Average Error: 1.9 → 0.2
Time: 12.5s
Precision: binary64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
↓
\[x + \frac{z - y}{\left(t - z\right) + 1} \cdot a \]
(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))
↓
(FPCore (x y z t a)
 :precision binary64
 (+ x (* (/ (- z y) (+ (- t z) 1.0)) a)))
double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}
↓
double code(double x, double y, double z, double t, double a) {
	return x + (((z - y) / ((t - z) + 1.0)) * a);
}

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

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

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

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

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

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

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.9
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a \]

Derivation

  1. Initial program 1.9

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

  2. Applied associate-/r/_binary640.2

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

  3. Applied cancel-sign-sub-inv_binary640.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2022129 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))