        tmp = t_1
    else
        tmp = x - (x * (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 t_1 = Math.exp((a * -b));
	double tmp;
	if (b <= -2.5e+39) {
		tmp = t_1;
	} else if (b <= -1.55e-61) {
		tmp = x - (t * (x * y));
	} else if ((b <= -3.2e-114) || !(b <= 1.5e-160)) {
		tmp = t_1;
	} else {
		tmp = x - (x * (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp((a * -b))
	tmp = 0
	if b <= -2.5e+39:
		tmp = t_1
	elif b <= -1.55e-61:
		tmp = x - (t * (x * y))
	elif (b <= -3.2e-114) or not (b <= 1.5e-160):
		tmp = t_1
	else:
		tmp = x - (x * (y * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = exp(Float64(a * Float64(-b)))
	tmp = 0.0
	if (b <= -2.5e+39)
		tmp = t_1;
	elseif (b <= -1.55e-61)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif ((b <= -3.2e-114) || !(b <= 1.5e-160))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x * Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp((a * -b));
	tmp = 0.0;
	if (b <= -2.5e+39)
		tmp = t_1;
	elseif (b <= -1.55e-61)
		tmp = x - (t * (x * y));
	elseif ((b <= -3.2e-114) || ~((b <= 1.5e-160)))
		tmp = t_1;
	else
		tmp = x - (x * (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[b, -2.5e+39], t$95$1, If[LessEqual[b, -1.55e-61], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -3.2e-114], N[Not[LessEqual[b, 1.5e-160]], $MachinePrecision]], t$95$1, N[(x - N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.50000000000000008e39 or -1.54999999999999997e-61 < b < -3.2000000000000002e-114 or 1.49999999999999998e-160 < b

   1. Initial program 96.8%

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

      1. fma-def 98.7%

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

      2. sub-neg 98.7%

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

      3. log1p-def 98.7%

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

   3. Simplified 98.7%

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

      1. add-exp-log 69.8%

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

      2. *-commutative 69.8%

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

      3. log-prod 52.6%

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

      4. add-log-exp 52.6%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-unprod 50.8%

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

      7. sqr-neg 50.8%

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

      8. sqrt-unprod 50.8%

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

      9. add-sqr-sqrt 50.8%

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

   6. Applied egg-rr 50.8%

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

   7. Taylor expanded in b around inf 37.0%

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

      1. mul-1-neg 37.0%

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

      2. distribute-rgt-neg-in 37.0%

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

   9. Simplified 37.0%

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

   10. Taylor expanded in a around inf 43.1%

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

       1. mul-1-neg 43.1%

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

       2. *-commutative 43.1%

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

       3. distribute-rgt-neg-in 43.1%

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

   12. Simplified 43.1%

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

   if -2.50000000000000008e39 < b < -1.54999999999999997e-61

   1. Initial program 98.8%

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

      1. fma-def 98.8%

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

      2. sub-neg 98.8%

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

      3. log1p-def 99.9%

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

   3. Simplified 99.9%

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

      1. add-exp-log 65.5%

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

      2. *-commutative 65.5%

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

      3. log-prod 61.0%

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

      4. add-log-exp 61.0%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-unprod 61.0%

