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

Average Error: 12.0 → 2.3

Time: 14.0s

Precision: binary64

Cost: 840

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-181}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.15e-53)
   (/ x (/ (- t z) (- y z)))
   (if (<= z 3.3e-181) (* (- y z) (/ x (- 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 tmp;
	if (z <= -1.15e-53) {
		tmp = x / ((t - z) / (y - z));
	} else if (z <= 3.3e-181) {
		tmp = (y - z) * (x / (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) :: tmp
    if (z <= (-1.15d-53)) then
        tmp = x / ((t - z) / (y - z))
    else if (z <= 3.3d-181) then
        tmp = (y - z) * (x / (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 tmp;
	if (z <= -1.15e-53) {
		tmp = x / ((t - z) / (y - z));
	} else if (z <= 3.3e-181) {
		tmp = (y - z) * (x / (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):
	tmp = 0
	if z <= -1.15e-53:
		tmp = x / ((t - z) / (y - z))
	elif z <= 3.3e-181:
		tmp = (y - z) * (x / (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)
	tmp = 0.0
	if (z <= -1.15e-53)
		tmp = Float64(x / Float64(Float64(t - z) / Float64(y - z)));
	elseif (z <= 3.3e-181)
		tmp = Float64(Float64(y - z) * Float64(x / 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)
	tmp = 0.0;
	if (z <= -1.15e-53)
		tmp = x / ((t - z) / (y - z));
	elseif (z <= 3.3e-181)
		tmp = (y - z) * (x / (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_] := If[LessEqual[z, -1.15e-53], N[(x / N[(N[(t - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e-181], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	12.0
Target	2.2
Herbie	2.3

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

Derivation

1. Split input into 3 regimes

2. if z < -1.1500000000000001e-53

   1. Initial program 16.2

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

   2. Simplified 0.3

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

      [Start] 16.2	\[ \frac{x \cdot \left(y - z\right)}{t - z} \]
      rational.json-simplify-2 [=>] 16.2	\[ \frac{\color{blue}{\left(y - z\right) \cdot x}}{t - z} \]
      rational.json-simplify-49 [=>] 0.3	\[ \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Applied egg-rr 0.3

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

   if -1.1500000000000001e-53 < z < 3.30000000000000009e-181

   1. Initial program 6.1

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

   2. Simplified 5.9

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

      [Start] 6.1	\[ \frac{x \cdot \left(y - z\right)}{t - z} \]
      rational.json-simplify-49 [=>] 5.9	\[ \color{blue}{\left(y - z\right) \cdot \frac{x}{t - z}} \]

   if 3.30000000000000009e-181 < z

   1. Initial program 13.1

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

   2. Simplified 1.1

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

      [Start] 13.1	\[ \frac{x \cdot \left(y - z\right)}{t - z} \]
      rational.json-simplify-2 [=>] 13.1	\[ \frac{\color{blue}{\left(y - z\right) \cdot x}}{t - z} \]
      rational.json-simplify-49 [=>] 1.1	\[ \color{blue}{x \cdot \frac{y - z}{t - z}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 2.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-181}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	17.0
Cost	1040

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-140}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{z}{t - z}\right)\\ \end{array} \]

Alternative 2
Error	17.1
Cost	976

\[\begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ t_2 := x \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	16.8
Cost	976

\[\begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;z \leq -5 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \]

Alternative 4
Error	17.0
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -1.72 \cdot 10^{-140}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-189}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \]

Alternative 5
Error	26.5
Cost	848

\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-137}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	2.3
Cost	840

\[\begin{array}{l} t_1 := x \cdot \frac{y - z}{t - z}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-179}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	21.6
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.092:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	21.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	17.0
Cost	712

\[\begin{array}{l} t_1 := x \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	25.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Error	26.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	26.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	2.2
Cost	576

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

Alternative 14
Error	40.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023074 
(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)))