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

Average Accuracy: 92.4% → 98.5%

Time: 14.5s

Precision: binary64

Cost: 3408

Math

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

↓

\[\begin{array}{l} t_1 := \frac{t}{1 - z}\\ t_2 := \frac{y}{z} - t_1\\ t_3 := \frac{y}{z} \cdot x - t_1 \cdot x\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-128}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{elif}\;t_2 \leq 10^{+289}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

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 (/ t (- 1.0 z)))
        (t_2 (- (/ y z) t_1))
        (t_3 (- (* (/ y z) x) (* t_1 x))))
   (if (<= t_2 (- INFINITY))
     (/ y (/ z x))
     (if (<= t_2 -5e-128)
       t_3
       (if (<= t_2 0.0)
         (/ (* x (+ y t)) z)
         (if (<= t_2 1e+289) t_3 (* 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 = t / (1.0 - z);
	double t_2 = (y / z) - t_1;
	double t_3 = ((y / z) * x) - (t_1 * x);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y / (z / x);
	} else if (t_2 <= -5e-128) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = (x * (y + t)) / z;
	} else if (t_2 <= 1e+289) {
		tmp = t_3;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

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 = t / (1.0 - z);
	double t_2 = (y / z) - t_1;
	double t_3 = ((y / z) * x) - (t_1 * x);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = y / (z / x);
	} else if (t_2 <= -5e-128) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = (x * (y + t)) / z;
	} else if (t_2 <= 1e+289) {
		tmp = t_3;
	} 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 = t / (1.0 - z)
	t_2 = (y / z) - t_1
	t_3 = ((y / z) * x) - (t_1 * x)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = y / (z / x)
	elif t_2 <= -5e-128:
		tmp = t_3
	elif t_2 <= 0.0:
		tmp = (x * (y + t)) / z
	elif t_2 <= 1e+289:
		tmp = t_3
	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(t / Float64(1.0 - z))
	t_2 = Float64(Float64(y / z) - t_1)
	t_3 = Float64(Float64(Float64(y / z) * x) - Float64(t_1 * x))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y / Float64(z / x));
	elseif (t_2 <= -5e-128)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	elseif (t_2 <= 1e+289)
		tmp = t_3;
	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 = t / (1.0 - z);
	t_2 = (y / z) - t_1;
	t_3 = ((y / z) * x) - (t_1 * x);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = y / (z / x);
	elseif (t_2 <= -5e-128)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = (x * (y + t)) / z;
	elseif (t_2 <= 1e+289)
		tmp = t_3;
	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[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / z), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision] - N[(t$95$1 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-128], t$95$3, If[LessEqual[t$95$2, 0.0], N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 1e+289], t$95$3, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Target

Original	92.4%
Target	92.9%
Herbie	98.5%

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

Derivation

1. Split input into 4 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -inf.0

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 99.6%

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

   3. Simplified 99.6%

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

      [Start] 99.6	\[ \frac{y \cdot x}{z} \]
      associate-/l* [=>] 99.6	\[ \color{blue}{\frac{y}{\frac{z}{x}}} \]

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -5.0000000000000001e-128 or 0.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 1.0000000000000001e289

   1. Initial program 99.6%

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

   2. Applied egg-rr 99.6%

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

      [Start] 99.6	\[ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
      sub-neg [=>] 99.6	\[ x \cdot \color{blue}{\left(\frac{y}{z} + \left(-\frac{t}{1 - z}\right)\right)} \]
      distribute-rgt-in [=>] 99.6	\[ \color{blue}{\frac{y}{z} \cdot x + \left(-\frac{t}{1 - z}\right) \cdot x} \]
      +-commutative [=>] 99.6	\[ \color{blue}{\left(-\frac{t}{1 - z}\right) \cdot x + \frac{y}{z} \cdot x} \]
      distribute-neg-frac [=>] 99.6	\[ \color{blue}{\frac{-t}{1 - z}} \cdot x + \frac{y}{z} \cdot x \]

   3. Taylor expanded in t around 0 86.1%

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

   4. Simplified 99.6%

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

      [Start] 86.1	\[ \frac{y \cdot x}{z} + -1 \cdot \frac{t \cdot x}{1 - z} \]
      associate-*l/ [<=] 93.5	\[ \color{blue}{\frac{y}{z} \cdot x} + -1 \cdot \frac{t \cdot x}{1 - z} \]
      associate-*l/ [<=] 99.6	\[ \frac{y}{z} \cdot x + -1 \cdot \color{blue}{\left(\frac{t}{1 - z} \cdot x\right)} \]
      *-commutative [<=] 99.6	\[ \frac{y}{z} \cdot x + -1 \cdot \color{blue}{\left(x \cdot \frac{t}{1 - z}\right)} \]
      mul-1-neg [=>] 99.6	\[ \frac{y}{z} \cdot x + \color{blue}{\left(-x \cdot \frac{t}{1 - z}\right)} \]
      sub-neg [<=] 99.6	\[ \color{blue}{\frac{y}{z} \cdot x - x \cdot \frac{t}{1 - z}} \]
      *-commutative [=>] 99.6	\[ \color{blue}{x \cdot \frac{y}{z}} - x \cdot \frac{t}{1 - z} \]

   if -5.0000000000000001e-128 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 0.0

