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

Average Accuracy: 92.5% → 99.2%

Time: 14.8s

Precision: binary64

Cost: 3280

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y}{\frac{z}{x}}\\ t_2 := \frac{y}{z} - \frac{t}{1 - z}\\ t_3 := t_2 \cdot x\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-172}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 10^{-311}:\\ \;\;\;\;y \cdot \frac{x}{z} + t \cdot \frac{x}{z}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 x))) (t_2 (- (/ y z) (/ t (- 1.0 z)))) (t_3 (* t_2 x)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-172)
       t_3
       (if (<= t_2 1e-311)
         (+ (* y (/ x z)) (* t (/ x z)))
         (if (<= t_2 5e+299) t_3 t_1))))))

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 / x);
	double t_2 = (y / z) - (t / (1.0 - z));
	double t_3 = t_2 * x;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-172) {
		tmp = t_3;
	} else if (t_2 <= 1e-311) {
		tmp = (y * (x / z)) + (t * (x / z));
	} else if (t_2 <= 5e+299) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	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 = y / (z / x);
	double t_2 = (y / z) - (t / (1.0 - z));
	double t_3 = t_2 * x;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-172) {
		tmp = t_3;
	} else if (t_2 <= 1e-311) {
		tmp = (y * (x / z)) + (t * (x / z));
	} else if (t_2 <= 5e+299) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	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 / x)
	t_2 = (y / z) - (t / (1.0 - z))
	t_3 = t_2 * x
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-172:
		tmp = t_3
	elif t_2 <= 1e-311:
		tmp = (y * (x / z)) + (t * (x / z))
	elif t_2 <= 5e+299:
		tmp = t_3
	else:
		tmp = t_1
	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(y / Float64(z / x))
	t_2 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	t_3 = Float64(t_2 * x)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-172)
		tmp = t_3;
	elseif (t_2 <= 1e-311)
		tmp = Float64(Float64(y * Float64(x / z)) + Float64(t * Float64(x / z)));
	elseif (t_2 <= 5e+299)
		tmp = t_3;
	else
		tmp = t_1;
	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 / x);
	t_2 = (y / z) - (t / (1.0 - z));
	t_3 = t_2 * x;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-172)
		tmp = t_3;
	elseif (t_2 <= 1e-311)
		tmp = (y * (x / z)) + (t * (x / z));
	elseif (t_2 <= 5e+299)
		tmp = t_3;
	else
		tmp = t_1;
	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[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * x), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-172], t$95$3, If[LessEqual[t$95$2, 1e-311], N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+299], t$95$3, t$95$1]]]]]]]

Target

Original	92.5%
Target	93.2%
Herbie	99.2%

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

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -inf.0 or 5.0000000000000003e299 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 5.1%

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

   2. Applied egg-rr 5.1%

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

      [Start] 5.1	\[ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
      frac-2neg [=>] 5.1	\[ x \cdot \left(\color{blue}{\frac{-y}{-z}} - \frac{t}{1 - z}\right) \]
      div-inv [=>] 5.1	\[ x \cdot \left(\color{blue}{\left(-y\right) \cdot \frac{1}{-z}} - \frac{t}{1 - z}\right) \]
      fma-neg [=>] 5.1	\[ x \cdot \color{blue}{\mathsf{fma}\left(-y, \frac{1}{-z}, -\frac{t}{1 - z}\right)} \]
      distribute-neg-frac [=>] 5.1	\[ x \cdot \mathsf{fma}\left(-y, \frac{1}{-z}, \color{blue}{\frac{-t}{1 - z}}\right) \]

