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

Average Accuracy: 97.6% → 99.1%

Time: 12.6s

Precision: binary64

Cost: 969

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+40} \lor \neg \left(y \leq 10^{-19}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \]

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 (<= y -2e+40) (not (<= y 1e-19)))
   (+ x (* y (/ (- z t) (- a t))))
   (+ x (/ (* (- z t) y) (- a t)))))

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 ((y <= -2e+40) || !(y <= 1e-19)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = x + (((z - t) * y) / (a - t));
	}
	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 ((y <= (-2d+40)) .or. (.not. (y <= 1d-19))) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = x + (((z - t) * y) / (a - t))
    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 ((y <= -2e+40) || !(y <= 1e-19)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = x + (((z - t) * y) / (a - t));
	}
	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 (y <= -2e+40) or not (y <= 1e-19):
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = x + (((z - t) * y) / (a - t))
	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 ((y <= -2e+40) || !(y <= 1e-19))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(x + Float64(Float64(Float64(z - t) * y) / Float64(a - t)));
	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 ((y <= -2e+40) || ~((y <= 1e-19)))
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = x + (((z - t) * y) / (a - t));
	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[y, -2e+40], N[Not[LessEqual[y, 1e-19]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	97.6%
Target	99.2%
Herbie	99.1%

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

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000006e40 or 9.9999999999999998e-20 < y

   1. Initial program 99.0%

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

   if -2.00000000000000006e40 < y < 9.9999999999999998e-20

   1. Initial program 96.5%

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

   2. Simplified 99.2%

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

      [Start] 96.5	\[ x + y \cdot \frac{z - t}{a - t} \]
      associate-*r/ [=>] 99.2	\[ x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+40} \lor \neg \left(y \leq 10^{-19}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	65.6%
Cost	976

\[\begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 64000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 2
Accuracy	65.1%
Cost	976

\[\begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-212}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 62000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3
Accuracy	51.0%
Cost	856

\[\begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+32}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-159}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-193}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-82}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Accuracy	65.4%
Cost	852

\[\begin{array}{l} t_1 := z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{-142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 64000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5
Accuracy	63.7%
Cost	852

\[\begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-307}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-235}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-210}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 64000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6
Accuracy	79.1%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+25} \lor \neg \left(t \leq 62000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 7
Accuracy	83.9%
Cost	841

\[\begin{array}{l} \mathbf{if}\;t \leq -14000000000000 \lor \neg \left(t \leq 2.35 \cdot 10^{-102}\right):\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 8
Accuracy	82.5%
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -15000000000000:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \]

Alternative 9
Accuracy	97.9%
Cost	832

\[x + \frac{1}{\frac{\frac{a - t}{z - t}}{y}} \]

Alternative 10
Accuracy	77.0%
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -19000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 64000000000:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11
Accuracy	77.3%
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -16000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 65000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12
Accuracy	77.3%
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -14500000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 64000000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13
Accuracy	97.6%
Cost	704

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

Alternative 14
Accuracy	67.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+39}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 62000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 15
Accuracy	54.7%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023141 
(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)))))