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

Percentage Accurate: 87.7% → 97.3%

Time: 21.5s

Precision: binary64

Cost: 2508

• could not determine a ground truth

  1. x = 2.387501152545511e-262
  2. y = 1.2178575715387347e-86
  3. z = -1.3729119915258474e+173
  4. t = -5.053792087175491e+68

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot \frac{y - z}{t - z}\\ t_2 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \]

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)))) (t_2 (/ (* x (- y z)) (- t z))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-250)
       t_2
       (if (<= t_2 2e-95) t_1 (* (- y z) (/ x (- 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 t_2 = (x * (y - z)) / (t - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-250) {
		tmp = t_2;
	} else if (t_2 <= 2e-95) {
		tmp = t_1;
	} else {
		tmp = (y - z) * (x / (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 t_2 = (x * (y - z)) / (t - z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-250) {
		tmp = t_2;
	} else if (t_2 <= 2e-95) {
		tmp = t_1;
	} else {
		tmp = (y - z) * (x / (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))
	t_2 = (x * (y - z)) / (t - z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-250:
		tmp = t_2
	elif t_2 <= 2e-95:
		tmp = t_1
	else:
		tmp = (y - z) * (x / (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(x * Float64(Float64(y - z) / Float64(t - z)))
	t_2 = Float64(Float64(x * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-250)
		tmp = t_2;
	elseif (t_2 <= 2e-95)
		tmp = t_1;
	else
		tmp = Float64(Float64(y - z) * Float64(x / 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));
	t_2 = (x * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-250)
		tmp = t_2;
	elseif (t_2 <= 2e-95)
		tmp = t_1;
	else
		tmp = (y - z) * (x / (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[(x * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-250], t$95$2, If[LessEqual[t$95$2, 2e-95], t$95$1, N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	87.7%
Target	96.3%
Herbie	97.3%

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -inf.0 or -5.00000000000000027e-250 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 1.99999999999999998e-95

   1. Initial program 82.2%

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

   2. Simplified 99.2%

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

      [Start] 82.2%	\[ \frac{x \cdot \left(y - z\right)}{t - z} \]
      associate-*r/ [<=] 99.2%	\[ \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -5.00000000000000027e-250

   1. Initial program 99.7%

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

   if 1.99999999999999998e-95 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 85.5%

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

   2. Simplified 99.7%

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

      [Start] 85.5%	\[ \frac{x \cdot \left(y - z\right)}{t - z} \]
      associate-*l/ [<=] 99.7%	\[ \color{blue}{\frac{x}{t - z} \cdot \left(y - z\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -5 \cdot 10^{-250}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 2 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	97.3%
Cost	2508

\[\begin{array}{l} t_1 := x \cdot \frac{y - z}{t - z}\\ t_2 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \]

Alternative 2
Accuracy	80.9%
Cost	844

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -12500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-135}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	81.0%
Cost	844

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -12500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-137}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	64.9%
Cost	780

\[\begin{array}{l} \mathbf{if}\;z \leq -12500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-87}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(-\frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Accuracy	64.9%
Cost	780

\[\begin{array}{l} \mathbf{if}\;z \leq -12500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+35}:\\ \;\;\;\;\frac{y}{\frac{-z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	76.9%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -420 \lor \neg \left(y \leq 6.5 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

Alternative 7
Accuracy	75.2%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -340 \lor \neg \left(y \leq 1.8 \cdot 10^{-39}\right):\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

Alternative 8
Accuracy	75.6%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Accuracy	93.4%
Cost	708

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-143}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array} \]

Alternative 10
Accuracy	67.1%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -60000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Accuracy	65.6%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	65.6%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -14500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Accuracy	96.3%
Cost	576

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

Alternative 14
Accuracy	33.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023277 
(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)))