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

Average Error: 4.6 → 0.3

Time: 19.2s

Precision: binary64

Cost: 3664

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-197}:\\ \;\;\;\;x \cdot t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+276}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \left(y \cdot \frac{2}{z} - \frac{t}{\frac{1 - z}{2}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z} + -1 \cdot \frac{t \cdot x}{1 - z}\\ \end{array} \]

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)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ x z))
     (if (<= t_1 -5e-197)
       (* x t_1)
       (if (<= t_1 0.0)
         (/ (+ y t) (/ z x))
         (if (<= t_1 2e+276)
           (* x (* 0.5 (- (* y (/ 2.0 z)) (/ t (/ (- 1.0 z) 2.0)))))
           (+ (/ (* y x) z) (* -1.0 (/ (* t x) (- 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 tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (x / z);
	} else if (t_1 <= -5e-197) {
		tmp = x * t_1;
	} else if (t_1 <= 0.0) {
		tmp = (y + t) / (z / x);
	} else if (t_1 <= 2e+276) {
		tmp = x * (0.5 * ((y * (2.0 / z)) - (t / ((1.0 - z) / 2.0))));
	} else {
		tmp = ((y * x) / z) + (-1.0 * ((t * x) / (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 tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x / z);
	} else if (t_1 <= -5e-197) {
		tmp = x * t_1;
	} else if (t_1 <= 0.0) {
		tmp = (y + t) / (z / x);
	} else if (t_1 <= 2e+276) {
		tmp = x * (0.5 * ((y * (2.0 / z)) - (t / ((1.0 - z) / 2.0))));
	} else {
		tmp = ((y * x) / z) + (-1.0 * ((t * x) / (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))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (x / z)
	elif t_1 <= -5e-197:
		tmp = x * t_1
	elif t_1 <= 0.0:
		tmp = (y + t) / (z / x)
	elif t_1 <= 2e+276:
		tmp = x * (0.5 * ((y * (2.0 / z)) - (t / ((1.0 - z) / 2.0))))
	else:
		tmp = ((y * x) / z) + (-1.0 * ((t * x) / (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)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(x / z));
	elseif (t_1 <= -5e-197)
		tmp = Float64(x * t_1);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(y + t) / Float64(z / x));
	elseif (t_1 <= 2e+276)
		tmp = Float64(x * Float64(0.5 * Float64(Float64(y * Float64(2.0 / z)) - Float64(t / Float64(Float64(1.0 - z) / 2.0)))));
	else
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-1.0 * Float64(Float64(t * x) / 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));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (x / z);
	elseif (t_1 <= -5e-197)
		tmp = x * t_1;
	elseif (t_1 <= 0.0)
		tmp = (y + t) / (z / x);
	elseif (t_1 <= 2e+276)
		tmp = x * (0.5 * ((y * (2.0 / z)) - (t / ((1.0 - z) / 2.0))));
	else
		tmp = ((y * x) / z) + (-1.0 * ((t * x) / (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]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-197], N[(x * t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(y + t), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+276], N[(x * N[(0.5 * N[(N[(y * N[(2.0 / z), $MachinePrecision]), $MachinePrecision] - N[(t / N[(N[(1.0 - z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + N[(-1.0 * N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	4.6
Target	4.2
Herbie	0.3

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

Derivation

1. Split input into 5 regimes

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

   1. Initial program 64.0

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

   2. Taylor expanded in y around inf 0.3

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

   3. Simplified 0.3

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

      [Start] 0.3	\[ \frac{y \cdot x}{z} \]
      rational.json-simplify-2 [=>] 0.3	\[ \frac{\color{blue}{x \cdot y}}{z} \]
      rational.json-simplify-49 [=>] 0.3	\[ \color{blue}{y \cdot \frac{x}{z}} \]

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -5.0000000000000002e-197

   1. Initial program 0.2

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

   if -5.0000000000000002e-197 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 0.0

   1. Initial program 13.4

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

   2. Taylor expanded in z around inf 1.5

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

   3. Simplified 13.6

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

      [Start] 1.5	\[ \frac{\left(y - -1 \cdot t\right) \cdot x}{z} \]
      rational.json-simplify-49 [=>] 13.6	\[ \color{blue}{x \cdot \frac{y - -1 \cdot t}{z}} \]
      rational.json-simplify-2 [=>] 13.6	\[ x \cdot \frac{y - \color{blue}{t \cdot -1}}{z} \]
      rational.json-simplify-8 [<=] 13.6	\[ x \cdot \frac{y - \color{blue}{\left(-t\right)}}{z} \]

   4. Applied egg-rr 1.2

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

   if 0.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 2.0000000000000001e276

