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

Percentage Accurate: 96.3% → 96.3%

Time: 10.8s

Alternatives: 9

Speedup: 1.0×

• Could not converge on a ground truth

  1. x = 9.004192644708278e-104
  2. y = -5.4369677023868365e+163
  3. z = 6.786915678197327e-201
  4. t = 2.070850317444193e+77
  5. a = -3.1660104766609794e+299
  6. b = -2.0045659431329768e-64

• 41.5% 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: 96.3% 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: 96.3% 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 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. Add Preprocessing

Alternative 2: 58.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)\\ \mathbf{if}\;t\_1 \leq -800 \lor \neg \left(t\_1 \leq 5 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot {\left(z \cdot z\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
   (if (or (<= t_1 -800.0) (not (<= t_1 5e+15)))
     (* x (pow (* z z) y))
     (* x (pow z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * (log(z) - t)) + (a * (log((1.0 - z)) - b));
	double tmp;
	if ((t_1 <= -800.0) || !(t_1 <= 5e+15)) {
		tmp = x * pow((z * z), y);
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))
    if ((t_1 <= (-800.0d0)) .or. (.not. (t_1 <= 5d+15))) then
        tmp = x * ((z * z) ** y)
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b));
	double tmp;
	if ((t_1 <= -800.0) || !(t_1 <= 5e+15)) {
		tmp = x * Math.pow((z * z), y);
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))
	tmp = 0
	if (t_1 <= -800.0) or not (t_1 <= 5e+15):
		tmp = x * math.pow((z * z), y)
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))
	tmp = 0.0
	if ((t_1 <= -800.0) || !(t_1 <= 5e+15))
		tmp = Float64(x * (Float64(z * z) ^ y));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * (log(z) - t)) + (a * (log((1.0 - z)) - b));
	tmp = 0.0;
	if ((t_1 <= -800.0) || ~((t_1 <= 5e+15)))
		tmp = x * ((z * z) ^ y);
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[t$95$1, -800.0], N[Not[LessEqual[t$95$1, 5e+15]], $MachinePrecision]], N[(x * N[Power[N[(z * z), $MachinePrecision], y], $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -800 or 5e15 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 96.8%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. exp-prod N/A

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

      3. lower-pow.f64 N/A

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

      4. exp-diff N/A

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

      5. rem-exp-log N/A

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

      6. lower-/.f64 N/A

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

      7. lower-exp.f64 74.2

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

   5. Applied rewrites 74.2%

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

   6. Taylor expanded in t around 0

      \[\leadsto x \cdot {z}^{\color{blue}{y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.8%

      \[\leadsto x \cdot {z}^{\color{blue}{y}} \]
   9. Step-by-step derivation

   10. Applied rewrites 54.4%

       \[\leadsto x \cdot {\left(z \cdot z\right)}^{y} \]

   if -800 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < 5e15

   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

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

      1. *-commutative N/A

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

      2. exp-prod N/A

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

      3. lower-pow.f64 N/A

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

      4. exp-diff N/A

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

      5. rem-exp-log N/A

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

      6. lower-/.f64 N/A

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

      7. lower-exp.f64 73.8

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in t around 0

      \[\leadsto x \cdot {z}^{\color{blue}{y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 85.5%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right) \leq -800 \lor \neg \left(y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right) \leq 5 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot {\left(z \cdot z\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{\left(-t\right) \cdot y}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+113}:\\ \;\;\;\;x \cdot e^{\left(\left(-z\right) - b\right) \cdot a}\\ \mathbf{elif}\;t \leq -960:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-73}:\\ \;\;\;\;x \cdot {\left({z}^{\left(-y\right)}\right)}^{-1}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;x \cdot e^{\left(-b\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* (- t) y)))))
   (if (<= t -1.25e+231)
     t_1
     (if (<= t -1.8e+113)
       (* x (exp (* (- (- z) b) a)))
       (if (<= t -960.0)
         t_1
         (if (<= t 1.12e-73)
           (* x (pow (pow z (- y)) -1.0))
           (if (<= t 5.2e-20) (* x (exp (* (- b) a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((-t * y));
	double tmp;
	if (t <= -1.25e+231) {
		tmp = t_1;
	} else if (t <= -1.8e+113) {
		tmp = x * exp(((-z - b) * a));
	} else if (t <= -960.0) {
		tmp = t_1;
	} else if (t <= 1.12e-73) {
		tmp = x * pow(pow(z, -y), -1.0);
	} else if (t <= 5.2e-20) {
		tmp = x * exp((-b * a));
	} 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((-t * y))
    if (t <= (-1.25d+231)) then
        tmp = t_1
    else if (t <= (-1.8d+113)) then
        tmp = x * exp(((-z - b) * a))
    else if (t <= (-960.0d0)) then
        tmp = t_1
    else if (t <= 1.12d-73) then
        tmp = x * ((z ** -y) ** (-1.0d0))
    else if (t <= 5.2d-20) then
        tmp = x * exp((-b * a))
    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((-t * y));
	double tmp;
	if (t <= -1.25e+231) {
		tmp = t_1;
	} else if (t <= -1.8e+113) {
		tmp = x * Math.exp(((-z - b) * a));
	} else if (t <= -960.0) {
		tmp = t_1;
	} else if (t <= 1.12e-73) {
		tmp = x * Math.pow(Math.pow(z, -y), -1.0);
	} else if (t <= 5.2e-20) {
		tmp = x * Math.exp((-b * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((-t * y))
	tmp = 0
	if t <= -1.25e+231:
		tmp = t_1
	elif t <= -1.8e+113:
		tmp = x * math.exp(((-z - b) * a))
	elif t <= -960.0:
		tmp = t_1
	elif t <= 1.12e-73:
		tmp = x * math.pow(math.pow(z, -y), -1.0)
	elif t <= 5.2e-20:
		tmp = x * math.exp((-b * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(Float64(-t) * y)))
	tmp = 0.0
	if (t <= -1.25e+231)
		tmp = t_1;
	elseif (t <= -1.8e+113)
		tmp = Float64(x * exp(Float64(Float64(Float64(-z) - b) * a)));
	elseif (t <= -960.0)
		tmp = t_1;
	elseif (t <= 1.12e-73)
		tmp = Float64(x * ((z ^ Float64(-y)) ^ -1.0));
	elseif (t <= 5.2e-20)
		tmp = Float64(x * exp(Float64(Float64(-b) * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((-t * y));
	tmp = 0.0;
	if (t <= -1.25e+231)
		tmp = t_1;
	elseif (t <= -1.8e+113)
		tmp = x * exp(((-z - b) * a));
	elseif (t <= -960.0)
		tmp = t_1;
	elseif (t <= 1.12e-73)
		tmp = x * ((z ^ -y) ^ -1.0);
	elseif (t <= 5.2e-20)
		tmp = x * exp((-b * a));
	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[((-t) * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+231], t$95$1, If[LessEqual[t, -1.8e+113], N[(x * N[Exp[N[(N[((-z) - b), $MachinePrecision] * a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -960.0], t$95$1, If[LessEqual[t, 1.12e-73], N[(x * N[Power[N[Power[z, (-y)], $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-20], N[(x * N[Exp[N[((-b) * a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.25000000000000007e231 or -1.79999999999999996e113 < t < -960 or 5.1999999999999999e-20 < t

   1. Initial program 99.1%

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

   3. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 87.0

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

   5. Applied rewrites 87.0%

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

   if -1.25000000000000007e231 < t < -1.79999999999999996e113

   1. Initial program 91.1%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-log1p.f64 N/A

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

      6. lower-neg.f64 86.5

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

   5. Applied rewrites 86.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 86.5%

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

   if -960 < t < 1.11999999999999995e-73

   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 a around 0

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

      1. *-commutative N/A

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

      2. exp-prod N/A

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

      3. lower-pow.f64 N/A

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

      4. exp-diff N/A

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

      5. rem-exp-log N/A

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

      6. lower-/.f64 N/A

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

      7. lower-exp.f64 73.2

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

   5. Applied rewrites 73.2%

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

   6. Taylor expanded in t around 0

      \[\leadsto x \cdot {z}^{\color{blue}{y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 74.1%

