Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Average Accuracy: 92.6% → 98.9%

Time: 13.9s

Precision: binary64

Cost: 3280

Math

\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

↓

\[\begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ t_2 := t_1 \cdot x\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+235}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} - t \cdot x\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+294}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))) (t_2 (* t_1 x)))
   (if (<= t_1 -1e+235)
     (- (/ y (/ z x)) (* t x))
     (if (<= t_1 -2e-173)
       t_2
       (if (<= t_1 2e-318)
         (/ (+ y t) (/ z x))
         (if (<= t_1 4e+294) t_2 (* y (/ x z))))))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

↓

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double t_2 = t_1 * x;
	double tmp;
	if (t_1 <= -1e+235) {
		tmp = (y / (z / x)) - (t * x);
	} else if (t_1 <= -2e-173) {
		tmp = t_2;
	} else if (t_1 <= 2e-318) {
		tmp = (y + t) / (z / x);
	} else if (t_1 <= 4e+294) {
		tmp = t_2;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y / z) - (t / (1.0d0 - z))
    t_2 = t_1 * x
    if (t_1 <= (-1d+235)) then
        tmp = (y / (z / x)) - (t * x)
    else if (t_1 <= (-2d-173)) then
        tmp = t_2
    else if (t_1 <= 2d-318) then
        tmp = (y + t) / (z / x)
    else if (t_1 <= 4d+294) then
        tmp = t_2
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double t_2 = t_1 * x;
	double tmp;
	if (t_1 <= -1e+235) {
		tmp = (y / (z / x)) - (t * x);
	} else if (t_1 <= -2e-173) {
		tmp = t_2;
	} else if (t_1 <= 2e-318) {
		tmp = (y + t) / (z / x);
	} else if (t_1 <= 4e+294) {
		tmp = t_2;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

↓

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	t_2 = t_1 * x
	tmp = 0
	if t_1 <= -1e+235:
		tmp = (y / (z / x)) - (t * x)
	elif t_1 <= -2e-173:
		tmp = t_2
	elif t_1 <= 2e-318:
		tmp = (y + t) / (z / x)
	elif t_1 <= 4e+294:
		tmp = t_2
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

↓

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	t_2 = Float64(t_1 * x)
	tmp = 0.0
	if (t_1 <= -1e+235)
		tmp = Float64(Float64(y / Float64(z / x)) - Float64(t * x));
	elseif (t_1 <= -2e-173)
		tmp = t_2;
	elseif (t_1 <= 2e-318)
		tmp = Float64(Float64(y + t) / Float64(z / x));
	elseif (t_1 <= 4e+294)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

↓

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	t_2 = t_1 * x;
	tmp = 0.0;
	if (t_1 <= -1e+235)
		tmp = (y / (z / x)) - (t * x);
	elseif (t_1 <= -2e-173)
		tmp = t_2;
	elseif (t_1 <= 2e-318)
		tmp = (y + t) / (z / x);
	elseif (t_1 <= 4e+294)
		tmp = t_2;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * x), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+235], N[(N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-173], t$95$2, If[LessEqual[t$95$1, 2e-318], N[(N[(y + t), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+294], t$95$2, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	92.6%
Target	93.2%
Herbie	98.9%

\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array} \]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -1.0000000000000001e235

   1. Initial program 57.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Applied egg-rr 57.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{1}{\frac{y}{z} - \frac{t}{1 - z}}}} \]

   3. Taylor expanded in z around 0 95.1%

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

   4. Simplified 95.0%

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

      [Start] 95.1	\[ \frac{y \cdot x}{z} + -1 \cdot \left(t \cdot x\right) \]
      +-commutative [=>] 95.1	\[ \color{blue}{-1 \cdot \left(t \cdot x\right) + \frac{y \cdot x}{z}} \]
      associate-*r* [=>] 95.1	\[ \color{blue}{\left(-1 \cdot t\right) \cdot x} + \frac{y \cdot x}{z} \]
      mul-1-neg [=>] 95.1	\[ \color{blue}{\left(-t\right)} \cdot x + \frac{y \cdot x}{z} \]
      associate-/l* [=>] 95.0	\[ \left(-t\right) \cdot x + \color{blue}{\frac{y}{\frac{z}{x}}} \]

   if -1.0000000000000001e235 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -2.0000000000000001e-173 or 2.0000024e-318 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 4.00000000000000027e294

   1. Initial program 99.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   if -2.0000000000000001e-173 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 2.0000024e-318

