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

Average Error: 11.5 → 1.6

Time: 7.8s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\frac{x \cdot y}{t - z} - \frac{x \cdot z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array} \]

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 -2e+63)
     (/ x (/ (- t z) (- y z)))
     (if (<= t_1 2e+299)
       (- (/ (* x y) (- t z)) (/ (* x z) (- t z)))
       (* 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 <= -2e+63) {
		tmp = x / ((t - z) / (y - z));
	} else if (t_1 <= 2e+299) {
		tmp = ((x * y) / (t - z)) - ((x * z) / (t - z));
	} else {
		tmp = x * ((y - z) / (t - z));
	}
	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
    t_1 = (x * (y - z)) / (t - z)
    if (t_1 <= (-2d+63)) then
        tmp = x / ((t - z) / (y - z))
    else if (t_1 <= 2d+299) then
        tmp = ((x * y) / (t - z)) - ((x * z) / (t - z))
    else
        tmp = x * ((y - z) / (t - z))
    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 = (x * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -2e+63) {
		tmp = x / ((t - z) / (y - z));
	} else if (t_1 <= 2e+299) {
		tmp = ((x * y) / (t - z)) - ((x * z) / (t - z));
	} 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 <= -2e+63:
		tmp = x / ((t - z) / (y - z))
	elif t_1 <= 2e+299:
		tmp = ((x * y) / (t - z)) - ((x * z) / (t - z))
	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 <= -2e+63)
		tmp = Float64(x / Float64(Float64(t - z) / Float64(y - z)));
	elseif (t_1 <= 2e+299)
		tmp = Float64(Float64(Float64(x * y) / Float64(t - z)) - Float64(Float64(x * z) / Float64(t - z)));
	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 <= -2e+63)
		tmp = x / ((t - z) / (y - z));
	elseif (t_1 <= 2e+299)
		tmp = ((x * y) / (t - z)) - ((x * z) / (t - z));
	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, -2e+63], N[(x / N[(N[(t - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+299], N[(N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	11.5
Target	2.3
Herbie	1.6

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -2.00000000000000012e63

   1. Initial program 29.2

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

   2. Simplified 2.9

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

   3. Applied egg-rr 2.7

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

   if -2.00000000000000012e63 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 2.0000000000000001e299

   1. Initial program 1.5

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

   2. Simplified 2.4

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

   3. Taylor expanded in y around 0 1.5

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

   if 2.0000000000000001e299 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 62.5

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

   2. Simplified 0.5

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 1.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -2 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\frac{x \cdot y}{t - z} - \frac{x \cdot z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array} \]

Reproduce

herbie shell --seed 2022210 
(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)))