Average Error: 0.0 → 0.0
Time: 7.3s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \cos im\]
↓
\[\cos im \cdot e^{re}\]

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019007 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 6.8s)Debug log

sample91.0ms

Algorithm
intervals

simplify2.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

2.0ms
(* (exp re) (cos im))

prune6.0ms

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
(* (exp re) (cos im))

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

7.0ms
(* (exp re) (cos im))

series70.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

70.0ms
(* (exp re) (cos im))

simplify149.0ms

Counts
11 → 20
Calls

11 calls. Slowest were:

84.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
43.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))
4.0ms
(* (cos im) (exp re))

prune273.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.3b
(log (exp (* (exp re) (cos im))))
0.1b
(exp (* (exp re) (cos im)))
0.0b
(* (exp re) (cos im))

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
3 → 41
Calls

3 calls. Slowest were:

4.0ms
(* (exp re) (cos im))
4.0ms
(exp (* (exp re) (cos im)))
3.0ms
(log (exp (* (exp re) (cos im))))

series146.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

80.0ms
(exp (* (exp re) (cos im)))
34.0ms
(log (exp (* (exp re) (cos im))))
32.0ms
(* (exp re) (cos im))

simplify221.0ms

Counts
26 → 50
Calls

26 calls. Slowest were:

62.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
41.0ms
(+ (* (pow re 2) E) (+ (* re E) E))
39.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))

prune546.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos im))
0.3b
(cbrt (cos im))
0.3b
(cbrt (cos im))
0.3b
(* (cbrt (cos im)) (cbrt (cos im)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Counts
4 → 61
Calls

4 calls. Slowest were:

13.0ms
(* (cbrt (cos im)) (cbrt (cos im)))
1.0ms
(cbrt (cos im))
1.0ms
(cbrt (cos im))

series655.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

199.0ms
(* (cbrt (cos im)) (cbrt (cos im)))
172.0ms
(cbrt (cos im))
154.0ms
(cbrt (cos im))
131.0ms
(cbrt (cos im))

simplify296.0ms

Counts
41 → 73
Calls

41 calls. Slowest were:

79.0ms
(- 1 (+ (* 1/6 (pow im 2)) (* 1/72 (pow im 4))))
68.0ms
(- 1 (+ (* 1/6 (pow im 2)) (* 1/72 (pow im 4))))
57.0ms
(- 1 (+ (* 1/3 (pow im 2)) (* 1/405 (pow im 6))))

prune863.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes175.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.2s

Algorithm
intervals