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

      7. sqr-neg 61.0%

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

      8. sqrt-unprod 61.0%

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

      9. add-sqr-sqrt 61.0%

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

   6. Applied egg-rr 61.0%

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

   7. Taylor expanded in t around inf 38.8%

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

      1. associate-*r* 38.8%

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

      2. neg-mul-1 38.8%

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

   9. Simplified 38.8%

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

   10. Taylor expanded in t around 0 53.3%

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

       1. mul-1-neg 53.3%

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

       2. unsub-neg 53.3%

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

   12. Simplified 53.3%

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

   if -3.2000000000000002e-114 < b < 1.49999999999999998e-160

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf 93.2%

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

   4. Taylor expanded in y around 0 51.6%

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

      1. *-commutative 51.6%

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

   6. Simplified 51.6%

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

   7. Taylor expanded in t around inf 48.9%

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

      1. neg-mul-1 48.9%

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

   9. Simplified 48.9%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+39}:\\ \;\;\;\;e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-61}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-114} \lor \neg \left(b \leq 1.5 \cdot 10^{-160}\right):\\ \;\;\;\;e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 44.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{y \cdot \left(-t\right)}\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-190}:\\ \;\;\;\;e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-248}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 1900000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (exp (* y (- t)))))
   (if (<= y -8.6e-25)
     t_1
     (if (<= y -3.7e-190)
       (exp (* a (- b)))
       (if (<= y 2.9e-248)
         (/ x (+ 1.0 (* a b)))
         (if (<= y 1900000000.0) (* x (- 1.0 (* a b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp((y * -t));
	double tmp;
	if (y <= -8.6e-25) {
		tmp = t_1;
	} else if (y <= -3.7e-190) {
		tmp = exp((a * -b));
	} else if (y <= 2.9e-248) {
		tmp = x / (1.0 + (a * b));
	} else if (y <= 1900000000.0) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = exp((y * -t))
    if (y <= (-8.6d-25)) then
        tmp = t_1
    else if (y <= (-3.7d-190)) then
        tmp = exp((a * -b))
    else if (y <= 2.9d-248) then
        tmp = x / (1.0d0 + (a * b))
    else if (y <= 1900000000.0d0) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.exp((y * -t));
	double tmp;
	if (y <= -8.6e-25) {
		tmp = t_1;
	} else if (y <= -3.7e-190) {
		tmp = Math.exp((a * -b));
	} else if (y <= 2.9e-248) {
		tmp = x / (1.0 + (a * b));
	} else if (y <= 1900000000.0) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp((y * -t))
	tmp = 0
	if y <= -8.6e-25:
		tmp = t_1
	elif y <= -3.7e-190:
		tmp = math.exp((a * -b))
	elif y <= 2.9e-248:
		tmp = x / (1.0 + (a * b))
	elif y <= 1900000000.0:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = exp(Float64(y * Float64(-t)))
	tmp = 0.0
	if (y <= -8.6e-25)
		tmp = t_1;
	elseif (y <= -3.7e-190)
		tmp = exp(Float64(a * Float64(-b)));
	elseif (y <= 2.9e-248)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	elseif (y <= 1900000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp((y * -t));
	tmp = 0.0;
	if (y <= -8.6e-25)
		tmp = t_1;
	elseif (y <= -3.7e-190)
		tmp = exp((a * -b));
	elseif (y <= 2.9e-248)
		tmp = x / (1.0 + (a * b));
	elseif (y <= 1900000000.0)
		tmp = x * (1.0 - (a * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -8.6e-25], t$95$1, If[LessEqual[y, -3.7e-190], N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision], If[LessEqual[y, 2.9e-248], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1900000000.0], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.59999999999999953e-25 or 1.9e9 < y

   1. Initial program 95.4%

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

      1. fma-def 97.7%

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

      2. sub-neg 97.7%

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

      3. log1p-def 98.5%

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

   3. Simplified 98.5%

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

      1. add-exp-log 72.5%

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

      2. *-commutative 72.5%

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

      3. log-prod 57.2%

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

      4. add-log-exp 57.2%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-unprod 54.9%

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

      7. sqr-neg 54.9%

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

      8. sqrt-unprod 54.9%

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

      9. add-sqr-sqrt 54.9%

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

   6. Applied egg-rr 54.9%

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

   7. Taylor expanded in t around inf 33.5%

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

      1. associate-*r* 33.5%

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

      2. neg-mul-1 33.5%

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

   9. Simplified 33.5%

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

   10. Taylor expanded in t around inf 43.0%

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

       1. mul-1-neg 43.0%

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

       2. distribute-rgt-neg-in 43.0%

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

   12. Simplified 43.0%

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

   if -8.59999999999999953e-25 < y < -3.7000000000000002e-190

   1. Initial program 98.9%

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

      1. fma-def 98.9%

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

      2. sub-neg 98.9%

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

      3. log1p-def 99.9%

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

   3. Simplified 99.9%

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

      1. add-exp-log 65.4%

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

      2. *-commutative 65.4%

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

      3. log-prod 39.5%

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

      4. add-log-exp 39.5%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-unprod 39.5%

