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

Percentage Accurate: 96.4% → 99.6%

Time: 15.4s

Alternatives: 14

Speedup: 1.0×

• 20.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

   1. +-commutative 97.0%

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

   2. fma-def 97.3%

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

   3. sub-neg 97.3%

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

   4. log1p-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

2. Final simplification 97.0%

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

Alternative 3: 85.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -33000000000 \lor \neg \left(y \leq 2.05 \cdot 10^{-110}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -33000000000.0) (not (<= y 2.05e-110)))
   (* x (exp (* y (- (log z) t))))
   (* x (exp (* a (- (- z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -33000000000.0) || !(y <= 2.05e-110)) {
		tmp = x * exp((y * (log(z) - t)));
	} else {
		tmp = x * exp((a * (-z - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-33000000000.0d0)) .or. (.not. (y <= 2.05d-110))) then
        tmp = x * exp((y * (log(z) - t)))
    else
        tmp = x * exp((a * (-z - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -33000000000.0) || !(y <= 2.05e-110)) {
		tmp = x * Math.exp((y * (Math.log(z) - t)));
	} else {
		tmp = x * Math.exp((a * (-z - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -33000000000.0) or not (y <= 2.05e-110):
		tmp = x * math.exp((y * (math.log(z) - t)))
	else:
		tmp = x * math.exp((a * (-z - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -33000000000.0) || !(y <= 2.05e-110))
		tmp = Float64(x * exp(Float64(y * Float64(log(z) - t))));
	else
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -33000000000.0) || ~((y <= 2.05e-110)))
		tmp = x * exp((y * (log(z) - t)));
	else
		tmp = x * exp((a * (-z - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -33000000000.0], N[Not[LessEqual[y, 2.05e-110]], $MachinePrecision]], N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e10 or 2.04999999999999991e-110 < y

   1. Initial program 98.2%

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

   2. Taylor expanded in y around inf 87.3%

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

   if -3.3e10 < y < 2.04999999999999991e-110

   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. Taylor expanded in y around 0 88.1%

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

      1. sub-neg 88.1%

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

      2. neg-mul-1 88.1%

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

      3. log1p-def 93.1%

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

      4. neg-mul-1 93.1%

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

   4. Simplified 93.1%

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

   5. Taylor expanded in z around 0 93.1%

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

      1. +-commutative 93.1%

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

      2. associate-*r* 93.1%

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

      3. associate-*r* 93.1%

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

      4. distribute-lft-out 93.1%

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

      5. neg-mul-1 93.1%

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

   7. Simplified 93.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -33000000000 \lor \neg \left(y \leq 2.05 \cdot 10^{-110}\right):\\ \;\;\;\;x \cdot e^{y \cdot \left(\log z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \end{array} \]

Alternative 4: 72.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ t_2 := x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.035:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))) (t_2 (* x (exp (* y (- t))))))
   (if (<= y -7e+88)
     t_2
     (if (<= y -1.75e+16)
       t_1
       (if (<= y -0.035) t_2 (if (<= y 2.0) (* x (exp (* a (- b)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double t_2 = x * exp((y * -t));
	double tmp;
	if (y <= -7e+88) {
		tmp = t_2;
	} else if (y <= -1.75e+16) {
		tmp = t_1;
	} else if (y <= -0.035) {
		tmp = t_2;
	} else if (y <= 2.0) {
		tmp = x * exp((a * -b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z ** y)
    t_2 = x * exp((y * -t))
    if (y <= (-7d+88)) then
        tmp = t_2
    else if (y <= (-1.75d+16)) then
        tmp = t_1
    else if (y <= (-0.035d0)) then
        tmp = t_2
    else if (y <= 2.0d0) then
        tmp = x * exp((a * -b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double t_2 = x * Math.exp((y * -t));
	double tmp;
	if (y <= -7e+88) {
		tmp = t_2;
	} else if (y <= -1.75e+16) {
		tmp = t_1;
	} else if (y <= -0.035) {
		tmp = t_2;
	} else if (y <= 2.0) {
		tmp = x * Math.exp((a * -b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	t_2 = x * math.exp((y * -t))
	tmp = 0
	if y <= -7e+88:
		tmp = t_2
	elif y <= -1.75e+16:
		tmp = t_1
	elif y <= -0.035:
		tmp = t_2
	elif y <= 2.0:
		tmp = x * math.exp((a * -b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	t_2 = Float64(x * exp(Float64(y * Float64(-t))))
	tmp = 0.0
	if (y <= -7e+88)
		tmp = t_2;
	elseif (y <= -1.75e+16)
		tmp = t_1;
	elseif (y <= -0.035)
		tmp = t_2;
	elseif (y <= 2.0)
		tmp = Float64(x * exp(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 * (z ^ y);
	t_2 = x * exp((y * -t));
	tmp = 0.0;
	if (y <= -7e+88)
		tmp = t_2;
	elseif (y <= -1.75e+16)
		tmp = t_1;
	elseif (y <= -0.035)
		tmp = t_2;
	elseif (y <= 2.0)
		tmp = x * exp((a * -b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+88], t$95$2, If[LessEqual[y, -1.75e+16], t$95$1, If[LessEqual[y, -0.035], t$95$2, If[LessEqual[y, 2.0], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9999999999999995e88 or -1.75e16 < y < -0.035000000000000003

   1. Initial program 96.6%

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

   2. Taylor expanded in t around inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. distribute-rgt-neg-out 75.2%

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

   4. Simplified 75.2%

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

   if -6.9999999999999995e88 < y < -1.75e16 or 2 < y

   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. Taylor expanded in y around inf 86.9%

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

   3. Taylor expanded in t around 0 68.3%

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

   if -0.035000000000000003 < y < 2

   1. Initial program 95.5%

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

   2. Taylor expanded in b around inf 83.0%

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

      1. mul-1-neg 83.0%

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

      2. *-commutative 83.0%

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

      3. distribute-rgt-neg-in 83.0%

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

   4. Simplified 83.0%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+88}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+16}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq -0.035:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;y \leq 2:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]

Alternative 5: 73.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{if}\;t \leq -6800000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-160}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+33}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* y (- t))))))
   (if (<= t -6800000.0)
     t_1
     (if (<= t -4.6e-160)
       (* x (pow z y))
       (if (<= t 1.15e+33) (* x (exp (* a (- (- z) b)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((y * -t));
	double tmp;
	if (t <= -6800000.0) {
		tmp = t_1;
	} else if (t <= -4.6e-160) {
		tmp = x * pow(z, y);
	} else if (t <= 1.15e+33) {
		tmp = x * exp((a * (-z - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * exp((y * -t))
    if (t <= (-6800000.0d0)) then
        tmp = t_1
    else if (t <= (-4.6d-160)) then
        tmp = x * (z ** y)
    else if (t <= 1.15d+33) then
        tmp = x * exp((a * (-z - b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.exp((y * -t));
	double tmp;
	if (t <= -6800000.0) {
		tmp = t_1;
	} else if (t <= -4.6e-160) {
		tmp = x * Math.pow(z, y);
	} else if (t <= 1.15e+33) {
		tmp = x * Math.exp((a * (-z - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((y * -t))
	tmp = 0
	if t <= -6800000.0:
		tmp = t_1
	elif t <= -4.6e-160:
		tmp = x * math.pow(z, y)
	elif t <= 1.15e+33:
		tmp = x * math.exp((a * (-z - b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(y * Float64(-t))))
	tmp = 0.0
	if (t <= -6800000.0)
		tmp = t_1;
	elseif (t <= -4.6e-160)
		tmp = Float64(x * (z ^ y));
	elseif (t <= 1.15e+33)
		tmp = Float64(x * exp(Float64(a * Float64(Float64(-z) - b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((y * -t));
	tmp = 0.0;
	if (t <= -6800000.0)
		tmp = t_1;
	elseif (t <= -4.6e-160)
		tmp = x * (z ^ y);
	elseif (t <= 1.15e+33)
		tmp = x * exp((a * (-z - b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6800000.0], t$95$1, If[LessEqual[t, -4.6e-160], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+33], N[(x * N[Exp[N[(a * N[((-z) - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.8e6 or 1.15000000000000005e33 < t

   1. Initial program 97.8%

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

   2. Taylor expanded in t around inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. distribute-rgt-neg-out 80.0%

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

   4. Simplified 80.0%

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

   if -6.8e6 < t < -4.5999999999999997e-160

   1. Initial program 97.1%

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

   2. Taylor expanded in y around inf 72.5%

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

   3. Taylor expanded in t around 0 72.5%

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

   if -4.5999999999999997e-160 < t < 1.15000000000000005e33

   1. Initial program 95.6%

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

   2. Taylor expanded in y around 0 68.4%

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

      1. sub-neg 68.4%

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

      2. neg-mul-1 68.4%

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

      3. log1p-def 75.1%

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

      4. neg-mul-1 75.1%

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

   4. Simplified 75.1%

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

   5. Taylor expanded in z around 0 75.1%

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

      1. +-commutative 75.1%

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

      2. associate-*r* 75.1%

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

      3. associate-*r* 75.1%

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

      4. distribute-lft-out 75.1%

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

      5. neg-mul-1 75.1%

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

   7. Simplified 75.1%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6800000:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-160}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+33}:\\ \;\;\;\;x \cdot e^{a \cdot \left(\left(-z\right) - b\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]

Alternative 6: 54.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -26000000000:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-218} \lor \neg \left(t \leq -2.7 \cdot 10^{-268}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -26000000000.0)
   (* x (- 1.0 (* y t)))
   (if (or (<= t -1.5e-218) (not (<= t -2.7e-268)))
     (* x (pow z y))
     (* y (* x (- t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -26000000000.0) {
		tmp = x * (1.0 - (y * t));
	} else if ((t <= -1.5e-218) || !(t <= -2.7e-268)) {
		tmp = x * pow(z, y);
	} else {
		tmp = 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 (t <= (-26000000000.0d0)) then
        tmp = x * (1.0d0 - (y * t))
    else if ((t <= (-1.5d-218)) .or. (.not. (t <= (-2.7d-268)))) then
        tmp = x * (z ** y)
    else
        tmp = 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 (t <= -26000000000.0) {
		tmp = x * (1.0 - (y * t));
	} else if ((t <= -1.5e-218) || !(t <= -2.7e-268)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = y * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -26000000000.0:
		tmp = x * (1.0 - (y * t))
	elif (t <= -1.5e-218) or not (t <= -2.7e-268):
		tmp = x * math.pow(z, y)
	else:
		tmp = y * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -26000000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	elseif ((t <= -1.5e-218) || !(t <= -2.7e-268))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(y * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -26000000000.0)
		tmp = x * (1.0 - (y * t));
	elseif ((t <= -1.5e-218) || ~((t <= -2.7e-268)))
		tmp = x * (z ^ y);
	else
		tmp = y * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -26000000000.0], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.5e-218], N[Not[LessEqual[t, -2.7e-268]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(y * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6e10