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

   10. Applied rewrites 74.1%

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

   if 1.11999999999999995e-73 < t < 5.1999999999999999e-20

   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

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+231}:\\ \;\;\;\;x \cdot e^{\left(-t\right) \cdot y}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+113}:\\ \;\;\;\;x \cdot e^{\left(\left(-z\right) - b\right) \cdot a}\\ \mathbf{elif}\;t \leq -960:\\ \;\;\;\;x \cdot e^{\left(-t\right) \cdot y}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-73}:\\ \;\;\;\;x \cdot {\left({z}^{\left(-y\right)}\right)}^{-1}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;x \cdot e^{\left(-b\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(-t\right) \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \lor \neg \left(y \leq 45000000\right):\\ \;\;\;\;x \cdot {\left(\frac{z}{e^{t}}\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(\left(-z\right) - b\right) \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.65) (not (<= y 45000000.0)))
   (* x (pow (/ z (exp t)) y))
   (* x (exp (* (- (- z) b) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.65) || !(y <= 45000000.0)) {
		tmp = x * pow((z / exp(t)), y);
	} else {
		tmp = x * exp(((-z - b) * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.65d0)) .or. (.not. (y <= 45000000.0d0))) then
        tmp = x * ((z / exp(t)) ** y)
    else
        tmp = x * exp(((-z - b) * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.65) || !(y <= 45000000.0)) {
		tmp = x * Math.pow((z / Math.exp(t)), y);
	} else {
		tmp = x * Math.exp(((-z - b) * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.65) or not (y <= 45000000.0):
		tmp = x * math.pow((z / math.exp(t)), y)
	else:
		tmp = x * math.exp(((-z - b) * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.65) || !(y <= 45000000.0))
		tmp = Float64(x * (Float64(z / exp(t)) ^ y));
	else
		tmp = Float64(x * exp(Float64(Float64(Float64(-z) - b) * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.65) || ~((y <= 45000000.0)))
		tmp = x * ((z / exp(t)) ^ y);
	else
		tmp = x * exp(((-z - b) * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.65], N[Not[LessEqual[y, 45000000.0]], $MachinePrecision]], N[(x * N[Power[N[(z / N[Exp[t], $MachinePrecision]), $MachinePrecision], y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(N[((-z) - b), $MachinePrecision] * a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.64999999999999991 or 4.5e7 < y

