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

Average Error: 11.3 → 2.3

Time: 21.8s

Precision: binary64

Cost: 972

Math

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

↓

\[\begin{array}{l} t_1 := \frac{z - y}{z - t} \cdot x\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-220}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;x \ne 0:\\ \;\;\;\;\frac{z - y}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - y\right) \cdot x}{z - t}\\ \end{array}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- z y) (- z t)) x)))
   (if (<= z -1.4e-151)
     t_1
     (if (<= z 9.5e-220)
       (if (!= x 0.0) (/ (- z y) (/ (- z t) x)) (/ (* (- z y) x) (- z t)))
       t_1))))

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 = ((z - y) / (z - t)) * x;
	double tmp;
	if (z <= -1.4e-151) {
		tmp = t_1;
	} else if (z <= 9.5e-220) {
		double tmp_1;
		if (x != 0.0) {
			tmp_1 = (z - y) / ((z - t) / x);
		} else {
			tmp_1 = ((z - y) * x) / (z - t);
		}
		tmp = tmp_1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (y - z)) / (t - z)
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    real(8) :: tmp_1
    t_1 = ((z - y) / (z - t)) * x
    if (z <= (-1.4d-151)) then
        tmp = t_1
    else if (z <= 9.5d-220) then
        if (x /= 0.0d0) then
            tmp_1 = (z - y) / ((z - t) / x)
        else
            tmp_1 = ((z - y) * x) / (z - t)
        end if
        tmp = tmp_1
    else
        tmp = t_1
    end if
    code = tmp
end function

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 = ((z - y) / (z - t)) * x;
	double tmp;
	if (z <= -1.4e-151) {
		tmp = t_1;
	} else if (z <= 9.5e-220) {
		double tmp_1;
		if (x != 0.0) {
			tmp_1 = (z - y) / ((z - t) / x);
		} else {
			tmp_1 = ((z - y) * x) / (z - t);
		}
		tmp = tmp_1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = ((z - y) / (z - t)) * x
	tmp = 0
	if z <= -1.4e-151:
		tmp = t_1
	elif z <= 9.5e-220:
		tmp_1 = 0
		if x != 0.0:
			tmp_1 = (z - y) / ((z - t) / x)
		else:
			tmp_1 = ((z - y) * x) / (z - t)
		tmp = tmp_1
	else:
		tmp = t_1
	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(Float64(z - y) / Float64(z - t)) * x)
	tmp = 0.0
	if (z <= -1.4e-151)
		tmp = t_1;
	elseif (z <= 9.5e-220)
		tmp_1 = 0.0
		if (x != 0.0)
			tmp_1 = Float64(Float64(z - y) / Float64(Float64(z - t) / x));
		else
			tmp_1 = Float64(Float64(Float64(z - y) * x) / Float64(z - t));
		end
		tmp = tmp_1;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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

↓

function tmp_3 = code(x, y, z, t)
	t_1 = ((z - y) / (z - t)) * x;
	tmp = 0.0;
	if (z <= -1.4e-151)
		tmp = t_1;
	elseif (z <= 9.5e-220)
		tmp_2 = 0.0;
		if (x ~= 0.0)
			tmp_2 = (z - y) / ((z - t) / x);
		else
			tmp_2 = ((z - y) * x) / (z - t);
		end
		tmp = tmp_2;
	else
		tmp = t_1;
	end
	tmp_3 = 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[(N[(z - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -1.4e-151], t$95$1, If[LessEqual[z, 9.5e-220], If[Unequal[x, 0.0], N[(N[(z - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]], t$95$1]]]

Target

Original	11.3
Target	2.2
Herbie	2.3

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

Derivation

1. Split input into 2 regimes

2. if z < -1.4e-151 or 9.50000000000000062e-220 < z

   1. Initial program 12.5

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

   2. Simplified 12.5

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

   3. Applied egg-rr 1.3

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

   if -1.4e-151 < z < 9.50000000000000062e-220

   1. Initial program 6.0

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

   2. Simplified 6.0

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

   3. Applied egg-rr 6.4

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;x \ne 0:\\ \;\;\;\;\frac{z - y}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ } \end{array}} \]

   4. Simplified 6.4

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;x \ne 0:\\ \;\;\;\;\frac{z - y}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - y\right) \cdot x}{z - t}\\ } \end{array}} \]
      Proof
3. Recombined 2 regimes into one program.

Alternatives

Alternative 1
Error	22.4
Cost	1240

\[\begin{array}{l} t_1 := \frac{x}{z} \cdot \left(z - y\right)\\ t_2 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -6 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{t} \cdot \left(y - z\right)\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-287}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	22.3
Cost	1240

\[\begin{array}{l} t_1 := \frac{x}{z} \cdot \left(z - y\right)\\ t_2 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	22.4
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ t_2 := \frac{x}{z} \cdot \left(z - y\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.7 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z - t} \cdot z\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-287}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	26.4
Cost	912

\[\begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-134}:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-113}:\\ \;\;\;\;\left(-\frac{y}{z}\right) \cdot x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-12}:\\ \;\;\;\;-\frac{z \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	18.0
Cost	844

\[\begin{array}{l} t_1 := \frac{z - y}{z} \cdot x\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-113}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+141}:\\ \;\;\;\;\frac{x}{z - t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	7.2
Cost	840

\[\begin{array}{l} t_1 := \frac{z - y}{z} \cdot x\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+149}:\\ \;\;\;\;\frac{x}{z - t} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	2.4
Cost	840

\[\begin{array}{l} t_1 := \frac{z - y}{z - t} \cdot x\\ \mathbf{if}\;z \leq -1 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-219}:\\ \;\;\;\;\frac{x}{z - t} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	26.9
Cost	780

\[\begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-139}:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-96}:\\ \;\;\;\;\frac{-y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	20.3
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	21.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2:\\ \;\;\;\;\frac{x}{t} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Error	25.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	40.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023010 
(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)))