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

Average Error: 12.2 → 0.5

Time: 4.9s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ t_1 := x - \frac{x}{\frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+272}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{y}, x, x\right)\\ \mathbf{elif}\;t_0 \leq -4 \cdot 10^{+41}:\\ \;\;\;\;x - \frac{1}{y} \cdot \frac{z}{\frac{1}{x}}\\ \mathbf{elif}\;t_0 \leq 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+291}:\\ \;\;\;\;x - {\left(\frac{y}{x \cdot z}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (/ x (/ y z)))))
   (if (<= t_0 -2e+272)
     (fma (/ (- z) y) x x)
     (if (<= t_0 -4e+41)
       (- x (* (/ 1.0 y) (/ z (/ 1.0 x))))
       (if (<= t_0 1e-112)
         t_1
         (if (<= t_0 5e+291) (- x (pow (/ y (* x z)) -1.0)) 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 - (x / (y / z));
	double tmp;
	if (t_0 <= -2e+272) {
		tmp = fma((-z / y), x, x);
	} else if (t_0 <= -4e+41) {
		tmp = x - ((1.0 / y) * (z / (1.0 / x)));
	} else if (t_0 <= 1e-112) {
		tmp = t_1;
	} else if (t_0 <= 5e+291) {
		tmp = x - pow((y / (x * z)), -1.0);
	} 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(x / Float64(y / z)))
	tmp = 0.0
	if (t_0 <= -2e+272)
		tmp = fma(Float64(Float64(-z) / y), x, x);
	elseif (t_0 <= -4e+41)
		tmp = Float64(x - Float64(Float64(1.0 / y) * Float64(z / Float64(1.0 / x))));
	elseif (t_0 <= 1e-112)
		tmp = t_1;
	elseif (t_0 <= 5e+291)
		tmp = Float64(x - (Float64(y / Float64(x * z)) ^ -1.0));
	else
		tmp = t_1;
	end
	return 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[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+272], N[(N[((-z) / y), $MachinePrecision] * x + x), $MachinePrecision], If[LessEqual[t$95$0, -4e+41], N[(x - N[(N[(1.0 / y), $MachinePrecision] * N[(z / N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e-112], t$95$1, If[LessEqual[t$95$0, 5e+291], N[(x - N[Power[N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Target

Original	12.2
Target	2.8
Herbie	0.5

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

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -2.0000000000000001e272

   1. Initial program 51.6

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

   2. Simplified 4.8

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

   3. Applied egg-rr 2.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\frac{z}{y}, x, x\right)} \]

   if -2.0000000000000001e272 < (/.f64 (*.f64 x (-.f64 y z)) y) < -4.00000000000000002e41

   1. Initial program 0.2

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

   2. Simplified 5.9

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

   3. Applied egg-rr 0.2

      \[\leadsto x - \color{blue}{\frac{1}{y} \cdot \frac{z}{\frac{1}{x}}} \]

   if -4.00000000000000002e41 < (/.f64 (*.f64 x (-.f64 y z)) y) < 9.9999999999999995e-113 or 5.0000000000000001e291 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 16.2

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

   2. Simplified 3.6

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

   3. Applied egg-rr 6.6

      \[\leadsto x - \color{blue}{{\left(\frac{y}{z \cdot x}\right)}^{-1}} \]

   4. Applied egg-rr 0.3

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

   if 9.9999999999999995e-113 < (/.f64 (*.f64 x (-.f64 y z)) y) < 5.0000000000000001e291

   1. Initial program 0.3

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

   2. Simplified 4.8

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

   3. Applied egg-rr 0.2

      \[\leadsto x - \color{blue}{{\left(\frac{y}{z \cdot x}\right)}^{-1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -2 \cdot 10^{+272}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{y}, x, x\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq -4 \cdot 10^{+41}:\\ \;\;\;\;x - \frac{1}{y} \cdot \frac{z}{\frac{1}{x}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 10^{-112}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 5 \cdot 10^{+291}:\\ \;\;\;\;x - {\left(\frac{y}{x \cdot z}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022210 
(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))