   1. Initial program 99.3%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. exp-prod N/A

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

      3. lower-pow.f64 N/A

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

      4. exp-diff N/A

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

      5. rem-exp-log N/A

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

      6. lower-/.f64 N/A

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

      7. lower-exp.f64 92.7

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

   5. Applied rewrites 92.7%

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

   if -2.64999999999999991 < y < 4.5e7

   1. Initial program 93.5%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-log1p.f64 N/A

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

      6. lower-neg.f64 84.2

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

   5. Applied rewrites 84.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 84.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \lor \neg \left(y \leq 45000000\right):\\ \;\;\;\;x \cdot {\left(\frac{z}{e^{t}}\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{\left(\left(-z\right) - b\right) \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{\left(-t\right) \cdot y}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+113}:\\ \;\;\;\;x \cdot e^{\left(\left(-z\right) - b\right) \cdot a}\\ \mathbf{elif}\;t \leq -960:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-73}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;x \cdot e^{\left(-b\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* (- t) y)))))
   (if (<= t -1.25e+231)
     t_1
     (if (<= t -1.8e+113)
       (* x (exp (* (- (- z) b) a)))
       (if (<= t -960.0)
         t_1
         (if (<= t 1.12e-73)
           (* x (pow z y))
           (if (<= t 5.2e-20) (* x (exp (* (- b) a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((-t * y));
	double tmp;
	if (t <= -1.25e+231) {
		tmp = t_1;
	} else if (t <= -1.8e+113) {
		tmp = x * exp(((-z - b) * a));
	} else if (t <= -960.0) {
		tmp = t_1;
	} else if (t <= 1.12e-73) {
		tmp = x * pow(z, y);
	} else if (t <= 5.2e-20) {
		tmp = x * exp((-b * a));
	} 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((-t * y))
    if (t <= (-1.25d+231)) then
        tmp = t_1
    else if (t <= (-1.8d+113)) then
        tmp = x * exp(((-z - b) * a))
    else if (t <= (-960.0d0)) then
        tmp = t_1
    else if (t <= 1.12d-73) then
        tmp = x * (z ** y)
    else if (t <= 5.2d-20) then
        tmp = x * exp((-b * a))
    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((-t * y));
	double tmp;
	if (t <= -1.25e+231) {
		tmp = t_1;
	} else if (t <= -1.8e+113) {
		tmp = x * Math.exp(((-z - b) * a));
	} else if (t <= -960.0) {
		tmp = t_1;
	} else if (t <= 1.12e-73) {
		tmp = x * Math.pow(z, y);
	} else if (t <= 5.2e-20) {
		tmp = x * Math.exp((-b * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((-t * y))
	tmp = 0
	if t <= -1.25e+231:
		tmp = t_1
	elif t <= -1.8e+113:
		tmp = x * math.exp(((-z - b) * a))
	elif t <= -960.0:
		tmp = t_1
	elif t <= 1.12e-73:
		tmp = x * math.pow(z, y)
	elif t <= 5.2e-20:
		tmp = x * math.exp((-b * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(Float64(-t) * y)))
	tmp = 0.0
	if (t <= -1.25e+231)
		tmp = t_1;
	elseif (t <= -1.8e+113)
		tmp = Float64(x * exp(Float64(Float64(Float64(-z) - b) * a)));
	elseif (t <= -960.0)
		tmp = t_1;
	elseif (t <= 1.12e-73)
		tmp = Float64(x * (z ^ y));
	elseif (t <= 5.2e-20)
		tmp = Float64(x * exp(Float64(Float64(-b) * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((-t * y));
	tmp = 0.0;
	if (t <= -1.25e+231)
		tmp = t_1;
	elseif (t <= -1.8e+113)
		tmp = x * exp(((-z - b) * a));
	elseif (t <= -960.0)
		tmp = t_1;
	elseif (t <= 1.12e-73)
		tmp = x * (z ^ y);
	elseif (t <= 5.2e-20)
		tmp = x * exp((-b * a));
	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[((-t) * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+231], t$95$1, If[LessEqual[t, -1.8e+113], N[(x * N[Exp[N[(N[((-z) - b), $MachinePrecision] * a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -960.0], t$95$1, If[LessEqual[t, 1.12e-73], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-20], N[(x * N[Exp[N[((-b) * a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.25000000000000007e231 or -1.79999999999999996e113 < t < -960 or 5.1999999999999999e-20 < t

   1. Initial program 99.1%

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

   3. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 87.0

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

   5. Applied rewrites 87.0%

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

   if -1.25000000000000007e231 < t < -1.79999999999999996e113

   1. Initial program 91.1%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-log1p.f64 N/A

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

      6. lower-neg.f64 86.5

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

   5. Applied rewrites 86.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 86.5%

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

   if -960 < t < 1.11999999999999995e-73

   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 a around 0

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

      1. *-commutative N/A

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

      2. exp-prod N/A

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

      3. lower-pow.f64 N/A

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

      4. exp-diff N/A

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

      5. rem-exp-log N/A

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

      6. lower-/.f64 N/A

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

      7. lower-exp.f64 73.2

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

   5. Applied rewrites 73.2%

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

   6. Taylor expanded in t around 0

      \[\leadsto x \cdot {z}^{\color{blue}{y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 74.1%

