fma_test2

Average Error: 64.0 → 0.3

Time: 25.4s

Precision: binary64

Cost: 320

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

Math

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

↓

\[\left(t + -1\right) \cdot 1.7 \cdot 10^{+308} \]

FPCore

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

↓

(FPCore (t) :precision binary64 (* (+ t -1.0) 1.7e+308))

C

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

↓

double code(double t) {
	return (t + -1.0) * 1.7e+308;
}

Fortran

real(8) function code(t)
    real(8), intent (in) :: t
    code = (1.7d+308 * t) - 1.7d+308
end function

↓

real(8) function code(t)
    real(8), intent (in) :: t
    code = (t + (-1.0d0)) * 1.7d+308
end function

Java

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

↓

public static double code(double t) {
	return (t + -1.0) * 1.7e+308;
}

Python

def code(t):
	return (1.7e+308 * t) - 1.7e+308

↓

def code(t):
	return (t + -1.0) * 1.7e+308

Julia

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

↓

function code(t)
	return Float64(Float64(t + -1.0) * 1.7e+308)
end

MATLAB

function tmp = code(t)
	tmp = (1.7e+308 * t) - 1.7e+308;
end

↓

function tmp = code(t)
	tmp = (t + -1.0) * 1.7e+308;
end

Wolfram

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

↓

code[t_] := N[(N[(t + -1.0), $MachinePrecision] * 1.7e+308), $MachinePrecision]

Target

Original	64.0
Target	0.3
Herbie	0.3

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

Derivation

1. Initial program 64.0

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

2. Applied egg-rr 0.3

   \[\leadsto \color{blue}{\left(t + -1\right) \cdot 1.7 \cdot 10^{+308}} \]

Alternatives

Alternative 1
Error	64.0
Cost	64

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

Reproduce

herbie shell --seed 2023010 
(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))