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

Average Error: 1.3 → 9.1

Time: 8.7s

Precision: binary64

Cost: 968

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -8.835610133199546 \cdot 10^{+67}:\\ \;\;\;\;x + \frac{z}{\frac{z - a}{y}}\\ \mathbf{elif}\;z \leq 231542533.1532033:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{1}{z} \cdot \left(z - t\right)\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.835610133199546e+67)
   (+ x (/ z (/ (- z a) y)))
   (if (<= z 231542533.1532033)
     (+ x (/ y (/ (- a z) t)))
     (+ x (* y (* (/ 1.0 z) (- 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 <= -8.835610133199546e+67) {
		tmp = x + (z / ((z - a) / y));
	} else if (z <= 231542533.1532033) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y * ((1.0 / z) * (z - t)));
	}
	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 <= (-8.835610133199546d+67)) then
        tmp = x + (z / ((z - a) / y))
    else if (z <= 231542533.1532033d0) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = x + (y * ((1.0d0 / z) * (z - t)))
    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 <= -8.835610133199546e+67) {
		tmp = x + (z / ((z - a) / y));
	} else if (z <= 231542533.1532033) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y * ((1.0 / z) * (z - t)));
	}
	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 <= -8.835610133199546e+67:
		tmp = x + (z / ((z - a) / y))
	elif z <= 231542533.1532033:
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x + (y * ((1.0 / z) * (z - t)))
	return 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 (z <= -8.835610133199546e+67)
		tmp = Float64(x + Float64(z / Float64(Float64(z - a) / y)));
	elseif (z <= 231542533.1532033)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(1.0 / z) * Float64(z - t))));
	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 <= -8.835610133199546e+67)
		tmp = x + (z / ((z - a) / y));
	elseif (z <= 231542533.1532033)
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x + (y * ((1.0 / z) * (z - t)));
	end
	tmp_2 = 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_] := If[LessEqual[z, -8.835610133199546e+67], N[(x + N[(z / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 231542533.1532033], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(1.0 / z), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	1.3
Target	1.2
Herbie	9.1

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

Derivation

1. Split input into 3 regimes

2. if z < -8.83561013319954648e67

   1. Initial program 0.1

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

   2. Applied egg-rr 0.1

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

   3. Taylor expanded in t around 0 24.5

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

   4. Simplified 10.3

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

   if -8.83561013319954648e67 < z < 231542533.15320331

   1. Initial program 2.4

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

   2. Applied egg-rr 2.2

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

   3. Taylor expanded in t around inf 8.7

      \[\leadsto x + \frac{y}{\color{blue}{-1 \cdot \frac{z - a}{t}}} \]

   4. Simplified 8.7

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

   5. Taylor expanded in a around 0 8.8

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a}{t} + -1 \cdot \frac{z}{t}}} \]

   6. Simplified 8.7

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

   if 231542533.15320331 < z

   1. Initial program 0.1

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

   2. Taylor expanded in a around 0 8.7

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

   3. Applied egg-rr 8.7

      \[\leadsto x + y \cdot \color{blue}{\left(\frac{1}{z} \cdot \left(z - t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 9.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.835610133199546 \cdot 10^{+67}:\\ \;\;\;\;x + \frac{z}{\frac{z - a}{y}}\\ \mathbf{elif}\;z \leq 231542533.1532033:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{1}{z} \cdot \left(z - t\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	14.0
Cost	1500

\[\begin{array}{l} t_1 := x + \frac{z}{\frac{z - a}{y}}\\ t_2 := x + \frac{y}{\frac{a - z}{t}}\\ t_3 := x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -3.440354216829813 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -62294261937.066055:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.471337250621794 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-110}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-270}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 7.7 \cdot 10^{-143}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	12.8
Cost	1040

\[\begin{array}{l} t_1 := x + \frac{z}{\frac{z - a}{y}}\\ \mathbf{if}\;z \leq -5.656673676119437 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.047159423548221 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 10694994263919630:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6720333941235434 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Error	18.7
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -3.440354216829813 \cdot 10^{+94}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-163}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-239}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.3675986399721009 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4
Error	18.7
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -3.440354216829813 \cdot 10^{+94}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-163}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-239}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.3675986399721009 \cdot 10^{+35}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 5
Error	13.2
Cost	972

\[\begin{array}{l} t_1 := x + \frac{z}{\frac{z - a}{y}}\\ \mathbf{if}\;a \leq -3.440354216829813 \cdot 10^{+94}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -6.32 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.7 \cdot 10^{-143}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	14.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -3.302919194384396 \cdot 10^{-44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.555318880041199 \cdot 10^{-94}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Error	19.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -5.656673676119437 \cdot 10^{-65}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 30202.516212601757:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Error	28.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022228 
(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)))))