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

Average Error: 1.6 → 1.4

Time: 7.4s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- a t)))))

↓

(FPCore (x y z t a) :precision binary64 (+ x (/ y (/ (- a t) (- z t)))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	return x + (y / ((a - t) / (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) / (a - t)))
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 / ((a - t) / (z - t)))
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	1.6
Target	0.5
Herbie	1.4

\[\begin{array}{l} \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Derivation

1. Initial program 1.6

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

2. Applied egg-rr 1.4

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

3. Final simplification 1.4

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

Alternatives

Alternative 1
Error	10.5
Cost	840

\[\begin{array}{l} t_1 := x - y \cdot \frac{t}{a - t}\\ \mathbf{if}\;t \leq -4.071511416001858 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.314898097072049 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	11.3
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -4.071511416001858 \cdot 10^{-8}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{elif}\;t \leq 4.462849520098056 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot \frac{z}{t} - y\right)\\ \end{array} \]

Alternative 3
Error	11.3
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -4.071511416001858 \cdot 10^{-8}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq 4.462849520098056 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot \frac{z}{t} - y\right)\\ \end{array} \]

Alternative 4
Error	19.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -2.2809849630464558 \cdot 10^{+53}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.283819516414495 \cdot 10^{-61}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Error	14.3
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -2.2809849630464558 \cdot 10^{+53}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.283819516414495 \cdot 10^{-61}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	19.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1.985141535833203 \cdot 10^{-93}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.462849520098056 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Error	28.5
Cost	64

\[x \]

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, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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