Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Average Error: 0.0 → 0.0

Time: 27.0s

Precision: binary64

Cost: 832

Math

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

↓

\[t \cdot \left(y - z\right) + x \cdot \left(z - \left(y - 1\right)\right) \]

FPCore

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

↓

(FPCore (x y z t) :precision binary64 (+ (* t (- y z)) (* x (- z (- y 1.0)))))

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 (t * (y - z)) + (x * (z - (y - 1.0)));
}

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 = (t * (y - z)) + (x * (z - (y - 1.0d0)))
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 (t * (y - z)) + (x * (z - (y - 1.0)));
}

Python

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

↓

def code(x, y, z, t):
	return (t * (y - z)) + (x * (z - (y - 1.0)))

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(Float64(t * Float64(y - z)) + Float64(x * Float64(z - Float64(y - 1.0))))
end

MATLAB

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

↓

function tmp = code(x, y, z, t)
	tmp = (t * (y - z)) + (x * (z - (y - 1.0)));
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[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z - N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

2. Taylor expanded in x around 0 0.0

   \[\leadsto \color{blue}{t \cdot \left(y - z\right) + \left(1 + -1 \cdot \left(y - z\right)\right) \cdot x} \]

3. Simplified 0.0

   \[\leadsto \color{blue}{t \cdot \left(y - z\right) + x \cdot \left(z - \left(y - 1\right)\right)} \]
   Proof

   [Start] 0.0	\[ t \cdot \left(y - z\right) + \left(1 + -1 \cdot \left(y - z\right)\right) \cdot x \]
   rational.json-simplify-2 [=>] 0.0	\[ t \cdot \left(y - z\right) + \color{blue}{x \cdot \left(1 + -1 \cdot \left(y - z\right)\right)} \]
   rational.json-simplify-17 [=>] 0.0	\[ t \cdot \left(y - z\right) + x \cdot \color{blue}{\left(-1 \cdot \left(y - z\right) - -1\right)} \]
   rational.json-simplify-2 [=>] 0.0	\[ t \cdot \left(y - z\right) + x \cdot \left(\color{blue}{\left(y - z\right) \cdot -1} - -1\right) \]
   rational.json-simplify-9 [=>] 0.0	\[ t \cdot \left(y - z\right) + x \cdot \left(\color{blue}{\left(-\left(y - z\right)\right)} - -1\right) \]
   rational.json-simplify-12 [=>] 0.0	\[ t \cdot \left(y - z\right) + x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} - -1\right) \]
   rational.json-simplify-42 [=>] 0.0	\[ t \cdot \left(y - z\right) + x \cdot \color{blue}{\left(\left(0 - -1\right) - \left(y - z\right)\right)} \]
   metadata-eval [=>] 0.0	\[ t \cdot \left(y - z\right) + x \cdot \left(\color{blue}{1} - \left(y - z\right)\right) \]
   rational.json-simplify-45 [=>] 0.0	\[ t \cdot \left(y - z\right) + x \cdot \color{blue}{\left(z - \left(y - 1\right)\right)} \]

4. Final simplification 0.0

   \[\leadsto t \cdot \left(y - z\right) + x \cdot \left(z - \left(y - 1\right)\right) \]

Alternatives

Alternative 1
Error	25.1
Cost	2724

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x + \left(-t\right)\right)\\ \mathbf{if}\;y - z \leq -1 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y - z \leq -2 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq -5 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;y - z \leq 10^{-169}:\\ \;\;\;\;y \cdot t + x\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \left(-t\right)\\ \mathbf{elif}\;y - z \leq 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{+245}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	28.8
Cost	2140

\[\begin{array}{l} t_1 := t \cdot \left(y - z\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y - z \leq -5 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq -2 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y - z \leq -5 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 10^{+134}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	25.0
Cost	2140

\[\begin{array}{l} t_1 := t \cdot \left(y - z\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y - z \leq -5 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq -2 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y - z \leq -5 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{-16}:\\ \;\;\;\;y \cdot t + x\\ \mathbf{elif}\;y - z \leq 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 10^{+134}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	22.5
Cost	1244

\[\begin{array}{l} t_1 := z \cdot x + x\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \left(x + \left(-t\right)\right)\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-96}:\\ \;\;\;\;y \cdot t + x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	38.4
Cost	1180

\[\begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-57}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-204}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+83}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+274}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 6
Error	24.3
Cost	1112

\[\begin{array}{l} t_1 := z \cdot x + x\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -0.0048:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.35 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+196}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \end{array} \]

Alternative 7
Error	11.0
Cost	976

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + z \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq -1120000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-109}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;y \leq 1020:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	10.7
Cost	976

\[\begin{array}{l} t_1 := x + z \cdot \left(x - t\right)\\ t_2 := y \cdot \left(t - x\right) + x\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-106}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;y \leq 2050:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	37.8
Cost	916

\[\begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-72}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+82}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+281}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 10
Error	24.3
Cost	848

\[\begin{array}{l} t_1 := \left(1 - y\right) \cdot x\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+145}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	29.0
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+146}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	16.1
Cost	712

\[\begin{array}{l} t_1 := x \cdot \left(z - \left(y - 1\right)\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-105}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	12.8
Cost	712

\[\begin{array}{l} t_1 := x \cdot \left(z - \left(y - 1\right)\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-50}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	0.0
Cost	576

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

Alternative 15
Error	37.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-57}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 16
Error	47.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023073 
(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))))