Cancel like terms

Average Error: 28.7 → 0

Time: 823.0ms

Precision: binary64

Cost: 64

Math

\[\left(1 + x\right) - x \]

↓

\[1 \]

FPCore

(FPCore (x) :precision binary64 (- (+ 1.0 x) x))

↓

(FPCore (x) :precision binary64 1.0)

C

double code(double x) {
	return (1.0 + x) - x;
}

↓

double code(double x) {
	return 1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 + x) - x
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0
end function

Java

public static double code(double x) {
	return (1.0 + x) - x;
}

↓

public static double code(double x) {
	return 1.0;
}

Python

def code(x):
	return (1.0 + x) - x

↓

def code(x):
	return 1.0

Julia

function code(x)
	return Float64(Float64(1.0 + x) - x)
end

↓

function code(x)
	return 1.0
end

MATLAB

function tmp = code(x)
	tmp = (1.0 + x) - x;
end

↓

function tmp = code(x)
	tmp = 1.0;
end

Wolfram

code[x_] := N[(N[(1.0 + x), $MachinePrecision] - x), $MachinePrecision]

↓

code[x_] := 1.0

Derivation

1. Initial program 28.7

   \[\left(1 + x\right) - x \]

2. Simplified 0

   \[\leadsto \color{blue}{1} \]
   Proof

   [Start] 28.7	\[ \left(1 + x\right) - x \]
   rational_best_oopsla_all_46_json_45_simplify-35 [=>] 28.7	\[ \color{blue}{\left(x + 1\right)} - x \]
   rational_best_oopsla_all_46_json_45_simplify-11 [=>] 28.7	\[ \color{blue}{\left(x - -1\right)} - x \]
   rational_best_oopsla_all_46_json_45_simplify-105 [=>] 0	\[ \color{blue}{\left(x - x\right) - -1} \]
   rational_best_oopsla_all_46_json_45_simplify-86 [=>] 0	\[ \color{blue}{0} - -1 \]
   metadata-eval [=>] 0	\[ \color{blue}{1} \]

3. Final simplification 0

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x)
  :name "Cancel like terms"
  :precision binary64
  (- (+ 1.0 x) x))