Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A

Average Error: 1.2 → 1.2

Time: 11.0s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

(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 t) (- z a)))))

C

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 - t) / (z - a)));
}

Fortran

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

Java

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 - t) / (z - a)));
}

Python

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 - t) / (z - a)))

Julia

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

↓

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

MATLAB

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 - t) / (z - a)));
end

Wolfram

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

↓

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

Target

Original	1.2
Target	1.1
Herbie	1.2

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

Derivation

1. Initial program 1.2

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

2. Final simplification 1.2

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

Alternatives

Alternative 1
Error	11.3
Cost	1364

\[\begin{array}{l} t_1 := y + \left(x - y \cdot \frac{t}{z}\right)\\ t_2 := x + \frac{y}{1 - \frac{a}{z}}\\ t_3 := x + y \cdot \left(\left(z - t\right) \cdot \frac{-1}{a}\right)\\ \mathbf{if}\;z \leq -9.858574165298792 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.660609814288562 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.410193304348883 \cdot 10^{-32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4619055.746585874:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7127019747925625 \cdot 10^{+52}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	14.4
Cost	976

\[\begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -5.8026087384071584 \cdot 10^{-33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.410193304348883 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4619055.746585874:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 2.7127019747925625 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Error	11.1
Cost	972

\[\begin{array}{l} t_1 := x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{if}\;z \leq -9.858574165298792 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.660609814288562 \cdot 10^{-96}:\\ \;\;\;\;y + \left(x - y \cdot \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 2.4588862502106457 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	10.5
Cost	840

\[\begin{array}{l} t_1 := x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{if}\;z \leq -5.741463029644397 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4588862502106457 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	14.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -5.8026087384071584 \cdot 10^{-33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.71291728535124 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	14.6
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -4.660609814288562 \cdot 10^{-96}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.7127019747925625 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Error	20.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -4.660609814288562 \cdot 10^{-96}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.7127019747925625 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Error	27.2
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.0650365936822119 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.1712371333490866 \cdot 10^{-71}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	28.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022308 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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