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

Average Error: 7.5 → 1.0

Time: 19.5s

Precision: binary64

Cost: 1608

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

Math

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

↓

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+241}:\\ \;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array} \]

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+241)
     (/ (/ 1.0 (/ (- y z) x)) (- t z))
     (if (<= t_1 5e+117) (/ x t_1) (/ (/ 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 t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -1e+241) {
		tmp = (1.0 / ((y - z) / x)) / (t - z);
	} else if (t_1 <= 5e+117) {
		tmp = x / t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if (t_1 <= (-1d+241)) then
        tmp = (1.0d0 / ((y - z) / x)) / (t - z)
    else if (t_1 <= 5d+117) then
        tmp = x / t_1
    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 t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -1e+241) {
		tmp = (1.0 / ((y - z) / x)) / (t - z);
	} else if (t_1 <= 5e+117) {
		tmp = x / t_1;
	} 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):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -1e+241:
		tmp = (1.0 / ((y - z) / x)) / (t - z)
	elif t_1 <= 5e+117:
		tmp = x / t_1
	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)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= -1e+241)
		tmp = Float64(Float64(1.0 / Float64(Float64(y - z) / x)) / Float64(t - z));
	elseif (t_1 <= 5e+117)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / 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)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -1e+241)
		tmp = (1.0 / ((y - z) / x)) / (t - z);
	elseif (t_1 <= 5e+117)
		tmp = x / t_1;
	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_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+241], N[(N[(1.0 / N[(N[(y - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+117], N[(x / t$95$1), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	7.5
Target	8.3
Herbie	1.0

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -1.0000000000000001e241

   1. Initial program 13.7

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

   2. Simplified 0.3

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

      [Start] 13.7	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      rational.json-simplify-46 [=>] 0.2	\[ \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]
      rational.json-simplify-44 [=>] 0.3	\[ \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Taylor expanded in x around 0 13.7

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

   4. Simplified 0.2

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

      [Start] 13.7	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      rational.json-simplify-46 [=>] 0.2	\[ \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

   5. Applied egg-rr 0.2

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

   6. Applied egg-rr 0.2

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

   if -1.0000000000000001e241 < (*.f64 (-.f64 y z) (-.f64 t z)) < 4.99999999999999983e117

   1. Initial program 1.6

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

   if 4.99999999999999983e117 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 10.5

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

   2. Simplified 0.7

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

      [Start] 10.5	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      rational.json-simplify-46 [=>] 0.6	\[ \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]
      rational.json-simplify-44 [=>] 0.7	\[ \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Taylor expanded in x around 0 10.5

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

   4. Simplified 0.6

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

      [Start] 10.5	\[ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
      rational.json-simplify-46 [=>] 0.6	\[ \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -1 \cdot 10^{+241}:\\ \;\;\;\;\frac{\frac{1}{\frac{y - z}{x}}}{t - z}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 5 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	1.1
Cost	1608

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ t_2 := \frac{\frac{x}{t - z}}{y - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	1.0
Cost	1608

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ t_2 := \frac{\frac{x}{y - z}}{t - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+241}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	0.9
Cost	1608

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+259}:\\ \;\;\;\;\frac{x}{z - y} \cdot \frac{1}{z - t}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array} \]

Alternative 4
Error	14.6
Cost	1500

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t - z}\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-165}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{z - y} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 5
Error	31.4
Cost	1176

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{\frac{x}{t}}{y}\\ t_3 := -\frac{x}{z \cdot y}\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-107}:\\ \;\;\;\;-\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	30.8
Cost	1176

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{\frac{x}{t}}{y}\\ t_3 := -\frac{x}{z \cdot y}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-104}:\\ \;\;\;\;-\frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	31.2
Cost	1176

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{\frac{x}{t}}{y}\\ t_3 := -\frac{\frac{x}{z}}{y}\\ \mathbf{if}\;t \leq -6 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-163}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+222}:\\ \;\;\;\;-\frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	18.5
Cost	976

\[\begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot t}\\ t_2 := \frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-87}:\\ \;\;\;\;-\frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	14.7
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t - z}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-166}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 10
Error	13.7
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{t - z}\\ \mathbf{if}\;t \leq -2.55 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-165}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 11
Error	4.2
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+123}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;z \leq 2.22 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 12
Error	22.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-64}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-163}:\\ \;\;\;\;-\frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 13
Error	15.3
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 14
Error	14.6
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-66}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 15
Error	31.9
Cost	648

\[\begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-107}:\\ \;\;\;\;-\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 16
Error	36.4
Cost	452

\[\begin{array}{l} \mathbf{if}\;t \leq 5 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 17
Error	40.1
Cost	320

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

Alternative 18
Error	37.7
Cost	320

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

Reproduce

herbie shell --seed 2023074 
(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))))