?

Average Error: 38.6% → 9.14%
Time: 39.5s
Precision: binary64
Cost: 33356

?

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \end{array} \]
\[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+112}:\\ \;\;\;\;\frac{x \cdot y}{\mathsf{fma}\left(0.5, \frac{a}{z \cdot z} \cdot t, -1\right)}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{\sqrt{z \cdot z - a \cdot t}}\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-210}:\\ \;\;\;\;{\left(\sqrt[3]{e^{-0.5 \cdot \left(\log \left(-t\right) - \log \left(\frac{1}{a}\right)\right)} \cdot \left(z \cdot \left(x \cdot y\right)\right)}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot {\left(1 - \frac{\frac{t}{z}}{\frac{z}{a}}\right)}^{-0.5}\right)\\ \end{array} \]
(FPCore (x y z t a)
 :precision binary64
 (/ (* (* x y) z) (sqrt (- (* z z) (* t a)))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e+112)
   (/ (* x y) (fma 0.5 (* (/ a (* z z)) t) -1.0))
   (if (<= z -2e-209)
     (* x (* y (/ z (sqrt (- (* z z) (* a t))))))
     (if (<= z 4.5e-210)
       (pow
        (cbrt (* (exp (* -0.5 (- (log (- t)) (log (/ 1.0 a))))) (* z (* x y))))
        3.0)
       (* y (* x (pow (- 1.0 (/ (/ t z) (/ z a))) -0.5)))))))
double code(double x, double y, double z, double t, double a) {
	return ((x * y) * z) / sqrt(((z * z) - (t * a)));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+112) {
		tmp = (x * y) / fma(0.5, ((a / (z * z)) * t), -1.0);
	} else if (z <= -2e-209) {
		tmp = x * (y * (z / sqrt(((z * z) - (a * t)))));
	} else if (z <= 4.5e-210) {
		tmp = pow(cbrt((exp((-0.5 * (log(-t) - log((1.0 / a))))) * (z * (x * y)))), 3.0);
	} else {
		tmp = y * (x * pow((1.0 - ((t / z) / (z / a))), -0.5));
	}
	return tmp;
}

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) * z) / sqrt(Float64(Float64(z * z) - Float64(t * a))))
end
↓
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e+112)
		tmp = Float64(Float64(x * y) / fma(0.5, Float64(Float64(a / Float64(z * z)) * t), -1.0));
	elseif (z <= -2e-209)
		tmp = Float64(x * Float64(y * Float64(z / sqrt(Float64(Float64(z * z) - Float64(a * t))))));
	elseif (z <= 4.5e-210)
		tmp = cbrt(Float64(exp(Float64(-0.5 * Float64(log(Float64(-t)) - log(Float64(1.0 / a))))) * Float64(z * Float64(x * y)))) ^ 3.0;
	else
		tmp = Float64(y * Float64(x * (Float64(1.0 - Float64(Float64(t / z) / Float64(z / a))) ^ -0.5)));
	end
	return tmp
end

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] / N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e+112], N[(N[(x * y), $MachinePrecision] / N[(0.5 * N[(N[(a / N[(z * z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-209], N[(x * N[(y * N[(z / N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-210], N[Power[N[Power[N[(N[Exp[N[(-0.5 * N[(N[Log[(-t)], $MachinePrecision] - N[Log[N[(1.0 / a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision], N[(y * N[(x * N[Power[N[(1.0 - N[(N[(t / z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -5 \cdot 10^{+112}:\\
\;\;\;\;\frac{x \cdot y}{\mathsf{fma}\left(0.5, \frac{a}{z \cdot z} \cdot t, -1\right)}\\

\mathbf{elif}\;z \leq -2 \cdot 10^{-209}:\\
\;\;\;\;x \cdot \left(y \cdot \frac{z}{\sqrt{z \cdot z - a \cdot t}}\right)\\

\mathbf{elif}\;z \leq 4.5 \cdot 10^{-210}:\\
\;\;\;\;{\left(\sqrt[3]{e^{-0.5 \cdot \left(\log \left(-t\right) - \log \left(\frac{1}{a}\right)\right)} \cdot \left(z \cdot \left(x \cdot y\right)\right)}\right)}^{3}\\

\mathbf{else}:\\
\;\;\;\;y \cdot \left(x \cdot {\left(1 - \frac{\frac{t}{z}}{\frac{z}{a}}\right)}^{-0.5}\right)\\


\end{array}

Error?

