FastMath test1

?

Percentage Accurate: 99.6% → 100.0%

Time: 839.0ms

Precision: binary64

Cost: 192

?

\[d \cdot 10 + d \cdot 20 \]

↓

\[d \cdot 30 \]

(FPCore (d) :precision binary64 (+ (* d 10.0) (* d 20.0)))

↓

(FPCore (d) :precision binary64 (* d 30.0))

double code(double d) {
	return (d * 10.0) + (d * 20.0);
}

↓

double code(double d) {
	return d * 30.0;
}

real(8) function code(d)
    real(8), intent (in) :: d
    code = (d * 10.0d0) + (d * 20.0d0)
end function

↓

real(8) function code(d)
    real(8), intent (in) :: d
    code = d * 30.0d0
end function

public static double code(double d) {
	return (d * 10.0) + (d * 20.0);
}

↓

public static double code(double d) {
	return d * 30.0;
}

def code(d):
	return (d * 10.0) + (d * 20.0)

↓

def code(d):
	return d * 30.0

function code(d)
	return Float64(Float64(d * 10.0) + Float64(d * 20.0))
end

↓

function code(d)
	return Float64(d * 30.0)
end

function tmp = code(d)
	tmp = (d * 10.0) + (d * 20.0);
end

↓

function tmp = code(d)
	tmp = d * 30.0;
end

code[d_] := N[(N[(d * 10.0), $MachinePrecision] + N[(d * 20.0), $MachinePrecision]), $MachinePrecision]

↓

code[d_] := N[(d * 30.0), $MachinePrecision]

d \cdot 10 + d \cdot 20

↓

d \cdot 30

Local Percentage Accuracy vs ?

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.

Herbie found 1 alternatives:

Alternative	Accuracy	Speedup

Accuracy vs Speed

The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Bogosity?

Bogosity

Try it out?

In
Out

Enter valid numbers for all inputs

Target

Original	99.6%
Target	100.0%
Herbie	100.0%

\[d \cdot 30 \]

Derivation?

Initial program 99.6%
\[d \cdot 10 + d \cdot 20 \]
Simplified100.0%
\[\leadsto \color{blue}{d \cdot 30} \]
Step-by-step derivation
[Start]99.6%
\[ d \cdot 10 + d \cdot 20 \]
distribute-lft-out [=>]100.0%
\[ \color{blue}{d \cdot \left(10 + 20\right)} \]
metadata-eval [=>]100.0%
\[ d \cdot \color{blue}{30} \]
Final simplification100.0%
\[\leadsto d \cdot 30 \]

Reproduce?

herbie shell --seed 2023178 
(FPCore (d)
  :name "FastMath test1"
  :precision binary64

  :herbie-target
  (* d 30.0)

  (+ (* d 10.0) (* d 20.0)))