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

Average Error: 1.3 → 1.3

Time: 10.9s

Precision: binary64

Cost: 832

Math

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

↓

\[x + \frac{1}{\frac{\frac{z - a}{z - t}}{y}} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- z a)))))

↓

(FPCore (x y z t a)
 :precision binary64
 (+ x (/ 1.0 (/ (/ (- z a) (- z t)) y))))

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 + (1.0 / (((z - a) / (z - t)) / y));
}

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 + (1.0d0 / (((z - a) / (z - t)) / y))
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 + (1.0 / (((z - a) / (z - t)) / y));
}

Python

def code(x, y, z, t, a):
	return x + (y * ((z - t) / (z - a)))

↓

def code(x, y, z, t, a):
	return x + (1.0 / (((z - a) / (z - t)) / y))

Julia

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

↓

function code(x, y, z, t, a)
	return Float64(x + Float64(1.0 / Float64(Float64(Float64(z - a) / Float64(z - t)) / y)))
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 + (1.0 / (((z - a) / (z - t)) / y));
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := N[(x + N[(1.0 / N[(N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	1.3
Target	1.2
Herbie	1.3

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

Derivation

1. Initial program 1.3

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

2. Applied egg-rr 1.3

   \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{z - t}}{y}}} \]

3. Final simplification 1.3

   \[\leadsto x + \frac{1}{\frac{\frac{z - a}{z - t}}{y}} \]

Alternatives

Alternative 1
Error	11.1
Cost	3152

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{z - a}{z}}\\ t_2 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{-94}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	8.2
Cost	2124

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := \frac{-y}{\frac{z - a}{t}}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	12.3
Cost	2060

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-38}:\\ \;\;\;\;y \cdot t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+51}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{z - a}{t}}\\ \end{array} \]

Alternative 4
Error	15.3
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+49}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-18}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+37}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Error	15.2
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+49}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+37}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	23.4
Cost	852

\[\begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-278}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{-302}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-266}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Error	22.9
Cost	852

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-302}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-266}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Error	1.3
Cost	704

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

Alternative 9
Error	20.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -3.15 \cdot 10^{+237}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+103}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	29.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022343 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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