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

Average Error: 1.8 → 1.7

Time: 8.9s

Precision: binary64

Cost: 2509

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+134} \lor \neg \left(t_1 \leq 5 \cdot 10^{-263}\right) \land t_1 \leq 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z t)))))
   (if (or (<= t_1 -5e+134) (and (not (<= t_1 5e-263)) (<= t_1 1e+307)))
     t_1
     (+ x (/ z (/ t (- y x)))))))

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 t_1 = x + ((y - x) * (z / t));
	double tmp;
	if ((t_1 <= -5e+134) || (!(t_1 <= 5e-263) && (t_1 <= 1e+307))) {
		tmp = t_1;
	} else {
		tmp = x + (z / (t / (y - x)));
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) * (z / t))
    if ((t_1 <= (-5d+134)) .or. (.not. (t_1 <= 5d-263)) .and. (t_1 <= 1d+307)) then
        tmp = t_1
    else
        tmp = x + (z / (t / (y - x)))
    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 t_1 = x + ((y - x) * (z / t));
	double tmp;
	if ((t_1 <= -5e+134) || (!(t_1 <= 5e-263) && (t_1 <= 1e+307))) {
		tmp = t_1;
	} else {
		tmp = x + (z / (t / (y - x)));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = x + ((y - x) * (z / t))
	tmp = 0
	if (t_1 <= -5e+134) or (not (t_1 <= 5e-263) and (t_1 <= 1e+307)):
		tmp = t_1
	else:
		tmp = x + (z / (t / (y - x)))
	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)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(z / t)))
	tmp = 0.0
	if ((t_1 <= -5e+134) || (!(t_1 <= 5e-263) && (t_1 <= 1e+307)))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / Float64(t / Float64(y - x))));
	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)
	t_1 = x + ((y - x) * (z / t));
	tmp = 0.0;
	if ((t_1 <= -5e+134) || (~((t_1 <= 5e-263)) && (t_1 <= 1e+307)))
		tmp = t_1;
	else
		tmp = x + (z / (t / (y - x)));
	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_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+134], And[N[Not[LessEqual[t$95$1, 5e-263]], $MachinePrecision], LessEqual[t$95$1, 1e+307]]], t$95$1, N[(x + N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	1.8
Target	2.0
Herbie	1.7

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t))) < -4.99999999999999981e134 or 5.00000000000000006e-263 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t))) < 9.99999999999999986e306

   1. Initial program 1.3

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

   if -4.99999999999999981e134 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t))) < 5.00000000000000006e-263 or 9.99999999999999986e306 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

   1. Initial program 2.7

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

   2. Applied egg-rr 2.5

      \[\leadsto x + \color{blue}{\frac{z}{\frac{t}{y - x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 1.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} \leq -5 \cdot 10^{+134} \lor \neg \left(x + \left(y - x\right) \cdot \frac{z}{t} \leq 5 \cdot 10^{-263}\right) \land x + \left(y - x\right) \cdot \frac{z}{t} \leq 10^{+307}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternatives

Alternative 1
Error	22.9
Cost	1944

\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+127}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+234}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 2
Error	22.9
Cost	1944

\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+127}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{+234}:\\ \;\;\;\;x \cdot \left(-\frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 3
Error	15.8
Cost	1488

\[\begin{array}{l} t_1 := z \cdot \frac{y - x}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-130}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	13.6
Cost	1488

\[\begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-130}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	23.3
Cost	1362

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-36} \lor \neg \left(\frac{z}{t} \leq 10^{-173}\right) \land \left(\frac{z}{t} \leq 4 \cdot 10^{-130} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-23}\right)\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	23.3
Cost	1360

\[\begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 7
Error	1.3
Cost	1097

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-259} \lor \neg \left(\frac{z}{t} \leq 10^{-244}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 8
Error	2.9
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -200000 \lor \neg \left(\frac{z}{t} \leq 10^{-8}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 9
Error	31.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023039 
(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))))