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

Percentage Accurate: 96.6% → 99.5%

Time: 17.7s

Alternatives: 20

Speedup: 0.8×

• 40.9% 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: 96.6% 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: 99.5% 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 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-define 96.1%

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

   2. sub-neg 96.1%

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

   3. log1p-define 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. Final simplification 100.0%

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

Alternative 2: 96.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+237}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3e+237)
   (* x (exp (* a (- (- z) b))))
   (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3e+237) {
		tmp = x * exp((a * (-z - b)));
	} else {
		tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-3d+237)) then
        tmp = x * exp((a * (-z - b)))
    else
        tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3e+237) {
		tmp = x * Math.exp((a * (-z - b)));
	} else {
		tmp = x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3e+237:
		tmp = x * math.exp((a * (-z - b)))
	else:
		tmp = x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3e+237)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	else
		tmp = Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3e+237)
		tmp = x * exp((a * (-z - b)));
	else
		tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3e+237], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3e237

   1. Initial program 60.5%

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

   3. Taylor expanded in y around 0 67.2%

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

      1. sub-neg 67.2%

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

      2. log1p-define 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in z around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. associate-*r* 93.4%

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

      3. associate-*r* 93.4%

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

      4. distribute-lft-out 93.4%

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

      5. mul-1-neg 93.4%

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

   8. Simplified 93.4%

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

   if -3e237 < a

   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. Recombined 2 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+237}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-43} \lor \neg \left(y \leq 8.5 \cdot 10^{+17}\right):\\ \;\;\;\;x \cdot {\left(\frac{z}{e^{t}}\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.8e-43) (not (<= y 8.5e+17)))
   (* x (pow (/ z (exp t)) y))
   (* x (exp (* a (- (- z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.8e-43) || !(y <= 8.5e+17)) {
		tmp = x * pow((z / exp(t)), y);
	} else {
		tmp = x * exp((a * (-z - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9.8d-43)) .or. (.not. (y <= 8.5d+17))) then
        tmp = x * ((z / exp(t)) ** y)
    else
        tmp = x * exp((a * (-z - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.8e-43) || !(y <= 8.5e+17)) {
		tmp = x * Math.pow((z / Math.exp(t)), y);
	} else {
		tmp = x * Math.exp((a * (-z - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9.8e-43) or not (y <= 8.5e+17):
		tmp = x * math.pow((z / math.exp(t)), y)
	else:
		tmp = x * math.exp((a * (-z - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9.8e-43) || !(y <= 8.5e+17))
		tmp = Float64(x * (Float64(z / exp(t)) ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9.8e-43) || ~((y <= 8.5e+17)))
		tmp = x * ((z / exp(t)) ^ y);
	else
		tmp = x * exp((a * (-z - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9.8e-43], N[Not[LessEqual[y, 8.5e+17]], $MachinePrecision]], N[(x * N[Power[N[(z / N[Exp[t], $MachinePrecision]), $MachinePrecision], y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.79999999999999976e-43 or 8.5e17 < y

   1. Initial program 96.0%

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

   3. Taylor expanded in a around 0 88.1%

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

      1. *-commutative 88.1%

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

      2. exp-prod 88.1%

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

      3. exp-diff 88.1%

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

      4. rem-exp-log 88.1%

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

   5. Simplified 88.1%

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

   if -9.79999999999999976e-43 < y < 8.5e17

   1. Initial program 94.8%

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

   3. Taylor expanded in y around 0 83.9%

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

      1. sub-neg 83.9%

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

      2. log1p-define 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in z around 0 89.1%

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

      1. +-commutative 89.1%

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

      2. associate-*r* 89.1%

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

      3. associate-*r* 89.1%

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

      4. distribute-lft-out 89.1%

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

      5. mul-1-neg 89.1%

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

   8. Simplified 89.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-43} \lor \neg \left(y \leq 8.5 \cdot 10^{+17}\right):\\ \;\;\;\;x \cdot {\left(\frac{z}{e^{t}}\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -0.046:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.14:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -0.046)
     t_1
     (if (<= y 0.14)
       (* x (exp (* a (- b))))
       (if (<= y 1.8e+73) t_1 (* x (exp (* y (- t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -0.046) {
		tmp = t_1;
	} else if (y <= 0.14) {
		tmp = x * exp((a * -b));
	} else if (y <= 1.8e+73) {
		tmp = t_1;
	} else {
		tmp = x * exp((y * -t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-0.046d0)) then
        tmp = t_1
    else if (y <= 0.14d0) then
        tmp = x * exp((a * -b))
    else if (y <= 1.8d+73) then
        tmp = t_1
    else
        tmp = x * exp((y * -t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -0.046) {
		tmp = t_1;
	} else if (y <= 0.14) {
		tmp = x * Math.exp((a * -b));
	} else if (y <= 1.8e+73) {
		tmp = t_1;
	} else {
		tmp = x * Math.exp((y * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -0.046:
		tmp = t_1
	elif y <= 0.14:
		tmp = x * math.exp((a * -b))
	elif y <= 1.8e+73:
		tmp = t_1
	else:
		tmp = x * math.exp((y * -t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -0.046)
		tmp = t_1;
	elseif (y <= 0.14)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif (y <= 1.8e+73)
		tmp = t_1;
	else
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -0.046)
		tmp = t_1;
	elseif (y <= 0.14)
		tmp = x * exp((a * -b));
	elseif (y <= 1.8e+73)
		tmp = t_1;
	else
		tmp = x * exp((y * -t));
	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]}, If[LessEqual[y, -0.046], t$95$1, If[LessEqual[y, 0.14], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+73], t$95$1, N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.045999999999999999 or 0.14000000000000001 < y < 1.7999999999999999e73

   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 a around 0 88.4%

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

      1. *-commutative 88.4%

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

      2. exp-prod 88.4%

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

      3. exp-diff 88.4%

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

      4. rem-exp-log 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in t around 0 78.3%

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

   if -0.045999999999999999 < y < 0.14000000000000001

   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 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%

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

   if 1.7999999999999999e73 < y

   1. Initial program 91.2%

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

   3. Taylor expanded in t around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. distribute-lft-neg-out 74.0%

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

      3. *-commutative 74.0%

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

   5. Simplified 74.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.046:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 0.14:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+73}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -24000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.235:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -24000.0)
     t_1
     (if (<= y 0.235)
       (* x (exp (* a (- (- z) b))))
       (if (<= y 3.45e+72) t_1 (* x (exp (* y (- t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -24000.0) {
		tmp = t_1;
	} else if (y <= 0.235) {
		tmp = x * exp((a * (-z - b)));
	} else if (y <= 3.45e+72) {
		tmp = t_1;
	} else {
		tmp = x * exp((y * -t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-24000.0d0)) then
        tmp = t_1
    else if (y <= 0.235d0) then
        tmp = x * exp((a * (-z - b)))
    else if (y <= 3.45d+72) then
        tmp = t_1
    else
        tmp = x * exp((y * -t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -24000.0) {
		tmp = t_1;
	} else if (y <= 0.235) {
		tmp = x * Math.exp((a * (-z - b)));
	} else if (y <= 3.45e+72) {
		tmp = t_1;
	} else {
		tmp = x * Math.exp((y * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -24000.0:
		tmp = t_1
	elif y <= 0.235:
		tmp = x * math.exp((a * (-z - b)))
	elif y <= 3.45e+72:
		tmp = t_1
	else:
		tmp = x * math.exp((y * -t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -24000.0)
		tmp = t_1;
	elseif (y <= 0.235)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	elseif (y <= 3.45e+72)
		tmp = t_1;
	else
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -24000.0)
		tmp = t_1;
	elseif (y <= 0.235)
		tmp = x * exp((a * (-z - b)));
	elseif (y <= 3.45e+72)
		tmp = t_1;
	else
		tmp = x * exp((y * -t));
	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]}, If[LessEqual[y, -24000.0], t$95$1, If[LessEqual[y, 0.235], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.45e+72], t$95$1, N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -24000 or 0.23499999999999999 < y < 3.45000000000000017e72

   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 a around 0 88.4%

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

      1. *-commutative 88.4%

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

      2. exp-prod 88.4%

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

      3. exp-diff 88.4%

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

      4. rem-exp-log 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in t around 0 78.3%

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

   if -24000 < y < 0.23499999999999999

   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 0 82.7%

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

      1. sub-neg 82.7%

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

      2. log1p-define 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in z around 0 87.8%

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

      1. +-commutative 87.8%

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

      2. associate-*r* 87.8%

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

      3. associate-*r* 87.8%

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

      4. distribute-lft-out 87.8%

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

      5. mul-1-neg 87.8%

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

   8. Simplified 87.8%

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

   if 3.45000000000000017e72 < y

   1. Initial program 91.2%

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

   3. Taylor expanded in t around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. distribute-lft-neg-out 74.0%

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

      3. *-commutative 74.0%

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

   5. Simplified 74.0%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -24000:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 0.235:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{+72}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.15:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+271}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -1.55e-13)
     t_1
     (if (<= y 0.15)
       (- x (* x (* a b)))
       (if (<= y 1.35e+271) t_1 (* y (- (/ x y) (* x t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -1.55e-13) {
		tmp = t_1;
	} else if (y <= 0.15) {
		tmp = x - (x * (a * b));
	} else if (y <= 1.35e+271) {
		tmp = t_1;
	} else {
		tmp = y * ((x / y) - (x * 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 = x * (z ** y)
    if (y <= (-1.55d-13)) then
        tmp = t_1
    else if (y <= 0.15d0) then
        tmp = x - (x * (a * b))
    else if (y <= 1.35d+271) then
        tmp = t_1
    else
        tmp = y * ((x / y) - (x * 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 = x * Math.pow(z, y);
	double tmp;
	if (y <= -1.55e-13) {
		tmp = t_1;
	} else if (y <= 0.15) {
		tmp = x - (x * (a * b));
	} else if (y <= 1.35e+271) {
		tmp = t_1;
	} else {
		tmp = y * ((x / y) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -1.55e-13:
		tmp = t_1
	elif y <= 0.15:
		tmp = x - (x * (a * b))
	elif y <= 1.35e+271:
		tmp = t_1
	else:
		tmp = y * ((x / y) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -1.55e-13)
		tmp = t_1;
	elseif (y <= 0.15)
		tmp = Float64(x - Float64(x * Float64(a * b)));
	elseif (y <= 1.35e+271)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(x / y) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -1.55e-13)
		tmp = t_1;
	elseif (y <= 0.15)
		tmp = x - (x * (a * b));
	elseif (y <= 1.35e+271)
		tmp = t_1;
	else
		tmp = y * ((x / y) - (x * t));
	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]}, If[LessEqual[y, -1.55e-13], t$95$1, If[LessEqual[y, 0.15], N[(x - N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+271], t$95$1, N[(y * N[(N[(x / y), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55e-13 or 0.149999999999999994 < y < 1.34999999999999995e271

   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. Add Preprocessing

   3. Taylor expanded in a around 0 87.9%

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

      1. *-commutative 87.9%

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

      2. exp-prod 87.9%

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

      3. exp-diff 87.9%

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

      4. rem-exp-log 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in t around 0 73.5%

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

   if -1.55e-13 < y < 0.149999999999999994

   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 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 46.3%

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

      1. mul-1-neg 46.3%

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

      2. unsub-neg 46.3%

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

      3. associate-*r* 49.9%

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

      4. *-commutative 49.9%

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

   8. Simplified 49.9%

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

   if 1.34999999999999995e271 < y

   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 t around inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. distribute-lft-neg-out 71.9%

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

      3. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in y around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. unsub-neg 72.4%

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

      3. associate-*r* 72.6%

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

      4. *-commutative 72.6%

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

      5. cancel-sign-sub-inv 72.6%

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

      6. mul-1-neg 72.6%

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

      7. *-commutative 72.6%

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

      8. associate-*r* 72.6%

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

      9. *-commutative 72.6%

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

      10. mul-1-neg 72.6%

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

      11. distribute-lft-neg-in 72.6%

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

      12. *-commutative 72.6%

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

   8. Simplified 72.6%

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

   9. Taylor expanded in y around inf 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-13}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 0.15:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+271}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -0.38:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.135:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+271}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -0.38)
     t_1
     (if (<= y 0.135)
       (* x (exp (* a (- b))))
       (if (<= y 1.35e+271) t_1 (* y (- (/ x y) (* x t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -0.38) {
		tmp = t_1;
	} else if (y <= 0.135) {
		tmp = x * exp((a * -b));
	} else if (y <= 1.35e+271) {
		tmp = t_1;
	} else {
		tmp = y * ((x / y) - (x * 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 = x * (z ** y)
    if (y <= (-0.38d0)) then
        tmp = t_1
    else if (y <= 0.135d0) then
        tmp = x * exp((a * -b))
    else if (y <= 1.35d+271) then
        tmp = t_1
    else
        tmp = y * ((x / y) - (x * 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 = x * Math.pow(z, y);
	double tmp;
	if (y <= -0.38) {
		tmp = t_1;
	} else if (y <= 0.135) {
		tmp = x * Math.exp((a * -b));
	} else if (y <= 1.35e+271) {
		tmp = t_1;
	} else {
		tmp = y * ((x / y) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -0.38:
		tmp = t_1
	elif y <= 0.135:
		tmp = x * math.exp((a * -b))
	elif y <= 1.35e+271:
		tmp = t_1
	else:
		tmp = y * ((x / y) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -0.38)
		tmp = t_1;
	elseif (y <= 0.135)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif (y <= 1.35e+271)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(x / y) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -0.38)
		tmp = t_1;
	elseif (y <= 0.135)
		tmp = x * exp((a * -b));
	elseif (y <= 1.35e+271)
		tmp = t_1;
	else
		tmp = y * ((x / y) - (x * t));
	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]}, If[LessEqual[y, -0.38], t$95$1, If[LessEqual[y, 0.135], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+271], t$95$1, N[(y * N[(N[(x / y), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.38 or 0.13500000000000001 < y < 1.34999999999999995e271

   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. Add Preprocessing

   3. Taylor expanded in a around 0 87.9%

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

      1. *-commutative 87.9%

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

      2. exp-prod 87.9%

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

      3. exp-diff 87.9%

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

      4. rem-exp-log 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in t around 0 73.5%

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

   if -0.38 < y < 0.13500000000000001

   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 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%

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

   if 1.34999999999999995e271 < y

   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 t around inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. distribute-lft-neg-out 71.9%

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

      3. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in y around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. unsub-neg 72.4%

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

      3. associate-*r* 72.6%

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

      4. *-commutative 72.6%

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

      5. cancel-sign-sub-inv 72.6%

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

      6. mul-1-neg 72.6%

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

      7. *-commutative 72.6%

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

      8. associate-*r* 72.6%

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

      9. *-commutative 72.6%

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

      10. mul-1-neg 72.6%

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

      11. distribute-lft-neg-in 72.6%

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

      12. *-commutative 72.6%

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

   8. Simplified 72.6%

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

   9. Taylor expanded in y around inf 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.38:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 0.135:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+271}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.1% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+172}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* y (- t)))))
   (if (<= y -7.8e+205)
     t_1
     (if (<= y -2.05e-161)
       (* a (/ x a))
       (if (<= y 4.3e-27)
         x
         (if (<= y 1.32e+172)
           (* a (* x (- b)))
           (if (<= y 1.55e+301) t_1 (* a (* x b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y * -t);
	double tmp;
	if (y <= -7.8e+205) {
		tmp = t_1;
	} else if (y <= -2.05e-161) {
		tmp = a * (x / a);
	} else if (y <= 4.3e-27) {
		tmp = x;
	} else if (y <= 1.32e+172) {
		tmp = a * (x * -b);
	} else if (y <= 1.55e+301) {
		tmp = t_1;
	} else {
		tmp = a * (x * 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y * -t)
    if (y <= (-7.8d+205)) then
        tmp = t_1
    else if (y <= (-2.05d-161)) then
        tmp = a * (x / a)
    else if (y <= 4.3d-27) then
        tmp = x
    else if (y <= 1.32d+172) then
        tmp = a * (x * -b)
    else if (y <= 1.55d+301) then
        tmp = t_1
    else
        tmp = a * (x * 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 t_1 = x * (y * -t);
	double tmp;
	if (y <= -7.8e+205) {
		tmp = t_1;
	} else if (y <= -2.05e-161) {
		tmp = a * (x / a);
	} else if (y <= 4.3e-27) {
		tmp = x;
	} else if (y <= 1.32e+172) {
		tmp = a * (x * -b);
	} else if (y <= 1.55e+301) {
		tmp = t_1;
	} else {
		tmp = a * (x * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (y * -t)
	tmp = 0
	if y <= -7.8e+205:
		tmp = t_1
	elif y <= -2.05e-161:
		tmp = a * (x / a)
	elif y <= 4.3e-27:
		tmp = x
	elif y <= 1.32e+172:
		tmp = a * (x * -b)
	elif y <= 1.55e+301:
		tmp = t_1
	else:
		tmp = a * (x * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(y * Float64(-t)))
	tmp = 0.0
	if (y <= -7.8e+205)
		tmp = t_1;
	elseif (y <= -2.05e-161)
		tmp = Float64(a * Float64(x / a));
	elseif (y <= 4.3e-27)
		tmp = x;
	elseif (y <= 1.32e+172)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (y <= 1.55e+301)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(x * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (y * -t);
	tmp = 0.0;
	if (y <= -7.8e+205)
		tmp = t_1;
	elseif (y <= -2.05e-161)
		tmp = a * (x / a);
	elseif (y <= 4.3e-27)
		tmp = x;
	elseif (y <= 1.32e+172)
		tmp = a * (x * -b);
	elseif (y <= 1.55e+301)
		tmp = t_1;
	else
		tmp = a * (x * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.8e+205], t$95$1, If[LessEqual[y, -2.05e-161], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e-27], x, If[LessEqual[y, 1.32e+172], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+301], t$95$1, N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.7999999999999997e205 or 1.31999999999999996e172 < y < 1.55000000000000005e301

   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 t around inf 81.6%

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

      1. mul-1-neg 81.6%

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

      2. distribute-lft-neg-out 81.6%

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

      3. *-commutative 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in y around 0 45.2%

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

      1. mul-1-neg 45.2%

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

      2. unsub-neg 45.2%

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

      3. associate-*r* 37.4%

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

      4. *-commutative 37.4%

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

      5. cancel-sign-sub-inv 37.4%

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

      6. mul-1-neg 37.4%

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

      7. *-commutative 37.4%

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

      8. associate-*r* 37.4%

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

      9. *-commutative 37.4%

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

      10. mul-1-neg 37.4%

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

      11. distribute-lft-neg-in 37.4%

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

      12. *-commutative 37.4%

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

   8. Simplified 37.4%

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

   9. Taylor expanded in t around inf 45.2%

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

       1. mul-1-neg 45.2%

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

       2. associate-*r* 39.3%

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

       3. *-commutative 39.3%

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

       4. associate-*r* 41.2%

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

       5. distribute-lft-neg-in 41.2%

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

   11. Simplified 41.2%

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

   if -7.7999999999999997e205 < y < -2.0499999999999999e-161

   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 b around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. distribute-rgt-neg-out 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in a around 0 22.0%

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

      1. mul-1-neg 22.0%

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

      2. unsub-neg 22.0%

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

      3. associate-*r* 21.9%

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

      4. *-commutative 21.9%

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

   8. Simplified 21.9%

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

   9. Taylor expanded in a around inf 26.2%

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

   10. Taylor expanded in a around 0 29.0%

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

   if -2.0499999999999999e-161 < y < 4.30000000000000002e-27

   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 85.6%

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

      1. mul-1-neg 85.6%

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

      2. distribute-rgt-neg-out 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in a around 0 44.6%