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

      7. sqr-neg 39.5%

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

      8. sqrt-unprod 39.5%

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

      9. add-sqr-sqrt 39.5%

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

   6. Applied egg-rr 39.5%

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

   7. Taylor expanded in b around inf 36.0%

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

      1. mul-1-neg 36.0%

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

      2. distribute-rgt-neg-in 36.0%

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

   9. Simplified 36.0%

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

   10. Taylor expanded in a around inf 42.3%

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

       1. mul-1-neg 42.3%

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

       2. *-commutative 42.3%

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

       3. distribute-rgt-neg-in 42.3%

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

   12. Simplified 42.3%

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

   if -3.7000000000000002e-190 < y < 2.9000000000000001e-248

   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. Add Preprocessing

   3. Taylor expanded in y around 0 88.6%

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

      1. sub-neg 88.6%

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

      2. neg-mul-1 88.6%

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

      3. log1p-def 91.4%

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

      4. neg-mul-1 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in z around 0 88.6%

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

      1. rem-exp-log 48.3%

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

      2. exp-sum 48.3%

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

      3. mul-1-neg 48.3%

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

      4. sub-neg 48.3%

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

      5. exp-diff 48.3%

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

      6. rem-exp-log 88.6%

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

   8. Simplified 88.6%

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

   9. Taylor expanded in a around 0 62.6%

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

   if 2.9000000000000001e-248 < y < 1.9e9

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-rgt-neg-out 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in a around 0 54.9%

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

      1. mul-1-neg 54.9%

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

      2. unsub-neg 54.9%

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

   8. Simplified 54.9%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-25}:\\ \;\;\;\;e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-190}:\\ \;\;\;\;e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-248}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 1900000000:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+253}:\\ \;\;\;\;e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;y \leq -1.46 \cdot 10^{-16} \lor \neg \left(y \leq 7.5\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.25e+253)
   (exp (* y (- t)))
   (if (or (<= y -1.46e-16) (not (<= y 7.5)))
     (* 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 <= -1.25e+253) {
		tmp = exp((y * -t));
	} else if ((y <= -1.46e-16) || !(y <= 7.5)) {
		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 <= (-1.25d+253)) then
        tmp = exp((y * -t))
    else if ((y <= (-1.46d-16)) .or. (.not. (y <= 7.5d0))) 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 <= -1.25e+253) {
		tmp = Math.exp((y * -t));
	} else if ((y <= -1.46e-16) || !(y <= 7.5)) {
		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 <= -1.25e+253:
		tmp = math.exp((y * -t))
	elif (y <= -1.46e-16) or not (y <= 7.5):
		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 <= -1.25e+253)
		tmp = exp(Float64(y * Float64(-t)));
	elseif ((y <= -1.46e-16) || !(y <= 7.5))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x / exp(Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.25e+253)
		tmp = exp((y * -t));
	elseif ((y <= -1.46e-16) || ~((y <= 7.5)))
		tmp = x * (z ^ y);
	else
		tmp = x / exp((a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.25e+253], N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision], If[Or[LessEqual[y, -1.46e-16], N[Not[LessEqual[y, 7.5]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2499999999999999e253

   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. Step-by-step derivation

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. log1p-def 100.0%

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

   3. Simplified 100.0%

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

      1. add-exp-log 66.7%

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

      2. *-commutative 66.7%

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

      3. log-prod 50.0%

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

      4. add-log-exp 50.0%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-unprod 50.0%