Target

Original38.6%
Target11.53%
Herbie9.14%
\[\begin{array}{l} \mathbf{if}\;z < -3.1921305903852764 \cdot 10^{+46}:\\ \;\;\;\;-y \cdot x\\ \mathbf{elif}\;z < 5.976268120920894 \cdot 10^{+90}:\\ \;\;\;\;\frac{x \cdot z}{\frac{\sqrt{z \cdot z - a \cdot t}}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Derivation?

  1. Split input into 4 regimes

  2. if z < -5e112

    1. Initial program 71.92

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

    2. Simplified68.64

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

      [Start]71.92

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

      associate-/l* [=>]68.64

      \[ \color{blue}{\frac{x \cdot y}{\frac{\sqrt{z \cdot z - t \cdot a}}{z}}} \]

    3. Taylor expanded in z around -inf 11.12

      \[\leadsto \frac{x \cdot y}{\color{blue}{0.5 \cdot \frac{a \cdot t}{{z}^{2}} - 1}} \]

    4. Simplified2.86

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

      [Start]11.12

      \[ \frac{x \cdot y}{0.5 \cdot \frac{a \cdot t}{{z}^{2}} - 1} \]

      fma-neg [=>]11.12

      \[ \frac{x \cdot y}{\color{blue}{\mathsf{fma}\left(0.5, \frac{a \cdot t}{{z}^{2}}, -1\right)}} \]

      associate-/l* [=>]2.86

      \[ \frac{x \cdot y}{\mathsf{fma}\left(0.5, \color{blue}{\frac{a}{\frac{{z}^{2}}{t}}}, -1\right)} \]

      associate-/r/ [=>]2.86

      \[ \frac{x \cdot y}{\mathsf{fma}\left(0.5, \color{blue}{\frac{a}{{z}^{2}} \cdot t}, -1\right)} \]

      unpow2 [=>]2.86

      \[ \frac{x \cdot y}{\mathsf{fma}\left(0.5, \frac{a}{\color{blue}{z \cdot z}} \cdot t, -1\right)} \]

      metadata-eval [=>]2.86

      \[ \frac{x \cdot y}{\mathsf{fma}\left(0.5, \frac{a}{z \cdot z} \cdot t, \color{blue}{-1}\right)} \]

    if -5e112 < z < -2.0000000000000001e-209

    1. Initial program 12.74

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

    2. Simplified8.7

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

      [Start]12.74

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

      associate-*r/ [<=]8.95

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

      associate-*l* [=>]8.7

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

    if -2.0000000000000001e-209 < z < 4.5000000000000002e-210

    1. Initial program 29.22

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

    2. Applied egg-rr27.96

      \[\leadsto \color{blue}{{\left(z \cdot z - t \cdot a\right)}^{-0.5} \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]

    3. Applied egg-rr29.69

      \[\leadsto \color{blue}{{\left(\sqrt[3]{{\left(z \cdot z - t \cdot a\right)}^{-0.5} \cdot \left(z \cdot \left(x \cdot y\right)\right)}\right)}^{3}} \]

    4. Taylor expanded in a around inf 22.45

      \[\leadsto {\left(\sqrt[3]{\color{blue}{e^{-0.5 \cdot \left(\log \left(-t\right) + -1 \cdot \log \left(\frac{1}{a}\right)\right)}} \cdot \left(z \cdot \left(x \cdot y\right)\right)}\right)}^{3} \]

    if 4.5000000000000002e-210 < z

    1. Initial program 40.12

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

    2. Simplified36.54

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

      [Start]40.12

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

      associate-/l* [=>]36.54

      \[ \color{blue}{\frac{x \cdot y}{\frac{\sqrt{z \cdot z - t \cdot a}}{z}}} \]

    3. Applied egg-rr47.58

      \[\leadsto \frac{x \cdot y}{\color{blue}{\sqrt{\frac{z \cdot z - t \cdot a}{z \cdot z}}}} \]

