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

Average Accuracy: 84.2% → 97.7%

Time: 11.6s

Precision: binary64

Cost: 969

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-8} \lor \neg \left(z \leq 6 \cdot 10^{-268}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e-8) (not (<= z 6e-268)))
   (+ x (* (/ (- y z) (- a z)) t))
   (+ x (/ (- y z) (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) * t) / (a - z));
}

↓

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e-8) || !(z <= 6e-268)) {
		tmp = x + (((y - z) / (a - z)) * t);
	} else {
		tmp = x + ((y - z) / ((a - 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) / (a - z))
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 <= (-2.3d-8)) .or. (.not. (z <= 6d-268))) then
        tmp = x + (((y - z) / (a - z)) * t)
    else
        tmp = x + ((y - z) / ((a - 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) / (a - z));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e-8) || !(z <= 6e-268)) {
		tmp = x + (((y - z) / (a - z)) * t);
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	return x + (((y - z) * t) / (a - z))

↓

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e-8) or not (z <= 6e-268):
		tmp = x + (((y - z) / (a - z)) * t)
	else:
		tmp = x + ((y - z) / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)))
end

↓

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e-8) || !(z <= 6e-268))
		tmp = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.3e-8) || ~((z <= 6e-268)))
		tmp = x + (((y - z) / (a - z)) * t);
	else
		tmp = x + ((y - z) / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.3e-8], N[Not[LessEqual[z, 6e-268]], $MachinePrecision]], N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	84.2%
Target	99.0%
Herbie	97.7%

\[\begin{array}{l} \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if z < -2.3000000000000001e-8 or 5.9999999999999995e-268 < z

   1. Initial program 80.2%

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

   2. Simplified 98.7%

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

      [Start] 80.2	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      associate-*l/ [<=] 98.7	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   if -2.3000000000000001e-8 < z < 5.9999999999999995e-268

   1. Initial program 95.5%

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

   2. Simplified 94.9%

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

      [Start] 95.5	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      associate-/l* [=>] 94.9	\[ x + \color{blue}{\frac{y - z}{\frac{a - z}{t}}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-8} \lor \neg \left(z \leq 6 \cdot 10^{-268}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	83.3%
Cost	1104

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+99}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-268}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \end{array} \]

Alternative 2
Accuracy	77.4%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+101}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-24}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2900000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 3
Accuracy	79.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-24} \lor \neg \left(z \leq 1.65 \cdot 10^{-40}\right):\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 4
Accuracy	83.8%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+100}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+37}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \end{array} \]

Alternative 5
Accuracy	77.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+58}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2550000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 6
Accuracy	97.7%
Cost	704

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

Alternative 7
Accuracy	68.9%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-93}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 8
Accuracy	55.2%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023133 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

  (+ x (/ (* (- y z) t) (- a z))))