Average Error: 29.5 → 0.0
Time: 2.5s
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 29.5

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

  2. Initial simplification0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 1.3s)Debug log

start38.0ms

Algorithm
intervals

setup15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b
(hypot re im)

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(hypot re im)

series23.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

23.0ms
(hypot re im)

simplify8.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

7.0ms
(* -1 re)
0.0ms
im
0.0ms
re

prune399.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 2 expressions with local error:

29.8b
(sqrt (+ (* re re) (* im im)))
0.0b
(+ (* re re) (* im im))

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
2 → 31
Calls

2 calls. Slowest were:

4.0ms
(+ (* re re) (* im im))
4.0ms
(sqrt (+ (* re re) (* im im)))

series57.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

32.0ms
(sqrt (+ (* re re) (* im im)))
25.0ms
(+ (* re re) (* im im))

simplify281.0ms

Counts
13 → 37
Calls

13 calls. Slowest were:

179.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
53.0ms
(sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))
11.0ms
(sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))

prune297.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes160.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms