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

Average Error: 10.7 → 4.7

Time: 9.1s

Precision: binary64

Cost: 1992

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+238}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

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 (<= t_1 (- INFINITY)) (+ x y) (if (<= t_1 2e+238) (+ x t_1) (+ x y)))))

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)) {
		tmp = x + y;
	} else if (t_1 <= 2e+238) {
		tmp = x + t_1;
	} else {
		tmp = x + y;
	}
	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) {
		tmp = x + y;
	} else if (t_1 <= 2e+238) {
		tmp = x + t_1;
	} else {
		tmp = x + y;
	}
	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:
		tmp = x + y
	elif t_1 <= 2e+238:
		tmp = x + t_1
	else:
		tmp = x + y
	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))
		tmp = Float64(x + y);
	elseif (t_1 <= 2e+238)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + y);
	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)
		tmp = x + y;
	elseif (t_1 <= 2e+238)
		tmp = x + t_1;
	else
		tmp = x + y;
	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[LessEqual[t$95$1, (-Infinity)], N[(x + y), $MachinePrecision], If[LessEqual[t$95$1, 2e+238], N[(x + t$95$1), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Target

Original	10.7
Target	1.1
Herbie	4.7

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 2.0000000000000001e238 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 58.3

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

   2. Taylor expanded in z around inf 25.1

      \[\leadsto x + \color{blue}{y} \]

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.0000000000000001e238

   1. Initial program 0.2

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

4. Final simplification 4.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;x + y\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+238}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternatives

Alternative 1
Error	12.8
Cost	1036

\[\begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+54}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-64}:\\ \;\;\;\;x + \left(-\frac{y \cdot \left(z - t\right)}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 2
Error	11.2
Cost	904

\[\begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+43}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{y \cdot \left(-t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Error	13.9
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{+43}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-74}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4
Error	12.9
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+54}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{y \cdot z}{z - a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Error	14.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-36}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Error	13.6
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-7}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Error	20.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+43}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Error	28.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023077 
(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))))