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

Average Error: 1.4 → 1.3

Time: 10.4s

Precision: binary64

Cost: 704

Math

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

↓

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

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 a) (- z t)))))

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

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

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 - a) / (z - t)))

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 - a) / Float64(z - t))))
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 - a) / (z - t)));
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 - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	1.4
Target	1.3
Herbie	1.3

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

Derivation

1. Initial program 1.4

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

2. Applied egg-rr 1.3

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

3. Final simplification 1.3

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

Alternatives

Alternative 1
Error	10.7
Cost	840

\[\begin{array}{l} t_1 := x - y \cdot \frac{z}{a - z}\\ \mathbf{if}\;z \leq -5.0659073761473915 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8109334964296506 \cdot 10^{-48}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	11.0
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -9.796644944149417 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y - y \cdot \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.8109334964296506 \cdot 10^{-48}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a - z}\\ \end{array} \]

Alternative 3
Error	18.4
Cost	712

\[\begin{array}{l} t_1 := x - y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -3.778146315230698 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.450794290782853 \cdot 10^{+127}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	14.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -2.552989375547654 \cdot 10^{+23}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.4872058519325763 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Error	19.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -3.475726187018565 \cdot 10^{-108}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.717830092976928 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	26.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+196}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+194}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7
Error	51.2
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022317 
(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)))))