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

   if 1.11999999999999995e-73 < t < 5.1999999999999999e-20

   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

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

Alternative 6: 69.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{\left(-b\right) \cdot a}\\ t_2 := x \cdot e^{\left(-t\right) \cdot y}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+195}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -960:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-73}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (* (- b) a)))) (t_2 (* x (exp (* (- t) y)))))
   (if (<= t -6.2e+195)
     t_2
     (if (<= t -2.7e+113)
       t_1
       (if (<= t -960.0)
         t_2
         (if (<= t 1.12e-73) (* x (pow z y)) (if (<= t 5.2e-20) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp((-b * a));
	double t_2 = x * exp((-t * y));
	double tmp;
	if (t <= -6.2e+195) {
		tmp = t_2;
	} else if (t <= -2.7e+113) {
		tmp = t_1;
	} else if (t <= -960.0) {
		tmp = t_2;
	} else if (t <= 1.12e-73) {
		tmp = x * pow(z, y);
	} else if (t <= 5.2e-20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 * exp((-b * a))
    t_2 = x * exp((-t * y))
    if (t <= (-6.2d+195)) then
        tmp = t_2
    else if (t <= (-2.7d+113)) then
        tmp = t_1
    else if (t <= (-960.0d0)) then
        tmp = t_2
    else if (t <= 1.12d-73) then
        tmp = x * (z ** y)
    else if (t <= 5.2d-20) then
        tmp = t_1
    else
        tmp = t_2
    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((-b * a));
	double t_2 = x * Math.exp((-t * y));
	double tmp;
	if (t <= -6.2e+195) {
		tmp = t_2;
	} else if (t <= -2.7e+113) {
		tmp = t_1;
	} else if (t <= -960.0) {
		tmp = t_2;
	} else if (t <= 1.12e-73) {
		tmp = x * Math.pow(z, y);
	} else if (t <= 5.2e-20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.exp((-b * a))
	t_2 = x * math.exp((-t * y))
	tmp = 0
	if t <= -6.2e+195:
		tmp = t_2
	elif t <= -2.7e+113:
		tmp = t_1
	elif t <= -960.0:
		tmp = t_2
	elif t <= 1.12e-73:
		tmp = x * math.pow(z, y)
	elif t <= 5.2e-20:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(Float64(Float64(-b) * a)))
	t_2 = Float64(x * exp(Float64(Float64(-t) * y)))
	tmp = 0.0
	if (t <= -6.2e+195)
		tmp = t_2;
	elseif (t <= -2.7e+113)
		tmp = t_1;
	elseif (t <= -960.0)
		tmp = t_2;
	elseif (t <= 1.12e-73)
		tmp = Float64(x * (z ^ y));
	elseif (t <= 5.2e-20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * exp((-b * a));
	t_2 = x * exp((-t * y));
	tmp = 0.0;
	if (t <= -6.2e+195)
		tmp = t_2;
	elseif (t <= -2.7e+113)
		tmp = t_1;
	elseif (t <= -960.0)
		tmp = t_2;
	elseif (t <= 1.12e-73)
		tmp = x * (z ^ y);
	elseif (t <= 5.2e-20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[((-b) * a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Exp[N[((-t) * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+195], t$95$2, If[LessEqual[t, -2.7e+113], t$95$1, If[LessEqual[t, -960.0], t$95$2, If[LessEqual[t, 1.12e-73], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-20], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.2000000000000004e195 or -2.70000000000000011e113 < t < -960 or 5.1999999999999999e-20 < t

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 86.3

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

   5. Applied rewrites 86.3%

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

   if -6.2000000000000004e195 < t < -2.70000000000000011e113 or 1.11999999999999995e-73 < t < 5.1999999999999999e-20

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. lower-neg.f64 86.9

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

   5. Applied rewrites 86.9%

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

   if -960 < t < 1.11999999999999995e-73

   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 a around 0

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

      1. *-commutative N/A

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

      2. exp-prod N/A

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

      3. lower-pow.f64 N/A

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

      4. exp-diff N/A

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

      5. rem-exp-log N/A

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

      6. lower-/.f64 N/A

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

      7. lower-exp.f64 73.2

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

   5. Applied rewrites 73.2%

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

   6. Taylor expanded in t around 0

      \[\leadsto x \cdot {z}^{\color{blue}{y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 74.1%

