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

Average Accuracy: 92.6% → 98.7%

Time: 13.6s

Precision: binary64

Cost: 3280

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ t_2 := t_1 \cdot x\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+300}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+256}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} - t \cdot x\\ \end{array} \]

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 -5e+300)
     (/ (* y x) z)
     (if (<= t_1 -2e-182)
       t_2
       (if (<= t_1 2e-165)
         (* (/ x z) (+ y t))
         (if (<= t_1 5e+256) t_2 (- (/ y (/ z x)) (* t x))))))))

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 <= -5e+300) {
		tmp = (y * x) / z;
	} else if (t_1 <= -2e-182) {
		tmp = t_2;
	} else if (t_1 <= 2e-165) {
		tmp = (x / z) * (y + t);
	} else if (t_1 <= 5e+256) {
		tmp = t_2;
	} else {
		tmp = (y / (z / x)) - (t * x);
	}
	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 <= (-5d+300)) then
        tmp = (y * x) / z
    else if (t_1 <= (-2d-182)) then
        tmp = t_2
    else if (t_1 <= 2d-165) then
        tmp = (x / z) * (y + t)
    else if (t_1 <= 5d+256) then
        tmp = t_2
    else
        tmp = (y / (z / x)) - (t * x)
    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 <= -5e+300) {
		tmp = (y * x) / z;
	} else if (t_1 <= -2e-182) {
		tmp = t_2;
	} else if (t_1 <= 2e-165) {
		tmp = (x / z) * (y + t);
	} else if (t_1 <= 5e+256) {
		tmp = t_2;
	} else {
		tmp = (y / (z / x)) - (t * x);
	}
	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 <= -5e+300:
		tmp = (y * x) / z
	elif t_1 <= -2e-182:
		tmp = t_2
	elif t_1 <= 2e-165:
		tmp = (x / z) * (y + t)
	elif t_1 <= 5e+256:
		tmp = t_2
	else:
		tmp = (y / (z / x)) - (t * x)
	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 <= -5e+300)
		tmp = Float64(Float64(y * x) / z);
	elseif (t_1 <= -2e-182)
		tmp = t_2;
	elseif (t_1 <= 2e-165)
		tmp = Float64(Float64(x / z) * Float64(y + t));
	elseif (t_1 <= 5e+256)
		tmp = t_2;
	else
		tmp = Float64(Float64(y / Float64(z / x)) - Float64(t * x));
	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 <= -5e+300)
		tmp = (y * x) / z;
	elseif (t_1 <= -2e-182)
		tmp = t_2;
	elseif (t_1 <= 2e-165)
		tmp = (x / z) * (y + t);
	elseif (t_1 <= 5e+256)
		tmp = t_2;
	else
		tmp = (y / (z / x)) - (t * x);
	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, -5e+300], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -2e-182], t$95$2, If[LessEqual[t$95$1, 2e-165], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+256], t$95$2, N[(N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	92.6%
Target	93.3%
Herbie	98.7%

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

Derivation

1. Split input into 4 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -5.00000000000000026e300

   1. Initial program 10.2%

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

   2. Taylor expanded in y around inf 96.3%

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

   if -5.00000000000000026e300 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -2.0000000000000001e-182 or 2e-165 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 5.00000000000000015e256

   1. Initial program 99.7%

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

   if -2.0000000000000001e-182 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 2e-165

