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

Average Accuracy: 97.0% → 99.7%

Time: 14.3s

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	97.0%
Target	99.7%
Herbie	99.7%

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

Derivation

1. Initial program 97.0%

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

2. Simplified 99.7%

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

   [Start] 97.0	\[ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   associate-/r/ [=>] 99.7	\[ x - \color{blue}{\frac{y - z}{\left(t - z\right) + 1} \cdot a} \]

3. Final simplification 99.7%

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

Alternatives

Alternative 1
Accuracy	72.7%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+28}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-278}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-170}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 450000000000:\\ \;\;\;\;x + \frac{z}{\frac{t + 1}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \end{array} \]

Alternative 2
Accuracy	72.7%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+28}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-278}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-175}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 4800000000000:\\ \;\;\;\;x + \frac{z \cdot a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \end{array} \]

Alternative 3
Accuracy	71.4%
Cost	976

\[\begin{array}{l} t_1 := x - \frac{y \cdot a}{t}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+28}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-176}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 40000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 4
Accuracy	71.4%
Cost	976

\[\begin{array}{l} t_1 := x - \frac{y \cdot a}{t}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+28}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-177}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 380000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \end{array} \]

Alternative 5
Accuracy	88.8%
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+46} \lor \neg \left(z \leq 0.76\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \end{array} \]

Alternative 6
Accuracy	92.5%
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+45} \lor \neg \left(z \leq 0.014\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{t + 1}{a}}\\ \end{array} \]

Alternative 7
Accuracy	85.4%
Cost	904

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+46}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2200000000000:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \]

Alternative 8
Accuracy	84.8%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+46}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 75000000000:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \end{array} \]

Alternative 9
Accuracy	71.2%
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-26}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-45}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 10
Accuracy	70.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-26}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 85000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 11
Accuracy	56.3%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023125 
(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))))