?

Average Accuracy: 82.8% → 98.0%
Time: 15.2s
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

Original82.8%
Target98.0%
Herbie98.0%
\[x + \frac{y}{\frac{z - a}{z - t}} \]

Derivation?

  1. Initial program 82.8%

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

  2. Simplified98.0%

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

    [Start]82.8

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

    associate-/l* [=>]98.0

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

  3. Final simplification98.0%

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

Alternatives

Alternative 1
Accuracy76.5%
Cost1372
\[\begin{array}{l} t_1 := x - z \cdot \frac{y}{a}\\ t_2 := x - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+96}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+93}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 2
Accuracy76.6%
Cost1372
\[\begin{array}{l} t_1 := x - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+97}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.49:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+92}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+117}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 3
Accuracy76.4%
Cost1372
\[\begin{array}{l} t_1 := x - \frac{y}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+92}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.82:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+93}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+115}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 4
Accuracy77.3%
Cost1368
\[\begin{array}{l} t_1 := x - \frac{y \cdot t}{z - a}\\ t_2 := x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{if}\;y \leq -6 \cdot 10^{+186}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{-y}}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+162}:\\ \;\;\;\;x + \left(y - \frac{t}{\frac{z}{y}}\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+16}:\\ \;\;\;\;x + \left(y - t \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 5
Accuracy76.2%
Cost1108
\[\begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+80}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1350000000:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-52}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-278}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 6
Accuracy82.3%
Cost1105
\[\begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-132}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+102} \lor \neg \left(z \leq 1.5 \cdot 10^{+115}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]
Alternative 7
Accuracy79.7%
Cost972
\[\begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+90}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-70}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{elif}\;a \leq 10^{-41}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
Alternative 8
Accuracy80.5%
Cost841
\[\begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-53} \lor \neg \left(z \leq 1.95 \cdot 10^{-206}\right):\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
Alternative 9
Accuracy78.7%
Cost840
\[\begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+54}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-39}:\\ \;\;\;\;x + \left(y - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
Alternative 10
Accuracy78.9%
Cost840
\[\begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+54}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-39}:\\ \;\;\;\;x + \left(y - \frac{t}{\frac{z}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
Alternative 11
Accuracy79.2%
Cost840
\[\begin{array}{l} \mathbf{if}\;a \leq -1.18 \cdot 10^{+54}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
Alternative 12
Accuracy77.2%
Cost712
\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 13
Accuracy94.8%
Cost704
\[x + \left(z - t\right) \cdot \frac{y}{z - a} \]
Alternative 14
Accuracy67.9%
Cost456
\[\begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+59}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 15
Accuracy54.8%
Cost64
\[x \]

Error

Reproduce?

herbie shell --seed 2023140 
(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))))