Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Average Accuracy: 100.0% → 100.0%

Time: 13.8s

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	35.5%
Cost	1444

\[\begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-56}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-129}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-264}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	63.9%
Cost	1112

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-130}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-92}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	67.7%
Cost	980

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-130}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 720:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	76.5%
Cost	976

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -6500000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-264}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 18000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	37.9%
Cost	852

\[\begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+25}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-261}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00038:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 6
Accuracy	54.7%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-123}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+169}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Accuracy	60.6%
Cost	848

\[\begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-125}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	83.5%
Cost	844

\[\begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -35000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-71}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 0.00022:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	84.2%
Cost	844

\[\begin{array}{l} t_1 := x + z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -8.9 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-65}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 0.00036:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	35.8%
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-82}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+169}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Accuracy	53.4%
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-31}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+169}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	100.0%
Cost	576

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

Alternative 13
Accuracy	38.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-129}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 14
Accuracy	25.3%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023146 
(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))))