Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.0% → 98.1%

Time: 13.7s

Precision: binary64

Cost: 1864

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y z)) (- t z))))
   (if (<= t_1 (- INFINITY))
     (/ x (/ (- t z) (- y z)))
     (if (<= t_1 5e+244) t_1 (* x (/ (- y z) (- t z)))))))

C

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

↓

double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x / ((t - z) / (y - z));
	} else if (t_1 <= 5e+244) {
		tmp = t_1;
	} else {
		tmp = x * ((y - z) / (t - z));
	}
	return tmp;
}

Java

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

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x / ((t - z) / (y - z));
	} else if (t_1 <= 5e+244) {
		tmp = t_1;
	} else {
		tmp = x * ((y - z) / (t - z));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = (x * (y - z)) / (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x / ((t - z) / (y - z))
	elif t_1 <= 5e+244:
		tmp = t_1
	else:
		tmp = x * ((y - z) / (t - z))
	return tmp

Julia

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

↓

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x / Float64(Float64(t - z) / Float64(y - z)));
	elseif (t_1 <= 5e+244)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y - z) / Float64(t - z)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	t_1 = (x * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x / ((t - z) / (y - z));
	elseif (t_1 <= 5e+244)
		tmp = t_1;
	else
		tmp = x * ((y - z) / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x / N[(N[(t - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+244], t$95$1, N[(x * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	84.0%
Target	97.1%
Herbie	98.1%

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 38.2%

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

   2. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]
      Step-by-step derivation

      [Start] 38.2%	\[ \frac{x \cdot \left(y - z\right)}{t - z} \]
      associate-/l* [=>] 100.0%	\[ \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5.00000000000000022e244

   1. Initial program 97.8%

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

   if 5.00000000000000022e244 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 50.1%

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

   2. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
      Step-by-step derivation

      [Start] 50.1%	\[ \frac{x \cdot \left(y - z\right)}{t - z} \]
      associate-*r/ [<=] 99.9%	\[ \color{blue}{x \cdot \frac{y - z}{t - z}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 5 \cdot 10^{+244}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.1%
Cost	1864

\[\begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array} \]

Alternative 2
Accuracy	68.7%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-165}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	68.7%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ t_2 := x + x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-164}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	74.1%
Cost	776

\[\begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \frac{-z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \end{array} \]

Alternative 5
Accuracy	58.8%
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-110}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{t}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	60.0%
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(-\frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Accuracy	60.0%
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Accuracy	59.8%
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-71}:\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Accuracy	60.0%
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{y \cdot \left(-x\right)}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Accuracy	71.9%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-62} \lor \neg \left(z \leq 3.6 \cdot 10^{-65}\right):\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \end{array} \]

Alternative 11
Accuracy	69.0%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	60.3%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Accuracy	97.0%
Cost	576

\[x \cdot \frac{y - z}{t - z} \]

Alternative 14
Accuracy	35.9%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023263 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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