Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \sin im\]
↓
\[\sin im \cdot e^{re}\]

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

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019008 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 11.2s)Debug log

sample118.0ms

Algorithm
intervals

simplify4.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

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

series57.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

57.0ms
(* (exp re) (sin im))

simplify198.0ms

Counts
11 → 20
Calls

11 calls. Slowest were:

125.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
58.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (sin im) (sin im)) (sin im)))
4.0ms
(* (exp re) (sin im))

prune163.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

13.7b
(cbrt (pow (* (sin im) (exp re)) 3))
0.2b
(pow (* (sin im) (exp re)) 3)
0.0b
(* (sin im) (exp re))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
3 → 51
Calls

3 calls. Slowest were:

5.0ms
(* (sin im) (exp re))
3.0ms
(pow (* (sin im) (exp re)) 3)
1.0ms
(cbrt (pow (* (sin im) (exp re)) 3))

series160.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

55.0ms
(* (sin im) (exp re))
55.0ms
(cbrt (pow (* (sin im) (exp re)) 3))
49.0ms
(pow (* (sin im) (exp re)) 3)

simplify701.0ms

Counts
33 → 60
Calls

33 calls. Slowest were:

125.0ms
(- (+ (* re im) im) (* 1/6 (pow im 3)))
111.0ms
(- (+ (pow im 3) (* 3 (* re (pow im 3)))) (* 1/2 (pow im 5)))
88.0ms
(- (+ (* re im) im) (* 1/6 (pow im 3)))

prune691.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

13.7b
(cbrt (* (pow (sin im) 3) (* (* (exp re) (exp re)) (exp re))))
0.3b
(pow (sin im) 3)
0.0b
(* (exp re) (exp re))
0.0b
(* (pow (sin im) 3) (* (* (exp re) (exp re)) (exp re)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Counts
4 → 82
Calls

4 calls. Slowest were:

31.0ms
(* (pow (sin im) 3) (* (* (exp re) (exp re)) (exp re)))
13.0ms
(cbrt (* (pow (sin im) 3) (* (* (exp re) (exp re)) (exp re))))
3.0ms
(* (exp re) (exp re))

series138.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

55.0ms
(* (pow (sin im) 3) (* (* (exp re) (exp re)) (exp re)))
45.0ms
(cbrt (* (pow (sin im) 3) (* (* (exp re) (exp re)) (exp re))))
24.0ms
(pow (sin im) 3)
15.0ms
(* (exp re) (exp re))

simplify2.6s

Counts
58 → 94
Calls

58 calls. Slowest were:

557.0ms
(* (* (* (pow (sin im) 3) (pow (sin im) 3)) (pow (sin im) 3)) (* (* (* (* (exp re) (exp re)) (* (exp re) (exp re))) (* (exp re) (exp re))) (* (* (exp re) (exp re)) (exp re))))
493.0ms
(* (* (* (pow (sin im) 3) (pow (sin im) 3)) (pow (sin im) 3)) (* (* (* (* (exp re) (exp re)) (exp re)) (* (* (exp re) (exp re)) (exp re))) (* (* (exp re) (exp re)) (exp re))))
477.0ms
(* (* (* (pow (sin im) 3) (pow (sin im) 3)) (pow (sin im) 3)) (* (* (* (* (exp re) (exp re)) (exp re)) (* (* (exp re) (exp re)) (exp re))) (* (* (exp re) (exp re)) (exp re))))

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 3 expressions with local error:

8.7b
(* (pow re 2) im)
4.0b
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
0.0b
(* 1/2 (* (pow re 2) im))

rewrite24.0ms

Algorithm
rewrite-expression-head
Counts
3 → 33
Calls

3 calls. Slowest were:

13.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
6.0ms
(* 1/2 (* (pow re 2) im))
4.0ms
(* (pow re 2) im)

series69.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

30.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
20.0ms
(* 1/2 (* (pow re 2) im))
19.0ms
(* (pow re 2) im)

simplify586.0ms

Counts
12 → 42
Calls

12 calls. Slowest were:

126.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
122.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
110.0ms
(* (exp (* 1/2 (* (pow re 2) im))) (exp (+ (* re im) im)))

prune367.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes200.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.5s

Algorithm
intervals