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

Average Error: 11.0 → 1.3

Time: 16.6s

Precision: binary64

Cost: 704

Math

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

↓

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

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

Target

Original	11.0
Target	1.2
Herbie	1.3

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

Derivation

1. Initial program 11.0

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

2. Simplified 1.3

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

   [Start] 11.0	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   rational_best-simplify-2 [=>] 11.0	\[ x + \frac{\color{blue}{\left(z - t\right) \cdot y}}{z - a} \]
   rational_best-simplify-47 [=>] 1.3	\[ x + \color{blue}{y \cdot \frac{z - t}{z - a}} \]

3. Final simplification 1.3

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

Alternatives

Alternative 1
Error	13.7
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a} + x\\ t_2 := y \cdot \frac{z}{z - a} + x\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \frac{z - t}{z} + x\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -55000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -520000000000:\\ \;\;\;\;\frac{t}{-z} \cdot y\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	11.3
Cost	1232

\[\begin{array}{l} t_1 := y \cdot \frac{z}{z - a} + x\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-74}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right) + x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-117}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z} + x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+38}:\\ \;\;\;\;x + y \cdot \left(\frac{1}{a} \cdot \left(t - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	10.5
Cost	1104

\[\begin{array}{l} t_1 := y \cdot \frac{z}{z - a} + x\\ t_2 := \frac{y}{a} \cdot \left(t - z\right) + x\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \frac{z - t}{z} + x\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	17.5
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{t}{a} + x\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-301}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-182}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right) + x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-92}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a} + x\\ \end{array} \]

Alternative 5
Error	17.7
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \frac{t}{a} + x\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-302}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-171}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z} + x\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-92}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a} + x\\ \end{array} \]

Alternative 6
Error	10.4
Cost	840

\[\begin{array}{l} t_1 := y \cdot \frac{z}{z - a} + x\\ \mathbf{if}\;z \leq -5 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{t}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	14.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+39}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8
Error	14.3
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+39}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \frac{t}{a} + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9
Error	19.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-25}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10
Error	26.6
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+178}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 11
Error	28.5
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, A"
  :precision binary64

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

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