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

Average Error: 1.4 → 1.3

Time: 12.3s

Precision: binary64

Cost: 704

Math

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

↓

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $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	1.4
Target	1.3
Herbie	1.3

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

Derivation

1. Initial program 1.4

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

2. Applied egg-rr 1.3

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

3. Final simplification 1.3

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

Alternatives

Alternative 1
Error	19.0
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -5.739658963249961 \cdot 10^{+109}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -8.144225789632364 \cdot 10^{-135}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-199}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 3211383327.1486025:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 2
Error	19.0
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -5.739658963249961 \cdot 10^{+109}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -8.144225789632364 \cdot 10^{-135}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 3211383327.1486025:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 3
Error	19.0
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -5.739658963249961 \cdot 10^{+109}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -8.144225789632364 \cdot 10^{-135}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-199}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;a \leq 3211383327.1486025:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 4
Error	12.2
Cost	972

\[\begin{array}{l} \mathbf{if}\;a \leq -1.1020398381747617 \cdot 10^{-17}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 4.489220518708774 \cdot 10^{-146}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 3.667043581367042 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 5
Error	12.3
Cost	972

\[\begin{array}{l} \mathbf{if}\;a \leq -1.1020398381747617 \cdot 10^{-17}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 4.489220518708774 \cdot 10^{-146}:\\ \;\;\;\;x + \left(y - y \cdot \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 3.667043581367042 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 6
Error	21.3
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -5.739658963249961 \cdot 10^{+109}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -8.144225789632364 \cdot 10^{-135}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-199}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 6.732455245354841 \cdot 10^{+37}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	11.5
Cost	840

\[\begin{array}{l} t_1 := x + z \cdot \frac{y}{z - a}\\ \mathbf{if}\;z \leq -3.205958724596176 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4208097427683209 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	12.5
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -1.1020398381747617 \cdot 10^{-17}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 3211383327.1486025:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 9
Error	19.7
Cost	580

\[\begin{array}{l} \mathbf{if}\;a \leq -5.739658963249961 \cdot 10^{+109}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6.732455245354841 \cdot 10^{+37}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	20.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -5.739658963249961 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.732455245354841 \cdot 10^{+37}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Error	26.9
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -6.197510220527438 \cdot 10^{-214}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.7781682491492695 \cdot 10^{-182}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	28.4
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022316 
(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)))))