Average Error: 0.0 → 0.0
Time: 13.7s
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 2018365 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 9.1s)Debug log

start133.0ms

Algorithm
intervals

setup9.0ms

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
(* (exp re) (cos im))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

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

series80.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

80.0ms
(* (exp re) (cos im))

simplify130.0ms

Counts
11 → 20
Calls

11 calls. Slowest were:

63.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
47.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))
4.0ms
(* (cos im) (exp re))

prune167.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))
0.2b
(* (* (exp re) (cos im)) (* (exp re) (cos im)))
0.1b
(* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im)))
0.0b
(* (exp re) (cos im))

rewrite87.0ms

Algorithm
rewrite-expression-head
Counts
4 → 118
Calls

4 calls. Slowest were:

37.0ms
(* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im)))
29.0ms
(cbrt (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))
14.0ms
(* (* (exp re) (cos im)) (* (exp re) (cos im)))

series185.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

64.0ms
(* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im)))
43.0ms
(* (* (exp re) (cos im)) (* (exp re) (cos im)))
43.0ms
(* (exp re) (cos im))
35.0ms
(cbrt (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))

simplify6.7s

Counts
114 → 130
Calls

114 calls. Slowest were:

868.0ms
(* (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im))) (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))
733.0ms
(* (* (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im))) (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))) (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im))))
685.0ms
(* (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))) (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes148.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms