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

Percentage Accurate: 96.6% → 96.6%

Time: 13.0s

Alternatives: 11

Speedup: 1.0×

• 41.1% 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: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return exp((((log((1.0 - z)) - b) * a) + ((log(z) - t) * y))) * 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 = exp((((log((1.0d0 - z)) - b) * a) + ((log(z) - t) * y))) * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing

3. Final simplification 96.2%

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

Alternative 2: 35.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-x, t \cdot y, x\right)\\ t_2 := 1 \cdot t\_1\\ t_3 := \mathsf{fma}\left(t \cdot y, x, x\right)\\ t_4 := \left(\log \left(1 - z\right) - b\right) \cdot a + \left(\log z - t\right) \cdot y\\ t_5 := 1 \cdot \left(t\_1 \cdot t\_3\right)\\ \mathbf{if}\;t\_4 \leq -1 \cdot 10^{+31}:\\ \;\;\;\;\frac{t\_5}{t\_3}\\ \mathbf{elif}\;t\_4 \leq 5:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+263}:\\ \;\;\;\;\frac{1}{t\_3} \cdot t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- x) (* t y) x))
        (t_2 (* 1.0 t_1))
        (t_3 (fma (* t y) x x))
        (t_4 (+ (* (- (log (- 1.0 z)) b) a) (* (- (log z) t) y)))
        (t_5 (* 1.0 (* t_1 t_3))))
   (if (<= t_4 -1e+31)
     (/ t_5 t_3)
     (if (<= t_4 5.0) t_2 (if (<= t_4 2e+263) (* (/ 1.0 t_3) t_5) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-x, (t * y), x);
	double t_2 = 1.0 * t_1;
	double t_3 = fma((t * y), x, x);
	double t_4 = ((log((1.0 - z)) - b) * a) + ((log(z) - t) * y);
	double t_5 = 1.0 * (t_1 * t_3);
	double tmp;
	if (t_4 <= -1e+31) {
		tmp = t_5 / t_3;
	} else if (t_4 <= 5.0) {
		tmp = t_2;
	} else if (t_4 <= 2e+263) {
		tmp = (1.0 / t_3) * t_5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-x), Float64(t * y), x)
	t_2 = Float64(1.0 * t_1)
	t_3 = fma(Float64(t * y), x, x)
	t_4 = Float64(Float64(Float64(log(Float64(1.0 - z)) - b) * a) + Float64(Float64(log(z) - t) * y))
	t_5 = Float64(1.0 * Float64(t_1 * t_3))
	tmp = 0.0
	if (t_4 <= -1e+31)
		tmp = Float64(t_5 / t_3);
	elseif (t_4 <= 5.0)
		tmp = t_2;
	elseif (t_4 <= 2e+263)
		tmp = Float64(Float64(1.0 / t_3) * t_5);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-x) * N[(t * y), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * y), $MachinePrecision] * x + x), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] * a), $MachinePrecision] + N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(1.0 * N[(t$95$1 * t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -1e+31], N[(t$95$5 / t$95$3), $MachinePrecision], If[LessEqual[t$95$4, 5.0], t$95$2, If[LessEqual[t$95$4, 2e+263], N[(N[(1.0 / t$95$3), $MachinePrecision] * t$95$5), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -9.9999999999999996e30

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. distribute-rgt-out-- N/A

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

      7. lower-*.f64 N/A

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

   5. Applied rewrites 65.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 34.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 3.0%

       \[\leadsto 1 \cdot \left(x - \left(x \cdot t\right) \cdot y\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 12.4%

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

   if -9.9999999999999996e30 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < 5 or 2.00000000000000003e263 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 94.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. distribute-rgt-out-- N/A

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

      7. lower-*.f64 N/A

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

   5. Applied rewrites 78.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 61.6%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 57.7%

       \[\leadsto 1 \cdot \left(x - \left(x \cdot t\right) \cdot y\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 65.0%

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

   if 5 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < 2.00000000000000003e263

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. distribute-rgt-out-- N/A

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

      7. lower-*.f64 N/A

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

   5. Applied rewrites 72.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 42.0%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 14.9%

       \[\leadsto 1 \cdot \left(x - \left(x \cdot t\right) \cdot y\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 24.4%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\log \left(1 - z\right) - b\right) \cdot a + \left(\log z - t\right) \cdot y \leq -1 \cdot 10^{+31}:\\ \;\;\;\;\frac{1 \cdot \left(\mathsf{fma}\left(-x, t \cdot y, x\right) \cdot \mathsf{fma}\left(t \cdot y, x, x\right)\right)}{\mathsf{fma}\left(t \cdot y, x, x\right)}\\ \mathbf{elif}\;\left(\log \left(1 - z\right) - b\right) \cdot a + \left(\log z - t\right) \cdot y \leq 5:\\ \;\;\;\;1 \cdot \mathsf{fma}\left(-x, t \cdot y, x\right)\\ \mathbf{elif}\;\left(\log \left(1 - z\right) - b\right) \cdot a + \left(\log z - t\right) \cdot y \leq 2 \cdot 10^{+263}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(t \cdot y, x, x\right)} \cdot \left(1 \cdot \left(\mathsf{fma}\left(-x, t \cdot y, x\right) \cdot \mathsf{fma}\left(t \cdot y, x, x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \mathsf{fma}\left(-x, t \cdot y, x\right)\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024230 
(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))))))