fma_test2

Average Accuracy: 0.0% → 99.5%

Time: 11.4s

Precision: binary64

Cost: 6592

\[1.9 \leq t \land t \leq 2.1\]

Math

\[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]

↓

\[\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right) \]

FPCore

(FPCore (t) :precision binary64 (- (* 1.7e+308 t) 1.7e+308))

↓

(FPCore (t) :precision binary64 (fma 1.7e+308 t -1.7e+308))

C

double code(double t) {
	return (1.7e+308 * t) - 1.7e+308;
}

↓

double code(double t) {
	return fma(1.7e+308, t, -1.7e+308);
}

Julia

function code(t)
	return Float64(Float64(1.7e+308 * t) - 1.7e+308)
end

↓

function code(t)
	return fma(1.7e+308, t, -1.7e+308)
end

Wolfram

code[t_] := N[(N[(1.7e+308 * t), $MachinePrecision] - 1.7e+308), $MachinePrecision]

↓

code[t_] := N[(1.7e+308 * t + -1.7e+308), $MachinePrecision]

Target

Original	0.0%
Target	99.5%
Herbie	99.5%

\[\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right) \]

Derivation

1. Initial program 0.0%

   \[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]

2. Simplified 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \]
   Proof

   [Start] 0.0	\[ 1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]
   fma-neg [=>] 99.5	\[ \color{blue}{\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right)} \]
   metadata-eval [=>] 99.5	\[ \mathsf{fma}\left(1.7 \cdot 10^{+308}, t, \color{blue}{-1.7 \cdot 10^{+308}}\right) \]

3. Final simplification 99.5%

   \[\leadsto \mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right) \]

Alternatives

Alternative 1
Accuracy	0.0%
Cost	64

\[-1.7 \cdot 10^{+308} \]

Reproduce

herbie shell --seed 2023122 
(FPCore (t)
  :name "fma_test2"
  :precision binary64
  :pre (and (<= 1.9 t) (<= t 2.1))

  :herbie-target
  (fma 1.7e+308 t (- 1.7e+308))

  (- (* 1.7e+308 t) 1.7e+308))