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

Average Error: 4.4 → 0.6

Time: 11.7s

Precision: binary64

Cost: 3280

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ t_2 := t_1 \cdot x\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{1}{z} \cdot \frac{x}{\frac{1}{y}}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-262}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;t_1 \leq 10^{+206}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} - t \cdot x\\ \end{array} \]

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 (- INFINITY))
     (* (/ 1.0 z) (/ x (/ 1.0 y)))
     (if (<= t_1 -2e-262)
       t_2
       (if (<= t_1 5e-208)
         (* (/ x z) (+ y t))
         (if (<= t_1 1e+206) 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 <= -((double) INFINITY)) {
		tmp = (1.0 / z) * (x / (1.0 / y));
	} else if (t_1 <= -2e-262) {
		tmp = t_2;
	} else if (t_1 <= 5e-208) {
		tmp = (x / z) * (y + t);
	} else if (t_1 <= 1e+206) {
		tmp = t_2;
	} else {
		tmp = (y / (z / x)) - (t * x);
	}
	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 = (1.0 / z) * (x / (1.0 / y));
	} else if (t_1 <= -2e-262) {
		tmp = t_2;
	} else if (t_1 <= 5e-208) {
		tmp = (x / z) * (y + t);
	} else if (t_1 <= 1e+206) {
		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 <= -math.inf:
		tmp = (1.0 / z) * (x / (1.0 / y))
	elif t_1 <= -2e-262:
		tmp = t_2
	elif t_1 <= 5e-208:
		tmp = (x / z) * (y + t)
	elif t_1 <= 1e+206:
		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 <= Float64(-Inf))
		tmp = Float64(Float64(1.0 / z) * Float64(x / Float64(1.0 / y)));
	elseif (t_1 <= -2e-262)
		tmp = t_2;
	elseif (t_1 <= 5e-208)
		tmp = Float64(Float64(x / z) * Float64(y + t));
	elseif (t_1 <= 1e+206)
		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 <= -Inf)
		tmp = (1.0 / z) * (x / (1.0 / y));
	elseif (t_1 <= -2e-262)
		tmp = t_2;
	elseif (t_1 <= 5e-208)
		tmp = (x / z) * (y + t);
	elseif (t_1 <= 1e+206)
		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, (-Infinity)], N[(N[(1.0 / z), $MachinePrecision] * N[(x / N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-262], t$95$2, If[LessEqual[t$95$1, 5e-208], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+206], t$95$2, N[(N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	4.4
Target	4.0
Herbie	0.6

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

Derivation

1. Split input into 4 regimes

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

   1. Initial program 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 64.0

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]
      Proof
      (*.f64 (/.f64 y z) x): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 y x) z)): 48 points increase in error, 55 points decrease in error

   4. Applied egg-rr 58.9

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

   5. Applied egg-rr 0.5

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -2.00000000000000002e-262 or 4.99999999999999963e-208 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 1e206

   1. Initial program 0.2

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

   if -2.00000000000000002e-262 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 4.99999999999999963e-208

   1. Initial program 11.2

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

   2. Taylor expanded in z around inf 0.8

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

   3. Simplified 0.8

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + t\right)} \]
      Proof
      (*.f64 (/.f64 x z) (+.f64 y t)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 x z) (+.f64 y (Rewrite<= *-lft-identity_binary64 (*.f64 1 t)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 x z) (+.f64 y (*.f64 (Rewrite<= metadata-eval (neg.f64 -1)) t))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 x z) (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 y (*.f64 -1 t)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 x (/.f64 z (-.f64 y (*.f64 -1 t))))): 59 points increase in error, 57 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 x (-.f64 y (*.f64 -1 t))) z)): 66 points increase in error, 56 points decrease in error
      (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 y (*.f64 -1 t)) x)) z): 0 points increase in error, 0 points decrease in error

   if 1e206 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 19.0

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

   2. Taylor expanded in z around 0 3.8

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

   3. Simplified 22.0

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x + \left(-t\right) \cdot x} \]
      Proof
      (+.f64 (*.f64 (/.f64 y z) x) (*.f64 (neg.f64 t) x)): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 y x) z)) (*.f64 (neg.f64 t) x)): 27 points increase in error, 26 points decrease in error
      (+.f64 (/.f64 (*.f64 y x) z) (*.f64 (Rewrite=> neg-mul-1_binary64 (*.f64 -1 t)) x)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 y x) z) (Rewrite<= associate-*r*_binary64 (*.f64 -1 (*.f64 t x)))): 0 points increase in error, 0 points decrease in error

   4. Taylor expanded in y around 0 3.8

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

   5. Simplified 4.0

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}} - t \cdot x} \]
      Proof
      (-.f64 (/.f64 y (/.f64 z x)) (*.f64 t x)): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 y z) x)) (*.f64 t x)): 29 points increase in error, 30 points decrease in error
      (Rewrite=> cancel-sign-sub-inv_binary64 (+.f64 (*.f64 (/.f64 y z) x) (*.f64 (neg.f64 t) x))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 y x) z)) (*.f64 (neg.f64 t) x)): 27 points increase in error, 26 points decrease in error
      (+.f64 (/.f64 (*.f64 y x) z) (*.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 t)) x)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 y x) z) (Rewrite<= associate-*r*_binary64 (*.f64 -1 (*.f64 t x)))): 0 points increase in error, 0 points decrease in error
3. Recombined 4 regimes into one program.

4. Final simplification 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -\infty:\\ \;\;\;\;\frac{1}{z} \cdot \frac{x}{\frac{1}{y}}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq -2 \cdot 10^{-262}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 5 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 10^{+206}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} - t \cdot x\\ \end{array} \]

Alternatives

Alternative 1
Error	27.1
Cost	1244

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 700000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	28.2
Cost	1112

\[\begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := t \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+196}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	27.0
Cost	1112

\[\begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+168}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+133}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 4
Error	26.9
Cost	1112

\[\begin{array}{l} \mathbf{if}\;z \leq -1.72 \cdot 10^{+170}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 5
Error	26.2
Cost	1112

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-66}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	26.8
Cost	1112

\[\begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+169}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-48}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 7
Error	5.1
Cost	1104

\[\begin{array}{l} t_1 := \frac{y}{\frac{z}{x}} - t \cdot x\\ t_2 := \frac{x}{\frac{z}{y + t}}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 16500000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	19.8
Cost	976

\[\begin{array}{l} t_1 := \frac{y \cdot x}{z}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{-96}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	19.3
Cost	976

\[\begin{array}{l} t_1 := \frac{y \cdot x}{z}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	22.8
Cost	716

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -1.18 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+154}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	22.8
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -1.58 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+154}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 12
Error	9.1
Cost	712

\[\begin{array}{l} t_1 := \frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	5.2
Cost	712

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{y + t}}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 16500000000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	35.4
Cost	584

\[\begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	50.6
Cost	256

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

Reproduce

herbie shell --seed 2022325 
(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)))))