Average Error: 0.0 → 0.0
Time: 4.0s
Precision: 64
Internal Precision: 128
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[re \cdot re - im \cdot im\]
  2. Using strategy rm

  3. Applied difference-of-squares0.0

    \[\leadsto \color{blue}{\left(re + im\right) \cdot \left(re - im\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(im + re\right) \cdot \left(re - im\right)\]

Reproduce

herbie shell --seed 2019010 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))

Details

Time bar (total: 3.8s)Debug log

sample148.0ms

Algorithm
intervals

simplify33.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
32.0ms
(- (* re re) (* im im))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (* re re) (* im im))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×difference-of-squares
1×flip--
1×add-cube-cbrt
1×add-exp-log
1×diff-log
1×add-cbrt-cube
1×flip3--
1×*-un-lft-identity
1×sub-neg
1×pow1
1×add-sqr-sqrt
Counts
1 → 13
Calls
1 calls:
Slowest
6.0ms
(- (* re re) (* im im))

series57.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
57.0ms
(- (* re re) (* im im))

simplify46.0ms

Counts
6 → 16
Calls
6 calls:
Slowest
25.0ms
(/ (exp (* re re)) (exp (* im im)))
7.0ms
(- (pow re 2) (pow im 2))
5.0ms
(- (pow re 2) (pow im 2))
5.0ms
(- (pow re 2) (pow im 2))
1.0ms
(- re im)

prune166.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ re im) (- re im))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
4×frac-times
3×flip--
3×flip-+
3×add-cube-cbrt
3×add-exp-log
3×associate-*l*
3×associate-*r*
3×add-cbrt-cube
3×flip3--
3×flip3-+
3×*-un-lft-identity
3×pow1
3×add-sqr-sqrt
2×associate-*r/
2×associate-*l/
2×distribute-lft-in
2×sub-neg
2×distribute-rgt-in
1×add-log-exp
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-prod-down
Counts
1 → 29
Calls
1 calls:
Slowest
8.0ms
(* (+ re im) (- re im))

series38.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
38.0ms
(* (+ re im) (- re im))

simplify1.7s

Counts
27 → 32
Calls
27 calls:
Slowest
344.0ms
(* (+ (* re re) (- (* im im) (* re im))) (+ (* re re) (+ (* im im) (* re im))))
230.0ms
(* (+ (pow re 3) (pow im 3)) (- (pow re 3) (pow im 3)))
139.0ms
(* (- (* re re) (* im im)) (- (pow re 3) (pow im 3)))
138.0ms
(* (- re im) (+ (* re re) (+ (* im im) (* re im))))
130.0ms
(* (+ (pow re 3) (pow im 3)) (- (* re re) (* im im)))

prune203.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

end0.0ms

sample1.4s

Algorithm
intervals