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

Average Error: 2.0 → 2.0

Time: 8.9s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

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) * (z / t));
}

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) * (z / t))
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) * (z / t));
}

Python

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

↓

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

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(z / t)))
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) * (z / t));
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[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	2.0
Target	2.2
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 2.0

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

2. Final simplification 2.0

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

Alternatives

Alternative 1
Error	28.3
Cost	1112

\[\begin{array}{l} \mathbf{if}\;x \leq -96000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-106}:\\ \;\;\;\;-\frac{z \cdot x}{t}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-190}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-61}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	29.1
Cost	1112

\[\begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-106}:\\ \;\;\;\;\left(-\frac{x}{t}\right) \cdot z\\ \mathbf{elif}\;x \leq -1.38 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.36 \cdot 10^{-190}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	18.7
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-190}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-62}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	18.3
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-191}:\\ \;\;\;\;\frac{y - x}{t} \cdot z\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10^{-61}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	6.5
Cost	968

\[\begin{array}{l} t_1 := \frac{y - x}{t} \cdot z\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 100:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	27.2
Cost	848

\[\begin{array}{l} t_1 := \frac{y}{t} \cdot z\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.9 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	26.8
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-191}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-62}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	31.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(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))))