   1. Initial program 88.0%

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

   2. Applied egg-rr 86.9%

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

      [Start] 88.0	\[ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
      flip3-- [=>] 0.0	\[ x \cdot \color{blue}{\frac{{\left(\frac{y}{z}\right)}^{3} - {\left(\frac{t}{1 - z}\right)}^{3}}{\frac{y}{z} \cdot \frac{y}{z} + \left(\frac{t}{1 - z} \cdot \frac{t}{1 - z} + \frac{y}{z} \cdot \frac{t}{1 - z}\right)}} \]
      associate-*r/ [=>] 0.0	\[ \color{blue}{\frac{x \cdot \left({\left(\frac{y}{z}\right)}^{3} - {\left(\frac{t}{1 - z}\right)}^{3}\right)}{\frac{y}{z} \cdot \frac{y}{z} + \left(\frac{t}{1 - z} \cdot \frac{t}{1 - z} + \frac{y}{z} \cdot \frac{t}{1 - z}\right)}} \]
      associate-/l* [=>] 0.0	\[ \color{blue}{\frac{x}{\frac{\frac{y}{z} \cdot \frac{y}{z} + \left(\frac{t}{1 - z} \cdot \frac{t}{1 - z} + \frac{y}{z} \cdot \frac{t}{1 - z}\right)}{{\left(\frac{y}{z}\right)}^{3} - {\left(\frac{t}{1 - z}\right)}^{3}}}} \]
      *-un-lft-identity [=>] 0.0	\[ \frac{x}{\frac{\color{blue}{1 \cdot \left(\frac{y}{z} \cdot \frac{y}{z} + \left(\frac{t}{1 - z} \cdot \frac{t}{1 - z} + \frac{y}{z} \cdot \frac{t}{1 - z}\right)\right)}}{{\left(\frac{y}{z}\right)}^{3} - {\left(\frac{t}{1 - z}\right)}^{3}}} \]
      associate-/l* [=>] 0.0	\[ \frac{x}{\color{blue}{\frac{1}{\frac{{\left(\frac{y}{z}\right)}^{3} - {\left(\frac{t}{1 - z}\right)}^{3}}{\frac{y}{z} \cdot \frac{y}{z} + \left(\frac{t}{1 - z} \cdot \frac{t}{1 - z} + \frac{y}{z} \cdot \frac{t}{1 - z}\right)}}}} \]
      flip3-- [<=] 86.9	\[ \frac{x}{\frac{1}{\color{blue}{\frac{y}{z} - \frac{t}{1 - z}}}} \]

   3. Taylor expanded in z around inf 94.9%

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

   4. Simplified 94.9%

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

      [Start] 94.9	\[ \frac{\left(y - -1 \cdot t\right) \cdot x}{z} \]
      *-commutative [<=] 94.9	\[ \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]
      associate-/l* [=>] 83.9	\[ \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]
      associate-/r/ [=>] 94.9	\[ \color{blue}{\frac{x}{z} \cdot \left(y - -1 \cdot t\right)} \]
      mul-1-neg [=>] 94.9	\[ \frac{x}{z} \cdot \left(y - \color{blue}{\left(-t\right)}\right) \]
      sub-neg [=>] 94.9	\[ \frac{x}{z} \cdot \color{blue}{\left(y + \left(-\left(-t\right)\right)\right)} \]
      remove-double-neg [=>] 94.9	\[ \frac{x}{z} \cdot \left(y + \color{blue}{t}\right) \]

   if 5.00000000000000015e256 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 45.7%

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

   2. Applied egg-rr 45.6%

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

      [Start] 45.7	\[ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
      flip3-- [=>] 0.0	\[ x \cdot \color{blue}{\frac{{\left(\frac{y}{z}\right)}^{3} - {\left(\frac{t}{1 - z}\right)}^{3}}{\frac{y}{z} \cdot \frac{y}{z} + \left(\frac{t}{1 - z} \cdot \frac{t}{1 - z} + \frac{y}{z} \cdot \frac{t}{1 - z}\right)}} \]
      associate-*r/ [=>] 0.0	\[ \color{blue}{\frac{x \cdot \left({\left(\frac{y}{z}\right)}^{3} - {\left(\frac{t}{1 - z}\right)}^{3}\right)}{\frac{y}{z} \cdot \frac{y}{z} + \left(\frac{t}{1 - z} \cdot \frac{t}{1 - z} + \frac{y}{z} \cdot \frac{t}{1 - z}\right)}} \]
      associate-/l* [=>] 0.0	\[ \color{blue}{\frac{x}{\frac{\frac{y}{z} \cdot \frac{y}{z} + \left(\frac{t}{1 - z} \cdot \frac{t}{1 - z} + \frac{y}{z} \cdot \frac{t}{1 - z}\right)}{{\left(\frac{y}{z}\right)}^{3} - {\left(\frac{t}{1 - z}\right)}^{3}}}} \]
      *-un-lft-identity [=>] 0.0	\[ \frac{x}{\frac{\color{blue}{1 \cdot \left(\frac{y}{z} \cdot \frac{y}{z} + \left(\frac{t}{1 - z} \cdot \frac{t}{1 - z} + \frac{y}{z} \cdot \frac{t}{1 - z}\right)\right)}}{{\left(\frac{y}{z}\right)}^{3} - {\left(\frac{t}{1 - z}\right)}^{3}}} \]
      associate-/l* [=>] 0.0	\[ \frac{x}{\color{blue}{\frac{1}{\frac{{\left(\frac{y}{z}\right)}^{3} - {\left(\frac{t}{1 - z}\right)}^{3}}{\frac{y}{z} \cdot \frac{y}{z} + \left(\frac{t}{1 - z} \cdot \frac{t}{1 - z} + \frac{y}{z} \cdot \frac{t}{1 - z}\right)}}}} \]
      flip3-- [<=] 45.6	\[ \frac{x}{\frac{1}{\color{blue}{\frac{y}{z} - \frac{t}{1 - z}}}} \]

