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

Average Error: 10.9 → 0.7

Time: 11.3s

Precision: binary64

Cost: 1992

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+222}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+231}:\\ \;\;\;\;t_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 -1e+222)
     (+ x (/ y (/ (- z a) (- z t))))
     (if (<= t_1 4e+231) (+ t_1 x) (+ x (* (- z t) (/ y (- 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 t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -1e+222) {
		tmp = x + (y / ((z - a) / (z - t)));
	} else if (t_1 <= 4e+231) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((z - t) * (y / (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) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / (z - a)
    if (t_1 <= (-1d+222)) then
        tmp = x + (y / ((z - a) / (z - t)))
    else if (t_1 <= 4d+231) then
        tmp = t_1 + x
    else
        tmp = x + ((z - t) * (y / (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 t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -1e+222) {
		tmp = x + (y / ((z - a) / (z - t)));
	} else if (t_1 <= 4e+231) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((z - t) * (y / (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):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if t_1 <= -1e+222:
		tmp = x + (y / ((z - a) / (z - t)))
	elif t_1 <= 4e+231:
		tmp = t_1 + x
	else:
		tmp = x + ((z - t) * (y / (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)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -1e+222)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / Float64(z - t))));
	elseif (t_1 <= 4e+231)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / 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)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if (t_1 <= -1e+222)
		tmp = x + (y / ((z - a) / (z - t)));
	elseif (t_1 <= 4e+231)
		tmp = t_1 + x;
	else
		tmp = x + ((z - t) * (y / (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_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+222], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+231], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	10.9
Target	1.1
Herbie	0.7

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -1e222

   1. Initial program 50.4

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

   2. Simplified 2.0

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

      [Start] 50.4	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
      associate-/l* [=>] 2.0	\[ x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}} \]

   if -1e222 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.0000000000000002e231

   1. Initial program 0.3

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

   if 4.0000000000000002e231 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 52.7

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

   2. Simplified 3.2

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

      [Start] 52.7	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
      associate-*l/ [<=] 3.2	\[ x + \color{blue}{\frac{y}{z - a} \cdot \left(z - t\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -1 \cdot 10^{+222}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 4 \cdot 10^{+231}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array} \]

Alternatives

Alternative 1
Error	10.2
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-72} \lor \neg \left(z \leq 2.6 \cdot 10^{-118}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 2
Error	10.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-53}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 10^{-115}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 3
Error	10.3
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 4
Error	20.7
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-307}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5
Error	20.7
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-307}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-248}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6
Error	14.3
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-50} \lor \neg \left(z \leq 3.6 \cdot 10^{-90}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7
Error	14.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-51}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8
Error	3.0
Cost	704

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

Alternative 9
Error	20.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10
Error	27.2
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-111}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Error	28.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023031 
(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))))