   1. Initial program 96.0%

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

   2. Taylor expanded in t around inf 77.6%

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

      1. mul-1-neg 77.6%

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

      2. distribute-rgt-neg-out 77.6%

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

   4. Simplified 77.6%

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

   5. Taylor expanded in y around 0 25.0%

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

      1. +-commutative 25.0%

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

      2. mul-1-neg 25.0%

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

      3. unsub-neg 25.0%

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

   7. Simplified 25.0%

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

   8. Taylor expanded in x around 0 30.2%

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

   if -2.6e10 < t < -1.4999999999999999e-218 or -2.7000000000000001e-268 < t

   1. Initial program 97.7%

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

   2. Taylor expanded in y around inf 71.0%

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

   3. Taylor expanded in t around 0 65.3%

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

   if -1.4999999999999999e-218 < t < -2.7000000000000001e-268

   1. Initial program 88.1%

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

   2. Taylor expanded in t around inf 5.8%

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

      1. mul-1-neg 5.8%

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

      2. distribute-rgt-neg-out 5.8%

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

   4. Simplified 5.8%

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

   5. Taylor expanded in y around 0 6.0%

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

      1. +-commutative 6.0%

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

      2. mul-1-neg 6.0%

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

      3. unsub-neg 6.0%

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

   7. Simplified 6.0%

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

   8. Taylor expanded in y around inf 86.1%

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

      1. neg-mul-1 86.1%

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

      2. distribute-rgt-neg-in 86.1%

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

      3. distribute-rgt-neg-in 86.1%

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

   10. Simplified 86.1%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -26000000000:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-218} \lor \neg \left(t \leq -2.7 \cdot 10^{-268}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 7: 74.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -450000000000 \lor \neg \left(y \leq 2.2\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -450000000000.0) (not (<= y 2.2)))
   (* x (pow z y))
   (* x (exp (* a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -450000000000.0) || !(y <= 2.2)) {
		tmp = x * pow(z, y);
	} else {
		tmp = x * exp((a * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-450000000000.0d0)) .or. (.not. (y <= 2.2d0))) then
        tmp = x * (z ** y)
    else
        tmp = x * exp((a * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -450000000000.0) || !(y <= 2.2)) {
		tmp = x * Math.pow(z, y);
	} else {
		tmp = x * Math.exp((a * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -450000000000.0) or not (y <= 2.2):
		tmp = x * math.pow(z, y)
	else:
		tmp = x * math.exp((a * -b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -450000000000.0) || !(y <= 2.2))
		tmp = Float64(x * (z ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -450000000000.0) || ~((y <= 2.2)))
		tmp = x * (z ^ y);
	else
		tmp = x * exp((a * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -450000000000.0], N[Not[LessEqual[y, 2.2]], $MachinePrecision]], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e11 or 2.2000000000000002 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in y around inf 88.5%

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

   3. Taylor expanded in t around 0 62.9%

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

   if -4.5e11 < y < 2.2000000000000002

   1. Initial program 95.6%

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

   2. Taylor expanded in b around inf 81.7%

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

      1. mul-1-neg 81.7%

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

      2. *-commutative 81.7%

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

      3. distribute-rgt-neg-in 81.7%

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

   4. Simplified 81.7%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -450000000000 \lor \neg \left(y \leq 2.2\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \end{array} \]

Alternative 8: 17.8% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.1 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-194} \lor \neg \left(z \leq 9.5 \cdot 10^{-58}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.1e-271)
   x
   (if (or (<= z 9.5e-194) (not (<= z 9.5e-58)))
     (* y (* x (- t)))
     (* a (* x (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.1e-271) {
		tmp = x;
	} else if ((z <= 9.5e-194) || !(z <= 9.5e-58)) {
		tmp = y * (x * -t);
	} 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 (z <= 1.1d-271) then
        tmp = x
    else if ((z <= 9.5d-194) .or. (.not. (z <= 9.5d-58))) then
        tmp = y * (x * -t)
    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 (z <= 1.1e-271) {
		tmp = x;
	} else if ((z <= 9.5e-194) || !(z <= 9.5e-58)) {
		tmp = y * (x * -t);
	} else {
		tmp = a * (x * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.1e-271:
		tmp = x
	elif (z <= 9.5e-194) or not (z <= 9.5e-58):
		tmp = y * (x * -t)
	else:
		tmp = a * (x * -b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.1e-271)
		tmp = x;
	elseif ((z <= 9.5e-194) || !(z <= 9.5e-58))
		tmp = Float64(y * Float64(x * Float64(-t)));
	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 (z <= 1.1e-271)
		tmp = x;
	elseif ((z <= 9.5e-194) || ~((z <= 9.5e-58)))
		tmp = y * (x * -t);
	else
		tmp = a * (x * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.1e-271], x, If[Or[LessEqual[z, 9.5e-194], N[Not[LessEqual[z, 9.5e-58]], $MachinePrecision]], N[(y * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < 1.1e-271

