Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Average Error: 2.1 → 2.0

Time: 8.2s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - x) * (z / t))
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - x) / (t / z))
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	2.1
Target	2.3
Herbie	2.0

\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} < -1013646692435.8867:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Derivation

1. Initial program 2.1

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

2. Applied egg-rr 2.0

   \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

3. Final simplification 2.0

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

Alternatives

Alternative 1
Error	11.7
Cost	1108

\[\begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot z}{t}\\ t_2 := x - z \cdot \frac{x}{t}\\ t_3 := x + \frac{z}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-41}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 86000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	4.2
Cost	968

\[\begin{array}{l} t_1 := \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	17.4
Cost	844

\[\begin{array}{l} t_1 := x + \frac{z}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+150}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.647329598602738 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	10.9
Cost	712

\[\begin{array}{l} t_1 := x + \frac{z}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-49}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	25.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -6.006350759445143 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.815751373398074 \cdot 10^{-71}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	31.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022291 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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