Average Error: 9.6 → 0.1
Time: 8.5s
Precision: binary64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
↓
\[\frac{x}{y} + \left(-2 + \left(\frac{2}{t} + 2 \cdot \frac{1}{t \cdot z}\right)\right) \]
(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
↓
(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (+ -2.0 (+ (/ 2.0 t) (* 2.0 (/ 1.0 (* t z)))))))
double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}
↓
double code(double x, double y, double z, double t) {
	return (x / y) + (-2.0 + ((2.0 / t) + (2.0 * (1.0 / (t * z)))));
}

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function
↓
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((-2.0d0) + ((2.0d0 / t) + (2.0d0 * (1.0d0 / (t * z)))))
end function

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}
↓
public static double code(double x, double y, double z, double t) {
	return (x / y) + (-2.0 + ((2.0 / t) + (2.0 * (1.0 / (t * z)))));
}

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))
↓
def code(x, y, z, t):
	return (x / y) + (-2.0 + ((2.0 / t) + (2.0 * (1.0 / (t * z)))))

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end
↓
function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(-2.0 + Float64(Float64(2.0 / t) + Float64(2.0 * Float64(1.0 / Float64(t * z))))))
end

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end
↓
function tmp = code(x, y, z, t)
	tmp = (x / y) + (-2.0 + ((2.0 / t) + (2.0 * (1.0 / (t * z)))));
end

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] + N[(2.0 * N[(1.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(-2 + \left(\frac{2}{t} + 2 \cdot \frac{1}{t \cdot z}\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

Original9.6
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right) \]

Derivation

  1. Initial program 9.6

    \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

  2. Simplified0.1

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

  3. Applied *-un-lft-identity_binary640.1

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

  4. Applied *-un-lft-identity_binary640.1

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

  5. Applied times-frac_binary640.1

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

  6. Simplified0.1

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

  7. Simplified0.1

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

  8. Applied add-sqr-sqrt_binary640.3

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

  9. Applied associate-/l*_binary640.2

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

  10. Applied div-inv_binary640.2

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

  11. Applied *-un-lft-identity_binary640.2

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

  12. Applied sqrt-prod_binary640.2

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

  13. Applied times-frac_binary640.3

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

  14. Simplified0.3

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

  15. Simplified0.1

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

  16. Final simplification0.1

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

Reproduce

herbie shell --seed 2022131 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))