   1. Initial program 97.2%

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

   2. Taylor expanded in b around inf 54.4%

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

      1. mul-1-neg 54.4%

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

      2. *-commutative 54.4%

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

      3. distribute-rgt-neg-in 54.4%

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

   4. Simplified 54.4%

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

   5. Taylor expanded in b around 0 32.0%

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

   if 1.1e-271 < z < 9.50000000000000009e-194 or 9.4999999999999994e-58 < z

   1. Initial program 95.8%

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

   2. Taylor expanded in t around inf 57.8%

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

      1. mul-1-neg 57.8%

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

      2. distribute-rgt-neg-out 57.8%

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

   4. Simplified 57.8%

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

   5. Taylor expanded in y around 0 26.9%

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

      1. +-commutative 26.9%

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

      2. mul-1-neg 26.9%

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

      3. unsub-neg 26.9%

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

   7. Simplified 26.9%

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

   8. Taylor expanded in y around inf 26.7%

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

      1. neg-mul-1 26.7%

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

      2. distribute-rgt-neg-in 26.7%

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

      3. distribute-rgt-neg-in 26.7%

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

   10. Simplified 26.7%

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

   if 9.50000000000000009e-194 < z < 9.4999999999999994e-58

   1. Initial program 98.1%

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

   2. Taylor expanded in b around inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. *-commutative 56.9%

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

      3. distribute-rgt-neg-in 56.9%

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

   4. Simplified 56.9%

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

   5. Taylor expanded in b around 0 25.2%

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

      1. +-commutative 25.2%

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

      2. mul-1-neg 25.2%

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

      3. unsub-neg 25.2%

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

   7. Simplified 25.2%

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

   8. Taylor expanded in a around inf 30.1%

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

      1. neg-mul-1 30.1%

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

      2. distribute-rgt-neg-in 30.1%

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

      3. distribute-lft-neg-in 30.1%

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

   10. Simplified 30.1%

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

4. Final simplification 28.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.1 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-194} \lor \neg \left(z \leq 9.5 \cdot 10^{-58}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 9: 32.6% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.031:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+153}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* x (- t)))))
   (if (<= y -7.2e+37)
     t_1
     (if (<= y 0.031)
       (* x (- 1.0 (* a b)))
       (if (<= y 6.4e+153) (* a (* x (- b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (x * -t);
	double tmp;
	if (y <= -7.2e+37) {
		tmp = t_1;
	} else if (y <= 0.031) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 6.4e+153) {
		tmp = a * (x * -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 = y * (x * -t)
    if (y <= (-7.2d+37)) then
        tmp = t_1
    else if (y <= 0.031d0) then
        tmp = x * (1.0d0 - (a * b))
    else if (y <= 6.4d+153) then
        tmp = a * (x * -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 = y * (x * -t);
	double tmp;
	if (y <= -7.2e+37) {
		tmp = t_1;
	} else if (y <= 0.031) {
		tmp = x * (1.0 - (a * b));
	} else if (y <= 6.4e+153) {
		tmp = a * (x * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (x * -t)
	tmp = 0
	if y <= -7.2e+37:
		tmp = t_1
	elif y <= 0.031:
		tmp = x * (1.0 - (a * b))
	elif y <= 6.4e+153:
		tmp = a * (x * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(x * Float64(-t)))
	tmp = 0.0
	if (y <= -7.2e+37)
		tmp = t_1;
	elseif (y <= 0.031)
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	elseif (y <= 6.4e+153)
		tmp = Float64(a * Float64(x * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (x * -t);
	tmp = 0.0;
	if (y <= -7.2e+37)
		tmp = t_1;
	elseif (y <= 0.031)
		tmp = x * (1.0 - (a * b));
	elseif (y <= 6.4e+153)
		tmp = a * (x * -b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+37], t$95$1, If[LessEqual[y, 0.031], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+153], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.19999999999999995e37 or 6.4000000000000003e153 < y

