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

Average Error: 10.8 → 1.5

Time: 11.4s

Precision: binary64

Cost: 969

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+20} \lor \neg \left(z \leq 6.2 \cdot 10^{-239}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5e+20) (not (<= z 6.2e-239)))
   (+ x (/ y (/ (- z a) (- z t))))
   (+ 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) {
	double tmp;
	if ((z <= -5e+20) || !(z <= 6.2e-239)) {
		tmp = x + (y / ((z - a) / (z - t)));
	} else {
		tmp = x + ((y * (z - t)) / (z - a));
	}
	return 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 <= (-5d+20)) .or. (.not. (z <= 6.2d-239))) then
        tmp = x + (y / ((z - a) / (z - t)))
    else
        tmp = x + ((y * (z - t)) / (z - a))
    end if
    code = 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 <= -5e+20) || !(z <= 6.2e-239)) {
		tmp = x + (y / ((z - a) / (z - t)));
	} else {
		tmp = x + ((y * (z - t)) / (z - a));
	}
	return 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 <= -5e+20) or not (z <= 6.2e-239):
		tmp = x + (y / ((z - a) / (z - t)))
	else:
		tmp = x + ((y * (z - t)) / (z - a))
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5e+20) || !(z <= 6.2e-239))
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(z - a)));
	end
	return 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 <= -5e+20) || ~((z <= 6.2e-239)))
		tmp = x + (y / ((z - a) / (z - t)));
	else
		tmp = x + ((y * (z - t)) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5e+20], N[Not[LessEqual[z, 6.2e-239]], $MachinePrecision]], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	10.8
Target	1.3
Herbie	1.5

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

Derivation

1. Split input into 2 regimes

2. if z < -5e20 or 6.1999999999999997e-239 < z

   1. Initial program 14.0

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

   2. Simplified 0.6

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

      [Start] 14.0	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
      associate-/l* [=>] 0.6	\[ x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}} \]

   if -5e20 < z < 6.1999999999999997e-239

   1. Initial program 3.6

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 1.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+20} \lor \neg \left(z \leq 6.2 \cdot 10^{-239}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]

Alternatives

Alternative 1
Error	16.0
Cost	1368

\[\begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-55}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+132}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 2
Error	15.9
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-55}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-71}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Error	15.8
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-56}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-70}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4
Error	16.2
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-183}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-209}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-70}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Error	2.7
Cost	969

\[\begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-164} \lor \neg \left(t \leq 4 \cdot 10^{-226}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]

Alternative 6
Error	13.9
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-183}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]

Alternative 7
Error	20.9
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-170}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-183}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-194}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Error	14.5
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-56} \lor \neg \left(z \leq 1.25 \cdot 10^{-20}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9
Error	15.1
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-56} \lor \neg \left(z \leq 2.1 \cdot 10^{-20}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 10
Error	14.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-56}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11
Error	1.3
Cost	704

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

Alternative 12
Error	20.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-119}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13
Error	27.2
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-219}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Error	28.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023016 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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