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

Average Accuracy: 83.2% → 97.8%

Time: 9.9s

Precision: binary64

Cost: 704

Math

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

↓

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

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

Target

Original	83.2%
Target	97.8%
Herbie	97.8%

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

Derivation

1. Initial program 83.2%

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

2. Simplified 97.8%

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

   [Start] 83.2	\[ x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   associate-/l* [=>] 97.8	\[ x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

3. Final simplification 97.8%

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

Alternatives

Alternative 1
Accuracy	87.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-70} \lor \neg \left(z \leq 2.3 \cdot 10^{+45}\right):\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \]

Alternative 2
Accuracy	83.3%
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+92}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Accuracy	77.6%
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-6}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4
Accuracy	76.7%
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-6}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Accuracy	95.4%
Cost	704

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

Alternative 6
Accuracy	68.7%
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Accuracy	57.6%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-176}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-242}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Accuracy	55.1%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023137 
(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))))