Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Average Error: 1.9 → 0.3

Time: 15.6s

Precision: binary64

Cost: 832

Math

\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]

↓

\[x + a \cdot \frac{z - y}{\left(t - z\right) + 1} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

↓

(FPCore (x y z t a)
 :precision binary64
 (+ x (* a (/ (- z y) (+ (- t z) 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

↓

double code(double x, double y, double z, double t, double a) {
	return x + (a * ((z - y) / ((t - z) + 1.0)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

↓

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (a * ((z - y) / ((t - z) + 1.0d0)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	return x + (a * ((z - y) / ((t - z) + 1.0)));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

↓

def code(x, y, z, t, a):
	return x + (a * ((z - y) / ((t - z) + 1.0)))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

↓

function code(x, y, z, t, a)
	return Float64(x + Float64(a * Float64(Float64(z - y) / Float64(Float64(t - z) + 1.0))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

↓

function tmp = code(x, y, z, t, a)
	tmp = x + (a * ((z - y) / ((t - z) + 1.0)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_] := N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	1.9
Target	0.3
Herbie	0.3

\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a \]

Derivation

1. Initial program 1.9

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]

2. Applied egg-rr 0.3

   \[\leadsto x - \color{blue}{\frac{y - z}{\left(t - z\right) + 1} \cdot a} \]

3. Final simplification 0.3

   \[\leadsto x + a \cdot \frac{z - y}{\left(t - z\right) + 1} \]

Alternatives

Alternative 1
Error	18.0
Cost	1104

\[\begin{array}{l} t_1 := x + a \cdot \frac{z - y}{t}\\ \mathbf{if}\;z \leq -538965903005182460:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.070975677854058 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.924366501265018 \cdot 10^{-117}:\\ \;\;\;\;x + a \cdot \left(y \cdot t - y\right)\\ \mathbf{elif}\;z \leq 3.190409246181771 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 2
Error	8.7
Cost	1036

\[\begin{array}{l} t_1 := x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{if}\;z \leq -538965903005182460:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.294570831372558 \cdot 10^{-48}:\\ \;\;\;\;x + \frac{z \cdot a}{\left(t + 1\right) - z}\\ \mathbf{elif}\;z \leq 3.190409246181771 \cdot 10^{+38}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	18.2
Cost	976

\[\begin{array}{l} t_1 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -2.2578011682471106 \cdot 10^{-34}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.070975677854058 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.597249596906733 \cdot 10^{-77}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3.190409246181771 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 4
Error	18.7
Cost	976

\[\begin{array}{l} t_1 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -2.2578011682471106 \cdot 10^{-34}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.070975677854058 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.597249596906733 \cdot 10^{-77}:\\ \;\;\;\;x + a \cdot \left(y \cdot t - y\right)\\ \mathbf{elif}\;z \leq 3.190409246181771 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 5
Error	9.0
Cost	904

\[\begin{array}{l} t_1 := x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{if}\;z \leq -5.466538720239697 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.190409246181771 \cdot 10^{+38}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	9.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -538965903005182460:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.190409246181771 \cdot 10^{+38}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7
Error	17.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -538965903005182460:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.2605179812303106 \cdot 10^{-17}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 8
Error	19.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -538965903005182460:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.190409246181771 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 9
Error	27.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022308 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))