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

Average Accuracy: 82.8% → 98.1%

Time: 13.9s

Precision: binary64

Cost: 704

Math

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

↓

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

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 a) (- z t)))))

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 - a) / (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)) / (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 - a) / (z - t)))
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 - a) / (z - t)));
}

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 - a) / (z - t)))

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

Target

Original	82.8%
Target	98.1%
Herbie	98.1%

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

Derivation

1. Initial program 82.8%

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

2. Simplified 98.1%

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

   [Start] 82.8	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   associate-/l* [=>] 98.1	\[ x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}} \]

3. Final simplification 98.1%

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

Alternatives

Alternative 1
Accuracy	60.3%
Cost	1112

\[\begin{array}{l} t_1 := y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{-28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-110}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-191}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-245}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 2
Accuracy	74.6%
Cost	1104

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{-25}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 85000000000:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Accuracy	75.8%
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+150}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4
Accuracy	94.3%
Cost	969

\[\begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-200} \lor \neg \left(x \leq 1.18 \cdot 10^{-206}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]

Alternative 5
Accuracy	61.6%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-112}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-192}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-238}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Accuracy	61.5%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-112}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-192}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-236}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Accuracy	61.5%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-109}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-191}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-230}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-247}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Accuracy	80.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-26} \lor \neg \left(x \leq 9.2 \cdot 10^{-148}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \end{array} \]

Alternative 9
Accuracy	77.4%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.86 \cdot 10^{+28} \lor \neg \left(z \leq 4 \cdot 10^{+41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 10
Accuracy	77.4%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+42}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11
Accuracy	77.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12
Accuracy	63.8%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-238}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13
Accuracy	68.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-98}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 14
Accuracy	58.3%
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+175}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15
Accuracy	55.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023138 
(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))))