Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A

Average Accuracy: 97.9% → 97.9%

Time: 13.7s

Precision: binary64

Cost: 704

Math

\[x + y \cdot \frac{z - t}{z - a} \]

↓

\[x + y \cdot \frac{z - t}{z - a} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- z a)))))

↓

(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (z - a)));
}

↓

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (z - 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 - 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 - a)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (z - a)));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (z - a)));
}

Python

def code(x, y, z, t, a):
	return x + (y * ((z - t) / (z - a)))

↓

def code(x, y, z, t, a):
	return x + (y * ((z - t) / (z - a)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(z - t) / Float64(z - a))))
end

↓

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(z - t) / Float64(z - a))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * ((z - t) / (z - a)));
end

↓

function tmp = code(x, y, z, t, a)
	tmp = x + (y * ((z - t) / (z - a)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	97.9%
Target	98.1%
Herbie	97.9%

\[x + \frac{y}{\frac{z - a}{z - t}} \]

Derivation

1. Initial program 97.9%

   \[x + y \cdot \frac{z - t}{z - a} \]

2. Final simplification 97.9%

   \[\leadsto x + y \cdot \frac{z - t}{z - a} \]

Alternatives

Alternative 1
Accuracy	60.4%
Cost	1112

\[\begin{array}{l} t_1 := y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{-28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-110}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-191}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-247}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 2
Accuracy	71.2%
Cost	1108

\[\begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{-38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 130000000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+198}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Accuracy	81.9%
Cost	1104

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -61000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-141}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	81.5%
Cost	1104

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := x + \left(y - t \cdot \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-139}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	61.9%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-112}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-192}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-234}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Accuracy	62.0%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-112}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-191}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-234}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Accuracy	61.9%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-112}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-191}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-229}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-249}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Accuracy	78.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-38} \lor \neg \left(x \leq 7 \cdot 10^{-231}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 9
Accuracy	77.4%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.68 \cdot 10^{+28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10
Accuracy	77.4%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+42}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11
Accuracy	77.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12
Accuracy	63.7%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-238}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13
Accuracy	68.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-110}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 14
Accuracy	55.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023138 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (* y (/ (- z t) (- z a)))))