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

      7. sqr-neg 50.0%

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

      8. sqrt-unprod 50.0%

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

      9. add-sqr-sqrt 50.0%

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

   6. Applied egg-rr 50.0%

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

   7. Taylor expanded in t around inf 50.0%

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

      1. associate-*r* 50.0%

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

      2. neg-mul-1 50.0%

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

   9. Simplified 50.0%

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

   10. Taylor expanded in t around inf 66.9%

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

       1. mul-1-neg 66.9%

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

       2. distribute-rgt-neg-in 66.9%

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

   12. Simplified 66.9%

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

   if -1.2499999999999999e253 < y < -1.4600000000000001e-16 or 7.5 < y

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf 90.7%

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

   4. Taylor expanded in t around 0 67.2%

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

   if -1.4600000000000001e-16 < y < 7.5

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 86.1%

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

      1. sub-neg 86.1%

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

      2. neg-mul-1 86.1%

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

      3. log1p-def 87.0%

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

      4. neg-mul-1 87.0%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in z around 0 86.1%

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

      1. rem-exp-log 38.7%

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

      2. exp-sum 38.7%

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

      3. mul-1-neg 38.7%

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

      4. sub-neg 38.7%

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

      5. exp-diff 38.7%

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

      6. rem-exp-log 86.1%

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

   8. Simplified 86.1%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+253}:\\ \;\;\;\;e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;y \leq -1.46 \cdot 10^{-16} \lor \neg \left(y \leq 7.5\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -85000000 \lor \neg \left(t \leq 7.6 \cdot 10^{+185}\right):\\ \;\;\;\;e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -85000000.0) (not (<= t 7.6e+185)))
   (exp (* y (- t)))
   (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -85000000.0) || !(t <= 7.6e+185)) {
		tmp = exp((y * -t));
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-85000000.0d0)) .or. (.not. (t <= 7.6d+185))) then
        tmp = exp((y * -t))
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -85000000.0) || !(t <= 7.6e+185)) {
		tmp = Math.exp((y * -t));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -85000000.0) or not (t <= 7.6e+185):
		tmp = math.exp((y * -t))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -85000000.0) || !(t <= 7.6e+185))
		tmp = exp(Float64(y * Float64(-t)));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -85000000.0) || ~((t <= 7.6e+185)))
		tmp = exp((y * -t));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -85000000.0], N[Not[LessEqual[t, 7.6e+185]], $MachinePrecision]], N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5e7 or 7.5999999999999996e185 < t

   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. Step-by-step derivation

      1. fma-def 97.8%

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

      2. sub-neg 97.8%

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

      3. log1p-def 97.8%

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

   3. Simplified 97.8%

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

      1. add-exp-log 72.9%

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

      2. *-commutative 72.9%

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

      3. log-prod 55.1%

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

      4. add-log-exp 55.1%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-unprod 55.1%

