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

Average Accuracy: 88.0% → 98.1%

Time: 12.9s

Precision: binary64

Cost: 1736

\[ \begin{array}{c}[y, t] = \mathsf{sort}([y, t])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+301}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot \frac{1}{z - t}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 -1e+301)
     (/ (/ x (- z t)) (- z y))
     (if (<= t_1 -5e-100) (/ x t_1) (* (/ x (- z y)) (/ 1.0 (- z t)))))))

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 t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -1e+301) {
		tmp = (x / (z - t)) / (z - y);
	} else if (t_1 <= -5e-100) {
		tmp = x / t_1;
	} else {
		tmp = (x / (z - y)) * (1.0 / (z - t));
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if (t_1 <= (-1d+301)) then
        tmp = (x / (z - t)) / (z - y)
    else if (t_1 <= (-5d-100)) then
        tmp = x / t_1
    else
        tmp = (x / (z - y)) * (1.0d0 / (z - t))
    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 t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -1e+301) {
		tmp = (x / (z - t)) / (z - y);
	} else if (t_1 <= -5e-100) {
		tmp = x / t_1;
	} else {
		tmp = (x / (z - y)) * (1.0 / (z - t));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -1e+301:
		tmp = (x / (z - t)) / (z - y)
	elif t_1 <= -5e-100:
		tmp = x / t_1
	else:
		tmp = (x / (z - y)) * (1.0 / (z - t))
	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)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= -1e+301)
		tmp = Float64(Float64(x / Float64(z - t)) / Float64(z - y));
	elseif (t_1 <= -5e-100)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / Float64(z - y)) * Float64(1.0 / Float64(z - t)));
	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)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -1e+301)
		tmp = (x / (z - t)) / (z - y);
	elseif (t_1 <= -5e-100)
		tmp = x / t_1;
	else
		tmp = (x / (z - y)) * (1.0 / (z - t));
	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_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+301], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-100], N[(x / t$95$1), $MachinePrecision], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	88.0%
Target	86.8%
Herbie	98.1%

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -1.00000000000000005e301

   1. Initial program 69.2%

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

   2. Simplified 99.9%

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

      [Start] 69.2	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 69.2	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 69.2	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 69.2	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 69.2	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 69.2	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 69.2	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 69.2	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 69.2	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 69.2	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 69.2	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 69.2	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 69.2	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]
      associate-/l/ [<=] 99.9	\[ \color{blue}{\frac{\frac{x}{z - t}}{z - y}} \]

   if -1.00000000000000005e301 < (*.f64 (-.f64 y z) (-.f64 t z)) < -5.0000000000000001e-100

   1. Initial program 99.7%

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

   if -5.0000000000000001e-100 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 87.6%

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

   2. Simplified 87.6%

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

      [Start] 87.6	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 87.6	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 87.6	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 87.6	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 87.6	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 87.6	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 87.6	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 87.6	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 87.6	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 87.6	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 87.6	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 87.6	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 87.6	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]

   3. Applied egg-rr 97.4%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -1 \cdot 10^{+301}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq -5 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot \frac{1}{z - t}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.3%
Cost	1609

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+301} \lor \neg \left(t_1 \leq -2 \cdot 10^{-147}\right):\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t_1}\\ \end{array} \]

Alternative 2
Accuracy	92.5%
Cost	1104

\[\begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+108}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-213}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - t} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 3
Accuracy	79.3%
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t - z}\\ t_2 := \frac{\frac{x}{z}}{z - t}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z - y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	79.5%
Cost	908

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - t}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-193}:\\ \;\;\;\;\frac{\frac{-x}{z - t}}{y}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{-x}{z - y}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	79.2%
Cost	908

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+40}:\\ \;\;\;\;\frac{1}{\left(z - t\right) \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-185}:\\ \;\;\;\;\frac{\frac{-x}{z - t}}{y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{-x}{z - y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]

Alternative 6
Accuracy	70.1%
Cost	844

\[\begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 7
Accuracy	75.3%
Cost	844

\[\begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 8
Accuracy	79.0%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-22} \lor \neg \left(z \leq 1.8 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \end{array} \]

Alternative 9
Accuracy	44.0%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+82} \lor \neg \left(z \leq 1.1 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 10
Accuracy	61.1%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{-36} \lor \neg \left(z \leq 1.1 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 11
Accuracy	62.8%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-38} \lor \neg \left(z \leq 6.2 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 12
Accuracy	62.7%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-38} \lor \neg \left(z \leq 4.2 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 13
Accuracy	66.7%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-36} \lor \neg \left(z \leq 4.6 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 14
Accuracy	37.3%
Cost	320

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

Reproduce

herbie shell --seed 2023141 
(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))))