Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Average Accuracy: 100.0% → 100.0%

Time: 12.6s

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	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. Simplified 100.0%

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

   [Start] 100.0	\[ x + \left(y - z\right) \cdot \left(t - x\right) \]
   +-commutative [=>] 100.0	\[ \color{blue}{\left(y - z\right) \cdot \left(t - x\right) + x} \]
   fma-def [=>] 100.0	\[ \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	52.6%
Cost	3442

\[\begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y - z \leq -2 \cdot 10^{+258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y - z \leq -5 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq -5 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y - z \leq -0.04:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{-52}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 10^{+101} \lor \neg \left(y - z \leq 2 \cdot 10^{+125}\right) \land \left(y - z \leq 10^{+164} \lor \neg \left(y - z \leq 2 \cdot 10^{+195}\right) \land y - z \leq 2 \cdot 10^{+246}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	51.7%
Cost	2922

\[\begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y - z \leq -5 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq -5 \cdot 10^{+154}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y - z \leq -0.04:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{+94} \lor \neg \left(y - z \leq 10^{+182} \lor \neg \left(y - z \leq 2 \cdot 10^{+246}\right) \land y - z \leq 10^{+301}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	59.7%
Cost	2922

\[\begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y - z \leq -2 \cdot 10^{+258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y - z \leq -5 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq -5 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y - z \leq -0.04:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{-36}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y - z \leq 10^{+101} \lor \neg \left(y - z \leq 2 \cdot 10^{+125}\right) \land \left(y - z \leq 10^{+164} \lor \neg \left(y - z \leq 2 \cdot 10^{+195}\right) \land y - z \leq 2 \cdot 10^{+246}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	49.3%
Cost	2401

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y - z \leq -1 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq -1 \cdot 10^{+154}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y - z \leq -2 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq -2 \cdot 10^{+48}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y - z \leq -0.04:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 10^{+182} \lor \neg \left(y - z \leq 2 \cdot 10^{+246}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 5
Accuracy	38.4%
Cost	1710

\[\begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+161}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-272}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-209}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+35} \lor \neg \left(z \leq 4.8 \cdot 10^{+113} \lor \neg \left(z \leq 8.4 \cdot 10^{+182}\right) \land z \leq 2.15 \cdot 10^{+247}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 6
Accuracy	39.9%
Cost	1180

\[\begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-18}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-72}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-96}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+177}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 7
Accuracy	38.9%
Cost	984

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+20}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-273}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-207}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 4100:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 8
Accuracy	83.6%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+15} \lor \neg \left(z \leq 100\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 9
Accuracy	100.0%
Cost	576

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

Alternative 10
Accuracy	40.1%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-18}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 11
Accuracy	25.2%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023138 
(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))))