   1. Initial program 0.3

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

   2. Applied egg-rr 0.3

      \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \left(y \cdot \frac{2}{z} - t \cdot \frac{2}{1 - z}\right)\right)} \]

   3. Simplified 0.3

      \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \left(y \cdot \frac{2}{z} - \frac{t}{\frac{1 - z}{2}}\right)\right)} \]
      Proof

      [Start] 0.3	\[ x \cdot \left(0.5 \cdot \left(y \cdot \frac{2}{z} - t \cdot \frac{2}{1 - z}\right)\right) \]
      rational.json-simplify-2 [=>] 0.3	\[ x \cdot \left(0.5 \cdot \left(y \cdot \frac{2}{z} - \color{blue}{\frac{2}{1 - z} \cdot t}\right)\right) \]
      rational.json-simplify-7 [<=] 0.3	\[ x \cdot \left(0.5 \cdot \left(y \cdot \frac{2}{z} - \frac{2}{1 - z} \cdot \color{blue}{\frac{t}{1}}\right)\right) \]
      rational.json-simplify-35 [=>] 0.3	\[ x \cdot \left(0.5 \cdot \left(y \cdot \frac{2}{z} - \frac{2}{1 - z} \cdot \color{blue}{\frac{t + t}{1 + 1}}\right)\right) \]
      metadata-eval [=>] 0.3	\[ x \cdot \left(0.5 \cdot \left(y \cdot \frac{2}{z} - \frac{2}{1 - z} \cdot \frac{t + t}{\color{blue}{2}}\right)\right) \]
      rational.json-simplify-55 [=>] 0.3	\[ x \cdot \left(0.5 \cdot \left(y \cdot \frac{2}{z} - \color{blue}{\frac{\frac{t + t}{2}}{\frac{1 - z}{2}}}\right)\right) \]
      metadata-eval [<=] 0.3	\[ x \cdot \left(0.5 \cdot \left(y \cdot \frac{2}{z} - \frac{\frac{t + t}{\color{blue}{1 + 1}}}{\frac{1 - z}{2}}\right)\right) \]
      rational.json-simplify-35 [<=] 0.3	\[ x \cdot \left(0.5 \cdot \left(y \cdot \frac{2}{z} - \frac{\color{blue}{\frac{t}{1}}}{\frac{1 - z}{2}}\right)\right) \]
      rational.json-simplify-7 [=>] 0.3	\[ x \cdot \left(0.5 \cdot \left(y \cdot \frac{2}{z} - \frac{\color{blue}{t}}{\frac{1 - z}{2}}\right)\right) \]

   if 2.0000000000000001e276 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 39.5

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

   2. Taylor expanded in y around 0 0.2

      \[\leadsto \color{blue}{\frac{y \cdot x}{z} + -1 \cdot \frac{t \cdot x}{1 - z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq -5 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 0:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 2 \cdot 10^{+276}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \left(y \cdot \frac{2}{z} - \frac{t}{\frac{1 - z}{2}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z} + -1 \cdot \frac{t \cdot x}{1 - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.3
Cost	3536

\[\begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ t_2 := x \cdot t_1\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+276}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z} + -1 \cdot \frac{t \cdot x}{1 - z}\\ \end{array} \]

Alternative 2
Error	0.8
Cost	3280

\[\begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ t_2 := x \cdot t_1\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+277}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Alternative 3
Error	28.3
Cost	1376

\[\begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := x \cdot \frac{t}{z}\\ t_3 := x \cdot \frac{y}{z}\\ t_4 := x \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+261}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-166}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-263}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	28.1
Cost	1376

\[\begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := x \cdot \frac{y}{z}\\ t_3 := x \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+262}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{+129}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-104}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-166}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 5
Error	28.1
Cost	1376

\[\begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ t_2 := x \cdot \left(-t\right)\\ t_3 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+262}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+132}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-120}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+192}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 6
Error	28.0
Cost	1376

\[\begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ t_2 := x \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+263}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+128}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+192}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 7
Error	27.7
Cost	1112

\[\begin{array}{l} t_1 := \frac{y \cdot x}{z}\\ t_2 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+266}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+136}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 8
Error	28.5
Cost	980

\[\begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ t_2 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	27.5
Cost	980

\[\begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+262}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+129}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+193}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 10
Error	16.2
Cost	976

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z + -1}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 10^{+25}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	15.5
Cost	976

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z + -1}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{y + t}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	5.6
Cost	776

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{y + t}}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.00062:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	11.7
Cost	712

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{y + t}}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.00062:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	35.4
Cost	584

\[\begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -11500000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.00062:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	33.4
Cost	584

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -11500000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.00062:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	51.0
Cost	256

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

Reproduce

herbie shell --seed 2023074 
(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)))))