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

   if 4.30000000000000002e-27 < y < 1.31999999999999996e172

   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. Add Preprocessing

   3. Taylor expanded in b around inf 39.8%

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

      1. mul-1-neg 39.8%

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

      2. distribute-rgt-neg-out 39.8%

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

   5. Simplified 39.8%

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

   6. Taylor expanded in a around 0 14.8%

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

      1. mul-1-neg 14.8%

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

      2. unsub-neg 14.8%

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

      3. associate-*r* 15.1%

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

      4. *-commutative 15.1%

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

   8. Simplified 15.1%

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

   9. Taylor expanded in a around inf 32.5%

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

       1. neg-mul-1 32.5%

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

       2. distribute-rgt-neg-in 32.5%

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

       3. distribute-lft-neg-in 32.5%

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

   11. Simplified 32.5%

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

   if 1.55000000000000005e301 < y

   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 b around inf 4.0%

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

      1. mul-1-neg 4.0%

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

      2. distribute-rgt-neg-out 4.0%

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

   5. Simplified 4.0%

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

   6. Taylor expanded in a around 0 4.0%

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

      1. mul-1-neg 4.0%

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

      2. unsub-neg 4.0%

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

      3. associate-*r* 4.0%

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

      4. *-commutative 4.0%

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

   8. Simplified 4.0%

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

      1. sub-neg 4.0%

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

      2. *-commutative 4.0%

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

      3. distribute-lft-neg-in 4.0%

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

      4. distribute-lft-neg-out 4.0%

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

      5. add-sqr-sqrt 1.9%

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

      6. sqrt-unprod 4.0%

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

      7. sqr-neg 4.0%

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

      8. sqrt-unprod 2.1%

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

      9. add-sqr-sqrt 4.0%

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

      10. distribute-rgt1-in 4.0%

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

   10. Applied egg-rr 4.0%

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

   11. Taylor expanded in a around inf 4.5%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+205}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+172}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.6% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+176}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-36}:\\ \;\;\;\;x + t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-13}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.7e+176)
   (* t (* y (- x)))
   (if (<= y -2.1e-161)
     (* a (/ x a))
     (if (<= y 1.5e-36)
       (+ x (* t (* x y)))
       (if (<= y 3.1e-13)
         (* a (* x (- b)))
         (if (<= y 2.65e+172) (* x (* a (- b))) (* x (* y (- t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.7e+176) {
		tmp = t * (y * -x);
	} else if (y <= -2.1e-161) {
		tmp = a * (x / a);
	} else if (y <= 1.5e-36) {
		tmp = x + (t * (x * y));
	} else if (y <= 3.1e-13) {
		tmp = a * (x * -b);
	} else if (y <= 2.65e+172) {
		tmp = x * (a * -b);
	} else {
		tmp = 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) :: tmp
    if (y <= (-4.7d+176)) then
        tmp = t * (y * -x)
    else if (y <= (-2.1d-161)) then
        tmp = a * (x / a)
    else if (y <= 1.5d-36) then
        tmp = x + (t * (x * y))
    else if (y <= 3.1d-13) then
        tmp = a * (x * -b)
    else if (y <= 2.65d+172) then
        tmp = x * (a * -b)
    else
        tmp = 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 tmp;
	if (y <= -4.7e+176) {
		tmp = t * (y * -x);
	} else if (y <= -2.1e-161) {
		tmp = a * (x / a);
	} else if (y <= 1.5e-36) {
		tmp = x + (t * (x * y));
	} else if (y <= 3.1e-13) {
		tmp = a * (x * -b);
	} else if (y <= 2.65e+172) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.7e+176:
		tmp = t * (y * -x)
	elif y <= -2.1e-161:
		tmp = a * (x / a)
	elif y <= 1.5e-36:
		tmp = x + (t * (x * y))
	elif y <= 3.1e-13:
		tmp = a * (x * -b)
	elif y <= 2.65e+172:
		tmp = x * (a * -b)
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.7e+176)
		tmp = Float64(t * Float64(y * Float64(-x)));
	elseif (y <= -2.1e-161)
		tmp = Float64(a * Float64(x / a));
	elseif (y <= 1.5e-36)
		tmp = Float64(x + Float64(t * Float64(x * y)));
	elseif (y <= 3.1e-13)
		tmp = Float64(a * Float64(x * Float64(-b)));
	elseif (y <= 2.65e+172)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.7e+176)
		tmp = t * (y * -x);
	elseif (y <= -2.1e-161)
		tmp = a * (x / a);
	elseif (y <= 1.5e-36)
		tmp = x + (t * (x * y));
	elseif (y <= 3.1e-13)
		tmp = a * (x * -b);
	elseif (y <= 2.65e+172)
		tmp = x * (a * -b);
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.7e+176], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-161], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-36], N[(x + N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-13], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e+172], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.69999999999999981e176

   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 t around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. distribute-lft-neg-out 83.3%

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

      3. *-commutative 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in y around 0 43.1%

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

      1. mul-1-neg 43.1%

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

      2. unsub-neg 43.1%

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

      3. associate-*r* 26.9%

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

      4. *-commutative 26.9%

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

      5. cancel-sign-sub-inv 26.9%

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

      6. mul-1-neg 26.9%

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

      7. *-commutative 26.9%

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

      8. associate-*r* 26.9%

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

      9. *-commutative 26.9%

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

      10. mul-1-neg 26.9%

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

      11. distribute-lft-neg-in 26.9%

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

      12. *-commutative 26.9%

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

   8. Simplified 26.9%

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

   9. Taylor expanded in t around inf 43.1%

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

   if -4.69999999999999981e176 < y < -2.1e-161

   1. Initial program 98.4%

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

   3. Taylor expanded in b around inf 56.7%

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

      1. mul-1-neg 56.7%

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

      2. distribute-rgt-neg-out 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in a around 0 24.5%

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

      1. mul-1-neg 24.5%

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

      2. unsub-neg 24.5%

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

      3. associate-*r* 24.4%

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

      4. *-commutative 24.4%

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

   8. Simplified 24.4%

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

   9. Taylor expanded in a around inf 27.7%

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

   10. Taylor expanded in a around 0 30.9%

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

   if -2.1e-161 < y < 1.5000000000000001e-36

   1. Initial program 93.7%

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

   3. Taylor expanded in t around inf 51.5%

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

      1. mul-1-neg 51.5%

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

      2. distribute-lft-neg-out 51.5%

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

      3. *-commutative 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in y around 0 45.4%

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

      1. mul-1-neg 45.4%

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

      2. unsub-neg 45.4%

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

      3. associate-*r* 45.2%

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

      4. *-commutative 45.2%

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

      5. cancel-sign-sub-inv 45.2%

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

      6. mul-1-neg 45.2%

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

      7. *-commutative 45.2%

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

      8. associate-*r* 45.2%

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

      9. *-commutative 45.2%

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

      10. mul-1-neg 45.2%

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

      11. distribute-lft-neg-in 45.2%

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

      12. *-commutative 45.2%

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

   8. Simplified 45.2%

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

      1. *-un-lft-identity 45.2%

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

      2. *-commutative 45.2%

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

      3. add-sqr-sqrt 30.6%

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

      4. sqrt-unprod 44.1%

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

      5. sqr-neg 44.1%

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

      6. sqrt-unprod 32.3%

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

      7. add-sqr-sqrt 44.1%

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

      8. associate-*l* 46.4%

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

   10. Applied egg-rr 46.4%

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

       1. *-rgt-identity 46.4%

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

       2. associate-*r* 44.1%

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

       3. *-commutative 44.1%

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

       4. associate-*r* 46.4%

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

   12. Simplified 46.4%

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

   if 1.5000000000000001e-36 < y < 3.0999999999999999e-13

   1. Initial program 81.6%

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

   3. Taylor expanded in b around inf 42.8%

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

      1. mul-1-neg 42.8%

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

      2. distribute-rgt-neg-out 42.8%

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

   5. Simplified 42.8%

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

   6. Taylor expanded in a around 0 23.8%

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

      1. mul-1-neg 23.8%

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

      2. unsub-neg 23.8%

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

      3. associate-*r* 23.8%

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

      4. *-commutative 23.8%

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

   8. Simplified 23.8%

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

   9. Taylor expanded in a around inf 41.8%

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

       1. neg-mul-1 41.8%

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

       2. distribute-rgt-neg-in 41.8%

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

       3. distribute-lft-neg-in 41.8%

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

   11. Simplified 41.8%

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

   if 3.0999999999999999e-13 < y < 2.65e172

   1. Initial program 97.3%

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

   3. Taylor expanded in b around inf 37.6%

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

      1. mul-1-neg 37.6%

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

      2. distribute-rgt-neg-out 37.6%

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

   5. Simplified 37.6%

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

   6. Taylor expanded in a around 0 13.1%

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

      1. mul-1-neg 13.1%

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

      2. unsub-neg 13.1%

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

      3. associate-*r* 13.4%

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

      4. *-commutative 13.4%

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

   8. Simplified 13.4%

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

   9. Taylor expanded in a around inf 29.8%

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

       1. associate-*r* 32.1%

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

       2. associate-*r* 32.1%

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

       3. mul-1-neg 32.1%

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

       4. *-commutative 32.1%

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

       5. distribute-rgt-neg-in 32.1%

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

   11. Simplified 32.1%

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

   if 2.65e172 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-lft-neg-out 76.3%

