Average Error: 6.0 → 0.1
Time: 2.6s
Precision: binary64
Cost: 448
\[x + \frac{y \cdot y}{z} \]
↓
\[x + y \cdot \frac{y}{z} \]
(FPCore (x y z) :precision binary64 (+ x (/ (* y y) z)))
↓
(FPCore (x y z) :precision binary64 (+ x (* y (/ y z))))
double code(double x, double y, double z) {
	return x + ((y * y) / z);
}
↓
double code(double x, double y, double z) {
	return x + (y * (y / z));
}

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y * y) / z)
end function
↓
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y * (y / z))
end function

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

def code(x, y, z):
	return x + ((y * y) / z)
↓
def code(x, y, z):
	return x + (y * (y / z))

function code(x, y, z)
	return Float64(x + Float64(Float64(y * y) / z))
end
↓
function code(x, y, z)
	return Float64(x + Float64(y * Float64(y / z)))
end

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

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

x + \frac{y \cdot y}{z}
↓
x + y \cdot \frac{y}{z}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.0
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z} \]

Derivation

  1. Initial program 6.0

    \[x + \frac{y \cdot y}{z} \]

  2. Simplified0.1

    \[\leadsto \color{blue}{x + \frac{y}{z} \cdot y} \]
    Proof
    (+.f64 x (*.f64 (/.f64 y z) y)): 0 points increase in error, 0 points decrease in error
    (+.f64 x (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 y y) z))): 35 points increase in error, 9 points decrease in error

  3. Final simplification0.1

    \[\leadsto x + y \cdot \frac{y}{z} \]

Alternatives

Alternative 1
Error21.1
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022330 
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"
  :precision binary64

  :herbie-target
  (+ x (* y (/ y z)))

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