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

      7. sqr-neg 55.1%

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

      8. sqrt-unprod 55.1%

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

      9. add-sqr-sqrt 55.1%

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

   6. Applied egg-rr 55.1%

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

   7. Taylor expanded in t around inf 47.5%

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

      1. associate-*r* 47.5%

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

      2. neg-mul-1 47.5%

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

   9. Simplified 47.5%

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

   10. Taylor expanded in t around inf 61.7%

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

       1. mul-1-neg 61.7%

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

       2. distribute-rgt-neg-in 61.7%

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

   12. Simplified 61.7%

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

   if -8.5e7 < t < 7.5999999999999996e185

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf 71.1%

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

   4. Taylor expanded in t around 0 67.7%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -85000000 \lor \neg \left(t \leq 7.6 \cdot 10^{+185}\right):\\ \;\;\;\;e^{y \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 33.7% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+45}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.05e+45)
   (- x (* t (* x y)))
   (if (<= y 6.5e-5) (* x (- 1.0 (* a b))) (* x (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.05e+45) {
		tmp = x - (t * (x * y));
	} else if (y <= 6.5e-5) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (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 <= (-1.05d+45)) then
        tmp = x - (t * (x * y))
    else if (y <= 6.5d-5) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (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 <= -1.05e+45) {
		tmp = x - (t * (x * y));
	} else if (y <= 6.5e-5) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (a * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.05e+45:
		tmp = x - (t * (x * y))
	elif y <= 6.5e-5:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (a * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.05e+45)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif (y <= 6.5e-5)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(a * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.05e+45)
		tmp = x - (t * (x * y));
	elseif (y <= 6.5e-5)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (a * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.05e+45], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-5], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04999999999999997e45

   1. Initial program 98.1%

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

      1. fma-def 98.1%

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

      2. sub-neg 98.1%

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

      3. log1p-def 98.1%

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

   3. Simplified 98.1%

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

      1. add-exp-log 57.7%

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

      2. *-commutative 57.7%

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

      3. log-prod 46.2%

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

      4. add-log-exp 46.2%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-unprod 44.3%

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

      7. sqr-neg 44.3%

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

      8. sqrt-unprod 44.3%

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

      9. add-sqr-sqrt 44.3%

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

   6. Applied egg-rr 44.3%

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

   7. Taylor expanded in t around inf 33.1%

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

      1. associate-*r* 33.1%

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

      2. neg-mul-1 33.1%

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

   9. Simplified 33.1%

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

   10. Taylor expanded in t around 0 19.1%

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

       1. mul-1-neg 19.1%

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

       2. unsub-neg 19.1%

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

   12. Simplified 19.1%

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

   if -1.04999999999999997e45 < y < 6.49999999999999943e-5

   1. Initial program 99.0%

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

   3. Taylor expanded in b around inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. distribute-rgt-neg-out 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in a around 0 46.0%

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

      1. mul-1-neg 46.0%

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

      2. unsub-neg 46.0%

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

   8. Simplified 46.0%

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

   if 6.49999999999999943e-5 < y

   1. Initial program 93.8%

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

   3. Taylor expanded in b around inf 39.1%

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

      1. mul-1-neg 39.1%

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

      2. distribute-rgt-neg-out 39.1%

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

   5. Simplified 39.1%

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

   6. Taylor expanded in a around 0 16.6%

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

      1. mul-1-neg 16.6%

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

      2. unsub-neg 16.6%

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

   8. Simplified 16.6%

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

   9. Taylor expanded in a around inf 29.9%

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

       1. mul-1-neg 29.9%

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

       2. associate-*r* 33.6%

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

       3. distribute-rgt-neg-in 33.6%

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

   11. Simplified 33.6%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+45}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 32.2% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{-246}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 0.052:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 2.3e-246)
   (/ x (+ 1.0 (* a b)))
   (if (<= y 0.052) (* x (- 1.0 (* a b))) (* x (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.3e-246) {
		tmp = x / (1.0 + (a * b));
	} else if (y <= 0.052) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (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 <= 2.3d-246) then
        tmp = x / (1.0d0 + (a * b))
    else if (y <= 0.052d0) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (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 <= 2.3e-246) {
		tmp = x / (1.0 + (a * b));
	} else if (y <= 0.052) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (a * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 2.3e-246:
		tmp = x / (1.0 + (a * b))
	elif y <= 0.052:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (a * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 2.3e-246)
		tmp = Float64(x / Float64(1.0 + Float64(a * b)));
	elseif (y <= 0.052)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(a * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 2.3e-246)
		tmp = x / (1.0 + (a * b));
	elseif (y <= 0.052)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (a * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 2.3e-246], N[(x / N[(1.0 + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.052], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.2999999999999998e-246

   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. Add Preprocessing

   3. Taylor expanded in y around 0 60.1%

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

      1. sub-neg 60.1%

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

      2. neg-mul-1 60.1%

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

      3. log1p-def 61.7%

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

      4. neg-mul-1 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in z around 0 60.1%

