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

Average Accuracy: 81.8% → 98.0%

Time: 12.6s

Precision: binary64

Cost: 1865

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+292} \lor \neg \left(t_1 \leq -2 \cdot 10^{-305}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y z)) (- t z))))
   (if (or (<= t_1 -2e+292) (not (<= t_1 -2e-305)))
     (/ x (/ (- t z) (- y z)))
     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 = (x * (y - z)) / (t - z);
	double tmp;
	if ((t_1 <= -2e+292) || !(t_1 <= -2e-305)) {
		tmp = x / ((t - z) / (y - z));
	} 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
    t_1 = (x * (y - z)) / (t - z)
    if ((t_1 <= (-2d+292)) .or. (.not. (t_1 <= (-2d-305)))) then
        tmp = x / ((t - z) / (y - z))
    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 = (x * (y - z)) / (t - z);
	double tmp;
	if ((t_1 <= -2e+292) || !(t_1 <= -2e-305)) {
		tmp = x / ((t - z) / (y - z));
	} 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 = (x * (y - z)) / (t - z)
	tmp = 0
	if (t_1 <= -2e+292) or not (t_1 <= -2e-305):
		tmp = x / ((t - z) / (y - z))
	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(x * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if ((t_1 <= -2e+292) || !(t_1 <= -2e-305))
		tmp = Float64(x / Float64(Float64(t - z) / Float64(y - z)));
	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_2 = code(x, y, z, t)
	t_1 = (x * (y - z)) / (t - z);
	tmp = 0.0;
	if ((t_1 <= -2e+292) || ~((t_1 <= -2e-305)))
		tmp = x / ((t - z) / (y - z));
	else
		tmp = t_1;
	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[Or[LessEqual[t$95$1, -2e+292], N[Not[LessEqual[t$95$1, -2e-305]], $MachinePrecision]], N[(x / N[(N[(t - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Target

Original	81.8%
Target	96.7%
Herbie	98.0%

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -2e292 or -1.99999999999999999e-305 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 71.9%

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

   2. Simplified 97.1%

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

      [Start] 71.9	\[ \frac{x \cdot \left(y - z\right)}{t - z} \]
      associate-/l* [=>] 97.1	\[ \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   if -2e292 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -1.99999999999999999e-305

   1. Initial program 99.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -2 \cdot 10^{+292} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \leq -2 \cdot 10^{-305}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	74.0%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -9 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(-\frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	74.2%
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-253}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 3
Accuracy	74.3%
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-294}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 4
Accuracy	74.6%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 5
Accuracy	74.6%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 6
Accuracy	96.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-79} \lor \neg \left(z \leq 4.8 \cdot 10^{-307}\right):\\ \;\;\;\;x \cdot \frac{z - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \]

Alternative 7
Accuracy	96.6%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \frac{z - y}{z - t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-307}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \end{array} \]

Alternative 8
Accuracy	71.2%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-39} \lor \neg \left(z \leq 4.1 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \]

Alternative 9
Accuracy	75.0%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-17} \lor \neg \left(z \leq 7 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 10
Accuracy	74.6%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 11
Accuracy	41.3%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-136}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	60.1%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Accuracy	61.2%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Accuracy	61.2%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Accuracy	96.7%
Cost	576

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

Alternative 16
Accuracy	37.6%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023141 
(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)))