   3. Simplified 5.1%

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

      [Start] 5.1	\[ x \cdot \mathsf{fma}\left(-y, \frac{1}{-z}, \frac{-t}{1 - z}\right) \]
      fma-udef [=>] 5.1	\[ x \cdot \color{blue}{\left(\left(-y\right) \cdot \frac{1}{-z} + \frac{-t}{1 - z}\right)} \]
      +-commutative [=>] 5.1	\[ x \cdot \color{blue}{\left(\frac{-t}{1 - z} + \left(-y\right) \cdot \frac{1}{-z}\right)} \]
      distribute-lft-neg-out [=>] 5.1	\[ x \cdot \left(\frac{-t}{1 - z} + \color{blue}{\left(-y \cdot \frac{1}{-z}\right)}\right) \]
      unsub-neg [=>] 5.1	\[ x \cdot \color{blue}{\left(\frac{-t}{1 - z} - y \cdot \frac{1}{-z}\right)} \]
      neg-mul-1 [=>] 5.1	\[ x \cdot \left(\frac{\color{blue}{-1 \cdot t}}{1 - z} - y \cdot \frac{1}{-z}\right) \]
      *-commutative [=>] 5.1	\[ x \cdot \left(\frac{\color{blue}{t \cdot -1}}{1 - z} - y \cdot \frac{1}{-z}\right) \]
      associate-*r/ [<=] 5.1	\[ x \cdot \left(\color{blue}{t \cdot \frac{-1}{1 - z}} - y \cdot \frac{1}{-z}\right) \]
      metadata-eval [<=] 5.1	\[ x \cdot \left(t \cdot \frac{\color{blue}{\frac{1}{-1}}}{1 - z} - y \cdot \frac{1}{-z}\right) \]
      associate-/r* [<=] 5.1	\[ x \cdot \left(t \cdot \color{blue}{\frac{1}{-1 \cdot \left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]
      neg-mul-1 [<=] 5.1	\[ x \cdot \left(t \cdot \frac{1}{\color{blue}{-\left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]
      associate-*r/ [=>] 5.1	\[ x \cdot \left(\color{blue}{\frac{t \cdot 1}{-\left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]
      *-rgt-identity [=>] 5.1	\[ x \cdot \left(\frac{\color{blue}{t}}{-\left(1 - z\right)} - y \cdot \frac{1}{-z}\right) \]
      neg-sub0 [=>] 5.1	\[ x \cdot \left(\frac{t}{\color{blue}{0 - \left(1 - z\right)}} - y \cdot \frac{1}{-z}\right) \]
      associate--r- [=>] 5.1	\[ x \cdot \left(\frac{t}{\color{blue}{\left(0 - 1\right) + z}} - y \cdot \frac{1}{-z}\right) \]
      metadata-eval [=>] 5.1	\[ x \cdot \left(\frac{t}{\color{blue}{-1} + z} - y \cdot \frac{1}{-z}\right) \]
      neg-mul-1 [=>] 5.1	\[ x \cdot \left(\frac{t}{-1 + z} - y \cdot \frac{1}{\color{blue}{-1 \cdot z}}\right) \]
      associate-/r* [=>] 5.1	\[ x \cdot \left(\frac{t}{-1 + z} - y \cdot \color{blue}{\frac{\frac{1}{-1}}{z}}\right) \]
      metadata-eval [=>] 5.1	\[ x \cdot \left(\frac{t}{-1 + z} - y \cdot \frac{\color{blue}{-1}}{z}\right) \]

   4. Taylor expanded in t around 0 97.2%

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

   5. Simplified 97.2%

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

      [Start] 97.2	\[ \frac{y \cdot x}{z} \]
      associate-/l* [=>] 97.2	\[ \color{blue}{\frac{y}{\frac{z}{x}}} \]

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -2.0000000000000001e-172 or 9.99999999999948e-312 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 5.0000000000000003e299

   1. Initial program 99.7%

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

   if -2.0000000000000001e-172 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 9.99999999999948e-312

   1. Initial program 82.7%

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

   2. Taylor expanded in z around inf 97.3%

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

   3. Simplified 78.8%

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

      [Start] 97.3	\[ \frac{\left(y - -1 \cdot t\right) \cdot x}{z} \]
      *-commutative [<=] 97.3	\[ \frac{\color{blue}{x \cdot \left(y - -1 \cdot t\right)}}{z} \]
      associate-/l* [=>] 78.8	\[ \color{blue}{\frac{x}{\frac{z}{y - -1 \cdot t}}} \]
      neg-mul-1 [<=] 78.8	\[ \frac{x}{\frac{z}{y - \color{blue}{\left(-t\right)}}} \]

   4. Applied egg-rr 96.7%

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

      [Start] 78.8	\[ \frac{x}{\frac{z}{y - \left(-t\right)}} \]
      associate-/r/ [=>] 96.7	\[ \color{blue}{\frac{x}{z} \cdot \left(y - \left(-t\right)\right)} \]
      sub-neg [=>] 96.7	\[ \frac{x}{z} \cdot \color{blue}{\left(y + \left(-\left(-t\right)\right)\right)} \]
      remove-double-neg [=>] 96.7	\[ \frac{x}{z} \cdot \left(y + \color{blue}{t}\right) \]
      distribute-lft-in [=>] 96.7	\[ \color{blue}{\frac{x}{z} \cdot y + \frac{x}{z} \cdot t} \]

3. Recombined 3 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq -2 \cdot 10^{-172}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 10^{-311}:\\ \;\;\;\;y \cdot \frac{x}{z} + t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.2%
Cost	3280

\[\begin{array}{l} t_1 := \frac{y}{\frac{z}{x}}\\ t_2 := \frac{y}{z} - \frac{t}{1 - z}\\ t_3 := t_2 \cdot x\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-172}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 10^{-311}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	56.7%
Cost	1244

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{+185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -55000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-275}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+19}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	67.6%
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -880000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{-269}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-307}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 8.5:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	67.8%
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z + -1}\\ t_2 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+44}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -4400000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-268}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-306}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 0.0076:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	58.0%
Cost	1112

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -39000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	58.3%
Cost	1112

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := \frac{y}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -225000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	58.4%
Cost	1112

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -900000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+21}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	85.6%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ t_2 := \frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-304}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	91.6%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.00046\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 10
Accuracy	44.2%
Cost	585

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

Alternative 11
Accuracy	47.1%
Cost	585

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

Alternative 12
Accuracy	20.6%
Cost	256

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

Reproduce

herbie shell --seed 2023147 
(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)))))