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

Average Error: 1.3 → 1.2

Time: 1.5min

Precision: binary64

Cost: 964

Math

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

↓

\[x + \begin{array}{l} \mathbf{if}\;z - t \ne 0:\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (+
  x
  (if (!= (- z t) 0.0) (/ y (/ (- z a) (- z t))) (* (/ y (- z a)) (- z t)))))

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) {
	double tmp;
	if ((z - t) != 0.0) {
		tmp = y / ((z - a) / (z - t));
	} else {
		tmp = (y / (z - a)) * (z - t);
	}
	return x + tmp;
}

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
    real(8) :: tmp
    if ((z - t) /= 0.0d0) then
        tmp = y / ((z - a) / (z - t))
    else
        tmp = (y / (z - a)) * (z - t)
    end if
    code = x + tmp
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) {
	double tmp;
	if ((z - t) != 0.0) {
		tmp = y / ((z - a) / (z - t));
	} else {
		tmp = (y / (z - a)) * (z - t);
	}
	return x + tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) != 0.0:
		tmp = y / ((z - a) / (z - t))
	else:
		tmp = (y / (z - a)) * (z - t)
	return x + tmp

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)
	tmp = 0.0
	if (Float64(z - t) != 0.0)
		tmp = Float64(y / Float64(Float64(z - a) / Float64(z - t)));
	else
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(z - t));
	end
	return Float64(x + tmp)
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z - t) ~= 0.0)
		tmp = y / ((z - a) / (z - t));
	else
		tmp = (y / (z - a)) * (z - t);
	end
	tmp_2 = x + tmp;
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 + If[Unequal[N[(z - t), $MachinePrecision], 0.0], N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Target

Original	1.3
Target	1.2
Herbie	1.2

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

Derivation

1. Initial program 1.3

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

2. Applied egg-rr 1.2

   \[\leadsto x + \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;z - t \ne 0:\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ } \end{array}} \]

3. Simplified 1.2

   \[\leadsto x + \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;z - t \ne 0:\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ } \end{array}} \]
   Proof

Alternatives

Alternative 1
Error	21.2
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-61}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 2
Error	13.3
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-33}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3
Error	10.5
Cost	840

\[\begin{array}{l} t_1 := x + y \cdot \frac{z - t}{z}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	21.5
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5
Error	21.5
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-61}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6
Error	21.6
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-61}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7
Error	14.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-31}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8
Error	1.3
Cost	704

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

Alternative 9
Error	20.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10
Error	28.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023033 
(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)))))