Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B

Average Error: 2.18% → 2.18%

Time: 10.5s

Precision: binary64

Cost: 969

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-120} \lor \neg \left(t \leq 1.1 \cdot 10^{-234}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6e-120) (not (<= t 1.1e-234)))
   (+ x (* y (/ (- z t) (- a t))))
   (+ x (/ (- z t) (/ (- a t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (a - t)));
}

↓

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6e-120) || !(t <= 1.1e-234)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = x + ((z - t) / ((a - t) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y * ((z - t) / (a - t)))
end function

↓

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-6d-120)) .or. (.not. (t <= 1.1d-234))) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = x + ((z - t) / ((a - t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (a - t)));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6e-120) || !(t <= 1.1e-234)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = x + ((z - t) / ((a - t) / y));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6e-120) or not (t <= 1.1e-234):
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = x + ((z - t) / ((a - t) / y))
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6e-120) || !(t <= 1.1e-234))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6e-120) || ~((t <= 1.1e-234)))
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = x + ((z - t) / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6e-120], N[Not[LessEqual[t, 1.1e-234]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	2.18%
Target	0.7%
Herbie	2.18%

\[\begin{array}{l} \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if t < -6.00000000000000022e-120 or 1.1e-234 < t

   1. Initial program 1.42

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

   if -6.00000000000000022e-120 < t < 1.1e-234

   1. Initial program 5.23

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

   2. Applied egg-rr 5.22

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

4. Final simplification 2.18

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-120} \lor \neg \left(t \leq 1.1 \cdot 10^{-234}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \end{array} \]

Alternatives

Alternative 1
Error	18.04%
Cost	1997

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+121}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t_1 \leq 10^{-7} \lor \neg \left(t_1 \leq 5 \cdot 10^{+32}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 2
Error	12.68%
Cost	1996

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+123}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t_1 \leq 0.4:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+32}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3
Error	1.06%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-141} \lor \neg \left(y \leq 10^{-100}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \]

Alternative 4
Error	25.91%
Cost	713

\[\begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-5} \lor \neg \left(a \leq 7 \cdot 10^{+89}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Error	2.18%
Cost	704

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

Alternative 6
Error	31.77%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+188}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	42.55%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-255}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-220}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	45.01%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023121 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

  (+ x (* y (/ (- z t) (- a t)))))