   1. Initial program 84.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in z around -inf 97.3%

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

   3. Simplified 97.3%

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

      [Start] 97.3	\[ -1 \cdot \frac{\left(-1 \cdot y - t\right) \cdot x}{z} \]
      mul-1-neg [=>] 97.3	\[ \color{blue}{-\frac{\left(-1 \cdot y - t\right) \cdot x}{z}} \]
      associate-/l* [=>] 97.3	\[ -\color{blue}{\frac{-1 \cdot y - t}{\frac{z}{x}}} \]
      mul-1-neg [=>] 97.3	\[ -\frac{\color{blue}{\left(-y\right)} - t}{\frac{z}{x}} \]

   if 4.00000000000000027e294 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 17.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]

   2. Taylor expanded in y around inf 95.0%

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

   3. Simplified 12.8%

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

      [Start] 95.0	\[ \frac{y \cdot x}{z} \]
      associate-*l/ [<=] 12.8	\[ \color{blue}{\frac{y}{z} \cdot x} \]

   4. Taylor expanded in y around 0 95.0%

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

   5. Simplified 95.0%

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

      [Start] 95.0	\[ \frac{y \cdot x}{z} \]
      associate-*r/ [<=] 95.0	\[ \color{blue}{y \cdot \frac{x}{z}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -1 \cdot 10^{+235}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} - t \cdot x\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq -2 \cdot 10^{-173}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 4 \cdot 10^{+294}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	55.9%
Cost	1773

\[\begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := x \cdot \frac{t}{z}\\ t_3 := t \cdot \left(-x\right)\\ t_4 := \frac{y}{z} \cdot x\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+62}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-13}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-207}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+127} \lor \neg \left(z \leq 1.7 \cdot 10^{+213}\right) \land z \leq 1.4 \cdot 10^{+283}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 2
Accuracy	55.1%
Cost	1772

\[\begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := x \cdot \frac{t}{z}\\ t_3 := \frac{y}{z} \cdot x\\ t_4 := t \cdot \left(-x\right)\\ t_5 := \frac{t}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-13}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-110}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-206}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+127}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+215}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+261}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	54.9%
Cost	1772

\[\begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := x \cdot \frac{t}{z}\\ t_3 := \frac{x}{\frac{z}{y}}\\ t_4 := t \cdot \left(-x\right)\\ t_5 := \frac{t}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-114}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-207}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+127}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+213}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+257}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	55.1%
Cost	1772

\[\begin{array}{l} t_1 := \frac{y}{\frac{z}{x}}\\ t_2 := x \cdot \frac{t}{z}\\ t_3 := \frac{x}{\frac{z}{y}}\\ t_4 := t \cdot \left(-x\right)\\ t_5 := \frac{t}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-113}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-206}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+127}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+213}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+260}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	55.2%
Cost	1772

\[\begin{array}{l} t_1 := \frac{y}{\frac{z}{x}}\\ t_2 := x \cdot \frac{t}{z}\\ t_3 := t \cdot \left(-x\right)\\ t_4 := \frac{x}{\frac{z}{y}}\\ t_5 := \frac{t}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{+59}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-13}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-114}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.212 \cdot 10^{-206}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+127}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+214}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+258}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	55.5%
Cost	1641

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := t \cdot \left(-x\right)\\ t_3 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+59}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-13}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+106} \lor \neg \left(z \leq 3.2 \cdot 10^{+156}\right) \land z \leq 3.8 \cdot 10^{+212}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	66.1%
Cost	1508

\[\begin{array}{l} t_1 := \frac{t}{\frac{z}{x}}\\ t_2 := \frac{x}{\frac{z}{y}}\\ t_3 := x \cdot \frac{t}{z}\\ t_4 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -3.45 \cdot 10^{+115}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.72 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{+18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.212 \cdot 10^{-206}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-200}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+36}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+214}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+259}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 8
Accuracy	66.3%
Cost	1508

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{y}}\\ t_2 := x \cdot \frac{t}{z}\\ t_3 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.212 \cdot 10^{-206}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-198}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+261}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 9
Accuracy	90.4%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ t_2 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -24:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.212 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{-198}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	87.0%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -24:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq -1.212 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-202}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 245000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \end{array} \]

Alternative 11
Accuracy	54.1%
Cost	850

\[\begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-13} \lor \neg \left(z \leq -1.48 \cdot 10^{-108} \lor \neg \left(z \leq -4.2 \cdot 10^{-140}\right) \land z \leq -1.12 \cdot 10^{-206}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 12
Accuracy	90.3%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -0.95:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} - t \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \end{array} \]

Alternative 13
Accuracy	20.6%
Cost	256

\[t \cdot \left(-x\right) \]

Reproduce

herbie shell --seed 2023141 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))