   3. Taylor expanded in z around 0 97.0%

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

   4. Simplified 97.4%

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

      [Start] 97.0	\[ \frac{y \cdot x}{z} + -1 \cdot \left(t \cdot x\right) \]
      +-commutative [=>] 97.0	\[ \color{blue}{-1 \cdot \left(t \cdot x\right) + \frac{y \cdot x}{z}} \]
      associate-*r* [=>] 97.0	\[ \color{blue}{\left(-1 \cdot t\right) \cdot x} + \frac{y \cdot x}{z} \]
      mul-1-neg [=>] 97.0	\[ \color{blue}{\left(-t\right)} \cdot x + \frac{y \cdot x}{z} \]
      associate-/l* [=>] 97.4	\[ \left(-t\right) \cdot x + \color{blue}{\frac{y}{\frac{z}{x}}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -5 \cdot 10^{+300}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq -2 \cdot 10^{-182}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 2 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 5 \cdot 10^{+256}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} - t \cdot x\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	55.2%
Cost	1642

\[\begin{array}{l} t_1 := \frac{y}{z} \cdot x\\ t_2 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+267}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+31} \lor \neg \left(z \leq 10^{+93} \lor \neg \left(z \leq 5.5 \cdot 10^{+132}\right) \land z \leq 1.4 \cdot 10^{+211}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	55.3%
Cost	1642

\[\begin{array}{l} t_1 := \frac{y}{z} \cdot x\\ t_2 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+265}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+231}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+29} \lor \neg \left(z \leq 2.55 \cdot 10^{+92} \lor \neg \left(z \leq 1.7 \cdot 10^{+134}\right) \land z \leq 2.7 \cdot 10^{+213}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	57.9%
Cost	1641

\[\begin{array}{l} t_1 := \frac{y}{z} \cdot x\\ t_2 := x \cdot \frac{t}{z}\\ t_3 := \frac{y \cdot x}{z}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+266}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+230}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+28}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+91} \lor \neg \left(z \leq 7 \cdot 10^{+133}\right) \land z \leq 8.6 \cdot 10^{+212}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	67.2%
Cost	1641

\[\begin{array}{l} t_1 := \frac{y}{z} \cdot x\\ t_2 := x \cdot \frac{t}{z}\\ t_3 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+265}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+231}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-166}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-256}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+93} \lor \neg \left(z \leq 2.9 \cdot 10^{+134}\right) \land z \leq 1.9 \cdot 10^{+213}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	56.9%
Cost	1113

\[\begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+28} \lor \neg \left(z \leq 2.7 \cdot 10^{+212}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	63.6%
Cost	1112

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ t_2 := \frac{y}{z} \cdot x\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-178}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	69.8%
Cost	1109

\[\begin{array}{l} t_1 := t \cdot \frac{x}{z + -1}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-180}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 210:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+65} \lor \neg \left(t \leq 4.5 \cdot 10^{+96}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Alternative 8
Accuracy	90.4%
Cost	1104

\[\begin{array}{l} t_1 := \frac{y}{z} \cdot x - t \cdot x\\ t_2 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -48:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-260}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	84.4%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ t_2 := \frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{if}\;z \leq -48:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-257}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	84.0%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -48:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-257}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \]

Alternative 11
Accuracy	90.4%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ t_2 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -48:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-253}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Accuracy	56.9%
Cost	452

\[\begin{array}{l} \mathbf{if}\;t \leq 6.8 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]

Alternative 13
Accuracy	20.9%
Cost	256

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

Reproduce

herbie shell --seed 2023138 
(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)))))