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

Average Error: 10.8 → 0.7

Time: 1.7min

Precision: binary64

Cost: 1992

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-39}:\\ \;\;\;\;x + \begin{array}{l} \mathbf{if}\;y \ne 0:\\ \;\;\;\;\frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \end{array}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z - a}\\ \end{array} \]

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 -4e-39)
     (+ x (if (!= y 0.0) (/ (- z t) (/ (- z a) y)) (* (/ y (- z a)) (- z t))))
     (if (<= t_1 5e+297) (+ x t_1) (- x (* y (/ (- t z) (- 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_1;
	if (t_1 <= -4e-39) {
		double tmp_2;
		if (y != 0.0) {
			tmp_2 = (z - t) / ((z - a) / y);
		} else {
			tmp_2 = (y / (z - a)) * (z - t);
		}
		tmp_1 = x + tmp_2;
	} else if (t_1 <= 5e+297) {
		tmp_1 = x + t_1;
	} else {
		tmp_1 = x - (y * ((t - z) / (z - a)));
	}
	return tmp_1;
}

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
    real(8) :: tmp_1
    real(8) :: tmp_2
    t_1 = (y * (z - t)) / (z - a)
    if (t_1 <= (-4d-39)) then
        if (y /= 0.0d0) then
            tmp_2 = (z - t) / ((z - a) / y)
        else
            tmp_2 = (y / (z - a)) * (z - t)
        end if
        tmp_1 = x + tmp_2
    else if (t_1 <= 5d+297) then
        tmp_1 = x + t_1
    else
        tmp_1 = x - (y * ((t - z) / (z - a)))
    end if
    code = tmp_1
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_1;
	if (t_1 <= -4e-39) {
		double tmp_2;
		if (y != 0.0) {
			tmp_2 = (z - t) / ((z - a) / y);
		} else {
			tmp_2 = (y / (z - a)) * (z - t);
		}
		tmp_1 = x + tmp_2;
	} else if (t_1 <= 5e+297) {
		tmp_1 = x + t_1;
	} else {
		tmp_1 = x - (y * ((t - z) / (z - a)));
	}
	return tmp_1;
}

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_1 = 0
	if t_1 <= -4e-39:
		tmp_2 = 0
		if y != 0.0:
			tmp_2 = (z - t) / ((z - a) / y)
		else:
			tmp_2 = (y / (z - a)) * (z - t)
		tmp_1 = x + tmp_2
	elif t_1 <= 5e+297:
		tmp_1 = x + t_1
	else:
		tmp_1 = x - (y * ((t - z) / (z - a)))
	return tmp_1

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_1 = 0.0
	if (t_1 <= -4e-39)
		tmp_2 = 0.0
		if (y != 0.0)
			tmp_2 = Float64(Float64(z - t) / Float64(Float64(z - a) / y));
		else
			tmp_2 = Float64(Float64(y / Float64(z - a)) * Float64(z - t));
		end
		tmp_1 = Float64(x + tmp_2);
	elseif (t_1 <= 5e+297)
		tmp_1 = Float64(x + t_1);
	else
		tmp_1 = Float64(x - Float64(y * Float64(Float64(t - z) / Float64(z - a))));
	end
	return tmp_1
end

MATLAB

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

↓

function tmp_4 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp_2 = 0.0;
	if (t_1 <= -4e-39)
		tmp_3 = 0.0;
		if (y ~= 0.0)
			tmp_3 = (z - t) / ((z - a) / y);
		else
			tmp_3 = (y / (z - a)) * (z - t);
		end
		tmp_2 = x + tmp_3;
	elseif (t_1 <= 5e+297)
		tmp_2 = x + t_1;
	else
		tmp_2 = x - (y * ((t - z) / (z - a)));
	end
	tmp_4 = tmp_2;
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, -4e-39], N[(x + If[Unequal[y, 0.0], N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision], If[LessEqual[t$95$1, 5e+297], N[(x + t$95$1), $MachinePrecision], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	10.8
Target	1.2
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)) < -3.99999999999999972e-39

   1. Initial program 20.4

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

   2. Applied egg-rr 1.8

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

   if -3.99999999999999972e-39 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.9999999999999998e297

   1. Initial program 0.4

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

   if 4.9999999999999998e297 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 62.4

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

   2. Simplified 0.6

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

   3. Applied egg-rr 0.6

      \[\leadsto \color{blue}{x - y \cdot \frac{t - z}{z - a}} \]
3. Recombined 3 regimes into one program.

Alternatives

Alternative 1
Error	3.5
Cost	1992

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{z}{z - a} \cdot y\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \end{array} \]

Alternative 2
Error	0.3
Cost	1992

\[\begin{array}{l} t_1 := x - y \cdot \frac{t - z}{z - a}\\ t_2 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;x + t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	8.8
Cost	1104

\[\begin{array}{l} t_1 := x - \frac{y}{z - a} \cdot t\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+84}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-258}:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{z - a} \cdot y\\ \end{array} \]

Alternative 4
Error	10.8
Cost	840

\[\begin{array}{l} t_1 := x + \frac{z}{z - a} \cdot y\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	11.1
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{t - z}{z}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{z - a} \cdot y\\ \end{array} \]

Alternative 6
Error	21.5
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7
Error	21.5
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-61}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8
Error	21.6
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-61}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9
Error	14.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10
Error	20.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11
Error	28.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023033 
(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))))