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

Average Error: 2.1 → 2.1

Time: 11.1s

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	2.1
Target	2.2
Herbie	2.1

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

Derivation

1. Initial program 2.1

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

2. Final simplification 2.1

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

Alternatives

Alternative 1
Error	16.7
Cost	1488

\[\begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -10000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	4.8
Cost	968

\[\begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -10000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 0.1:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	25.5
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -5.02890998355651 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.423967809968238 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq -1.8072509494263347 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.871973886937964 \cdot 10^{-118}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	24.1
Cost	840

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]

Alternative 5
Error	4.3
Cost	840

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -1.755942967805514 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.242198964747733 \cdot 10^{+162}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	25.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -5.02890998355651 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.89711344065272 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	25.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -5.02890998355651 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.89711344065272 \cdot 10^{-91}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	2.0
Cost	576

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

Alternative 9
Error	31.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022318 
(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))))