Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Average Accuracy: 100.0% → 100.0%

Time: 11.5s

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	56.3%
Cost	1376

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := x \cdot \left(1 - y\right)\\ t_3 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-102}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-167}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	38.4%
Cost	1312

\[\begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-261}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+28}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+261}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 3
Accuracy	73.0%
Cost	1108

\[\begin{array}{l} t_1 := x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-127}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	38.6%
Cost	984

\[\begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{-25}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 5
Accuracy	62.3%
Cost	849

\[\begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-7}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+67} \lor \neg \left(x \leq 3.4 \cdot 10^{+98}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 6
Accuracy	64.5%
Cost	848

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-135}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	52.4%
Cost	784

\[\begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-7}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+67}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+160}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Accuracy	81.3%
Cost	713

\[\begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{-123} \lor \neg \left(t \leq 5.8 \cdot 10^{-7}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \end{array} \]

Alternative 9
Accuracy	38.5%
Cost	588

\[\begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+14}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-169}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 82000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 10
Accuracy	70.7%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-26} \lor \neg \left(y \leq 8 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 11
Accuracy	100.0%
Cost	576

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

Alternative 12
Accuracy	39.9%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-26}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 13
Accuracy	25.3%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023135 
(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))))