   1. Initial program 97.9%

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

   2. Taylor expanded in t around inf 67.3%

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

      1. mul-1-neg 67.3%

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

      2. distribute-rgt-neg-out 67.3%

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

   4. Simplified 67.3%

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

   5. Taylor expanded in y around 0 19.2%

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

      1. +-commutative 19.2%

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

      2. mul-1-neg 19.2%

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

      3. unsub-neg 19.2%

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

   7. Simplified 19.2%

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

   8. Taylor expanded in y around inf 24.0%

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

      1. neg-mul-1 24.0%

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

      2. distribute-rgt-neg-in 24.0%

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

      3. distribute-rgt-neg-in 24.0%

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

   10. Simplified 24.0%

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

   if -7.19999999999999995e37 < y < 0.031

   1. Initial program 95.7%

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

   2. Taylor expanded in b around inf 79.4%

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

      1. mul-1-neg 79.4%

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

      2. *-commutative 79.4%

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

      3. distribute-rgt-neg-in 79.4%

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

   4. Simplified 79.4%

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

   5. Taylor expanded in b around 0 39.6%

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

      1. +-commutative 39.6%

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

      2. mul-1-neg 39.6%

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

      3. unsub-neg 39.6%

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

   7. Simplified 39.6%

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

   8. Taylor expanded in x around 0 41.2%

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

   if 0.031 < y < 6.4000000000000003e153

   1. Initial program 98.0%

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

   2. Taylor expanded in b around inf 38.7%

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

      1. mul-1-neg 38.7%

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

      2. *-commutative 38.7%

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

      3. distribute-rgt-neg-in 38.7%

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

   4. Simplified 38.7%

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

   5. Taylor expanded in b around 0 15.0%

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

      1. +-commutative 15.0%

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

      2. mul-1-neg 15.0%

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

      3. unsub-neg 15.0%

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

   7. Simplified 15.0%

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

   8. Taylor expanded in a around inf 30.8%

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

      1. neg-mul-1 30.8%

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

      2. distribute-rgt-neg-in 30.8%

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

      3. distribute-lft-neg-in 30.8%

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

   10. Simplified 30.8%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq 0.031:\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+153}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 10: 31.5% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+46} \lor \neg \left(b \leq 2.8 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.8e+46) (not (<= b 2.8e-14)))
   (* x (- 1.0 (* a b)))
   (* x (- 1.0 (* y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.8e+46) || !(b <= 2.8e-14)) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (1.0 - (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 ((b <= (-1.8d+46)) .or. (.not. (b <= 2.8d-14))) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x * (1.0d0 - (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 ((b <= -1.8e+46) || !(b <= 2.8e-14)) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x * (1.0 - (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.8e+46) or not (b <= 2.8e-14):
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x * (1.0 - (y * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.8e+46) || !(b <= 2.8e-14))
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.8e+46) || ~((b <= 2.8e-14)))
		tmp = x * (1.0 - (a * b));
	else
		tmp = x * (1.0 - (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.8e+46], N[Not[LessEqual[b, 2.8e-14]], $MachinePrecision]], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7999999999999999e46 or 2.8000000000000001e-14 < b

   1. Initial program 99.2%

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

   2. Taylor expanded in b around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. *-commutative 74.0%

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

      3. distribute-rgt-neg-in 74.0%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in b around 0 25.3%

