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

Average Error: 11.42% → 2.23%

Time: 13.0s

Precision: binary64

Cost: 1348

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;\frac{x}{z - y} \cdot \frac{1}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 0.0) (* (/ x (- z y)) (/ 1.0 (- z t))) t_1)))

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 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (x / (z - y)) * (1.0 / (z - t));
	} else {
		tmp = t_1;
	}
	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 = x / ((y - z) * (t - z))
    if (t_1 <= 0.0d0) then
        tmp = (x / (z - y)) * (1.0d0 / (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) {
	return x / ((y - z) * (t - z));
}

↓

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

Python

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

↓

def code(x, y, z, t):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= 0.0:
		tmp = (x / (z - y)) * (1.0 / (z - t))
	else:
		tmp = t_1
	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(x / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(Float64(x / Float64(z - y)) * Float64(1.0 / Float64(z - t)));
	else
		tmp = t_1;
	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 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= 0.0)
		tmp = (x / (z - y)) * (1.0 / (z - t));
	else
		tmp = t_1;
	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[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Target

Original	11.42%
Target	12.62%
Herbie	2.23%

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < 0.0

   1. Initial program 14.26

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

   2. Simplified 14.26

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

      [Start] 14.26	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      sub-neg [=>] 14.26	\[ \frac{x}{\color{blue}{\left(y + \left(-z\right)\right)} \cdot \left(t - z\right)} \]
      +-commutative [=>] 14.26	\[ \frac{x}{\color{blue}{\left(\left(-z\right) + y\right)} \cdot \left(t - z\right)} \]
      neg-sub0 [=>] 14.26	\[ \frac{x}{\left(\color{blue}{\left(0 - z\right)} + y\right) \cdot \left(t - z\right)} \]
      associate-+l- [=>] 14.26	\[ \frac{x}{\color{blue}{\left(0 - \left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      sub0-neg [=>] 14.26	\[ \frac{x}{\color{blue}{\left(-\left(z - y\right)\right)} \cdot \left(t - z\right)} \]
      distribute-lft-neg-out [=>] 14.26	\[ \frac{x}{\color{blue}{-\left(z - y\right) \cdot \left(t - z\right)}} \]
      distribute-rgt-neg-in [=>] 14.26	\[ \frac{x}{\color{blue}{\left(z - y\right) \cdot \left(-\left(t - z\right)\right)}} \]
      neg-sub0 [=>] 14.26	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}} \]
      associate-+l- [<=] 14.26	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(\left(0 - t\right) + z\right)}} \]
      neg-sub0 [<=] 14.26	\[ \frac{x}{\left(z - y\right) \cdot \left(\color{blue}{\left(-t\right)} + z\right)} \]
      +-commutative [<=] 14.26	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}} \]
      sub-neg [<=] 14.26	\[ \frac{x}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} \]

   3. Applied egg-rr 2.16

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

   if 0.0 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 2.44

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

4. Final simplification 2.23

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

Alternatives

Alternative 1
Error	1.79%
Cost	1609

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+245} \lor \neg \left(t_1 \leq -1 \cdot 10^{-216}\right):\\ \;\;\;\;\frac{\frac{x}{z - t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t_1}\\ \end{array} \]

Alternative 2
Error	19.79%
Cost	1041

\[\begin{array}{l} \mathbf{if}\;y \leq -250:\\ \;\;\;\;\frac{-x}{y \cdot \left(z - t\right)}\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-119} \lor \neg \left(y \leq 6.6 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{\frac{-x}{t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \end{array} \]

Alternative 3
Error	21.14%
Cost	976

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4:\\ \;\;\;\;\frac{-x}{y \cdot \left(z - t\right)}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 4
Error	33.07%
Cost	912

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -48000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 35000000000:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	34.17%
Cost	912

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{\frac{x}{z}}{-y}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 50000000:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	34.54%
Cost	912

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 280:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	29.5%
Cost	844

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 45000000000:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	29.02%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+112}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-66}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \]

Alternative 9
Error	24.44%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{+158}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \]

Alternative 10
Error	21.31%
Cost	844

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - t}\\ \mathbf{if}\;z \leq -3.85 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	7.1%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]

Alternative 12
Error	32.64%
Cost	780

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 72000:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	20.71%
Cost	776

\[\begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{-x}{z - y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]

Alternative 14
Error	20.93%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]

Alternative 15
Error	55.35%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-27} \lor \neg \left(z \leq 4 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 16
Error	38.18%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-36} \lor \neg \left(z \leq 170000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 17
Error	36.99%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-28} \lor \neg \left(z \leq 21000000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 18
Error	36.68%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-26} \lor \neg \left(z \leq 165000000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 19
Error	32.68%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-26} \lor \neg \left(z \leq 78000000\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 20
Error	63.09%
Cost	320

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

Reproduce

herbie shell --seed 2023088 
(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))))