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

Average Accuracy: 83.4% → 99.1%

Time: 10.7s

Precision: binary64

Cost: 969

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-165} \lor \neg \left(y \leq 2 \cdot 10^{+19}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]

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 (<= y -5e-165) (not (<= y 2e+19)))
   (+ 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 ((y <= -5e-165) || !(y <= 2e+19)) {
		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 ((y <= (-5d-165)) .or. (.not. (y <= 2d+19))) 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 ((y <= -5e-165) || !(y <= 2e+19)) {
		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 (y <= -5e-165) or not (y <= 2e+19):
		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 ((y <= -5e-165) || !(y <= 2e+19))
		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 ((y <= -5e-165) || ~((y <= 2e+19)))
		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[y, -5e-165], N[Not[LessEqual[y, 2e+19]], $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	83.4%
Target	98.1%
Herbie	99.1%

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

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999981e-165 or 2e19 < y

   1. Initial program 71.9%

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

   2. Simplified 98.8%

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

      [Start] 71.9	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
      associate-/l* [=>] 98.8	\[ x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}} \]

   if -4.99999999999999981e-165 < y < 2e19

   1. Initial program 99.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-165} \lor \neg \left(y \leq 2 \cdot 10^{+19}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	65.1%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{+192}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-79}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 0.00024:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Accuracy	64.8%
Cost	980

\[\begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.00024:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	64.8%
Cost	980

\[\begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-79}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 0.00024:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Accuracy	96.0%
Cost	969

\[\begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-90} \lor \neg \left(t \leq 4 \cdot 10^{-172}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 5
Accuracy	66.4%
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+193}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.00024:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	82.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-95} \lor \neg \left(z \leq 1.85 \cdot 10^{-10}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 7
Accuracy	77.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-95} \lor \neg \left(z \leq 2.5 \cdot 10^{+37}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8
Accuracy	98.1%
Cost	704

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

Alternative 9
Accuracy	68.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-138}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10
Accuracy	58.1%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-111}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Accuracy	55.7%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023137 
(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))))