Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B

Average Error: 7.5 → 2.1

Time: 13.1s

Precision: binary64

Cost: 841

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+49} \lor \neg \left(z \leq 4 \cdot 10^{-197}\right):\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.5e+49) (not (<= z 4e-197)))
   (/ (/ x (- z t)) (- z y))
   (/ x (* (- y z) (- t z)))))

C

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

↓

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.5e+49) || !(z <= 4e-197)) {
		tmp = (x / (z - t)) / (z - y);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	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 - z) * (t - z))
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) :: tmp
    if ((z <= (-3.5d+49)) .or. (.not. (z <= 4d-197))) then
        tmp = (x / (z - t)) / (z - y)
    else
        tmp = x / ((y - z) * (t - z))
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.5e+49) || !(z <= 4e-197)) {
		tmp = (x / (z - t)) / (z - y);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.5e+49) or not (z <= 4e-197):
		tmp = (x / (z - t)) / (z - y)
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

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

↓

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.5e+49) || !(z <= 4e-197))
		tmp = Float64(Float64(x / Float64(z - t)) / Float64(z - y));
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.5e+49) || ~((z <= 4e-197)))
		tmp = (x / (z - t)) / (z - y);
	else
		tmp = x / ((y - z) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.5e+49], N[Not[LessEqual[z, 4e-197]], $MachinePrecision]], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	7.5
Target	8.2
Herbie	2.1

\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999975e49 or 3.9999999999999999e-197 < z

   1. Initial program 9.2

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

   2. Simplified 0.9

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

      [Start] 9.2	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 9.2	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 9.2	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 9.2	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 9.2	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 9.2	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 9.2	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 9.2	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 9.2	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 9.2	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 9.2	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 9.2	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 9.2	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]
      associate-/l/ [<=] 0.9	\[ \color{blue}{\frac{\frac{x}{z - t}}{z - y}} \]

   if -3.49999999999999975e49 < z < 3.9999999999999999e-197

   1. Initial program 4.5

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

4. Final simplification 2.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+49} \lor \neg \left(z \leq 4 \cdot 10^{-197}\right):\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	31.2
Cost	1308

\[\begin{array}{l} t_1 := \frac{x}{y \cdot t}\\ t_2 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-307}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 4500000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 2
Error	32.1
Cost	1308

\[\begin{array}{l} t_1 := \frac{x}{y \cdot t}\\ t_2 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-305}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 4500000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 15000000000000:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 3
Error	32.1
Cost	1308

\[\begin{array}{l} t_1 := \frac{x}{y \cdot t}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-306}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 7500000000:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \mathbf{elif}\;t \leq 750000000000:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+161}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 4
Error	14.3
Cost	976

\[\begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+148}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.00021:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 5
Error	14.7
Cost	976

\[\begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq 0.014:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 6
Error	18.4
Cost	976

\[\begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-67}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 7
Error	21.3
Cost	844

\[\begin{array}{l} t_1 := \frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-305}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-37}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	19.7
Cost	844

\[\begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-155}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-32}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 9
Error	4.3
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+130}:\\ \;\;\;\;\frac{1}{z - t} \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]

Alternative 10
Error	18.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 11
Error	17.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x}{z - y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 12
Error	2.0
Cost	704

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

Alternative 13
Error	35.4
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+35} \lor \neg \left(z \leq 6.2 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 14
Error	24.5
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-19} \lor \neg \left(z \leq 2.7 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 15
Error	23.6
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-21} \lor \neg \left(z \leq 0.0022\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 16
Error	21.0
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-19} \lor \neg \left(z \leq 0.0013\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 17
Error	40.0
Cost	320

\[\frac{x}{y \cdot t} \]

Reproduce

herbie shell --seed 2022364 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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