Average Error: 0.0 → 0.0
Time: 16.8s
Precision: 64
Internal Precision: 128
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[x.re \cdot y.re - x.im \cdot y.im\]

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x.re \cdot y.re - x.im \cdot y.im\]

  2. Final simplification0.0

    \[\leadsto x.re \cdot y.re - x.im \cdot y.im\]

Reproduce

herbie shell --seed 2019004 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))

Details

Time bar (total: 16.4s)Debug log

sample29.0ms

Algorithm
intervals

simplify5.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

5.0ms
(- (* x.re y.re) (* x.im y.im))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (* x.re y.re) (* x.im y.im))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 12
Calls

1 calls. Slowest were:

2.0ms
(- (* x.re y.re) (* x.im y.im))

series57.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

57.0ms
(- (* x.re y.re) (* x.im y.im))

simplify52.0ms

Counts
4 → 15
Calls

4 calls. Slowest were:

29.0ms
(/ (exp (* x.re y.re)) (exp (* x.im y.im)))
11.0ms
(- (* y.re x.re) (* y.im x.im))
10.0ms
(- (* y.re x.re) (* y.im x.im))

prune119.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

2.2b
(cbrt (- (* x.re y.re) (* x.im y.im)))
2.2b
(cbrt (- (* x.re y.re) (* x.im y.im)))
2.2b
(cbrt (- (* x.re y.re) (* x.im y.im)))
0.5b
(* (cbrt (- (* x.re y.re) (* x.im y.im))) (cbrt (- (* x.re y.re) (* x.im y.im))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

9.0ms
(* (cbrt (- (* x.re y.re) (* x.im y.im))) (cbrt (- (* x.re y.re) (* x.im y.im))))
1.0ms
(cbrt (- (* x.re y.re) (* x.im y.im)))
1.0ms
(cbrt (- (* x.re y.re) (* x.im y.im)))

series615.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

182.0ms
(cbrt (- (* x.re y.re) (* x.im y.im)))
160.0ms
(* (cbrt (- (* x.re y.re) (* x.im y.im))) (cbrt (- (* x.re y.re) (* x.im y.im))))
137.0ms
(cbrt (- (* x.re y.re) (* x.im y.im)))
136.0ms
(cbrt (- (* x.re y.re) (* x.im y.im)))

simplify7.8s

Counts
59 → 87
Calls

59 calls. Slowest were:

569.0ms
(* (cbrt (- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im)))) (cbrt (- (* x.re y.re) (* x.im y.im))))
505.0ms
(* (cbrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3))) (cbrt (- (* x.re y.re) (* x.im y.im))))
417.0ms
(* (cbrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3))) (cbrt (- (pow (* x.re y.re) 3) (pow (* x.im y.im) 3))))

prune985.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

29.2b
(cbrt (- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im))))
3.1b
(- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im)))
2.2b
(cbrt (+ (* x.re y.re) (* x.im y.im)))
2.2b
(cbrt (- (* x.re y.re) (* x.im y.im)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Counts
4 → 53
Calls

4 calls. Slowest were:

11.0ms
(- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im)))
4.0ms
(cbrt (- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im))))
3.0ms
(cbrt (- (* x.re y.re) (* x.im y.im)))

series443.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

134.0ms
(cbrt (- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im))))
123.0ms
(cbrt (+ (* x.re y.re) (* x.im y.im)))
122.0ms
(cbrt (- (* x.re y.re) (* x.im y.im)))
63.0ms
(- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im)))

simplify3.8s

Counts
31 → 65
Calls

31 calls. Slowest were:

318.0ms
(exp (* -1/3 (+ (log (/ 1 x.re)) (log (/ 1 y.re)))))
318.0ms
(cbrt (sqrt (- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im)))))
317.0ms
(exp (* -1/3 (+ (log (/ 1 x.re)) (log (/ 1 y.re)))))

prune877.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes420.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch2.0ms

end0.0ms

sample1.1s

Algorithm
intervals