Average Error: 30.1 → 0.0
Time: 3.9s
Precision: 64
Internal Precision: 128
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\sqrt{re^2 + im^2}^*\]

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 30.1

    \[\sqrt{re \cdot re + im \cdot im}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\sqrt{re^2 + im^2}^*}\]

  3. Final simplification0.0

    \[\leadsto \sqrt{re^2 + im^2}^*\]

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 3.5s)Debug log

sample39.0ms

Algorithm
intervals

simplify8.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

8.0ms
(sqrt (+ (* re re) (* im im)))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(hypot re im)

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(hypot re im)

series39.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

39.0ms
(hypot re im)

simplify5.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

3.0ms
(* -1 re)
1.0ms
im
1.0ms
re

prune134.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))
0.6b
(cbrt (hypot re im))
0.5b
(* (cbrt (hypot re im)) (cbrt (hypot re im)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Counts
4 → 69
Calls

4 calls. Slowest were:

15.0ms
(* (cbrt (hypot re im)) (cbrt (hypot re im)))
1.0ms
(cbrt (hypot re im))
1.0ms
(cbrt (hypot re im))

series509.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

166.0ms
(* (cbrt (hypot re im)) (cbrt (hypot re im)))
117.0ms
(cbrt (hypot re im))
116.0ms
(cbrt (hypot re im))
110.0ms
(cbrt (hypot re im))

simplify176.0ms

Counts
41 → 81
Calls

41 calls. Slowest were:

42.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
36.0ms
(+ (* 1/6 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3))
25.0ms
(+ (pow im 2/3) (* 1/3 (* (pow re 2) (pow (/ 1 (pow im 4)) 1/3))))

prune756.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

28.3b
(sqrt (+ (* re re) (* im im)))
0.0b
(+ (* re re) (* im im))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
2 → 31
Calls

2 calls. Slowest were:

2.0ms
(+ (* re re) (* im im))
2.0ms
(sqrt (+ (* re re) (* im im)))

series37.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

20.0ms
(sqrt (+ (* re re) (* im im)))
17.0ms
(+ (* re re) (* im im))

simplify288.0ms

Counts
13 → 37
Calls

13 calls. Slowest were:

189.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
57.0ms
(sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))
8.0ms
(+ (pow im 2) (pow re 2))

prune284.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes272.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample897.0ms

Algorithm
intervals