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

Average Error: 1.3 → 1.2

Time: 12.1s

Precision: binary64

Cost: 969

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-17} \lor \neg \left(y \leq 1.15 \cdot 10^{+20}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]

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 (<= y -2e-17) (not (<= y 1.15e+20)))
   (+ x (/ (- z t) (/ (- z a) y)))
   (+ 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 ((y <= -2e-17) || !(y <= 1.15e+20)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} 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 ((y <= (-2d-17)) .or. (.not. (y <= 1.15d+20))) then
        tmp = x + ((z - t) / ((z - a) / y))
    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 ((y <= -2e-17) || !(y <= 1.15e+20)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} 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 (y <= -2e-17) or not (y <= 1.15e+20):
		tmp = x + ((z - t) / ((z - a) / y))
	else:
		tmp = x + ((y * (z - t)) / (z - a))
	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 ((y <= -2e-17) || !(y <= 1.15e+20))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	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 ((y <= -2e-17) || ~((y <= 1.15e+20)))
		tmp = x + ((z - t) / ((z - a) / y));
	else
		tmp = x + ((y * (z - t)) / (z - a));
	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[Or[LessEqual[y, -2e-17], N[Not[LessEqual[y, 1.15e+20]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	1.3
Target	1.1
Herbie	1.2

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

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000014e-17 or 1.15e20 < y

   1. Initial program 0.3

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

   2. Applied egg-rr 2.2

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

   if -2.00000000000000014e-17 < y < 1.15e20

   1. Initial program 2.1

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

   2. Simplified 0.4

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

      [Start] 2.1	\[ x + y \cdot \frac{z - t}{z - a} \]
      associate-*r/ [=>] 0.4	\[ x + \color{blue}{\frac{y \cdot \left(z - t\right)}{z - a}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 1.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-17} \lor \neg \left(y \leq 1.15 \cdot 10^{+20}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.9
Cost	1220

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+261}:\\ \;\;\;\;x + y \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]

Alternative 2
Error	14.9
Cost	1041

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-50}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-90}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+159} \lor \neg \left(z \leq 9.5 \cdot 10^{+207}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \end{array} \]

Alternative 3
Error	0.4
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+22} \lor \neg \left(y \leq 10^{-36}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]

Alternative 4
Error	10.3
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-50} \lor \neg \left(z \leq 3.8 \cdot 10^{-117}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 5
Error	10.8
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-116}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 6
Error	10.4
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 7
Error	20.7
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-307}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-246}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8
Error	20.7
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-307}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-248}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9
Error	14.5
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-66} \lor \neg \left(z \leq 3.2 \cdot 10^{-90}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10
Error	14.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-50}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-90}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11
Error	20.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 12
Error	28.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023031 
(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)))))