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

Average Error: 10.7 → 1.4

Time: 14.4s

Precision: binary64

Cost: 704

Math

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

↓

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

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 (/ (- z t) (- a 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 * ((z - t) / (a - 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 * ((z - t) / (a - 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 * ((z - t) / (a - 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 * ((z - t) / (a - t)))

Julia

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

↓

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

Wolfram

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

↓

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

Target

Original	10.7
Target	1.3
Herbie	1.4

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

Derivation

1. Initial program 10.7

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

2. Simplified 1.4

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

   [Start] 10.7	\[ x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   rational_best-simplify-2 [=>] 10.7	\[ x + \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]
   rational_best-simplify-47 [=>] 1.4	\[ x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

3. Final simplification 1.4

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

Alternatives

Alternative 1
Error	21.1
Cost	844

\[\begin{array}{l} \mathbf{if}\;t \leq -27500:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 2
Error	21.1
Cost	844

\[\begin{array}{l} \mathbf{if}\;t \leq -61000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.65 \cdot 10^{-122}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3
Error	11.2
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -11200000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4
Error	8.7
Cost	840

\[\begin{array}{l} t_1 := x + y \cdot \frac{t - z}{t}\\ \mathbf{if}\;t \leq -800000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.000105:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	14.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -39000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z}{a} + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6
Error	20.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1360000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 10^{-101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7
Error	27.3
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1.96 \cdot 10^{+108}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8
Error	28.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023096 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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