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

Average Error: 1.4 → 1.4

Time: 20.8s

Precision: binary64

Cost: 1088

Math

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

↓

\[x + \left(\frac{z}{a - t} \cdot y + \frac{t}{t - a} \cdot y\right) \]

FPCore

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

↓

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

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 + (((z / (a - t)) * y) + ((t / (t - a)) * y));
}

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 + (((z / (a - t)) * y) + ((t / (t - a)) * y))
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 + (((z / (a - t)) * y) + ((t / (t - a)) * y));
}

Python

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

↓

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

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(Float64(Float64(z / Float64(a - t)) * y) + Float64(Float64(t / Float64(t - a)) * y)))
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 + (((z / (a - t)) * y) + ((t / (t - a)) * y));
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[(N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + N[(N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	1.4
Target	0.4
Herbie	1.4

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

Derivation

1. Initial program 1.4

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

2. Applied egg-rr 1.4

   \[\leadsto x + \color{blue}{\left(\frac{z}{a - t} \cdot y + \frac{t}{t - a} \cdot y\right)} \]

Alternatives

Alternative 1
Error	13.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-42}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-45}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 2
Error	13.4
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-43}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-50}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3
Error	11.8
Cost	840

\[\begin{array}{l} t_1 := x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-48}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	10.6
Cost	840

\[\begin{array}{l} t_1 := \left(1 - \frac{z}{t}\right) \cdot y + x\\ \mathbf{if}\;t \leq -1.32 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	14.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-42}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6
Error	14.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-42}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7
Error	14.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-48}:\\ \;\;\;\;\frac{y \cdot z}{a} + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8
Error	1.4
Cost	704

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

Alternative 9
Error	20.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -8000000000000:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10
Error	27.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+228}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 11
Error	28.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023010 
(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)))))