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

      3. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. unsub-neg 39.4%

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

      3. associate-*r* 36.3%

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

      4. *-commutative 36.3%

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

      5. cancel-sign-sub-inv 36.3%

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

      6. mul-1-neg 36.3%

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

      7. *-commutative 36.3%

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

      8. associate-*r* 36.3%

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

      9. *-commutative 36.3%

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

      10. mul-1-neg 36.3%

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

      11. distribute-lft-neg-in 36.3%

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

      12. *-commutative 36.3%

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

   8. Simplified 36.3%

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

   9. Taylor expanded in t around inf 39.4%

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

       1. mul-1-neg 39.4%

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

       2. associate-*r* 46.1%

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

       3. *-commutative 46.1%

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

       4. associate-*r* 39.5%

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

       5. distribute-lft-neg-in 39.5%

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

   11. Simplified 39.5%

       \[\leadsto \color{blue}{\left(-x\right) \cdot \left(t \cdot y\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+176}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-36}:\\ \;\;\;\;x + t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-13}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.4% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* y (- t)))))
   (if (<= y -2.5e+204)
     t_1
     (if (<= y -2.1e-161)
       (* a (/ x a))
       (if (<= y 4.2e-27) x (if (<= y 2e+171) (* x (* a (- b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y * -t);
	double tmp;
	if (y <= -2.5e+204) {
		tmp = t_1;
	} else if (y <= -2.1e-161) {
		tmp = a * (x / a);
	} else if (y <= 4.2e-27) {
		tmp = x;
	} else if (y <= 2e+171) {
		tmp = x * (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 = x * (y * -t)
    if (y <= (-2.5d+204)) then
        tmp = t_1
    else if (y <= (-2.1d-161)) then
        tmp = a * (x / a)
    else if (y <= 4.2d-27) then
        tmp = x
    else if (y <= 2d+171) then
        tmp = x * (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 * (y * -t);
	double tmp;
	if (y <= -2.5e+204) {
		tmp = t_1;
	} else if (y <= -2.1e-161) {
		tmp = a * (x / a);
	} else if (y <= 4.2e-27) {
		tmp = x;
	} else if (y <= 2e+171) {
		tmp = x * (a * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (y * -t)
	tmp = 0
	if y <= -2.5e+204:
		tmp = t_1
	elif y <= -2.1e-161:
		tmp = a * (x / a)
	elif y <= 4.2e-27:
		tmp = x
	elif y <= 2e+171:
		tmp = x * (a * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(y * Float64(-t)))
	tmp = 0.0
	if (y <= -2.5e+204)
		tmp = t_1;
	elseif (y <= -2.1e-161)
		tmp = Float64(a * Float64(x / a));
	elseif (y <= 4.2e-27)
		tmp = x;
	elseif (y <= 2e+171)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (y * -t);
	tmp = 0.0;
	if (y <= -2.5e+204)
		tmp = t_1;
	elseif (y <= -2.1e-161)
		tmp = a * (x / a);
	elseif (y <= 4.2e-27)
		tmp = x;
	elseif (y <= 2e+171)
		tmp = x * (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[(y * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+204], t$95$1, If[LessEqual[y, -2.1e-161], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-27], x, If[LessEqual[y, 2e+171], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.50000000000000004e204 or 1.99999999999999991e171 < y

   1. Initial program 94.0%

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

   3. Taylor expanded in t around inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. distribute-lft-neg-out 78.4%

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

      3. *-commutative 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in y around 0 43.5%

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

      1. mul-1-neg 43.5%

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

      2. unsub-neg 43.5%

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

      3. associate-*r* 36.0%

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

      4. *-commutative 36.0%

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

      5. cancel-sign-sub-inv 36.0%

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

      6. mul-1-neg 36.0%

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

      7. *-commutative 36.0%

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

      8. associate-*r* 36.0%

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

      9. *-commutative 36.0%

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

      10. mul-1-neg 36.0%

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

      11. distribute-lft-neg-in 36.0%

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

      12. *-commutative 36.0%

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

   8. Simplified 36.0%

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

   9. Taylor expanded in t around inf 43.5%

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

       1. mul-1-neg 43.5%

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

       2. associate-*r* 41.7%

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

       3. *-commutative 41.7%

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

       4. associate-*r* 39.7%

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

       5. distribute-lft-neg-in 39.7%

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

   11. Simplified 39.7%

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

   if -2.50000000000000004e204 < y < -2.1e-161

   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 b around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. distribute-rgt-neg-out 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in a around 0 22.0%

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

      1. mul-1-neg 22.0%

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

      2. unsub-neg 22.0%

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

      3. associate-*r* 21.9%

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

      4. *-commutative 21.9%

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

   8. Simplified 21.9%

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

   9. Taylor expanded in a around inf 26.2%

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

   10. Taylor expanded in a around 0 29.0%

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

   if -2.1e-161 < y < 4.20000000000000031e-27

   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 85.6%

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

      1. mul-1-neg 85.6%

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

      2. distribute-rgt-neg-out 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in a around 0 44.6%

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

   if 4.20000000000000031e-27 < y < 1.99999999999999991e171

   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. Add Preprocessing

   3. Taylor expanded in b around inf 39.8%

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

      1. mul-1-neg 39.8%

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

      2. distribute-rgt-neg-out 39.8%

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

   5. Simplified 39.8%

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

   6. Taylor expanded in a around 0 14.8%

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

      1. mul-1-neg 14.8%

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

      2. unsub-neg 14.8%

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

      3. associate-*r* 15.1%

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

      4. *-commutative 15.1%

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

   8. Simplified 15.1%

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

   9. Taylor expanded in a around inf 32.5%

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

       1. associate-*r* 32.5%

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

       2. associate-*r* 32.5%

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

       3. mul-1-neg 32.5%

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

       4. *-commutative 32.5%

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

       5. distribute-rgt-neg-in 32.5%

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

   11. Simplified 32.5%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+204}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.6% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+174}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.05e+174)
   (* t (* y (- x)))
   (if (<= y -2.1e-161)
     (* a (/ x a))
     (if (<= y 4.2e-27)
       x
       (if (<= y 2.85e+172) (* x (* a (- b))) (* x (* y (- t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.05e+174) {
		tmp = t * (y * -x);
	} else if (y <= -2.1e-161) {
		tmp = a * (x / a);
	} else if (y <= 4.2e-27) {
		tmp = x;
	} else if (y <= 2.85e+172) {
		tmp = x * (a * -b);
	} else {
		tmp = 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) :: tmp
    if (y <= (-3.05d+174)) then
        tmp = t * (y * -x)
    else if (y <= (-2.1d-161)) then
        tmp = a * (x / a)
    else if (y <= 4.2d-27) then
        tmp = x
    else if (y <= 2.85d+172) then
        tmp = x * (a * -b)
    else
        tmp = 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 tmp;
	if (y <= -3.05e+174) {
		tmp = t * (y * -x);
	} else if (y <= -2.1e-161) {
		tmp = a * (x / a);
	} else if (y <= 4.2e-27) {
		tmp = x;
	} else if (y <= 2.85e+172) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.05e+174:
		tmp = t * (y * -x)
	elif y <= -2.1e-161:
		tmp = a * (x / a)
	elif y <= 4.2e-27:
		tmp = x
	elif y <= 2.85e+172:
		tmp = x * (a * -b)
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.05e+174)
		tmp = Float64(t * Float64(y * Float64(-x)));
	elseif (y <= -2.1e-161)
		tmp = Float64(a * Float64(x / a));
	elseif (y <= 4.2e-27)
		tmp = x;
	elseif (y <= 2.85e+172)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.05e+174)
		tmp = t * (y * -x);
	elseif (y <= -2.1e-161)
		tmp = a * (x / a);
	elseif (y <= 4.2e-27)
		tmp = x;
	elseif (y <= 2.85e+172)
		tmp = x * (a * -b);
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.05e+174], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-161], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-27], x, If[LessEqual[y, 2.85e+172], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.05e174

   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 t around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. distribute-lft-neg-out 83.3%

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

      3. *-commutative 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in y around 0 43.1%

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

      1. mul-1-neg 43.1%

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

      2. unsub-neg 43.1%

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

      3. associate-*r* 26.9%

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

      4. *-commutative 26.9%

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

      5. cancel-sign-sub-inv 26.9%

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

      6. mul-1-neg 26.9%

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

      7. *-commutative 26.9%

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

      8. associate-*r* 26.9%

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

      9. *-commutative 26.9%

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

      10. mul-1-neg 26.9%

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

      11. distribute-lft-neg-in 26.9%

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

      12. *-commutative 26.9%

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

   8. Simplified 26.9%

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

   9. Taylor expanded in t around inf 43.1%

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

   if -3.05e174 < y < -2.1e-161

   1. Initial program 98.4%

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

   3. Taylor expanded in b around inf 56.7%

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

      1. mul-1-neg 56.7%

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

      2. distribute-rgt-neg-out 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in a around 0 24.5%

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

      1. mul-1-neg 24.5%

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

      2. unsub-neg 24.5%

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

      3. associate-*r* 24.4%

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

      4. *-commutative 24.4%

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

   8. Simplified 24.4%

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

   9. Taylor expanded in a around inf 27.7%

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

   10. Taylor expanded in a around 0 30.9%

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

   if -2.1e-161 < y < 4.20000000000000031e-27

   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 85.6%

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

      1. mul-1-neg 85.6%

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

      2. distribute-rgt-neg-out 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in a around 0 44.6%

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

   if 4.20000000000000031e-27 < y < 2.85e172

   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. Add Preprocessing

   3. Taylor expanded in b around inf 39.8%

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

      1. mul-1-neg 39.8%

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

      2. distribute-rgt-neg-out 39.8%

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

   5. Simplified 39.8%

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

   6. Taylor expanded in a around 0 14.8%

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

      1. mul-1-neg 14.8%

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

      2. unsub-neg 14.8%

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

      3. associate-*r* 15.1%

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

      4. *-commutative 15.1%

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

   8. Simplified 15.1%

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

   9. Taylor expanded in a around inf 32.5%

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

       1. associate-*r* 32.5%

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

       2. associate-*r* 32.5%

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

       3. mul-1-neg 32.5%

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

       4. *-commutative 32.5%

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

       5. distribute-rgt-neg-in 32.5%

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

   11. Simplified 32.5%

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

   if 2.85e172 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-lft-neg-out 76.3%

