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

Average Error: 2.0 → 0.2

Time: 26.0s

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	2.0
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 2.0

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

2. Simplified 0.2

   \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   Proof
   (-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)): 0 points increase in error, 0 points decrease in error
   (-.f64 x (Rewrite<= associate-/r/_binary64 (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))): 34 points increase in error, 11 points decrease in error

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	8.8
Cost	968

\[\begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+38}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+98}:\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \]

Alternative 2
Error	7.5
Cost	968

\[\begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{a}{\frac{t + \left(1 - z\right)}{z}}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+98}:\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \]

Alternative 3
Error	9.4
Cost	904

\[\begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+37}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+45}:\\ \;\;\;\;x - \frac{y}{\frac{t + 1}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \]

Alternative 4
Error	17.5
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+27}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{-87}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+97}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 5
Error	17.5
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+27}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{-91}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+97}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 6
Error	10.0
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+37}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+97}:\\ \;\;\;\;x - \frac{y}{\frac{t + 1}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7
Error	17.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+27}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.9:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 8
Error	19.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+28}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 9
Error	27.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022325 
(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))))