fma_test2

?

Percentage Accurate: 33.7% → 99.6%
Time: 11.1s
Precision: binary64
Cost: 6592

?

\[1.9 \leq t \land t \leq 2.1\]
\[1.7 \cdot 10^{+308} \cdot t - 1.7 \cdot 10^{+308} \]
↓
\[\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right) \]
(FPCore (t) :precision binary64 (- (* 1.7e+308 t) 1.7e+308))
↓
(FPCore (t) :precision binary64 (fma 1.7e+308 t -1.7e+308))
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);
}

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

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

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)

Local Percentage Accuracy?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Target

Original33.7%
Target99.6%
Herbie99.6%
\[\mathsf{fma}\left(1.7 \cdot 10^{+308}, t, -1.7 \cdot 10^{+308}\right) \]

Derivation?

  1. Initial program 33.4%

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

  2. Simplified99.6%

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

    [Start]33.4

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

    fma-neg [=>]99.6

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

    metadata-eval [=>]99.6

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

  3. Final simplification99.6%

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

Alternatives

Alternative 1
Accuracy33.7%
Cost192
\[1.7 \cdot 10^{+308} \cdot t \]
Alternative 2
Accuracy0.0%
Cost64
\[-1.7 \cdot 10^{+308} \]

Error

Reproduce?

herbie shell --seed 2023160 
(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))