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

Average Error: 2.1 → 2.1

Time: 15.8s

Precision: binary64

Cost: 832

Math

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

↓

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

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

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 - ((y - z) / (((t - z) + 1.0) / a));
}

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 - ((y - z) / (((t - z) + 1.0d0) / a))
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 - ((y - z) / (((t - z) + 1.0) / a));
}

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

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(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
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 - ((y - z) / (((t - z) + 1.0) / a));
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[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	2.1
Target	0.2
Herbie	2.1

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

Derivation

1. Initial program 2.1

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

2. Final simplification 2.1

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

Alternatives

Alternative 1
Error	10.5
Cost	1168

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-11}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-20}:\\ \;\;\;\;x - \frac{y \cdot a}{1 + t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+61}:\\ \;\;\;\;x - \frac{a \cdot \left(y - z\right)}{1 - z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+75}:\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{-\frac{z}{a}}\\ \end{array} \]

Alternative 2
Error	19.6
Cost	1104

\[\begin{array}{l} t_1 := x - \frac{a \cdot \left(y - z\right)}{t}\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-171}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-252}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+160}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	10.5
Cost	904

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-11}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-6}:\\ \;\;\;\;x - \frac{y \cdot a}{1 + t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{-\frac{z}{a}}\\ \end{array} \]

Alternative 4
Error	10.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-11}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{y \cdot a}{1 + t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 5
Error	16.6
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -0.42:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-82}:\\ \;\;\;\;\frac{a \cdot z}{t} + x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-33}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 6
Error	16.4
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-11}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-33}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7
Error	19.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+71}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 8
Error	27.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023077 
(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))))