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

      1. rem-exp-log 29.6%

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

      2. exp-sum 29.6%

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

      3. mul-1-neg 29.6%

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

      4. sub-neg 29.6%

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

      5. exp-diff 29.6%

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

      6. rem-exp-log 60.1%

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

   8. Simplified 60.1%

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

   9. Taylor expanded in a around 0 31.9%

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

   if 2.2999999999999998e-246 < y < 0.0519999999999999976

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. distribute-rgt-neg-out 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in a around 0 55.8%

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

      1. mul-1-neg 55.8%

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

      2. unsub-neg 55.8%

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

   8. Simplified 55.8%

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

   if 0.0519999999999999976 < y

   1. Initial program 93.8%

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

   3. Taylor expanded in b around inf 39.1%

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

      1. mul-1-neg 39.1%

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

      2. distribute-rgt-neg-out 39.1%

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

   5. Simplified 39.1%

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

   6. Taylor expanded in a around 0 16.6%

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

      1. mul-1-neg 16.6%

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

      2. unsub-neg 16.6%

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

   8. Simplified 16.6%

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

   9. Taylor expanded in a around inf 29.9%

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

       1. mul-1-neg 29.9%

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

       2. associate-*r* 33.6%

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

       3. distribute-rgt-neg-in 33.6%

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

   11. Simplified 33.6%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{-246}:\\ \;\;\;\;\frac{x}{1 + a \cdot b}\\ \mathbf{elif}\;y \leq 0.052:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 27.3% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -61000000000000 \lor \neg \left(y \leq 0.00011\right):\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -61000000000000.0) (not (<= y 0.00011))) (* b (* x (- a))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -61000000000000.0) || !(y <= 0.00011)) {
		tmp = b * (x * -a);
	} 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 <= (-61000000000000.0d0)) .or. (.not. (y <= 0.00011d0))) then
        tmp = b * (x * -a)
    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 <= -61000000000000.0) || !(y <= 0.00011)) {
		tmp = b * (x * -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -61000000000000.0) or not (y <= 0.00011):
		tmp = b * (x * -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -61000000000000.0) || !(y <= 0.00011))
		tmp = Float64(b * Float64(x * Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -61000000000000.0) || ~((y <= 0.00011)))
		tmp = b * (x * -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -61000000000000.0], N[Not[LessEqual[y, 0.00011]], $MachinePrecision]], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.1e13 or 1.10000000000000004e-4 < y

   1. Initial program 95.1%

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

   3. Taylor expanded in b around inf 38.0%

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

      1. mul-1-neg 38.0%

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

      2. distribute-rgt-neg-out 38.0%

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

   5. Simplified 38.0%

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

   6. Taylor expanded in a around 0 12.7%

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

      1. mul-1-neg 12.7%

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

      2. unsub-neg 12.7%

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

   8. Simplified 12.7%

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

   9. Taylor expanded in a around inf 20.0%

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

       1. mul-1-neg 20.0%

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

       2. associate-*r* 22.8%

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

       3. *-commutative 22.8%

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

       4. associate-*r* 22.7%

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

   11. Simplified 22.7%

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

   if -6.1e13 < y < 1.10000000000000004e-4

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-rgt-neg-out 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in a around 0 39.2%

