Average Error: 2.0 → 0.9
Time: 7.2s
Precision: binary64
\[\frac{x}{y} \cdot \left(z - t\right) + t \]
↓
\[t + \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) \]
(FPCore (x y z t) :precision binary64 (+ (* (/ x y) (- z t)) t))
↓
(FPCore (x y z t)
 :precision binary64
 (+
  t
  (*
   (/ (* (cbrt x) (cbrt x)) (pow (cbrt y) 2.0))
   (* (/ (cbrt x) (cbrt y)) (- z t)))))
double code(double x, double y, double z, double t) {
	return ((x / y) * (z - t)) + t;
}
↓
double code(double x, double y, double z, double t) {
	return t + (((cbrt(x) * cbrt(x)) / pow(cbrt(y), 2.0)) * ((cbrt(x) / cbrt(y)) * (z - t)));
}

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

function code(x, y, z, t)
	return Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
end
↓
function code(x, y, z, t)
	return Float64(t + Float64(Float64(Float64(cbrt(x) * cbrt(x)) / (cbrt(y) ^ 2.0)) * Float64(Float64(cbrt(x) / cbrt(y)) * Float64(z - t))))
end

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

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

Original2.0
Target2.4
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array} \]

Derivation

  1. Initial program 2.0

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

  2. Applied add-cube-cbrt_binary642.5

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

  3. Applied add-cube-cbrt_binary642.7

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

  4. Applied times-frac_binary642.7

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

  5. Applied associate-*l*_binary640.9

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

  6. Applied pow2_binary640.9

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

  7. Final simplification0.9

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

Reproduce

herbie shell --seed 2022131 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

  (+ (* (/ x y) (- z t)) t))