Average Error: 10.9 → 1.4
Time: 9.8s
Precision: binary64
Cost: 704
\[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
↓
\[x + \frac{y}{\frac{z - a}{z - t}} \]
(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- z a))))
↓
(FPCore (x y z t a) :precision binary64 (+ x (/ y (/ (- z a) (- z t)))))
double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (z - a));
}
↓
double code(double x, double y, double z, double t, double a) {
	return x + (y / ((z - a) / (z - t)));
}

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 - 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 + (y / ((z - a) / (z - t)))
end function

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

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

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

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

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

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

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.9
Target1.4
Herbie1.4
\[x + \frac{y}{\frac{z - a}{z - t}} \]

Derivation

  1. Initial program 10.9

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

  2. Simplified1.4

    \[\leadsto \color{blue}{x + \frac{y}{\frac{z - a}{z - t}}} \]
    Proof

    [Start]10.9

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

    associate-/l* [=>]1.4

    \[ x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}} \]

  3. Final simplification1.4

    \[\leadsto x + \frac{y}{\frac{z - a}{z - t}} \]

Alternatives

Alternative 1
Error3.7
Cost969
\[\begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-253} \lor \neg \left(x \leq 1.5 \cdot 10^{-265}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]
Alternative 2
Error8.6
Cost905
\[\begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+78} \lor \neg \left(t \leq 1.15 \cdot 10^{-40}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{-t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
Alternative 3
Error15.1
Cost844
\[\begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+82}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-99}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 4
Error10.5
Cost841
\[\begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-92} \lor \neg \left(z \leq 3.9 \cdot 10^{-100}\right):\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
Alternative 5
Error8.8
Cost841
\[\begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+78} \lor \neg \left(t \leq 1.25 \cdot 10^{-43}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
Alternative 6
Error12.2
Cost840
\[\begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
Alternative 7
Error14.8
Cost713
\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-90} \lor \neg \left(z \leq 1.95 \cdot 10^{+77}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
Alternative 8
Error14.9
Cost712
\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-86}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+77}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 9
Error23.7
Cost588
\[\begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+258}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+60}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 10
Error23.9
Cost588
\[\begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+224}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+60}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 11
Error20.6
Cost456
\[\begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-94}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 12
Error29.3
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022364 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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