Average Error: 10.9 → 1.2
Time: 12.3s
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
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}} \]

Derivation

  1. Initial program 10.9

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

  2. Simplified1.2

    \[\leadsto \color{blue}{x + \frac{y}{\frac{z - a}{z - t}}} \]
    Proof
    (+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))): 0 points increase in error, 0 points decrease in error
    (+.f64 x (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))): 2 points increase in error, 0 points decrease in error

  3. Final simplification1.2

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

Alternatives

Alternative 1
Error16.8
Cost1632
\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+217}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;z \leq -0.012:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-109}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 2
Error15.3
Cost1568
\[\begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ t_2 := x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 3
Error16.1
Cost1173
\[\begin{array}{l} t_1 := x + \frac{y}{\frac{-z}{t}}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+217}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+33} \lor \neg \left(z \leq 2.4 \cdot 10^{+79}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 4
Error15.2
Cost976
\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+49}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+37}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 5
Error23.5
Cost852
\[\begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-279}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{-302}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-266}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 6
Error22.8
Cost852
\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-278}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{-302}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-266}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
Alternative 7
Error10.9
Cost841
\[\begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-110} \lor \neg \left(z \leq 5 \cdot 10^{-22}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
Alternative 8
Error14.7
Cost713
\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+49} \lor \neg \left(z \leq 1.35 \cdot 10^{-17}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
Alternative 9
Error3.1
Cost704
\[x + \left(z - t\right) \cdot \frac{y}{z - a} \]
Alternative 10
Error28.8
Cost592
\[\begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-83}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-187}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-245}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 11
Error20.9
Cost456
\[\begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+236}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 12
Error29.6
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022343 
(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))))