   1. Initial program 87.9%

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

   2. Applied egg-rr 87.9%

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

      [Start] 87.9	\[ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
      sub-neg [=>] 87.9	\[ x \cdot \color{blue}{\left(\frac{y}{z} + \left(-\frac{t}{1 - z}\right)\right)} \]
      distribute-rgt-in [=>] 87.9	\[ \color{blue}{\frac{y}{z} \cdot x + \left(-\frac{t}{1 - z}\right) \cdot x} \]
      +-commutative [=>] 87.9	\[ \color{blue}{\left(-\frac{t}{1 - z}\right) \cdot x + \frac{y}{z} \cdot x} \]
      distribute-neg-frac [=>] 87.9	\[ \color{blue}{\frac{-t}{1 - z}} \cdot x + \frac{y}{z} \cdot x \]

   3. Taylor expanded in z around inf 94.1%

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

   4. Simplified 94.1%

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

      [Start] 94.1	\[ \frac{t \cdot x + y \cdot x}{z} \]
      distribute-rgt-out [=>] 94.1	\[ \frac{\color{blue}{x \cdot \left(t + y\right)}}{z} \]

   if 1.0000000000000001e289 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 24.9%

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

   2. Taylor expanded in z around 0 24.7%

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

   3. Applied egg-rr 24.6%

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

      [Start] 24.7	\[ x \cdot \left(\frac{y}{z} - t\right) \]
      flip3-- [=>] 0.0	\[ x \cdot \color{blue}{\frac{{\left(\frac{y}{z}\right)}^{3} - {t}^{3}}{\frac{y}{z} \cdot \frac{y}{z} + \left(t \cdot t + \frac{y}{z} \cdot t\right)}} \]
      associate-*r/ [=>] 0.0	\[ \color{blue}{\frac{x \cdot \left({\left(\frac{y}{z}\right)}^{3} - {t}^{3}\right)}{\frac{y}{z} \cdot \frac{y}{z} + \left(t \cdot t + \frac{y}{z} \cdot t\right)}} \]
      associate-/l* [=>] 0.0	\[ \color{blue}{\frac{x}{\frac{\frac{y}{z} \cdot \frac{y}{z} + \left(t \cdot t + \frac{y}{z} \cdot t\right)}{{\left(\frac{y}{z}\right)}^{3} - {t}^{3}}}} \]
      *-un-lft-identity [=>] 0.0	\[ \frac{x}{\frac{\color{blue}{1 \cdot \left(\frac{y}{z} \cdot \frac{y}{z} + \left(t \cdot t + \frac{y}{z} \cdot t\right)\right)}}{{\left(\frac{y}{z}\right)}^{3} - {t}^{3}}} \]
      associate-/l* [=>] 0.0	\[ \frac{x}{\color{blue}{\frac{1}{\frac{{\left(\frac{y}{z}\right)}^{3} - {t}^{3}}{\frac{y}{z} \cdot \frac{y}{z} + \left(t \cdot t + \frac{y}{z} \cdot t\right)}}}} \]
      flip3-- [<=] 24.6	\[ \frac{x}{\frac{1}{\color{blue}{\frac{y}{z} - t}}} \]

   4. Taylor expanded in y around inf 90.2%

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

   5. Simplified 90.2%

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

      [Start] 90.2	\[ \frac{y \cdot x}{z} \]
      *-commutative [=>] 90.2	\[ \frac{\color{blue}{x \cdot y}}{z} \]
      associate-/l* [=>] 23.5	\[ \color{blue}{\frac{x}{\frac{z}{y}}} \]
      associate-/r/ [=>] 90.2	\[ \color{blue}{\frac{x}{z} \cdot y} \]

3. Recombined 4 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq -5 \cdot 10^{-128}:\\ \;\;\;\;\frac{y}{z} \cdot x - \frac{t}{1 - z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 0:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 10^{+289}:\\ \;\;\;\;\frac{y}{z} \cdot x - \frac{t}{1 - z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.5%
Cost	3280

\[\begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ t_2 := t_1 \cdot x\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{elif}\;t_1 \leq 10^{+289}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 2
Accuracy	58.4%
Cost	1509

\[\begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := \frac{y}{z} \cdot x\\ t_3 := x \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -1.66 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-112}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+117} \lor \neg \left(z \leq 8.5 \cdot 10^{+191}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	58.5%
Cost	1509

\[\begin{array}{l} t_1 := \frac{y}{z} \cdot x\\ t_2 := x \cdot \left(-t\right)\\ t_3 := \frac{y}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-144}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 23000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+117} \lor \neg \left(z \leq 2.9 \cdot 10^{+193}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	57.8%
Cost	1244

\[\begin{array}{l} t_1 := x \cdot \left(-t\right)\\ t_2 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 40000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 5
Accuracy	68.7%
Cost	981

\[\begin{array}{l} t_1 := \frac{y}{z} \cdot x\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 28000000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+117} \lor \neg \left(z \leq 1.02 \cdot 10^{+192}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	68.7%
Cost	980

\[\begin{array}{l} t_1 := \frac{y}{z} \cdot x\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 42000000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 7
Accuracy	91.2%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -0.9:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{y}{z} \cdot x - t \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]

Alternative 8
Accuracy	84.3%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 820000\right):\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 9
Accuracy	85.0%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 820000\right):\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 10
Accuracy	91.4%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -24 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 11
Accuracy	91.2%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]

Alternative 12
Accuracy	48.0%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -0.0041 \lor \neg \left(z \leq 5600000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]

Alternative 13
Accuracy	20.7%
Cost	256

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

Reproduce

herbie shell --seed 2023133 
(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)))))