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

      3. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. unsub-neg 39.4%

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

      3. associate-*r* 36.3%

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

      4. *-commutative 36.3%

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

      5. cancel-sign-sub-inv 36.3%

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

      6. mul-1-neg 36.3%

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

      7. *-commutative 36.3%

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

      8. associate-*r* 36.3%

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

      9. *-commutative 36.3%

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

      10. mul-1-neg 36.3%

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

      11. distribute-lft-neg-in 36.3%

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

      12. *-commutative 36.3%

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

   8. Simplified 36.3%

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

   9. Taylor expanded in t around inf 39.4%

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

       1. mul-1-neg 39.4%

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

       2. associate-*r* 46.1%

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

       3. *-commutative 46.1%

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

       4. associate-*r* 39.5%

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

       5. distribute-lft-neg-in 39.5%

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

   11. Simplified 39.5%

       \[\leadsto \color{blue}{\left(-x\right) \cdot \left(t \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+174}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 34.1% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+36}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.4e+32)
   (* t (- (/ x t) (* x y)))
   (if (<= y 7.5e+36)
     (- x (* x (* a b)))
     (if (<= y 2e+171) (* x (* a (- b))) (* y (- (/ x y) (* x t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.4e+32) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 7.5e+36) {
		tmp = x - (x * (a * b));
	} else if (y <= 2e+171) {
		tmp = x * (a * -b);
	} else {
		tmp = y * ((x / y) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.4d+32)) then
        tmp = t * ((x / t) - (x * y))
    else if (y <= 7.5d+36) then
        tmp = x - (x * (a * b))
    else if (y <= 2d+171) then
        tmp = x * (a * -b)
    else
        tmp = y * ((x / y) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.4e+32) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 7.5e+36) {
		tmp = x - (x * (a * b));
	} else if (y <= 2e+171) {
		tmp = x * (a * -b);
	} else {
		tmp = y * ((x / y) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.4e+32:
		tmp = t * ((x / t) - (x * y))
	elif y <= 7.5e+36:
		tmp = x - (x * (a * b))
	elif y <= 2e+171:
		tmp = x * (a * -b)
	else:
		tmp = y * ((x / y) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.4e+32)
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	elseif (y <= 7.5e+36)
		tmp = Float64(x - Float64(x * Float64(a * b)));
	elseif (y <= 2e+171)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = Float64(y * Float64(Float64(x / y) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.4e+32)
		tmp = t * ((x / t) - (x * y));
	elseif (y <= 7.5e+36)
		tmp = x - (x * (a * b));
	elseif (y <= 2e+171)
		tmp = x * (a * -b);
	else
		tmp = y * ((x / y) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.4e+32], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+36], N[(x - N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+171], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x / y), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.4e32

   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 t around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. distribute-lft-neg-out 68.4%

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

      3. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in y around 0 34.8%

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

      1. mul-1-neg 34.8%

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

      2. unsub-neg 34.8%

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

      3. associate-*r* 24.0%

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

      4. *-commutative 24.0%

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

      5. cancel-sign-sub-inv 24.0%

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

      6. mul-1-neg 24.0%

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

      7. *-commutative 24.0%

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

      8. associate-*r* 24.0%

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

      9. *-commutative 24.0%

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

      10. mul-1-neg 24.0%

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

      11. distribute-lft-neg-in 24.0%

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

      12. *-commutative 24.0%

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

   8. Simplified 24.0%

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

   9. Taylor expanded in t around inf 38.5%

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

   if -1.4e32 < y < 7.50000000000000054e36

   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 b around inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. distribute-rgt-neg-out 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in a around 0 43.2%

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

      1. mul-1-neg 43.2%

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

      2. unsub-neg 43.2%

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

      3. associate-*r* 46.5%

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

      4. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   if 7.50000000000000054e36 < y < 1.99999999999999991e171

   1. Initial program 96.5%

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

   3. Taylor expanded in b around inf 27.8%

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

      1. mul-1-neg 27.8%

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

      2. distribute-rgt-neg-out 27.8%

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

   5. Simplified 27.8%

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

   6. Taylor expanded in a around 0 10.4%

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

      1. mul-1-neg 10.4%

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

      2. unsub-neg 10.4%

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

      3. associate-*r* 10.4%

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

      4. *-commutative 10.4%

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

   8. Simplified 10.4%

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

   9. Taylor expanded in a around inf 34.4%

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

       1. associate-*r* 37.7%

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

       2. associate-*r* 37.7%

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

       3. mul-1-neg 37.7%

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

       4. *-commutative 37.7%

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

       5. distribute-rgt-neg-in 37.7%

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

   11. Simplified 37.7%

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

   if 1.99999999999999991e171 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-lft-neg-out 76.3%

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

      3. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. unsub-neg 39.4%

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

      3. associate-*r* 36.3%

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

      4. *-commutative 36.3%

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

      5. cancel-sign-sub-inv 36.3%

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

      6. mul-1-neg 36.3%

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

      7. *-commutative 36.3%

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

      8. associate-*r* 36.3%

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

      9. *-commutative 36.3%

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

      10. mul-1-neg 36.3%

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

      11. distribute-lft-neg-in 36.3%

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

      12. *-commutative 36.3%

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

   8. Simplified 36.3%

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

   9. Taylor expanded in y around inf 46.1%

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

       1. *-commutative 46.1%

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

   11. Simplified 46.1%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+36}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.4% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(1 - z \cdot a\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.1e+32)
   (* t (* y (- x)))
   (if (<= y 4.4e-27)
     (* x (- 1.0 (* z a)))
     (if (<= y 3.9e+171) (* x (* a (- b))) (* x (* y (- t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.1e+32) {
		tmp = t * (y * -x);
	} else if (y <= 4.4e-27) {
		tmp = x * (1.0 - (z * a));
	} else if (y <= 3.9e+171) {
		tmp = x * (a * -b);
	} else {
		tmp = 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) :: tmp
    if (y <= (-2.1d+32)) then
        tmp = t * (y * -x)
    else if (y <= 4.4d-27) then
        tmp = x * (1.0d0 - (z * a))
    else if (y <= 3.9d+171) then
        tmp = x * (a * -b)
    else
        tmp = 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 tmp;
	if (y <= -2.1e+32) {
		tmp = t * (y * -x);
	} else if (y <= 4.4e-27) {
		tmp = x * (1.0 - (z * a));
	} else if (y <= 3.9e+171) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.1e+32:
		tmp = t * (y * -x)
	elif y <= 4.4e-27:
		tmp = x * (1.0 - (z * a))
	elif y <= 3.9e+171:
		tmp = x * (a * -b)
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.1e+32)
		tmp = Float64(t * Float64(y * Float64(-x)));
	elseif (y <= 4.4e-27)
		tmp = Float64(x * Float64(1.0 - Float64(z * a)));
	elseif (y <= 3.9e+171)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.1e+32)
		tmp = t * (y * -x);
	elseif (y <= 4.4e-27)
		tmp = x * (1.0 - (z * a));
	elseif (y <= 3.9e+171)
		tmp = x * (a * -b);
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.1e+32], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e-27], N[(x * N[(1.0 - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+171], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.1000000000000001e32

   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 t around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. distribute-lft-neg-out 68.4%

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

      3. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in y around 0 34.8%

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

      1. mul-1-neg 34.8%

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

      2. unsub-neg 34.8%

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

      3. associate-*r* 24.0%

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

      4. *-commutative 24.0%

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

      5. cancel-sign-sub-inv 24.0%

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

      6. mul-1-neg 24.0%

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

      7. *-commutative 24.0%

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

      8. associate-*r* 24.0%

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

      9. *-commutative 24.0%

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

      10. mul-1-neg 24.0%

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

      11. distribute-lft-neg-in 24.0%

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

      12. *-commutative 24.0%

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

   8. Simplified 24.0%

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

   9. Taylor expanded in t around inf 34.8%

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

   if -2.1000000000000001e32 < y < 4.39999999999999974e-27

   1. Initial program 94.8%

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

   3. Taylor expanded in y around 0 81.7%

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

      1. sub-neg 81.7%

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

      2. log1p-define 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in z around 0 86.9%

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

      1. +-commutative 86.9%

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

      2. associate-*r* 86.9%

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

      3. associate-*r* 86.9%

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

      4. distribute-lft-out 86.9%

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

      5. mul-1-neg 86.9%

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

   8. Simplified 86.9%

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

   9. Taylor expanded in z around inf 54.9%

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

       1. associate-*r* 54.9%

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

       2. mul-1-neg 54.9%

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

   11. Simplified 54.9%

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

   12. Taylor expanded in a around 0 39.5%

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

       1. mul-1-neg 39.5%

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

       2. unsub-neg 39.5%

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

       3. *-lft-identity 39.5%

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

       4. *-commutative 39.5%

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

       5. associate-*r* 39.5%

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

       6. distribute-rgt-out-- 39.5%

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

   14. Simplified 39.5%

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

   if 4.39999999999999974e-27 < y < 3.9e171

   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. Add Preprocessing

   3. Taylor expanded in b around inf 39.8%

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

      1. mul-1-neg 39.8%

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

      2. distribute-rgt-neg-out 39.8%

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

   5. Simplified 39.8%

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

   6. Taylor expanded in a around 0 14.8%

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

      1. mul-1-neg 14.8%

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

      2. unsub-neg 14.8%

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

      3. associate-*r* 15.1%

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

      4. *-commutative 15.1%

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

   8. Simplified 15.1%

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

   9. Taylor expanded in a around inf 32.5%

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

       1. associate-*r* 32.5%

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

       2. associate-*r* 32.5%

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

       3. mul-1-neg 32.5%

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

       4. *-commutative 32.5%

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

       5. distribute-rgt-neg-in 32.5%

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

   11. Simplified 32.5%

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

   if 3.9e171 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-lft-neg-out 76.3%

