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

Percentage Accurate: 97.2% → 99.7%

Time: 22.4s

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	97.2%
Target	99.7%
Herbie	99.7%

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

Derivation

1. Initial program 96.5%

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

2. Simplified 99.5%

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

   [Start] 96.5	\[ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   associate-/r/ [=>] 99.5	\[ x - \color{blue}{\frac{y - z}{\left(t - z\right) + 1} \cdot a} \]

3. Final simplification 99.5%

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

Alternatives

Alternative 1
Accuracy	89.1%
Cost	1232

\[\begin{array}{l} t_1 := x + z \cdot \frac{a}{\left(t - z\right) + 1}\\ \mathbf{if}\;t \leq -1.06 \cdot 10^{+160}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(a \cdot \frac{1}{-1 + \left(z - t\right)}\right)\\ \mathbf{elif}\;t \leq 3500000000:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	72.5%
Cost	1108

\[\begin{array}{l} t_1 := x + \frac{z \cdot a}{t}\\ t_2 := x - \left(y - z\right) \cdot a\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+39}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 3
Accuracy	73.1%
Cost	1108

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot a\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+39}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-222}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{z \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 4
Accuracy	73.2%
Cost	1108

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot a\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+40}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-221}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+84}:\\ \;\;\;\;x + z \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 5
Accuracy	87.2%
Cost	1036

\[\begin{array}{l} t_1 := x + a \cdot \frac{z - y}{-z}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-43}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+84}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	61.0%
Cost	976

\[\begin{array}{l} t_1 := y \cdot \frac{a}{-1 - t}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+34}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7
Accuracy	83.5%
Cost	972

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+66}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-43}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+83}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 8
Accuracy	83.7%
Cost	972

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+68}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-45}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+96}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 9
Accuracy	91.2%
Cost	968

\[\begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+84}:\\ \;\;\;\;x + a \cdot \frac{z - y}{-z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{y - z}{\frac{t + 1}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \]

Alternative 10
Accuracy	61.5%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+34}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \frac{a}{-1 - t}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{z \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 11
Accuracy	83.0%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+65}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-43}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+84}:\\ \;\;\;\;x + z \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 12
Accuracy	54.3%
Cost	656

\[\begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-261}:\\ \;\;\;\;-a\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-85}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Accuracy	64.3%
Cost	588

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+34}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 14
Accuracy	64.4%
Cost	588

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+34}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-13}:\\ \;\;\;\;a \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 15
Accuracy	64.4%
Cost	588

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+34}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 16
Accuracy	65.7%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+65}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 17
Accuracy	54.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023160 
(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))))