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

Average Error: 2.1 → 1.5

Time: 7.8s

Precision: binary64

Cost: 840

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-35}:\\ \;\;\;\;x + \left(\frac{y}{t} - \frac{x}{t}\right) \cdot z\\ \mathbf{elif}\;t \leq 10^{-34}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6e-35)
   (+ x (* (- (/ y t) (/ x t)) z))
   (if (<= t 1e-34) (+ x (/ (* z (- y x)) t)) (+ 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) {
	double tmp;
	if (t <= -6e-35) {
		tmp = x + (((y / t) - (x / t)) * z);
	} else if (t <= 1e-34) {
		tmp = x + ((z * (y - x)) / t);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (t <= (-6d-35)) then
        tmp = x + (((y / t) - (x / t)) * z)
    else if (t <= 1d-34) then
        tmp = x + ((z * (y - x)) / t)
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
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) {
	double tmp;
	if (t <= -6e-35) {
		tmp = x + (((y / t) - (x / t)) * z);
	} else if (t <= 1e-34) {
		tmp = x + ((z * (y - x)) / t);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	tmp = 0
	if t <= -6e-35:
		tmp = x + (((y / t) - (x / t)) * z)
	elif t <= 1e-34:
		tmp = x + ((z * (y - x)) / t)
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

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

↓

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6e-35)
		tmp = Float64(x + Float64(Float64(Float64(y / t) - Float64(x / t)) * z));
	elseif (t <= 1e-34)
		tmp = Float64(x + Float64(Float64(z * Float64(y - x)) / t));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6e-35)
		tmp = x + (((y / t) - (x / t)) * z);
	elseif (t <= 1e-34)
		tmp = x + ((z * (y - x)) / t);
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
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_] := If[LessEqual[t, -6e-35], N[(x + N[(N[(N[(y / t), $MachinePrecision] - N[(x / t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-34], N[(x + N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	2.1
Target	2.3
Herbie	1.5

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

Derivation

1. Split input into 3 regimes

2. if t < -5.99999999999999978e-35

   1. Initial program 1.1

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

   2. Taylor expanded in z around 0 1.1

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

   if -5.99999999999999978e-35 < t < 9.99999999999999928e-35

   1. Initial program 4.3

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

   2. Taylor expanded in z around -inf 2.2

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

   if 9.99999999999999928e-35 < t

   1. Initial program 1.1

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

   2. Applied egg-rr 1.2

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 1.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-35}:\\ \;\;\;\;x + \left(\frac{y}{t} - \frac{x}{t}\right) \cdot z\\ \mathbf{elif}\;t \leq 10^{-34}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Alternatives

Alternative 1
Error	21.9
Cost	2204

\[\begin{array}{l} t_1 := \frac{-x}{\frac{t}{z}}\\ t_2 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+183}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \end{array} \]

Alternative 2
Error	21.9
Cost	2204

\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+183}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(-\frac{z}{t}\right)\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+37}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{t}{x}}\\ \end{array} \]

Alternative 3
Error	21.9
Cost	2204

\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+183}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(-\frac{z}{t}\right)\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+37}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \end{array} \]

Alternative 4
Error	22.0
Cost	1684

\[\begin{array}{l} t_1 := \frac{-x}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+183}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -2 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	14.7
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-49} \lor \neg \left(\frac{z}{t} \leq 10^{-51}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	4.3
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4000 \lor \neg \left(\frac{z}{t} \leq 200\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 7
Error	22.5
Cost	841

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-49} \lor \neg \left(\frac{z}{t} \leq 10^{-51}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	22.4
Cost	841

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{-49} \lor \neg \left(\frac{z}{t} \leq 10^{-51}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	1.5
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-75} \lor \neg \left(t \leq 4 \cdot 10^{-31}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \end{array} \]

Alternative 10
Error	1.4
Cost	836

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 4 \cdot 10^{+190}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 11
Error	1.4
Cost	836

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq 4 \cdot 10^{+190}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 12
Error	32.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023031 
(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))))