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

Average Error: 10.6 → 0.7

Time: 12.2s

Precision: binary64

Cost: 1993

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+115}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \]

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 (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+115)))
     (+ x (/ y (/ (- z a) (- z t))))
     (+ t_1 x))))

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;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+115)) {
		tmp = x + (y / ((z - a) / (z - t)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

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;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+115)) {
		tmp = x + (y / ((z - a) / (z - t)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

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 = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+115):
		tmp = x + (y / ((z - a) / (z - t)))
	else:
		tmp = t_1 + x
	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)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+115))
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / Float64(z - t))));
	else
		tmp = Float64(t_1 + x);
	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)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+115)))
		tmp = x + (y / ((z - a) / (z - t)));
	else
		tmp = t_1 + x;
	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_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+115]], $MachinePrecision]], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Target

Original	10.6
Target	1.4
Herbie	0.7

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 2e115 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 45.5

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

   2. Simplified 2.1

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

      [Start] 45.5	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
      associate-/l* [=>] 2.1	\[ x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}} \]

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2e115

   1. Initial program 0.3

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

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+115}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]

Alternatives

Alternative 1
Error	21.8
Cost	1108

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{-167}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-308}:\\ \;\;\;\;y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-167}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 2
Error	18.5
Cost	1108

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-82}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 0.00142:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+14}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	1.2
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-139} \lor \neg \left(z \leq 8.6 \cdot 10^{-138}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 4
Error	19.9
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-73}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-117}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5
Error	9.9
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-73} \lor \neg \left(z \leq 1.05 \cdot 10^{-114}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6
Error	7.7
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-17} \lor \neg \left(z \leq 1.62 \cdot 10^{-43}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 7
Error	20.1
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-73}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8
Error	20.1
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-73}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-117}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9
Error	15.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-177}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-44}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10
Error	13.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-73}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 10^{-43}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11
Error	2.8
Cost	704

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

Alternative 12
Error	27.3
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -2700000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-37}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-223}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	19.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-73}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 14
Error	28.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023125 
(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))))