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

Average Accuracy: 82.4% → 97.9%

Time: 10.8s

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	82.4%
Target	97.9%
Herbie	97.9%

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

Derivation

1. Initial program 82.4%

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

2. Simplified 97.9%

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

   [Start] 82.4	\[ x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   associate-/l* [=>] 97.9	\[ x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

3. Final simplification 97.9%

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

Alternatives

Alternative 1
Accuracy	65.4%
Cost	976

\[\begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 62000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 2
Accuracy	63.7%
Cost	976

\[\begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-141}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 10^{-192}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 62000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Accuracy	65.4%
Cost	852

\[\begin{array}{l} t_1 := z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 62000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4
Accuracy	63.7%
Cost	852

\[\begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{-142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-307}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-210}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 62000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Accuracy	78.9%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{+25} \lor \neg \left(t \leq 65000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 6
Accuracy	83.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -14000000000000 \lor \neg \left(t \leq 1.8 \cdot 10^{-161}\right):\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 7
Accuracy	83.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -14000000000000 \lor \neg \left(t \leq 4.4 \cdot 10^{-102}\right):\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 8
Accuracy	83.4%
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -17200000000000:\\ \;\;\;\;x - y \cdot \left(-1 + \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \end{array} \]

Alternative 9
Accuracy	77.3%
Cost	713

\[\begin{array}{l} \mathbf{if}\;t \leq -26000000000000 \lor \neg \left(t \leq 64000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 10
Accuracy	77.3%
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -20500000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 65000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11
Accuracy	95.5%
Cost	704

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

Alternative 12
Accuracy	67.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{+39}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 62000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13
Accuracy	54.7%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023141 
(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))))