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

      3. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. unsub-neg 39.4%

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

      3. associate-*r* 36.3%

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

      4. *-commutative 36.3%

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

      5. cancel-sign-sub-inv 36.3%

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

      6. mul-1-neg 36.3%

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

      7. *-commutative 36.3%

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

      8. associate-*r* 36.3%

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

      9. *-commutative 36.3%

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

      10. mul-1-neg 36.3%

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

      11. distribute-lft-neg-in 36.3%

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

      12. *-commutative 36.3%

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

   8. Simplified 36.3%

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

   9. Taylor expanded in t around inf 39.4%

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

       1. mul-1-neg 39.4%

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

       2. associate-*r* 46.1%

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

       3. *-commutative 46.1%

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

       4. associate-*r* 39.5%

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

       5. distribute-lft-neg-in 39.5%

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

   11. Simplified 39.5%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(1 - z \cdot a\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.1% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{+37}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;y \leq 10^{+172}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.7e+100)
   (* t (* y (- x)))
   (if (<= y 1.82e+37)
     (- x (* a (* x b)))
     (if (<= y 1e+172) (* x (* a (- b))) (* x (* y (- t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.7e+100) {
		tmp = t * (y * -x);
	} else if (y <= 1.82e+37) {
		tmp = x - (a * (x * b));
	} else if (y <= 1e+172) {
		tmp = x * (a * -b);
	} else {
		tmp = 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) :: tmp
    if (y <= (-2.7d+100)) then
        tmp = t * (y * -x)
    else if (y <= 1.82d+37) then
        tmp = x - (a * (x * b))
    else if (y <= 1d+172) then
        tmp = x * (a * -b)
    else
        tmp = 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 tmp;
	if (y <= -2.7e+100) {
		tmp = t * (y * -x);
	} else if (y <= 1.82e+37) {
		tmp = x - (a * (x * b));
	} else if (y <= 1e+172) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.7e+100:
		tmp = t * (y * -x)
	elif y <= 1.82e+37:
		tmp = x - (a * (x * b))
	elif y <= 1e+172:
		tmp = x * (a * -b)
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.7e+100)
		tmp = Float64(t * Float64(y * Float64(-x)));
	elseif (y <= 1.82e+37)
		tmp = Float64(x - Float64(a * Float64(x * b)));
	elseif (y <= 1e+172)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.7e+100)
		tmp = t * (y * -x);
	elseif (y <= 1.82e+37)
		tmp = x - (a * (x * b));
	elseif (y <= 1e+172)
		tmp = x * (a * -b);
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.7e+100], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.82e+37], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+172], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.69999999999999998e100

   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 t around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. distribute-lft-neg-out 71.4%

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

      3. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in y around 0 36.1%

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

      1. mul-1-neg 36.1%

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

      2. unsub-neg 36.1%

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

      3. associate-*r* 23.3%

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

      4. *-commutative 23.3%

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

      5. cancel-sign-sub-inv 23.3%

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

      6. mul-1-neg 23.3%

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

      7. *-commutative 23.3%

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

      8. associate-*r* 23.3%

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

      9. *-commutative 23.3%

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

      10. mul-1-neg 23.3%

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

      11. distribute-lft-neg-in 23.3%

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

      12. *-commutative 23.3%

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

   8. Simplified 23.3%

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

   9. Taylor expanded in t around inf 36.2%

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

   if -2.69999999999999998e100 < y < 1.81999999999999998e37

   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 b around inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. distribute-rgt-neg-out 77.0%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in a around 0 42.4%

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

      1. mul-1-neg 42.4%

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

      2. unsub-neg 42.4%

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

      3. *-commutative 42.4%

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

   8. Simplified 42.4%

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

   if 1.81999999999999998e37 < y < 1.0000000000000001e172

   1. Initial program 96.5%

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

   3. Taylor expanded in b around inf 27.8%

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

      1. mul-1-neg 27.8%

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

      2. distribute-rgt-neg-out 27.8%

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

   5. Simplified 27.8%

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

   6. Taylor expanded in a around 0 10.4%

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

      1. mul-1-neg 10.4%

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

      2. unsub-neg 10.4%

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

      3. associate-*r* 10.4%

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

      4. *-commutative 10.4%

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

   8. Simplified 10.4%

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

   9. Taylor expanded in a around inf 34.4%

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

       1. associate-*r* 37.7%

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

       2. associate-*r* 37.7%

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

       3. mul-1-neg 37.7%

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

       4. *-commutative 37.7%

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

       5. distribute-rgt-neg-in 37.7%

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

   11. Simplified 37.7%

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

   if 1.0000000000000001e172 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-lft-neg-out 76.3%

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

      3. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. unsub-neg 39.4%

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

      3. associate-*r* 36.3%

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

      4. *-commutative 36.3%

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

      5. cancel-sign-sub-inv 36.3%

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

      6. mul-1-neg 36.3%

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

      7. *-commutative 36.3%

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

      8. associate-*r* 36.3%

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

      9. *-commutative 36.3%

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

      10. mul-1-neg 36.3%

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

      11. distribute-lft-neg-in 36.3%

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

      12. *-commutative 36.3%

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

   8. Simplified 36.3%

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

   9. Taylor expanded in t around inf 39.4%

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

       1. mul-1-neg 39.4%

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

       2. associate-*r* 46.1%

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

       3. *-commutative 46.1%

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

       4. associate-*r* 39.5%

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

       5. distribute-lft-neg-in 39.5%

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

   11. Simplified 39.5%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{+37}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;y \leq 10^{+172}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.4% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+36}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.05e+38)
   (* t (* y (- x)))
   (if (<= y 7.5e+36)
     (- x (* x (* a b)))
     (if (<= y 9.4e+170) (* x (* a (- b))) (* x (* y (- t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.05e+38) {
		tmp = t * (y * -x);
	} else if (y <= 7.5e+36) {
		tmp = x - (x * (a * b));
	} else if (y <= 9.4e+170) {
		tmp = x * (a * -b);
	} else {
		tmp = 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) :: tmp
    if (y <= (-1.05d+38)) then
        tmp = t * (y * -x)
    else if (y <= 7.5d+36) then
        tmp = x - (x * (a * b))
    else if (y <= 9.4d+170) then
        tmp = x * (a * -b)
    else
        tmp = 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 tmp;
	if (y <= -1.05e+38) {
		tmp = t * (y * -x);
	} else if (y <= 7.5e+36) {
		tmp = x - (x * (a * b));
	} else if (y <= 9.4e+170) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.05e+38:
		tmp = t * (y * -x)
	elif y <= 7.5e+36:
		tmp = x - (x * (a * b))
	elif y <= 9.4e+170:
		tmp = x * (a * -b)
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.05e+38)
		tmp = Float64(t * Float64(y * Float64(-x)));
	elseif (y <= 7.5e+36)
		tmp = Float64(x - Float64(x * Float64(a * b)));
	elseif (y <= 9.4e+170)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.05e+38)
		tmp = t * (y * -x);
	elseif (y <= 7.5e+36)
		tmp = x - (x * (a * b));
	elseif (y <= 9.4e+170)
		tmp = x * (a * -b);
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.05e+38], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+36], N[(x - N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.4e+170], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.05e38

   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 t around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. distribute-lft-neg-out 68.4%

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

      3. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in y around 0 34.8%

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

      1. mul-1-neg 34.8%

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

      2. unsub-neg 34.8%

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

      3. associate-*r* 24.0%

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

      4. *-commutative 24.0%

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

      5. cancel-sign-sub-inv 24.0%

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

      6. mul-1-neg 24.0%

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

      7. *-commutative 24.0%

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

      8. associate-*r* 24.0%

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

      9. *-commutative 24.0%

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

      10. mul-1-neg 24.0%

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

      11. distribute-lft-neg-in 24.0%

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

      12. *-commutative 24.0%

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

   8. Simplified 24.0%

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

   9. Taylor expanded in t around inf 34.8%

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

   if -1.05e38 < y < 7.50000000000000054e36

   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 b around inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. distribute-rgt-neg-out 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in a around 0 43.2%

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

      1. mul-1-neg 43.2%

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

      2. unsub-neg 43.2%

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

      3. associate-*r* 46.5%

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

      4. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   if 7.50000000000000054e36 < y < 9.40000000000000008e170

   1. Initial program 96.5%

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

   3. Taylor expanded in b around inf 27.8%

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

      1. mul-1-neg 27.8%

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

      2. distribute-rgt-neg-out 27.8%

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

   5. Simplified 27.8%

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

   6. Taylor expanded in a around 0 10.4%

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

      1. mul-1-neg 10.4%

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

      2. unsub-neg 10.4%

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

      3. associate-*r* 10.4%

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

      4. *-commutative 10.4%

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

   8. Simplified 10.4%

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

   9. Taylor expanded in a around inf 34.4%

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

       1. associate-*r* 37.7%

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

       2. associate-*r* 37.7%

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

       3. mul-1-neg 37.7%

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

       4. *-commutative 37.7%

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

       5. distribute-rgt-neg-in 37.7%

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

   11. Simplified 37.7%

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

   if 9.40000000000000008e170 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-lft-neg-out 76.3%

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

      3. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. unsub-neg 39.4%

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

      3. associate-*r* 36.3%

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

      4. *-commutative 36.3%

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

      5. cancel-sign-sub-inv 36.3%

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

      6. mul-1-neg 36.3%

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

      7. *-commutative 36.3%

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

      8. associate-*r* 36.3%

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

      9. *-commutative 36.3%

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

      10. mul-1-neg 36.3%

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

      11. distribute-lft-neg-in 36.3%

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

      12. *-commutative 36.3%

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

   8. Simplified 36.3%

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

   9. Taylor expanded in t around inf 39.4%

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

       1. mul-1-neg 39.4%

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

       2. associate-*r* 46.1%

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

       3. *-commutative 46.1%

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

       4. associate-*r* 39.5%

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

       5. distribute-lft-neg-in 39.5%

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

   11. Simplified 39.5%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+36}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.8% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+36}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.85e+33)
   (* t (- (/ x t) (* x y)))
   (if (<= y 7.5e+36)
     (- x (* x (* a b)))
     (if (<= y 1.52e+172) (* x (* a (- b))) (* x (* y (- t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.85e+33) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 7.5e+36) {
		tmp = x - (x * (a * b));
	} else if (y <= 1.52e+172) {
		tmp = x * (a * -b);
	} else {
		tmp = 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) :: tmp
    if (y <= (-1.85d+33)) then
        tmp = t * ((x / t) - (x * y))
    else if (y <= 7.5d+36) then
        tmp = x - (x * (a * b))
    else if (y <= 1.52d+172) then
        tmp = x * (a * -b)
    else
        tmp = 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 tmp;
	if (y <= -1.85e+33) {
		tmp = t * ((x / t) - (x * y));
	} else if (y <= 7.5e+36) {
		tmp = x - (x * (a * b));
	} else if (y <= 1.52e+172) {
		tmp = x * (a * -b);
	} else {
		tmp = x * (y * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.85e+33:
		tmp = t * ((x / t) - (x * y))
	elif y <= 7.5e+36:
		tmp = x - (x * (a * b))
	elif y <= 1.52e+172:
		tmp = x * (a * -b)
	else:
		tmp = x * (y * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.85e+33)
		tmp = Float64(t * Float64(Float64(x / t) - Float64(x * y)));
	elseif (y <= 7.5e+36)
		tmp = Float64(x - Float64(x * Float64(a * b)));
	elseif (y <= 1.52e+172)
		tmp = Float64(x * Float64(a * Float64(-b)));
	else
		tmp = Float64(x * Float64(y * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.85e+33)
		tmp = t * ((x / t) - (x * y));
	elseif (y <= 7.5e+36)
		tmp = x - (x * (a * b));
	elseif (y <= 1.52e+172)
		tmp = x * (a * -b);
	else
		tmp = x * (y * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.85e+33], N[(t * N[(N[(x / t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+36], N[(x - N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.52e+172], N[(x * N[(a * (-b)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.8499999999999999e33

