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

?

Percentage Accurate: 88.9% → 97.0%
Time: 18.6s
Precision: binary64
Cost: 576

?

\[ \begin{array}{c}[y, t] = \mathsf{sort}([y, t])\\ \end{array} \]
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
↓
\[\frac{\frac{x}{y - z}}{t - z} \]
(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))
↓
(FPCore (x y z t) :precision binary64 (/ (/ x (- y z)) (- t z)))
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) {
	return (x / (y - z)) / (t - z);
}

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
    code = (x / (y - z)) / (t - z)
end function

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) {
	return (x / (y - z)) / (t - z);
}

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

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

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

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

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

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Herbie found 23 alternatives:

AlternativeAccuracySpeedup

Accuracy vs Speed

The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Bogosity?

Bogosity

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original88.9%
Target87.7%
Herbie97.0%
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Derivation?

  1. Initial program 89.6%

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

  2. Simplified96.2%

    \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]
    Step-by-step derivation

    [Start]89.6%

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

    associate-/r* [=>]96.2%

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

  3. Final simplification96.2%

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

Alternatives

Alternative 1
Accuracy97.0%
Cost576
\[\frac{\frac{x}{y - z}}{t - z} \]
Alternative 2
Accuracy82.1%
Cost1104
\[\begin{array}{l} t_1 := \frac{x}{y - z}\\ \mathbf{if}\;t \leq -1.56 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-144}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{z}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-109}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 0.039:\\ \;\;\;\;t_1 \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{t}\\ \end{array} \]
Alternative 3
Accuracy82.1%
Cost1104
\[\begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-144}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{z}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 0.05:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y - z}{x}}\\ \end{array} \]
Alternative 4
Accuracy81.0%
Cost1040
\[\begin{array}{l} t_1 := \frac{\frac{-x}{z}}{t - z}\\ t_2 := \frac{\frac{x}{y}}{t - z}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
Alternative 5
Accuracy81.7%
Cost1040
\[\begin{array}{l} t_1 := \frac{\frac{-x}{z}}{y - z}\\ \mathbf{if}\;t \leq -1.32 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-108}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 0.047:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
Alternative 6
Accuracy82.0%
Cost1040
\[\begin{array}{l} \mathbf{if}\;t \leq -1.56 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-145}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{z}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-112}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 0.038:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
Alternative 7
Accuracy65.3%
Cost980
\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{-x}{y \cdot z}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 8
Accuracy64.3%
Cost980
\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-75}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 9
Accuracy64.5%
Cost980
\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-75}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Accuracy64.4%
Cost980
\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 11
Accuracy64.4%
Cost980
\[\begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-103}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 4.75 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-70}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
Alternative 12
Accuracy70.7%
Cost848
\[\begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-75}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
Alternative 13
Accuracy74.6%
Cost844
\[\begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-175}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 2400000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
Alternative 14
Accuracy93.3%
Cost840
\[\begin{array}{l} t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{t_1}{y - z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{t - z}\\ \end{array} \]
Alternative 15
Accuracy73.0%
Cost712
\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
Alternative 16
Accuracy74.0%
Cost712
\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 1000000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
Alternative 17
Accuracy45.6%
Cost585
\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+87} \lor \neg \left(z \leq 1.65 \cdot 10^{+122}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
Alternative 18
Accuracy45.7%
Cost585
\[\begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-26} \lor \neg \left(z \leq 7 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
Alternative 19
Accuracy62.0%
Cost585
\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-28} \lor \neg \left(z \leq 1.1 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
Alternative 20
Accuracy63.1%
Cost585
\[\begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-29} \lor \neg \left(z \leq 4.7 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
Alternative 21
Accuracy66.7%
Cost585
\[\begin{array}{l} \mathbf{if}\;z \leq -12.6 \lor \neg \left(z \leq 1.7 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
Alternative 22
Accuracy96.8%
Cost576
\[\frac{\frac{x}{t - z}}{y - z} \]
Alternative 23
Accuracy38.7%
Cost320
\[\frac{x}{y \cdot t} \]

Reproduce?

herbie shell --seed 2023263 
(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))))