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

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -61000000000000 \lor \neg \left(y \leq 0.00011\right):\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.8% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -61000000000000:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -61000000000000.0)
   (* b (* x (- a)))
   (if (<= y 1.75e-15) x (* x (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -61000000000000.0) {
		tmp = b * (x * -a);
	} else if (y <= 1.75e-15) {
		tmp = x;
	} else {
		tmp = x * (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 <= (-61000000000000.0d0)) then
        tmp = b * (x * -a)
    else if (y <= 1.75d-15) then
        tmp = x
    else
        tmp = x * (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 <= -61000000000000.0) {
		tmp = b * (x * -a);
	} else if (y <= 1.75e-15) {
		tmp = x;
	} else {
		tmp = x * (a * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -61000000000000.0:
		tmp = b * (x * -a)
	elif y <= 1.75e-15:
		tmp = x
	else:
		tmp = x * (a * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -61000000000000.0)
		tmp = Float64(b * Float64(x * Float64(-a)));
	elseif (y <= 1.75e-15)
		tmp = x;
	else
		tmp = Float64(x * Float64(a * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -61000000000000.0)
		tmp = b * (x * -a);
	elseif (y <= 1.75e-15)
		tmp = x;
	else
		tmp = x * (a * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -61000000000000.0], N[(b * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-15], x, N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.1e13

   1. Initial program 96.6%

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

   3. Taylor expanded in b around inf 36.8%

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

      1. mul-1-neg 36.8%

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

      2. distribute-rgt-neg-out 36.8%

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

   5. Simplified 36.8%

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

   6. Taylor expanded in a around 0 8.3%

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

      1. mul-1-neg 8.3%

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

      2. unsub-neg 8.3%

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

   8. Simplified 8.3%

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

   9. Taylor expanded in a around inf 9.0%

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

       1. mul-1-neg 9.0%

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

       2. associate-*r* 10.7%

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

       3. *-commutative 10.7%

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

       4. associate-*r* 12.2%

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

   11. Simplified 12.2%

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

   if -6.1e13 < y < 1.75e-15

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-rgt-neg-out 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in a around 0 39.2%

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

   if 1.75e-15 < y

   1. Initial program 93.8%

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

   3. Taylor expanded in b around inf 39.1%

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

      1. mul-1-neg 39.1%

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

      2. distribute-rgt-neg-out 39.1%

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

   5. Simplified 39.1%

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

   6. Taylor expanded in a around 0 16.6%

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

      1. mul-1-neg 16.6%

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

      2. unsub-neg 16.6%

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

   8. Simplified 16.6%

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

   9. Taylor expanded in a around inf 29.9%

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

       1. mul-1-neg 29.9%

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

       2. associate-*r* 33.6%

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

       3. distribute-rgt-neg-in 33.6%

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

   11. Simplified 33.6%

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

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -61000000000000:\\ \;\;\;\;b \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.8% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 9e-5) (* x (- 1.0 (* a b))) (* x (* a (- b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 9e-5) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (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 <= 9d-5) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (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 <= 9e-5) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (a * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 9e-5:
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (a * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 9e-5)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(a * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 9e-5)
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (a * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 9e-5], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.00000000000000057e-5

   1. Initial program 98.7%

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

   3. Taylor expanded in b around inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-rgt-neg-out 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in a around 0 35.9%

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

      1. mul-1-neg 35.9%

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

      2. unsub-neg 35.9%

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

   8. Simplified 35.9%

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

   if 9.00000000000000057e-5 < y

   1. Initial program 93.8%

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

   3. Taylor expanded in b around inf 39.1%

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

      1. mul-1-neg 39.1%

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

      2. distribute-rgt-neg-out 39.1%

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

   5. Simplified 39.1%

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

   6. Taylor expanded in a around 0 16.6%

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

      1. mul-1-neg 16.6%

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

      2. unsub-neg 16.6%

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

   8. Simplified 16.6%

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

   9. Taylor expanded in a around inf 29.9%

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

       1. mul-1-neg 29.9%

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

       2. associate-*r* 33.6%

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

       3. distribute-rgt-neg-in 33.6%

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

   11. Simplified 33.6%

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

4. Final simplification 35.3%

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

Alternative 15: 19.6% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.5%

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

3. Taylor expanded in b around inf 60.9%

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

   1. mul-1-neg 60.9%

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

   2. distribute-rgt-neg-out 60.9%

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

5. Simplified 60.9%

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

6. Taylor expanded in a around 0 22.1%

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

7. Final simplification 22.1%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(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))))))