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

Average Error: 10.7 → 0.6

Time: 11.9s

Precision: binary64

Cost: 969

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-80} \lor \neg \left(t \leq 5 \cdot 10^{-134}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5e-80) (not (<= t 5e-134)))
   (+ x (* t (/ (- y z) (- a z))))
   (+ x (/ (* t (- y z)) (- a z)))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e-80) || !(t <= 5e-134)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x + ((t * (y - z)) / (a - z));
	}
	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 - z))
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 <= (-5d-80)) .or. (.not. (t <= 5d-134))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = x + ((t * (y - z)) / (a - z))
    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 - z));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e-80) || !(t <= 5e-134)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x + ((t * (y - z)) / (a - z));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5e-80) or not (t <= 5e-134):
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = x + ((t * (y - z)) / (a - z))
	return tmp

Julia

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

↓

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5e-80) || !(t <= 5e-134))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(x + Float64(Float64(t * Float64(y - z)) / Float64(a - z)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5e-80) || ~((t <= 5e-134)))
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = x + ((t * (y - z)) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5e-80], N[Not[LessEqual[t, 5e-134]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	10.7
Target	0.6
Herbie	0.6

\[\begin{array}{l} \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if t < -5e-80 or 5.0000000000000003e-134 < t

   1. Initial program 16.3

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

   2. Simplified 0.8

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

      [Start] 16.3	\[ x + \frac{\left(y - z\right) \cdot t}{a - z} \]
      associate-*l/ [<=] 0.8	\[ x + \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   if -5e-80 < t < 5.0000000000000003e-134

   1. Initial program 0.2

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-80} \lor \neg \left(t \leq 5 \cdot 10^{-134}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	14.3
Cost	1236

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+125}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+243}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+295}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	14.4
Cost	1236

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+125}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+246}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+296}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	22.7
Cost	1108

\[\begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+125}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+242}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+296}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	22.8
Cost	1108

\[\begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+125}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+248}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+296}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	15.7
Cost	1108

\[\begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-113}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-10}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+97}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+153}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 6
Error	14.9
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-17}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-135}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 500000:\\ \;\;\;\;x - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 7
Error	14.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{-18}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-113}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 8
Error	1.4
Cost	704

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

Alternative 9
Error	19.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 10
Error	28.4
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023039 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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