Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Average Error: 0.0 → 0.0

Time: 9.6s

Precision: binary64

Cost: 6848

Math

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

↓

\[\mathsf{fma}\left(y - z, t - x, x\right) \]

FPCore

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

↓

(FPCore (x y z t) :precision binary64 (fma (- y z) (- t x) 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 fma((y - z), (t - x), 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 fma(Float64(y - z), Float64(t - x), 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $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. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]
   Proof

   [Start] 0.0	\[ x + \left(y - z\right) \cdot \left(t - x\right) \]
   +-commutative [=>] 0.0	\[ \color{blue}{\left(y - z\right) \cdot \left(t - x\right) + x} \]
   fma-def [=>] 0.0	\[ \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(y - z, t - x, x\right) \]

Alternatives

Alternative 1
Error	39.6
Cost	1576

\[\begin{array}{l} t_1 := -z \cdot t\\ \mathbf{if}\;z \leq -2 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-73}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-265}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.35 \cdot 10^{-206}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-151}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-111}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 10000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+106}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	28.6
Cost	1508

\[\begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-232}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-166}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7800000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	23.0
Cost	1508

\[\begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := y \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-73}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-259}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-206}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-113}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7800000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	39.9
Cost	1380

\[\begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+15}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-72}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-264}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-206}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-152}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-111}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 10000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 5
Error	30.1
Cost	1244

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;x \leq -17000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+23}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.16 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+74}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	22.4
Cost	980

\[\begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-208}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 10000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	19.4
Cost	848

\[\begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + y \cdot t\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-276}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 12500000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	10.8
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+15} \lor \neg \left(z \leq 31000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 9
Error	10.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 23000000:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x - z \cdot t\\ \end{array} \]

Alternative 10
Error	0.0
Cost	576

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

Alternative 11
Error	38.3
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-31}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 12
Error	47.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023039 
(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))))