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

Average Error: 2.0 → 2.0

Time: 21.6s

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	2.3
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 2.0

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

2. Final simplification 2.0

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

Alternatives

Alternative 1
Error	22.5
Cost	2204

\[\begin{array}{l} t_1 := x \cdot \left(-\frac{z}{t}\right)\\ t_2 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq -2000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+185}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 2
Error	22.5
Cost	2204

\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -2000000000000:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+185}:\\ \;\;\;\;x \cdot \left(-\frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 3
Error	23.5
Cost	1424

\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-\frac{z \cdot x}{t}\\ \end{array} \]

Alternative 4
Error	22.3
Cost	1360

\[\begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	22.3
Cost	1360

\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6
Error	23.0
Cost	1360

\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]

Alternative 7
Error	18.7
Cost	1240

\[\begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ t_2 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-239}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	5.7
Cost	968

\[\begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -40000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 200000000:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	10.2
Cost	712

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3200000:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	10.1
Cost	712

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2200000:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	31.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023074 
(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))))