Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Average Accuracy: 100.0% → 100.0%

Time: 11.9s

Precision: binary64

Cost: 832

Math

\[x + \left(y - z\right) \cdot \left(t - x\right) \]

↓

\[x + \left(\left(t - x\right) \cdot y + z \cdot \left(x - t\right)\right) \]

FPCore

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

↓

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

C

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

↓

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

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 - x))
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 + (((t - x) * y) + (z * (x - t)))
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	100.0%
Target	100.0%
Herbie	100.0%

\[x + \left(t \cdot \left(y - z\right) + \left(-x\right) \cdot \left(y - z\right)\right) \]

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]

2. Applied egg-rr 100.0%

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

   [Start] 100.0	\[ x + \left(y - z\right) \cdot \left(t - x\right) \]
   *-commutative [=>] 100.0	\[ x + \color{blue}{\left(t - x\right) \cdot \left(y - z\right)} \]
   sub-neg [=>] 100.0	\[ x + \left(t - x\right) \cdot \color{blue}{\left(y + \left(-z\right)\right)} \]
   distribute-lft-in [=>] 100.0	\[ x + \color{blue}{\left(\left(t - x\right) \cdot y + \left(t - x\right) \cdot \left(-z\right)\right)} \]
   +-commutative [=>] 100.0	\[ x + \color{blue}{\left(\left(t - x\right) \cdot \left(-z\right) + \left(t - x\right) \cdot y\right)} \]

3. Final simplification 100.0%

   \[\leadsto x + \left(\left(t - x\right) \cdot y + z \cdot \left(x - t\right)\right) \]

Alternatives

Alternative 1
Accuracy	64.1%
Cost	1508

\[\begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := t \cdot \left(y - z\right)\\ t_3 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-293}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-218}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-93}:\\ \;\;\;\;x - t \cdot z\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	64.2%
Cost	1508

\[\begin{array}{l} t_1 := t \cdot \left(y - z\right)\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-293}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-221}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-93}:\\ \;\;\;\;x - t \cdot z\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	54.0%
Cost	1361

\[\begin{array}{l} t_1 := t \cdot \left(y - z\right)\\ \mathbf{if}\;y - z \leq -1 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq -5 \cdot 10^{+82}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y - z \leq -1 \cdot 10^{-9} \lor \neg \left(y - z \leq 2 \cdot 10^{-36}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Accuracy	64.7%
Cost	980

\[\begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -5.9 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-222}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	77.9%
Cost	976

\[\begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x - t \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq -4.35 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-273}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	78.2%
Cost	976

\[\begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x - t \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.68 \cdot 10^{-273}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \]

Alternative 7
Accuracy	38.4%
Cost	852

\[\begin{array}{l} \mathbf{if}\;z \leq -0.0105:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-218}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-11}:\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 8
Accuracy	61.1%
Cost	849

\[\begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+27}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-11} \lor \neg \left(x \leq 2.25 \cdot 10^{+16}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \end{array} \]

Alternative 9
Accuracy	65.5%
Cost	716

\[\begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	100.0%
Cost	576

\[x + \left(t - x\right) \cdot \left(y - z\right) \]

Alternative 11
Accuracy	41.0%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-34}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot y\\ \end{array} \]

Alternative 12
Accuracy	26.4%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023137 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

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