Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Average Error: 12.8 → 1.6

Time: 11.1s

Precision: binary64

Cost: 1480

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ t_1 := \frac{x}{\frac{y}{y - z}}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -2 \cdot 10^{-66}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)) (t_1 (/ x (/ y (- y z)))))
   (if (<= t_0 (- INFINITY)) t_1 (if (<= t_0 -2e-66) t_0 t_1))))

C

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

↓

double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double t_1 = x / (y / (y - z));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= -2e-66) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}

↓

public static double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double t_1 = x / (y / (y - z));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= -2e-66) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	t_1 = x / (y / (y - z))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= -2e-66:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

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

↓

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y - z)) / y)
	t_1 = Float64(x / Float64(y / Float64(y - z)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= -2e-66)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z)
	t_0 = (x * (y - z)) / y;
	t_1 = x / (y / (y - z));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= -2e-66)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, -2e-66], t$95$0, t$95$1]]]]

Target

Original	12.8
Target	3.2
Herbie	1.6

\[\begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -inf.0 or -2e-66 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 17.3

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

   2. Simplified 2.2

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

      [Start] 17.3	\[ \frac{x \cdot \left(y - z\right)}{y} \]
      rational.json-simplify-2 [=>] 17.3	\[ \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]
      rational.json-simplify-49 [=>] 2.2	\[ \color{blue}{x \cdot \frac{y - z}{y}} \]

   3. Applied egg-rr 2.0

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}} \]

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < -2e-66

   1. Initial program 0.2

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

4. Final simplification 1.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq -2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array} \]

Alternatives

Alternative 1
Error	19.7
Cost	1176

\[\begin{array}{l} t_0 := -z \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-50}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+123}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	19.6
Cost	1176

\[\begin{array}{l} t_0 := -z \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-50}:\\ \;\;\;\;-\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+123}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	19.6
Cost	1176

\[\begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-49}:\\ \;\;\;\;-\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 63000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+28}:\\ \;\;\;\;-z \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(-\frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	19.5
Cost	1176

\[\begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+28}:\\ \;\;\;\;-z \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(-\frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	3.4
Cost	580

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+254}:\\ \;\;\;\;-\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array} \]

Alternative 6
Error	3.3
Cost	580

\[\begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+245}:\\ \;\;\;\;-\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array} \]

Alternative 7
Error	25.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023075 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))