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

Average Error: 11.1 → 0.2

Time: 15.1s

Precision: binary64

Cost: 1992

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;t_1 \leq 10^{+307}:\\ \;\;\;\;t_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ y (/ (- z a) (- z t))))
     (if (<= t_1 1e+307) (+ t_1 x) (+ x (* (- z t) (/ y (- 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 t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (y / ((z - a) / (z - t)));
	} else if (t_1 <= 1e+307) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((z - t) * (y / (z - a)));
	}
	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 / ((z - a) / (z - t)));
	} else if (t_1 <= 1e+307) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((z - t) * (y / (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):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (y / ((z - a) / (z - t)))
	elif t_1 <= 1e+307:
		tmp = t_1 + x
	else:
		tmp = x + ((z - t) * (y / (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)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / Float64(z - t))));
	elseif (t_1 <= 1e+307)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / 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)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (y / ((z - a) / (z - t)));
	elseif (t_1 <= 1e+307)
		tmp = t_1 + x;
	else
		tmp = x + ((z - t) * (y / (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_] := 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 + N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	11.1
Target	1.1
Herbie	0.2

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.0

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

   2. Simplified 0.1

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

      [Start] 64.0	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
      associate-/l* [=>] 0.1	\[ x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}} \]

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 9.99999999999999986e306

   1. Initial program 0.2

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

   if 9.99999999999999986e306 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 63.9

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

   2. Simplified 0.3

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

      [Start] 63.9	\[ x + \frac{y \cdot \left(z - t\right)}{z - a} \]
      associate-*l/ [<=] 0.3	\[ x + \color{blue}{\frac{y}{z - a} \cdot \left(z - t\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 10^{+307}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array} \]

Alternatives

Alternative 1
Error	18.5
Cost	1240

\[\begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-37}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-200}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -1.72 \cdot 10^{-276}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-290}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-287}:\\ \;\;\;\;y - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-31}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 2
Error	18.6
Cost	1240

\[\begin{array}{l} \mathbf{if}\;a \leq -5.9 \cdot 10^{-27}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-200}:\\ \;\;\;\;x + \frac{t}{\frac{-z}{y}}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-276}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-289}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-284}:\\ \;\;\;\;y - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-32}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 3
Error	17.6
Cost	1108

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-178}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-243}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-33}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	17.6
Cost	1108

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-178}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-243}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-32}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 5
Error	17.4
Cost	1108

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-178}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-243}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 9.3 \cdot 10^{-32}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 6
Error	18.8
Cost	1108

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -6.4 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-178}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.4 \cdot 10^{-243}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 4.75 \cdot 10^{-32}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 7
Error	15.3
Cost	1104

\[\begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+170}:\\ \;\;\;\;x + \frac{t}{\frac{-z}{y}}\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+193}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z - a}{y}}\\ \end{array} \]

Alternative 8
Error	13.1
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{z}{\frac{z - a}{y}}\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-15}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 7.3 \cdot 10^{-31}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	11.4
Cost	1104

\[\begin{array}{l} t_1 := x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+110}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	11.4
Cost	1104

\[\begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq 8.3 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+110}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \end{array} \]

Alternative 11
Error	20.7
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -0.024:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-242}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-182}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 12
Error	20.4
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -0.006:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-183}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 13
Error	20.4
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -0.024:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-183}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 14
Error	3.1
Cost	704

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

Alternative 15
Error	1.1
Cost	704

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

Alternative 16
Error	30.5
Cost	592

\[\begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-207}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-283}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-76}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	20.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{+125}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	28.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023060 
(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))))