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

      1. +-commutative 25.3%

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

      2. mul-1-neg 25.3%

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

      3. unsub-neg 25.3%

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

   7. Simplified 25.3%

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

   8. Taylor expanded in x around 0 25.4%

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

   if -1.7999999999999999e46 < b < 2.8000000000000001e-14

   1. Initial program 95.0%

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

   2. Taylor expanded in t around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. distribute-rgt-neg-out 68.5%

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

   4. Simplified 68.5%

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

   5. Taylor expanded in y around 0 32.9%

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

      1. +-commutative 32.9%

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

      2. mul-1-neg 32.9%

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

      3. unsub-neg 32.9%

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

   7. Simplified 32.9%

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

   8. Taylor expanded in x around 0 37.8%

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

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+46} \lor \neg \left(b \leq 2.8 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot t\right)\\ \end{array} \]

Alternative 11: 31.5% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+43} \lor \neg \left(b \leq 8.6 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.7e+43) (not (<= b 8.6e-19)))
   (* x (- 1.0 (* a b)))
   (- x (* x (* y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.7e+43) || !(b <= 8.6e-19)) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x - (x * (y * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.7d+43)) .or. (.not. (b <= 8.6d-19))) then
        tmp = x * (1.0d0 - (a * b))
    else
        tmp = x - (x * (y * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.7e+43) || !(b <= 8.6e-19)) {
		tmp = x * (1.0 - (a * b));
	} else {
		tmp = x - (x * (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.7e+43) or not (b <= 8.6e-19):
		tmp = x * (1.0 - (a * b))
	else:
		tmp = x - (x * (y * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.7e+43) || !(b <= 8.6e-19))
		tmp = Float64(x * Float64(1.0 - Float64(a * b)));
	else
		tmp = Float64(x - Float64(x * Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.7e+43) || ~((b <= 8.6e-19)))
		tmp = x * (1.0 - (a * b));
	else
		tmp = x - (x * (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.7e+43], N[Not[LessEqual[b, 8.6e-19]], $MachinePrecision]], N[(x * N[(1.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.70000000000000006e43 or 8.6e-19 < b

   1. Initial program 99.2%

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

   2. Taylor expanded in b around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. *-commutative 74.0%

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

      3. distribute-rgt-neg-in 74.0%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in b around 0 25.3%

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

      1. +-commutative 25.3%

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

      2. mul-1-neg 25.3%

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

      3. unsub-neg 25.3%

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

   7. Simplified 25.3%

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

   8. Taylor expanded in x around 0 25.4%

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

   if -1.70000000000000006e43 < b < 8.6e-19

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 87.3%

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

   3. Taylor expanded in y around 0 37.2%

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

   4. Taylor expanded in t around inf 32.9%

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

      1. mul-1-neg 32.9%

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

      2. associate-*r* 37.8%

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

      3. distribute-lft-neg-in 37.8%

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

      4. distribute-rgt-neg-out 37.8%

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

      5. *-commutative 37.8%

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

      6. neg-mul-1 37.8%

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

      7. associate-*r* 37.8%

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

      8. *-commutative 37.8%

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

      9. mul-1-neg 37.8%

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

   6. Simplified 37.8%

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

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+43} \lor \neg \left(b \leq 8.6 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot \left(1 - a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 12: 24.6% accurate, 31.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-15} \lor \neg \left(y \leq 5.8 \cdot 10^{-212}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.9e-15) (not (<= y 5.8e-212))) (* a (* x (- b))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e-15) || !(y <= 5.8e-212)) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.9d-15)) .or. (.not. (y <= 5.8d-212))) then
        tmp = a * (x * -b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e-15) || !(y <= 5.8e-212)) {
		tmp = a * (x * -b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.9e-15) or not (y <= 5.8e-212):
		tmp = a * (x * -b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.9e-15) || !(y <= 5.8e-212))
		tmp = Float64(a * Float64(x * Float64(-b)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.9e-15) || ~((y <= 5.8e-212)))
		tmp = a * (x * -b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.9e-15], N[Not[LessEqual[y, 5.8e-212]], $MachinePrecision]], N[(a * N[(x * (-b)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.9000000000000001e-15 or 5.7999999999999999e-212 < y

