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

Average Error: 1.6 → 1.6

Time: 11.3s

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	1.6
Target	1.4
Herbie	1.6

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

Derivation

1. Initial program 1.6

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

2. Final simplification 1.6

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

Alternatives

Alternative 1
Error	13.1
Cost	3028

\[\begin{array}{l} t_1 := x - \frac{y}{\frac{z}{t}}\\ t_2 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;t_2 \leq -20000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -0.002:\\ \;\;\;\;y \cdot t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-21}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t_2 \leq 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	13.3
Cost	2512

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;t_1 \leq -0.002:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-21}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t_1 \leq 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \end{array} \]

Alternative 3
Error	2.8
Cost	2188

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq -500:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{elif}\;t_1 \leq 10^{-5}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t_1 \leq 1.00000002:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{-t}}\\ \end{array} \]

Alternative 4
Error	2.9
Cost	2124

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := x - y \cdot \frac{t}{z - a}\\ \mathbf{if}\;t_1 \leq -500:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{-5}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t_1 \leq 1.00000002:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	5.5
Cost	1609

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq 10^{-5} \lor \neg \left(t_1 \leq 1.00000002\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	15.2
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.04 \cdot 10^{+80}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-105}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Error	15.2
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+78}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-105}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Error	14.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-85}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+77}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9
Error	14.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-84}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10
Error	23.9
Cost	588

\[\begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+225}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{+60}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11
Error	20.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-97}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-214}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12
Error	29.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022364 
(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)))))