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

Average Error: 16.8 → 8.1

Time: 15.6s

Precision: binary64

Cost: 2760

Math

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

↓

\[\begin{array}{l} t_1 := \left(x + y\right) + \frac{-1}{\frac{\frac{a - t}{y}}{z - t}}\\ t_2 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;x - \frac{y \cdot a - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ -1.0 (/ (/ (- a t) y) (- z t)))))
        (t_2 (+ (+ x y) (/ (* y (- t z)) (- a t)))))
   (if (<= t_2 -2e-131)
     t_1
     (if (<= t_2 0.0) (- x (/ (- (* y a) (* y z)) t)) t_1))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + (-1.0 / (((a - t) / y) / (z - t)));
	double t_2 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -2e-131) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = x - (((y * a) - (y * z)) / t);
	} else {
		tmp = t_1;
	}
	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) * y) / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + y) + ((-1.0d0) / (((a - t) / y) / (z - t)))
    t_2 = (x + y) + ((y * (t - z)) / (a - t))
    if (t_2 <= (-2d-131)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = x - (((y * a) - (y * z)) / t)
    else
        tmp = t_1
    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) * y) / (a - t));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + (-1.0 / (((a - t) / y) / (z - t)));
	double t_2 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -2e-131) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = x - (((y * a) - (y * z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	t_1 = (x + y) + (-1.0 / (((a - t) / y) / (z - t)))
	t_2 = (x + y) + ((y * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -2e-131:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = x - (((y * a) - (y * z)) / t)
	else:
		tmp = t_1
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(-1.0 / Float64(Float64(Float64(a - t) / y) / Float64(z - t))))
	t_2 = Float64(Float64(x + y) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e-131)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(x - Float64(Float64(Float64(y * a) - Float64(y * z)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) + (-1.0 / (((a - t) / y) / (z - t)));
	t_2 = (x + y) + ((y * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -2e-131)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = x - (((y * a) - (y * z)) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + N[(-1.0 / N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-131], t$95$1, If[LessEqual[t$95$2, 0.0], N[(x - N[(N[(N[(y * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Target

Original	16.8
Target	8.5
Herbie	8.1

\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2e-131 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 13.2

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

   2. Applied egg-rr 7.9

      \[\leadsto \left(x + y\right) - \color{blue}{\left(z - t\right) \cdot \frac{1}{\frac{a - t}{y}}} \]

   3. Applied egg-rr 7.8

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{1}{\frac{\frac{a - t}{y}}{z - t}}} \]

   if -2e-131 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 44.6

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

   2. Taylor expanded in t around -inf 10.4

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot a - y \cdot z}{t} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 8.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-131}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{\frac{a - t}{y}}{z - t}}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;x - \frac{y \cdot a - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{\frac{a - t}{y}}{z - t}}\\ \end{array} \]

Alternatives

Alternative 1
Error	8.1
Cost	2632

\[\begin{array}{l} t_1 := \left(x + y\right) + \frac{t - z}{\frac{a - t}{y}}\\ t_2 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;x - \frac{y \cdot a - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	7.9
Cost	1096

\[\begin{array}{l} \mathbf{if}\;t \leq -2.911823397209678 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t \leq 3.21132916177948 \cdot 10^{+228}:\\ \;\;\;\;\left(x + y\right) + \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 3
Error	11.7
Cost	840

\[\begin{array}{l} t_1 := \left(x + y\right) - \frac{z}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -4.733746245387809 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.3353043705661173 \cdot 10^{-24}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	10.9
Cost	840

\[\begin{array}{l} t_1 := \left(x + y\right) - \frac{z}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -4.733746245387809 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.3353043705661173 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	9.7
Cost	840

\[\begin{array}{l} t_1 := \left(x + y\right) - \frac{z}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -4.733746245387809 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.63537267832634 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{y \cdot z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	19.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -4.733746245387809 \cdot 10^{-31}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.4948293668432891 \cdot 10^{+38}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7
Error	19.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -4.733746245387809 \cdot 10^{-31}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.4948293668432891 \cdot 10^{+38}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8
Error	13.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -4.733746245387809 \cdot 10^{-31}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.3353043705661173 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9
Error	14.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -4.733746245387809 \cdot 10^{-31}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.3353043705661173 \cdot 10^{-24}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10
Error	19.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -4.733746245387809 \cdot 10^{-31}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 5.63537267832634 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11
Error	28.2
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022316 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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