   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 t around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. distribute-lft-neg-out 68.4%

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

      3. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in y around 0 34.8%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 34.8%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 34.8%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 24.0%

         \[\leadsto x - \color{blue}{\left(t \cdot x\right) \cdot y} \]

      4. *-commutative 24.0%

         \[\leadsto x - \color{blue}{y \cdot \left(t \cdot x\right)} \]

      5. cancel-sign-sub-inv 24.0%

         \[\leadsto \color{blue}{x + \left(-y\right) \cdot \left(t \cdot x\right)} \]

      6. mul-1-neg 24.0%

         \[\leadsto x + \color{blue}{\left(-1 \cdot y\right)} \cdot \left(t \cdot x\right) \]

      7. *-commutative 24.0%

         \[\leadsto x + \color{blue}{\left(y \cdot -1\right)} \cdot \left(t \cdot x\right) \]

      8. associate-*r* 24.0%

         \[\leadsto x + \color{blue}{y \cdot \left(-1 \cdot \left(t \cdot x\right)\right)} \]

      9. *-commutative 24.0%

         \[\leadsto x + \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right) \cdot y} \]

      10. mul-1-neg 24.0%

          \[\leadsto x + \color{blue}{\left(-t \cdot x\right)} \cdot y \]

      11. distribute-lft-neg-in 24.0%

          \[\leadsto x + \color{blue}{\left(-\left(t \cdot x\right) \cdot y\right)} \]

      12. *-commutative 24.0%

          \[\leadsto x + \left(-\color{blue}{\left(x \cdot t\right)} \cdot y\right) \]

   8. Simplified 24.0%

      \[\leadsto \color{blue}{x + \left(-\left(x \cdot t\right) \cdot y\right)} \]

   9. Taylor expanded in t around inf 38.5%

      \[\leadsto \color{blue}{t \cdot \left(\frac{x}{t} - x \cdot y\right)} \]

   if -1.8499999999999999e33 < y < 7.50000000000000054e36

   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 b around inf 78.4%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 78.4%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 78.4%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 78.4%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 43.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.2%

         \[\leadsto x + \color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)} \]

      2. unsub-neg 43.2%

         \[\leadsto \color{blue}{x - a \cdot \left(b \cdot x\right)} \]

      3. associate-*r* 46.5%

         \[\leadsto x - \color{blue}{\left(a \cdot b\right) \cdot x} \]

      4. *-commutative 46.5%

         \[\leadsto x - \color{blue}{x \cdot \left(a \cdot b\right)} \]

   8. Simplified 46.5%

      \[\leadsto \color{blue}{x - x \cdot \left(a \cdot b\right)} \]

   if 7.50000000000000054e36 < y < 1.5200000000000001e172

   1. Initial program 96.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 27.8%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 27.8%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 27.8%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 27.8%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 10.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 10.4%

         \[\leadsto x + \color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)} \]

      2. unsub-neg 10.4%

         \[\leadsto \color{blue}{x - a \cdot \left(b \cdot x\right)} \]

      3. associate-*r* 10.4%

         \[\leadsto x - \color{blue}{\left(a \cdot b\right) \cdot x} \]

      4. *-commutative 10.4%

         \[\leadsto x - \color{blue}{x \cdot \left(a \cdot b\right)} \]

   8. Simplified 10.4%

      \[\leadsto \color{blue}{x - x \cdot \left(a \cdot b\right)} \]

   9. Taylor expanded in a around inf 34.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 37.7%

          \[\leadsto -1 \cdot \color{blue}{\left(\left(a \cdot b\right) \cdot x\right)} \]

       2. associate-*r* 37.7%

          \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot b\right)\right) \cdot x} \]

       3. mul-1-neg 37.7%

          \[\leadsto \color{blue}{\left(-a \cdot b\right)} \cdot x \]

       4. *-commutative 37.7%

          \[\leadsto \left(-\color{blue}{b \cdot a}\right) \cdot x \]

       5. distribute-rgt-neg-in 37.7%

          \[\leadsto \color{blue}{\left(b \cdot \left(-a\right)\right)} \cdot x \]

   11. Simplified 37.7%

       \[\leadsto \color{blue}{\left(b \cdot \left(-a\right)\right) \cdot x} \]

   if 1.5200000000000001e172 < y

   1. Initial program 89.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 76.3%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 76.3%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 76.3%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 76.3%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 76.3%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 39.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 39.4%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 39.4%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. associate-*r* 36.3%

         \[\leadsto x - \color{blue}{\left(t \cdot x\right) \cdot y} \]

      4. *-commutative 36.3%

         \[\leadsto x - \color{blue}{y \cdot \left(t \cdot x\right)} \]

      5. cancel-sign-sub-inv 36.3%

         \[\leadsto \color{blue}{x + \left(-y\right) \cdot \left(t \cdot x\right)} \]

      6. mul-1-neg 36.3%

         \[\leadsto x + \color{blue}{\left(-1 \cdot y\right)} \cdot \left(t \cdot x\right) \]

      7. *-commutative 36.3%

         \[\leadsto x + \color{blue}{\left(y \cdot -1\right)} \cdot \left(t \cdot x\right) \]

      8. associate-*r* 36.3%

         \[\leadsto x + \color{blue}{y \cdot \left(-1 \cdot \left(t \cdot x\right)\right)} \]

      9. *-commutative 36.3%

         \[\leadsto x + \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right) \cdot y} \]

      10. mul-1-neg 36.3%

          \[\leadsto x + \color{blue}{\left(-t \cdot x\right)} \cdot y \]

      11. distribute-lft-neg-in 36.3%

          \[\leadsto x + \color{blue}{\left(-\left(t \cdot x\right) \cdot y\right)} \]

      12. *-commutative 36.3%

          \[\leadsto x + \left(-\color{blue}{\left(x \cdot t\right)} \cdot y\right) \]

   8. Simplified 36.3%

      \[\leadsto \color{blue}{x + \left(-\left(x \cdot t\right) \cdot y\right)} \]

   9. Taylor expanded in t around inf 39.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 39.4%

          \[\leadsto \color{blue}{-t \cdot \left(x \cdot y\right)} \]

       2. associate-*r* 46.1%

          \[\leadsto -\color{blue}{\left(t \cdot x\right) \cdot y} \]

       3. *-commutative 46.1%

          \[\leadsto -\color{blue}{\left(x \cdot t\right)} \cdot y \]

       4. associate-*r* 39.5%

          \[\leadsto -\color{blue}{x \cdot \left(t \cdot y\right)} \]

       5. distribute-lft-neg-in 39.5%

          \[\leadsto \color{blue}{\left(-x\right) \cdot \left(t \cdot y\right)} \]

   11. Simplified 39.5%

       \[\leadsto \color{blue}{\left(-x\right) \cdot \left(t \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} - x \cdot y\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+36}:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.6% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{x}{a}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ x a))))
   (if (<= y -2.1e-161)
     t_1
     (if (<= y 6.6e-101) x (if (<= y 5.8e+37) t_1 (* a (* x b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (x / a);
	double tmp;
	if (y <= -2.1e-161) {
		tmp = t_1;
	} else if (y <= 6.6e-101) {
		tmp = x;
	} else if (y <= 5.8e+37) {
		tmp = t_1;
	} else {
		tmp = a * (x * 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) :: t_1
    real(8) :: tmp
    t_1 = a * (x / a)
    if (y <= (-2.1d-161)) then
        tmp = t_1
    else if (y <= 6.6d-101) then
        tmp = x
    else if (y <= 5.8d+37) then
        tmp = t_1
    else
        tmp = a * (x * 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 t_1 = a * (x / a);
	double tmp;
	if (y <= -2.1e-161) {
		tmp = t_1;
	} else if (y <= 6.6e-101) {
		tmp = x;
	} else if (y <= 5.8e+37) {
		tmp = t_1;
	} else {
		tmp = a * (x * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (x / a)
	tmp = 0
	if y <= -2.1e-161:
		tmp = t_1
	elif y <= 6.6e-101:
		tmp = x
	elif y <= 5.8e+37:
		tmp = t_1
	else:
		tmp = a * (x * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(x / a))
	tmp = 0.0
	if (y <= -2.1e-161)
		tmp = t_1;
	elseif (y <= 6.6e-101)
		tmp = x;
	elseif (y <= 5.8e+37)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(x * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (x / a);
	tmp = 0.0;
	if (y <= -2.1e-161)
		tmp = t_1;
	elseif (y <= 6.6e-101)
		tmp = x;
	elseif (y <= 5.8e+37)
		tmp = t_1;
	else
		tmp = a * (x * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e-161], t$95$1, If[LessEqual[y, 6.6e-101], x, If[LessEqual[y, 5.8e+37], t$95$1, N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1e-161 or 6.59999999999999968e-101 < y < 5.79999999999999957e37

   1. Initial program 98.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 53.1%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 53.1%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 53.1%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 53.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 21.8%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 21.8%

         \[\leadsto x + \color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)} \]

      2. unsub-neg 21.8%

         \[\leadsto \color{blue}{x - a \cdot \left(b \cdot x\right)} \]

