Average Error: 0.3 → 0.3
Time: 7.8s
Precision: binary64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]
↓
\[\left(x \cdot 0.5\right) \cdot \sqrt{\left(z \cdot 2\right) \cdot {\left(e^{t}\right)}^{t}} - y \cdot \sqrt{\left(z \cdot 2\right) \cdot \sqrt[3]{e^{3 \cdot \left(t \cdot t\right)}}} \]
(FPCore (x y z t)
 :precision binary64
 (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))
↓
(FPCore (x y z t)
 :precision binary64
 (-
  (* (* x 0.5) (sqrt (* (* z 2.0) (pow (exp t) t))))
  (* y (sqrt (* (* z 2.0) (cbrt (exp (* 3.0 (* t t)))))))))
double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
}
↓
double code(double x, double y, double z, double t) {
	return ((x * 0.5) * sqrt(((z * 2.0) * pow(exp(t), t)))) - (y * sqrt(((z * 2.0) * cbrt(exp((3.0 * (t * t)))))));
}

public static double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * Math.sqrt((z * 2.0))) * Math.exp(((t * t) / 2.0));
}
↓
public static double code(double x, double y, double z, double t) {
	return ((x * 0.5) * Math.sqrt(((z * 2.0) * Math.pow(Math.exp(t), t)))) - (y * Math.sqrt(((z * 2.0) * Math.cbrt(Math.exp((3.0 * (t * t)))))));
}

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * 0.5) - y) * sqrt(Float64(z * 2.0))) * exp(Float64(Float64(t * t) / 2.0)))
end
↓
function code(x, y, z, t)
	return Float64(Float64(Float64(x * 0.5) * sqrt(Float64(Float64(z * 2.0) * (exp(t) ^ t)))) - Float64(y * sqrt(Float64(Float64(z * 2.0) * cbrt(exp(Float64(3.0 * Float64(t * t))))))))
end

code[x_, y_, z_, t_] := N[(N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_] := N[(N[(N[(x * 0.5), $MachinePrecision] * N[Sqrt[N[(N[(z * 2.0), $MachinePrecision] * N[Power[N[Exp[t], $MachinePrecision], t], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(y * N[Sqrt[N[(N[(z * 2.0), $MachinePrecision] * N[Power[N[Exp[N[(3.0 * N[(t * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(x \cdot 0.5\right) \cdot \sqrt{\left(z \cdot 2\right) \cdot {\left(e^{t}\right)}^{t}} - y \cdot \sqrt{\left(z \cdot 2\right) \cdot \sqrt[3]{e^{3 \cdot \left(t \cdot t\right)}}}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.3
Herbie0.3
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)} \]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]

  2. Simplified0.3

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

  3. Applied egg-rr0.3

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

  4. Applied egg-rr0.3

    \[\leadsto \left(x \cdot 0.5\right) \cdot \sqrt{\left(z \cdot 2\right) \cdot {\left(e^{t}\right)}^{t}} + \left(-y\right) \cdot \sqrt{\left(z \cdot 2\right) \cdot \color{blue}{\sqrt[3]{e^{3 \cdot \left(t \cdot t\right)}}}} \]

  5. Final simplification0.3

    \[\leadsto \left(x \cdot 0.5\right) \cdot \sqrt{\left(z \cdot 2\right) \cdot {\left(e^{t}\right)}^{t}} - y \cdot \sqrt{\left(z \cdot 2\right) \cdot \sqrt[3]{e^{3 \cdot \left(t \cdot t\right)}}} \]

Reproduce

herbie shell --seed 2022162 
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"
  :precision binary64

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp 1.0) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))