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

Alternative 7: 73.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+29}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 2:\\ \;\;\;\;x \cdot e^{\left(-b\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {\left(z \cdot z\right)}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.4e+29)
   (* x (pow z y))
   (if (<= y 2.0) (* x (exp (* (- b) a))) (* x (pow (* z z) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.4e+29) {
		tmp = x * pow(z, y);
	} else if (y <= 2.0) {
		tmp = x * exp((-b * a));
	} else {
		tmp = x * pow((z * z), y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6.4d+29)) then
        tmp = x * (z ** y)
    else if (y <= 2.0d0) then
        tmp = x * exp((-b * a))
    else
        tmp = x * ((z * z) ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.4e+29) {
		tmp = x * Math.pow(z, y);
	} else if (y <= 2.0) {
		tmp = x * Math.exp((-b * a));
	} else {
		tmp = x * Math.pow((z * z), y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.4e+29:
		tmp = x * math.pow(z, y)
	elif y <= 2.0:
		tmp = x * math.exp((-b * a))
	else:
		tmp = x * math.pow((z * z), y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.4e+29)
		tmp = Float64(x * (z ^ y));
	elseif (y <= 2.0)
		tmp = Float64(x * exp(Float64(Float64(-b) * a)));
	else
		tmp = Float64(x * (Float64(z * z) ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.4e+29)
		tmp = x * (z ^ y);
	elseif (y <= 2.0)
		tmp = x * exp((-b * a));
	else
		tmp = x * ((z * z) ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.4e+29], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.0], N[(x * N[Exp[N[((-b) * a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Power[N[(z * z), $MachinePrecision], y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.39999999999999973e29

   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 a around 0

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

      1. *-commutative N/A

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

      2. exp-prod N/A

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

      3. lower-pow.f64 N/A

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

      4. exp-diff N/A

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

      5. rem-exp-log N/A

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

      6. lower-/.f64 N/A

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

      7. lower-exp.f64 92.1

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

   5. Applied rewrites 92.1%

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

   6. Taylor expanded in t around 0

      \[\leadsto x \cdot {z}^{\color{blue}{y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 66.7%

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

   if -6.39999999999999973e29 < y < 2

   1. Initial program 94.4%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. lower-neg.f64 78.9

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

   5. Applied rewrites 78.9%

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

   if 2 < y

   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

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

      1. *-commutative N/A

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

      2. exp-prod N/A

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

      3. lower-pow.f64 N/A

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

      4. exp-diff N/A

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

      5. rem-exp-log N/A

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

      6. lower-/.f64 N/A

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

      7. lower-exp.f64 91.7

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

   5. Applied rewrites 91.7%

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

   6. Taylor expanded in t around 0

      \[\leadsto x \cdot {z}^{\color{blue}{y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 75.0%

      \[\leadsto x \cdot {z}^{\color{blue}{y}} \]
   9. Step-by-step derivation

   10. Applied rewrites 75.0%

       \[\leadsto x \cdot {\left(z \cdot z\right)}^{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 51.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ x \cdot {z}^{y} \end{array} \]

FPCore

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

C

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

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 * (z ** y)
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return x * math.pow(z, y)

Julia

function code(x, y, z, t, a, b)
	return Float64(x * (z ^ y))
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]

Derivation

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 a around 0

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

   1. *-commutative N/A

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

   2. exp-prod N/A

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

   3. lower-pow.f64 N/A

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

   4. exp-diff N/A

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

   5. rem-exp-log N/A

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

   6. lower-/.f64 N/A

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

   7. lower-exp.f64 74.2

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

5. Applied rewrites 74.2%

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

6. Taylor expanded in t around 0

   \[\leadsto x \cdot {z}^{\color{blue}{y}} \]
7. Step-by-step derivation

8. Applied rewrites 52.6%

   \[\leadsto x \cdot {z}^{\color{blue}{y}} \]
9. Add Preprocessing

Alternative 9: 18.9% accurate, 54.7× speedup

Math

\[\begin{array}{l} \\ x \cdot 1 \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* x 1.0))

C

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

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 * 1.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 1.0;
}

Python

def code(x, y, z, t, a, b):
	return x * 1.0

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * 1.0), $MachinePrecision]

Derivation

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 a around 0

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

   1. *-commutative N/A

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

   2. exp-prod N/A

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

   3. lower-pow.f64 N/A

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

   4. exp-diff N/A

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

   5. rem-exp-log N/A

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

   6. lower-/.f64 N/A

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

   7. lower-exp.f64 74.2

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

5. Applied rewrites 74.2%

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

6. Taylor expanded in y around 0

   \[\leadsto x \cdot 1 \]
7. Step-by-step derivation

8. Applied rewrites 17.8%

   \[\leadsto x \cdot 1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024324 
(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))))))