      3. associate-*r* 21.9%

         \[\leadsto x - \color{blue}{\left(a \cdot b\right) \cdot x} \]

      4. *-commutative 21.9%

         \[\leadsto x - \color{blue}{x \cdot \left(a \cdot b\right)} \]

   8. Simplified 21.9%

      \[\leadsto \color{blue}{x - x \cdot \left(a \cdot b\right)} \]

   9. Taylor expanded in a around inf 25.9%

      \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - b \cdot x\right)} \]

   10. Taylor expanded in a around 0 25.1%

       \[\leadsto a \cdot \color{blue}{\frac{x}{a}} \]

   if -2.1e-161 < y < 6.59999999999999968e-101

   1. Initial program 93.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 87.3%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 87.3%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 87.3%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 87.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 45.4%

      \[\leadsto \color{blue}{x} \]

   if 5.79999999999999957e37 < y

   1. Initial program 93.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 30.7%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 30.7%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 30.7%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 30.7%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 10.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 10.2%

         \[\leadsto x + \color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)} \]

      2. unsub-neg 10.2%

         \[\leadsto \color{blue}{x - a \cdot \left(b \cdot x\right)} \]

      3. associate-*r* 11.9%

         \[\leadsto x - \color{blue}{\left(a \cdot b\right) \cdot x} \]

      4. *-commutative 11.9%

         \[\leadsto x - \color{blue}{x \cdot \left(a \cdot b\right)} \]

   8. Simplified 11.9%

      \[\leadsto \color{blue}{x - x \cdot \left(a \cdot b\right)} \]
   9. Step-by-step derivation

      1. sub-neg 11.9%

         \[\leadsto \color{blue}{x + \left(-x \cdot \left(a \cdot b\right)\right)} \]

      2. *-commutative 11.9%

         \[\leadsto x + \left(-\color{blue}{\left(a \cdot b\right) \cdot x}\right) \]

      3. distribute-lft-neg-in 11.9%

         \[\leadsto x + \color{blue}{\left(-a \cdot b\right) \cdot x} \]

      4. distribute-lft-neg-out 11.9%

         \[\leadsto x + \color{blue}{\left(\left(-a\right) \cdot b\right)} \cdot x \]

      5. add-sqr-sqrt 3.6%

         \[\leadsto x + \left(\color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot b\right) \cdot x \]

      6. sqrt-unprod 8.1%

         \[\leadsto x + \left(\color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot b\right) \cdot x \]

      7. sqr-neg 8.1%

         \[\leadsto x + \left(\sqrt{\color{blue}{a \cdot a}} \cdot b\right) \cdot x \]

      8. sqrt-unprod 3.0%

         \[\leadsto x + \left(\color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot b\right) \cdot x \]

      9. add-sqr-sqrt 6.5%

         \[\leadsto x + \left(\color{blue}{a} \cdot b\right) \cdot x \]

      10. distribute-rgt1-in 6.5%

          \[\leadsto \color{blue}{\left(a \cdot b + 1\right) \cdot x} \]

   10. Applied egg-rr 6.5%

       \[\leadsto \color{blue}{\left(a \cdot b + 1\right) \cdot x} \]

   11. Taylor expanded in a around inf 28.2%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+37}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.1% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.05e-161) (* a (/ x a)) (if (<= y 4.2e-27) x (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.05e-161) {
		tmp = a * (x / a);
	} else if (y <= 4.2e-27) {
		tmp = x;
	} else {
		tmp = a * (x * -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 <= (-2.05d-161)) then
        tmp = a * (x / a)
    else if (y <= 4.2d-27) then
        tmp = x
    else
        tmp = a * (x * -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 <= -2.05e-161) {
		tmp = a * (x / a);
	} else if (y <= 4.2e-27) {
		tmp = x;
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.05e-161:
		tmp = a * (x / a)
	elif y <= 4.2e-27:
		tmp = x
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.05e-161)
		tmp = Float64(a * Float64(x / a));
	elseif (y <= 4.2e-27)
		tmp = x;
	else
		tmp = Float64(a * Float64(x * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.05e-161)
		tmp = a * (x / a);
	elseif (y <= 4.2e-27)
		tmp = x;
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.05e-161], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-27], x, N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0499999999999999e-161

   1. Initial program 98.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 49.0%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 49.0%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 49.0%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 49.0%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 19.7%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 19.7%

         \[\leadsto x + \color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)} \]

      2. unsub-neg 19.7%

         \[\leadsto \color{blue}{x - a \cdot \left(b \cdot x\right)} \]

      3. associate-*r* 19.6%

         \[\leadsto x - \color{blue}{\left(a \cdot b\right) \cdot x} \]

      4. *-commutative 19.6%

         \[\leadsto x - \color{blue}{x \cdot \left(a \cdot b\right)} \]

   8. Simplified 19.6%

      \[\leadsto \color{blue}{x - x \cdot \left(a \cdot b\right)} \]

   9. Taylor expanded in a around inf 23.9%

      \[\leadsto \color{blue}{a \cdot \left(\frac{x}{a} - b \cdot x\right)} \]

   10. Taylor expanded in a around 0 23.9%

       \[\leadsto a \cdot \color{blue}{\frac{x}{a}} \]

   if -2.0499999999999999e-161 < y < 4.20000000000000031e-27

   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 85.6%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 85.6%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 85.6%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 85.6%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 44.6%

      \[\leadsto \color{blue}{x} \]

   if 4.20000000000000031e-27 < y

   1. Initial program 93.1%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 37.3%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 37.3%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 37.3%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 37.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 12.8%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 12.8%

         \[\leadsto x + \color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)} \]

      2. unsub-neg 12.8%

         \[\leadsto \color{blue}{x - a \cdot \left(b \cdot x\right)} \]

      3. associate-*r* 14.4%

         \[\leadsto x - \color{blue}{\left(a \cdot b\right) \cdot x} \]

      4. *-commutative 14.4%

         \[\leadsto x - \color{blue}{x \cdot \left(a \cdot b\right)} \]

   8. Simplified 14.4%

      \[\leadsto \color{blue}{x - x \cdot \left(a \cdot b\right)} \]

   9. Taylor expanded in a around inf 29.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 29.8%

          \[\leadsto \color{blue}{-a \cdot \left(b \cdot x\right)} \]

       2. distribute-rgt-neg-in 29.8%

          \[\leadsto \color{blue}{a \cdot \left(-b \cdot x\right)} \]

       3. distribute-lft-neg-in 29.8%

          \[\leadsto a \cdot \color{blue}{\left(\left(-b\right) \cdot x\right)} \]

   11. Simplified 29.8%

       \[\leadsto \color{blue}{a \cdot \left(\left(-b\right) \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 23.1% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 1.25e-15) x (* a (* x b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.25e-15) {
		tmp = x;
	} else {
		tmp = a * (x * 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-15) then
        tmp = x
    else
        tmp = a * (x * 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-15) {
		tmp = x;
	} else {
		tmp = a * (x * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.25e-15:
		tmp = x
	else:
		tmp = a * (x * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.25e-15)
		tmp = x;
	else
		tmp = Float64(a * Float64(x * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.25e-15)
		tmp = x;
	else
		tmp = a * (x * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.25e-15], x, N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.25e-15

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in 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 28.2%

      \[\leadsto \color{blue}{x} \]

   if 1.25e-15 < y

   1. Initial program 92.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 35.5%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 35.5%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 35.5%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 35.5%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 11.7%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 11.7%

         \[\leadsto x + \color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)} \]

      2. unsub-neg 11.7%

         \[\leadsto \color{blue}{x - a \cdot \left(b \cdot x\right)} \]

      3. associate-*r* 13.3%

         \[\leadsto x - \color{blue}{\left(a \cdot b\right) \cdot x} \]

      4. *-commutative 13.3%

         \[\leadsto x - \color{blue}{x \cdot \left(a \cdot b\right)} \]

   8. Simplified 13.3%

      \[\leadsto \color{blue}{x - x \cdot \left(a \cdot b\right)} \]
   9. Step-by-step derivation

      1. sub-neg 13.3%

         \[\leadsto \color{blue}{x + \left(-x \cdot \left(a \cdot b\right)\right)} \]

      2. *-commutative 13.3%

         \[\leadsto x + \left(-\color{blue}{\left(a \cdot b\right) \cdot x}\right) \]

      3. distribute-lft-neg-in 13.3%

         \[\leadsto x + \color{blue}{\left(-a \cdot b\right) \cdot x} \]

      4. distribute-lft-neg-out 13.3%

         \[\leadsto x + \color{blue}{\left(\left(-a\right) \cdot b\right)} \cdot x \]

      5. add-sqr-sqrt 6.2%

         \[\leadsto x + \left(\color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot b\right) \cdot x \]

      6. sqrt-unprod 8.8%

         \[\leadsto x + \left(\color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot b\right) \cdot x \]

      7. sqr-neg 8.8%

         \[\leadsto x + \left(\sqrt{\color{blue}{a \cdot a}} \cdot b\right) \cdot x \]

      8. sqrt-unprod 2.7%

         \[\leadsto x + \left(\color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot b\right) \cdot x \]

      9. add-sqr-sqrt 6.0%

         \[\leadsto x + \left(\color{blue}{a} \cdot b\right) \cdot x \]

      10. distribute-rgt1-in 6.0%

          \[\leadsto \color{blue}{\left(a \cdot b + 1\right) \cdot x} \]

   10. Applied egg-rr 6.0%

       \[\leadsto \color{blue}{\left(a \cdot b + 1\right) \cdot x} \]

   11. Taylor expanded in a around inf 24.7%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 19.4% 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 95.4%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
2. Add Preprocessing

3. Taylor expanded in b around inf 59.3%

   \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
4. Step-by-step derivation

   1. mul-1-neg 59.3%

      \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

   2. distribute-rgt-neg-out 59.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

5. Simplified 59.3%

   \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

6. Taylor expanded in a around 0 21.7%

   \[\leadsto \color{blue}{x} \]

7. Final simplification 21.7%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024067 
(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))))))