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

Average Accuracy: 92.2% → 99.0%

Time: 15.9s

Precision: binary64

Cost: 3664

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ t_2 := t_1 \cdot x\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;t_1 \leq 10^{+229}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \end{array} \]

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 (- INFINITY))
     (/ y (/ z x))
     (if (<= t_1 -4e-184)
       t_2
       (if (<= t_1 0.0)
         (* (/ x z) (+ y t))
         (if (<= t_1 1e+229)
           t_2
           (/ (* x (- (* y (- 1.0 z)) (* z t))) (* z (- 1.0 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 <= -((double) INFINITY)) {
		tmp = y / (z / x);
	} else if (t_1 <= -4e-184) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = (x / z) * (y + t);
	} else if (t_1 <= 1e+229) {
		tmp = t_2;
	} else {
		tmp = (x * ((y * (1.0 - z)) - (z * t))) / (z * (1.0 - 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 = (y / z) - (t / (1.0 - z));
	double t_2 = t_1 * x;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y / (z / x);
	} else if (t_1 <= -4e-184) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = (x / z) * (y + t);
	} else if (t_1 <= 1e+229) {
		tmp = t_2;
	} else {
		tmp = (x * ((y * (1.0 - z)) - (z * t))) / (z * (1.0 - 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 <= -math.inf:
		tmp = y / (z / x)
	elif t_1 <= -4e-184:
		tmp = t_2
	elif t_1 <= 0.0:
		tmp = (x / z) * (y + t)
	elif t_1 <= 1e+229:
		tmp = t_2
	else:
		tmp = (x * ((y * (1.0 - z)) - (z * t))) / (z * (1.0 - 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 <= Float64(-Inf))
		tmp = Float64(y / Float64(z / x));
	elseif (t_1 <= -4e-184)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(x / z) * Float64(y + t));
	elseif (t_1 <= 1e+229)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * Float64(Float64(y * Float64(1.0 - z)) - Float64(z * t))) / Float64(z * Float64(1.0 - 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 <= -Inf)
		tmp = y / (z / x);
	elseif (t_1 <= -4e-184)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = (x / z) * (y + t);
	elseif (t_1 <= 1e+229)
		tmp = t_2;
	else
		tmp = (x * ((y * (1.0 - z)) - (z * t))) / (z * (1.0 - 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, (-Infinity)], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e-184], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+229], t$95$2, N[(N[(x * N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	92.2%
Target	92.8%
Herbie	99.0%

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

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 99.5%

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

   3. Simplified 0.0%

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

      [Start] 99.5	\[ \frac{y \cdot x}{z} \]
      associate-*l/ [<=] 0.0	\[ \color{blue}{\frac{y}{z} \cdot x} \]

   4. Applied egg-rr 99.5%

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

      [Start] 0.0	\[ \frac{y}{z} \cdot x \]
      associate-*l/ [=>] 99.5	\[ \color{blue}{\frac{y \cdot x}{z}} \]
      associate-/l* [=>] 99.5	\[ \color{blue}{\frac{y}{\frac{z}{x}}} \]

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -4.0000000000000002e-184 or 0.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 9.9999999999999999e228

   1. Initial program 99.6%

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

   if -4.0000000000000002e-184 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 0.0

   1. Initial program 83.2%

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

   2. Taylor expanded in z around inf 96.9%

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

   3. Simplified 97.4%

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

      [Start] 96.9	\[ \frac{\left(y - -1 \cdot t\right) \cdot x}{z} \]
      associate-/l* [=>] 97.4	\[ \color{blue}{\frac{y - -1 \cdot t}{\frac{z}{x}}} \]
      mul-1-neg [=>] 97.4	\[ \frac{y - \color{blue}{\left(-t\right)}}{\frac{z}{x}} \]

   4. Applied egg-rr 97.7%

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

      [Start] 97.4	\[ \frac{y - \left(-t\right)}{\frac{z}{x}} \]
      div-inv [=>] 97.4	\[ \color{blue}{\left(y - \left(-t\right)\right) \cdot \frac{1}{\frac{z}{x}}} \]
      *-commutative [=>] 97.4	\[ \color{blue}{\frac{1}{\frac{z}{x}} \cdot \left(y - \left(-t\right)\right)} \]
      clear-num [<=] 97.7	\[ \color{blue}{\frac{x}{z}} \cdot \left(y - \left(-t\right)\right) \]
      neg-mul-1 [=>] 97.7	\[ \frac{x}{z} \cdot \left(y - \color{blue}{-1 \cdot t}\right) \]
      cancel-sign-sub-inv [=>] 97.7	\[ \frac{x}{z} \cdot \color{blue}{\left(y + \left(--1\right) \cdot t\right)} \]
      metadata-eval [=>] 97.7	\[ \frac{x}{z} \cdot \left(y + \color{blue}{1} \cdot t\right) \]
      *-un-lft-identity [<=] 97.7	\[ \frac{x}{z} \cdot \left(y + \color{blue}{t}\right) \]

   if 9.9999999999999999e228 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 57.1%

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

   2. Applied egg-rr 94.3%

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

      [Start] 57.1	\[ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
      *-commutative [=>] 57.1	\[ \color{blue}{\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x} \]
      frac-sub [=>] 53.0	\[ \color{blue}{\frac{y \cdot \left(1 - z\right) - z \cdot t}{z \cdot \left(1 - z\right)}} \cdot x \]
      associate-*l/ [=>] 94.3	\[ \color{blue}{\frac{\left(y \cdot \left(1 - z\right) - z \cdot t\right) \cdot x}{z \cdot \left(1 - z\right)}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq -4 \cdot 10^{-184}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 0:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 10^{+229}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.2%
Cost	3408

\[\begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ t_2 := t_1 \cdot x\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;t_1 \leq 10^{+269}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z}\\ \end{array} \]

Alternative 2
Accuracy	99.3%
Cost	3280

\[\begin{array}{l} t_1 := \frac{y}{\frac{z}{x}}\\ t_2 := \frac{y}{z} - \frac{t}{1 - z}\\ t_3 := t_2 \cdot x\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-184}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;t_2 \leq 10^{+303}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	58.6%
Cost	1376

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{y}}\\ t_2 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -5.7 \cdot 10^{+256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+196}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 4
Accuracy	67.6%
Cost	1240

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{y}}\\ t_2 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+163}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-234}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 5
Accuracy	65.0%
Cost	1112

\[\begin{array}{l} t_1 := \frac{y}{z} \cdot x\\ \mathbf{if}\;t \leq -8 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+26}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-152}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 6
Accuracy	74.2%
Cost	1108

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z + -1}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-151}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	88.3%
Cost	1104

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{y + t}}\\ \mathbf{if}\;z \leq -13.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-229}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{z} \cdot x - t \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	82.8%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ t_2 := \frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{if}\;z \leq -13.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-228}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	88.3%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ t_2 := \frac{x}{\frac{z}{y + t}}\\ \mathbf{if}\;z \leq -13.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-224}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	64.9%
Cost	716

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -2.45 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	64.9%
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 12
Accuracy	64.9%
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-152}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 13
Accuracy	57.4%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-208} \lor \neg \left(y \leq 1.32 \cdot 10^{-134}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 14
Accuracy	64.5%
Cost	585

\[\begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+84} \lor \neg \left(t \leq 3 \cdot 10^{+87}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 15
Accuracy	21.1%
Cost	256

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

Reproduce

herbie shell --seed 2023140 
(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)))))