    4. Simplified10.98

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

      [Start]47.58

      \[ \frac{x \cdot y}{\sqrt{\frac{z \cdot z - t \cdot a}{z \cdot z}}} \]

      *-commutative [=>]47.58

      \[ \frac{x \cdot y}{\sqrt{\frac{z \cdot z - \color{blue}{a \cdot t}}{z \cdot z}}} \]

      div-sub [=>]50.24

      \[ \frac{x \cdot y}{\sqrt{\color{blue}{\frac{z \cdot z}{z \cdot z} - \frac{a \cdot t}{z \cdot z}}}} \]

      unpow2 [<=]50.24

      \[ \frac{x \cdot y}{\sqrt{\frac{\color{blue}{{z}^{2}}}{z \cdot z} - \frac{a \cdot t}{z \cdot z}}} \]

      unpow2 [<=]50.24

      \[ \frac{x \cdot y}{\sqrt{\frac{{z}^{2}}{\color{blue}{{z}^{2}}} - \frac{a \cdot t}{z \cdot z}}} \]

      *-inverses [=>]13.84

      \[ \frac{x \cdot y}{\sqrt{\color{blue}{1} - \frac{a \cdot t}{z \cdot z}}} \]

      unpow2 [<=]13.84

      \[ \frac{x \cdot y}{\sqrt{1 - \frac{a \cdot t}{\color{blue}{{z}^{2}}}}} \]

      associate-/l* [=>]11.39

      \[ \frac{x \cdot y}{\sqrt{1 - \color{blue}{\frac{a}{\frac{{z}^{2}}{t}}}}} \]

      associate-/r/ [=>]10.98

      \[ \frac{x \cdot y}{\sqrt{1 - \color{blue}{\frac{a}{{z}^{2}} \cdot t}}} \]

      unpow2 [=>]10.98

      \[ \frac{x \cdot y}{\sqrt{1 - \frac{a}{\color{blue}{z \cdot z}} \cdot t}} \]

    5. Applied egg-rr11.57

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

    6. Simplified10.74

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

      [Start]11.57

      \[ x \cdot \left(y \cdot {\left(1 - a \cdot \left({z}^{-2} \cdot t\right)\right)}^{-0.5}\right) \]

      associate-*r* [=>]11.78

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

      *-commutative [=>]11.78

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

      associate-*r* [<=]11.64

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

    7. Applied egg-rr8.65

      \[\leadsto y \cdot \left(x \cdot {\left(1 - \color{blue}{\frac{\frac{t}{z}}{\frac{z}{a}}}\right)}^{-0.5}\right) \]
  3. Recombined 4 regimes into one program.