   1. Initial program 97.8%

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

   2. Taylor expanded in b around inf 41.4%

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

      1. mul-1-neg 41.4%

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

      2. *-commutative 41.4%

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

      3. distribute-rgt-neg-in 41.4%

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

   4. Simplified 41.4%

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

   5. Taylor expanded in b around 0 15.3%

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

      1. +-commutative 15.3%

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

      2. mul-1-neg 15.3%

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

      3. unsub-neg 15.3%

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

   7. Simplified 15.3%

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

   8. Taylor expanded in a around inf 22.1%

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

      1. neg-mul-1 22.1%

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

      2. distribute-rgt-neg-in 22.1%

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

      3. distribute-lft-neg-in 22.1%

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

   10. Simplified 22.1%

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

   if -1.9000000000000001e-15 < y < 5.7999999999999999e-212

   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. Taylor expanded in b around inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. *-commutative 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in b around 0 37.0%

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

4. Final simplification 26.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-15} \lor \neg \left(y \leq 5.8 \cdot 10^{-212}\right):\\ \;\;\;\;a \cdot \left(x \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 22.8% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.8:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 2.8) x (* a (* x b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.8) {
		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 <= 2.8d0) 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 <= 2.8) {
		tmp = x;
	} else {
		tmp = a * (x * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 2.8:
		tmp = x
	else:
		tmp = a * (x * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 2.8)
		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 <= 2.8)
		tmp = x;
	else
		tmp = a * (x * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 2.8], x, N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.7999999999999998

   1. Initial program 96.2%

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

   2. Taylor expanded in b around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. *-commutative 62.6%

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

      3. distribute-rgt-neg-in 62.6%

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

   4. Simplified 62.6%

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

   5. Taylor expanded in b around 0 19.9%

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

   if 2.7999999999999998 < y

   1. Initial program 98.7%

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

   2. Taylor expanded in b around inf 35.6%

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

      1. mul-1-neg 35.6%

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

      2. *-commutative 35.6%

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

      3. distribute-rgt-neg-in 35.6%

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

   4. Simplified 35.6%

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

   5. Taylor expanded in b around 0 13.4%

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

      1. +-commutative 13.4%

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

      2. mul-1-neg 13.4%

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

      3. unsub-neg 13.4%

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

   7. Simplified 13.4%

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

   8. Taylor expanded in a around inf 28.0%

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

      1. neg-mul-1 28.0%

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

      2. distribute-rgt-neg-in 28.0%

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

      3. distribute-lft-neg-in 28.0%

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

   10. Simplified 28.0%

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

       1. expm1-log1p-u 21.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(\left(-b\right) \cdot x\right)\right)\right)} \]

       2. expm1-udef 45.6%

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

       3. add-sqr-sqrt 26.0%

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

       4. sqrt-unprod 41.7%

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

       5. sqr-neg 41.7%

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

       6. sqrt-unprod 18.3%

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

       7. add-sqr-sqrt 41.6%

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

   12. Applied egg-rr 41.6%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(b \cdot x\right)\right)} - 1} \]
   13. Step-by-step derivation

       1. expm1-def 17.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(b \cdot x\right)\right)\right)} \]

       2. expm1-log1p 17.6%

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

   14. Simplified 17.6%

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

4. Final simplification 19.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.8:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot b\right)\\ \end{array} \]

Alternative 14: 19.1% accurate, 315.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

2. Taylor expanded in b around inf 54.4%

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

   1. mul-1-neg 54.4%

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

   2. *-commutative 54.4%

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

   3. distribute-rgt-neg-in 54.4%

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

4. Simplified 54.4%

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

5. Taylor expanded in b around 0 15.1%

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

6. Final simplification 15.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023196 
(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))))))