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

Average Error: 1.3 → 1.3

Time: 11.6s

Precision: binary64

Cost: 704

Math

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

↓

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

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 t) (- z a)))))

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

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

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 - t) / (z - a)))

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 - t) / Float64(z - a))))
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 - t) / (z - a)));
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 - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $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. Final simplification 1.3

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

Alternatives

Alternative 1
Error	11.5
Cost	3156

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;t_1 \leq -1000000000000:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t_1 \leq 0.0001:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t_1 \leq 5000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+152}:\\ \;\;\;\;y \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \end{array} \]

Alternative 2
Error	11.3
Cost	3156

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;t_1 \leq -1000000000000:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-35}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t_1 \leq 5000000000000:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+152}:\\ \;\;\;\;y \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \end{array} \]

Alternative 3
Error	11.3
Cost	3156

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;t_1 \leq -1000000000000:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-35}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t_1 \leq 5000000000000:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+152}:\\ \;\;\;\;y \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \end{array} \]

Alternative 4
Error	14.7
Cost	1240

\[\begin{array}{l} t_1 := x - \frac{y \cdot t}{z}\\ \mathbf{if}\;z \leq -3.55 \cdot 10^{+87}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-63}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-25}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+89}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Error	15.5
Cost	1108

\[\begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-45}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+87}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	14.9
Cost	1108

\[\begin{array}{l} t_1 := x - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+104}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+89}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Error	23.4
Cost	912

\[\begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+235}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-120}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-181}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+237}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \end{array} \]

Alternative 8
Error	23.5
Cost	912

\[\begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+235}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-119}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-181}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+237}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \end{array} \]

Alternative 9
Error	24.8
Cost	912

\[\begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+136}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-120}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-181}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+237}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \end{array} \]

Alternative 10
Error	19.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+190}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+159}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Error	27.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-93}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	28.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023018 
(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)))))