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

Average Error: 1.4 → 1.3

Time: 13.9s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (a - t)));
}

↓

double code(double x, double y, double z, double t, double a) {
	return x + (y / ((a - t) / (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) / (a - t)))
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 / ((a - t) / (z - t)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (a - t)));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	return x + (y / ((a - t) / (z - t)));
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * ((z - t) / (a - t)));
end

↓

function tmp = code(x, y, z, t, a)
	tmp = x + (y / ((a - t) / (z - t)));
end

Wolfram

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

↓

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

Target

Original	1.4
Target	0.5
Herbie	1.3

\[\begin{array}{l} \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Derivation

1. Initial program 1.4

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

2. Applied egg-rr 1.3

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

3. Final simplification 1.3

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

Alternatives

Alternative 1
Error	13.0
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{if}\;t \leq -5369.4470998362085:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.18287244730128 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.346630671576964 \cdot 10^{-7}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 9.971058851644664 \cdot 10^{+205}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 2
Error	9.6
Cost	1104

\[\begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -4.78193036343062 \cdot 10^{+140}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{elif}\;t \leq -2.160699600567494 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.098837352779528 \cdot 10^{-53}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq 9.18287244730128 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	21.0
Cost	976

\[\begin{array}{l} t_1 := x - \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -6.876543070959288 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-91}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 1.0464550742075862 \cdot 10^{+206}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	21.0
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -6.876543070959288 \cdot 10^{+217}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-91}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 1.0464550742075862 \cdot 10^{+206}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 5
Error	11.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -5369.4470998362085:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.971058851644664 \cdot 10^{+205}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	8.6
Cost	840

\[\begin{array}{l} t_1 := x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{if}\;t \leq -7.098837352779528 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4391262444104223 \cdot 10^{-42}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	23.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-84}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;a \leq 1.0464550742075862 \cdot 10^{+206}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	23.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-91}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 1.0464550742075862 \cdot 10^{+206}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	14.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -9.99514295416828 \cdot 10^{-59}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.18287244730128 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10
Error	14.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -9.99514295416828 \cdot 10^{-59}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.18287244730128 \cdot 10^{-67}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11
Error	28.0
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -6.397312807870599 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6217703460461606 \cdot 10^{-201}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 5.379670348197073 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.5634334007179 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	23.2
Cost	588

\[\begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.0464550742075862 \cdot 10^{+206}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	23.2
Cost	588

\[\begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1.0464550742075862 \cdot 10^{+206}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Error	20.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -3.2312653445370984 \cdot 10^{-65}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.18287244730128 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 15
Error	51.4
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022291 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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