Average Error: 0.0 → 0.0
Time: 6.0s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \cos im\]
↓
\[e^{re} \cdot \cos im\]

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

    \[e^{re} \cdot \cos im\]

  2. Initial simplification0.0

    \[\leadsto \cos im \cdot e^{re}\]

  3. Final simplification0.0

    \[\leadsto e^{re} \cdot \cos im\]

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 2.6s)Debug log

start71.0ms

Algorithm
intervals

setup10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (cos im) (exp re))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 19
Calls

1 calls. Slowest were:

4.0ms
(* (cos im) (exp re))

series48.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

48.0ms
(* (cos im) (exp re))

simplify109.0ms

Counts
11 → 22
Calls

11 calls. Slowest were:

65.0ms
(* (* (* (cos im) (cos im)) (cos im)) (* (* (exp re) (exp re)) (exp re)))
32.0ms
(- (+ re 1) (* 1/2 (pow im 2)))
2.0ms
(* (cos im) (exp re))

prune193.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (cos im) (sqrt (exp re))) (sqrt (exp re)))
0.0b
(* (cos im) (sqrt (exp re)))
0.0b
(sqrt (exp re))
0.0b
(sqrt (exp re))

rewrite31.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

18.0ms
(* (* (cos im) (sqrt (exp re))) (sqrt (exp re)))
9.0ms
(* (cos im) (sqrt (exp re)))
1.0ms
(sqrt (exp re))

series137.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

54.0ms
(* (cos im) (sqrt (exp re)))
43.0ms
(* (* (cos im) (sqrt (exp re))) (sqrt (exp re)))
20.0ms
(sqrt (exp re))
19.0ms
(sqrt (exp re))

simplify996.0ms

Counts
44 → 85
Calls

44 calls. Slowest were:

340.0ms
(* (* (* (* (cos im) (sqrt (exp re))) (* (cos im) (sqrt (exp re)))) (* (cos im) (sqrt (exp re)))) (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))))
288.0ms
(* (* (* (* (cos im) (cos im)) (cos im)) (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re)))) (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))))
77.0ms
(- (+ (* 1/2 re) 1) (* 1/2 (pow im 2)))

prune835.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes124.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms