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

Average Accuracy: 96.6% → 99.5%

Time: 15.1s

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	96.6%
Target	99.5%
Herbie	99.5%

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

Derivation

1. Initial program 96.6%

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

2. Simplified 99.5%

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

   [Start] 96.6	\[ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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	74.2%
Cost	1372

\[\begin{array}{l} t_1 := x - y \cdot \frac{a}{1 - z}\\ t_2 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-89}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-69}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 390000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 420000000000:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	76.3%
Cost	1368

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{a}{z}\\ t_2 := x - y \cdot \frac{a}{1 - z}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+81}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-276}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-115}:\\ \;\;\;\;x - z \cdot \frac{a}{z + -1}\\ \mathbf{elif}\;t \leq 1.04 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \]

Alternative 3
Accuracy	76.6%
Cost	1368

\[\begin{array}{l} t_1 := x + \left(y \cdot \frac{a}{z} - a\right)\\ t_2 := x - y \cdot \frac{a}{1 - z}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+80}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-275}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-116}:\\ \;\;\;\;x - z \cdot \frac{a}{z + -1}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \]

Alternative 4
Accuracy	76.2%
Cost	1104

\[\begin{array}{l} t_1 := x - z \cdot \frac{a}{z + -1}\\ t_2 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-275}:\\ \;\;\;\;x - y \cdot \frac{a}{1 - z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	77.6%
Cost	1104

\[\begin{array}{l} t_1 := x - z \cdot \frac{a}{z + -1}\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+80}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-275}:\\ \;\;\;\;x - y \cdot \frac{a}{1 - z}\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \]

Alternative 6
Accuracy	71.3%
Cost	976

\[\begin{array}{l} t_1 := x - y \cdot \frac{a}{t}\\ \mathbf{if}\;t \leq -6.1 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-94}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-268}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+21}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	71.8%
Cost	976

\[\begin{array}{l} t_1 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-92}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 10^{-268}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+22}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	88.3%
Cost	968

\[\begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+82}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{a}{1 - z} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \end{array} \]

Alternative 9
Accuracy	89.6%
Cost	968

\[\begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+82}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+41}:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \end{array} \]

Alternative 10
Accuracy	87.2%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -120 \lor \neg \left(z \leq 1100000000\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t + 1}{a}}\\ \end{array} \]

Alternative 11
Accuracy	72.3%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+21}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5200:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 12
Accuracy	69.3%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -0.00145:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 13
Accuracy	56.8%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023137 
(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))))