Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Average Error: 0.0 → 0.0

Time: 13.9s

Precision: binary64

Cost: 832

Math

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

↓

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

FPCore

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

↓

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

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

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

Python

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

↓

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

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(y - z) * t) - Float64(Float64(y - z) * x)))
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 + (((y - z) * t) - ((y - z) * x));
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[(y - z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(y - z), $MachinePrecision] * x), $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. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	10.2
Cost	976

\[\begin{array}{l} t_1 := x + z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-104}:\\ \;\;\;\;y \cdot \left(t - x\right) + x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+15}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	18.4
Cost	912

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(-t\right) + x\\ \mathbf{if}\;y \leq -0.085:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-92}:\\ \;\;\;\;y \cdot t + x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	22.5
Cost	848

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := y \cdot t + x\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-141}:\\ \;\;\;\;\left(1 + z\right) \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	22.5
Cost	848

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := y \cdot t + x\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-141}:\\ \;\;\;\;z \cdot x + x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	40.8
Cost	784

\[\begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-26}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-64}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	40.9
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-27}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-63}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+30}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	13.8
Cost	712

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+48}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	11.9
Cost	712

\[\begin{array}{l} t_1 := x + t \cdot \left(y - z\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-86}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	28.5
Cost	584

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	22.1
Cost	584

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-11}:\\ \;\;\;\;\left(1 + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	0.0
Cost	576

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

Alternative 12
Error	40.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -0.00025:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-58}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	47.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023101 
(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))))