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

Average Error: 2% → 2%

Time: 12.3s

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	2%
Target	1.81%
Herbie	2%

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

Derivation

1. Initial program 2

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

2. Final simplification 2

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

Alternatives

Alternative 1
Error	25.93%
Cost	1237

\[\begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-28}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+16} \lor \neg \left(z \leq 4.2 \cdot 10^{+44}\right) \land z \leq 5 \cdot 10^{+159}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 2
Error	26.73%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+51}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+41}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+159}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Error	26.73%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+50}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+41}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+56}:\\ \;\;\;\;\frac{-y}{\frac{z - a}{t}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+159}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4
Error	20.83%
Cost	1104

\[\begin{array}{l} t_1 := x + y \cdot \frac{z - t}{z}\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-26}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	19.67%
Cost	1104

\[\begin{array}{l} t_1 := x + y \cdot \frac{z - t}{z}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	36.66%
Cost	976

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-141}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-268}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-182}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+106}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	31.05%
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+193}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	18.26%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-9} \lor \neg \left(z \leq 4.1 \cdot 10^{-28}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 9
Error	22.89%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+50}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-26}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10
Error	30.36%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+192}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Error	41.34%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-178}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-103}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	44.63%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(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)))))