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

Average Accuracy: 84.7% → 97.0%

Time: 17.1s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z t) :precision binary64 (/ x (/ (- t z) (- y 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) {
	return x / ((t - z) / (y - z));
}

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
    code = x / ((t - z) / (y - z))
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) {
	return x / ((t - z) / (y - z));
}

Python

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

↓

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

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(y - z)) / Float64(t - z))
end

↓

function code(x, y, z, t)
	return Float64(x / Float64(Float64(t - z) / Float64(y - z)))
end

MATLAB

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

↓

function tmp = code(x, y, z, t)
	tmp = x / ((t - z) / (y - z));
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_] := N[(x / N[(N[(t - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	84.7%
Target	97.0%
Herbie	97.0%

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

Derivation

1. Initial program 84.0%

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

2. Simplified 97.6%

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

   [Start] 84.0	\[ \frac{x \cdot \left(y - z\right)}{t - z} \]
   associate-/l* [=>] 97.6	\[ \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

3. Final simplification 97.6%

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

Alternatives

Alternative 1
Accuracy	52.2%
Cost	1108

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{z - y}}\\ t_2 := \frac{x}{\frac{t - z}{y}}\\ \mathbf{if}\;y \leq 3.1 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-83}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	52.2%
Cost	1108

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{z - y}}\\ t_2 := \frac{x}{\frac{t - z}{y}}\\ \mathbf{if}\;y \leq 1.75 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-83}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	34.0%
Cost	1044

\[\begin{array}{l} \mathbf{if}\;z \leq 9.5 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(-\frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Accuracy	52.2%
Cost	1040

\[\begin{array}{l} t_1 := \frac{x}{\frac{t - z}{y}}\\ \mathbf{if}\;y \leq 1.05 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-72}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{-z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	34.4%
Cost	976

\[\begin{array}{l} t_1 := y \cdot \frac{x}{t - z}\\ \mathbf{if}\;z \leq 1.3 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-71}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	50.2%
Cost	976

\[\begin{array}{l} \mathbf{if}\;t \leq 8.2 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \mathbf{elif}\;t \leq 2.26 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \end{array} \]

Alternative 7
Accuracy	35.1%
Cost	848

\[\begin{array}{l} \mathbf{if}\;z \leq 9 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Accuracy	52.0%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq 4.2 \cdot 10^{-27} \lor \neg \left(z \leq 1.4 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \]

Alternative 9
Accuracy	34.4%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq 1.3 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Accuracy	35.0%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq 5.3 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Accuracy	35.2%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	35.1%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq 9.5 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Accuracy	97.0%
Cost	576

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

Alternative 14
Accuracy	35.2%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023159 
(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)))