  4. Final simplification9.14

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+112}:\\ \;\;\;\;\frac{x \cdot y}{\mathsf{fma}\left(0.5, \frac{a}{z \cdot z} \cdot t, -1\right)}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{\sqrt{z \cdot z - a \cdot t}}\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-210}:\\ \;\;\;\;{\left(\sqrt[3]{e^{-0.5 \cdot \left(\log \left(-t\right) - \log \left(\frac{1}{a}\right)\right)} \cdot \left(z \cdot \left(x \cdot y\right)\right)}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot {\left(1 - \frac{\frac{t}{z}}{\frac{z}{a}}\right)}^{-0.5}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error8.06%
Cost20492
\[\begin{array}{l} t_1 := \sqrt{z \cdot z - a \cdot t}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+113}:\\ \;\;\;\;\frac{x \cdot y}{\mathsf{fma}\left(0.5, \frac{a}{z \cdot z} \cdot t, -1\right)}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{t_1}\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-182}:\\ \;\;\;\;e^{-0.5 \cdot \left(\log \left(-t\right) - \log \left(\frac{1}{a}\right)\right)} \cdot \left(x \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-63}:\\ \;\;\;\;\frac{x \cdot y}{\frac{t_1}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot {\left(1 - \frac{\frac{t}{z}}{\frac{z}{a}}\right)}^{-0.5}\right)\\ \end{array} \]
Alternative 2
Error10.22%
Cost7560
\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+113}:\\ \;\;\;\;\frac{x \cdot y}{\mathsf{fma}\left(0.5, \frac{a}{z \cdot z} \cdot t, -1\right)}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{\sqrt{z \cdot z - a \cdot t}}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot {\left(1 - \frac{\frac{t}{z}}{\frac{z}{a}}\right)}^{-0.5}\right)\\ \end{array} \]
Alternative 3
Error9.22%
Cost7496
\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{\sqrt{z \cdot z - a \cdot t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{1 + -0.5 \cdot \frac{t}{\frac{z}{\frac{a}{z}}}}\\ \end{array} \]
Alternative 4
Error8.69%
Cost7496
\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{\sqrt{z \cdot z - a \cdot t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\sqrt{1 - \frac{a}{z \cdot z} \cdot t}}{x}}\\ \end{array} \]
Alternative 5
Error10.64%
Cost7496
\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-276}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{\sqrt{z \cdot z - a \cdot t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{\sqrt{1 - \frac{t}{z \cdot \frac{z}{a}}}}\\ \end{array} \]
Alternative 6
Error10.7%
Cost7496
\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+113}:\\ \;\;\;\;\frac{x \cdot y}{\mathsf{fma}\left(0.5, \frac{a}{z \cdot z} \cdot t, -1\right)}\\ \mathbf{elif}\;z \leq 10^{-275}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{\sqrt{z \cdot z - a \cdot t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{\sqrt{1 - \frac{t}{z \cdot \frac{z}{a}}}}\\ \end{array} \]
Alternative 7
Error17.63%
Cost7368
\[\begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-93}:\\ \;\;\;\;\left(x \cdot \left(z \cdot y\right)\right) \cdot {\left(a \cdot \left(-t\right)\right)}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{z + -0.5 \cdot \frac{a}{\frac{z}{t}}}\right)\\ \end{array} \]
Alternative 8
Error18.15%
Cost7304
\[\begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{\sqrt{a \cdot \left(-t\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{z + -0.5 \cdot \frac{a}{\frac{z}{t}}}\right)\\ \end{array} \]
Alternative 9
Error17.92%
Cost7304
\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-142}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \frac{y}{\sqrt{a \cdot \left(-t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{z + -0.5 \cdot \frac{a}{\frac{z}{t}}}\right)\\ \end{array} \]
Alternative 10
Error25.49%
Cost1096
\[\begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-164}:\\ \;\;\;\;2 \cdot \left(\frac{y}{t} \cdot \left(\frac{z}{a} \cdot \left(z \cdot x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 11
Error25.4%
Cost1096
\[\begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-165}:\\ \;\;\;\;z \cdot \left(x \cdot \left(\frac{y}{\frac{a}{z}} \cdot \frac{2}{t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 12
Error25.41%
Cost1096
\[\begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-163}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y \cdot \frac{\frac{z}{a} \cdot 2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 13
Error25.4%
Cost1096
\[\begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-164}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot \left(z \cdot 2\right)\right)}{t \cdot \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 14
Error23.48%
Cost1092
\[\begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{z + -0.5 \cdot \frac{a}{\frac{z}{t}}}\right)\\ \end{array} \]
Alternative 15
Error22.99%
Cost1092
\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{0.5 \cdot \frac{a \cdot t}{z} - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{z}{z + -0.5 \cdot \frac{a}{\frac{z}{t}}}\right)\\ \end{array} \]
Alternative 16
Error26.11%
Cost840
\[\begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-164}:\\ \;\;\;\;\left(x \cdot \left(z \cdot y\right)\right) \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 17
Error28.57%
Cost712
\[\begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-167}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 18
Error28.58%
Cost712
\[\begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-166}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 19
Error26.03%
Cost712
\[\begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-129}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 20
Error29.3%
Cost388
\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-310}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 21
Error57.67%
Cost192
\[x \cdot y \]

Error

Reproduce?

herbie shell --seed 2023121 
(FPCore (x y z t a)
  :name "Statistics.Math.RootFinding:ridders from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< z -3.1921305903852764e+46) (- (* y x)) (if (< z 5.976268120920894e+90) (/ (* x z) (/ (sqrt (- (* z z) (* a t))) y)) (* y x)))

  (/ (* (* x y) z) (sqrt (- (* z z) (* t a)))))