Average Error: 0.0 → 0.0
Time: 15.1s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \sin im\]
↓
\[e^{re} \cdot \sin im\]

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

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

  2. Initial simplification0.0

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

  3. Final simplification0.0

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

Reproduce

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

Details

Time bar (total: 10.2s)Debug log

start123.0ms

Algorithm
intervals

setup25.0ms

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
(* (sin im) (exp re))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 19
Calls

1 calls. Slowest were:

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

series49.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

49.0ms
(* (sin im) (exp re))

simplify580.0ms

Counts
11 → 22
Calls

11 calls. Slowest were:

423.0ms
(* (* (* (sin im) (sin im)) (sin im)) (* (* (exp re) (exp re)) (exp re)))
137.0ms
(- (+ (* re im) im) (* 1/6 (pow im 3)))
4.0ms
(* (sin im) (exp re))

prune171.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

11.0ms
(* (* (sin im) (sqrt (exp re))) (sqrt (exp re)))
4.0ms
(* (sin im) (sqrt (exp re)))
2.0ms
(sqrt (exp re))

series131.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

59.0ms
(* (sin im) (sqrt (exp re)))
35.0ms
(* (* (sin im) (sqrt (exp re))) (sqrt (exp re)))
20.0ms
(sqrt (exp re))
17.0ms
(sqrt (exp re))

simplify1.3s

Counts
44 → 85
Calls

44 calls. Slowest were:

331.0ms
(* (* (* (* (sin im) (sqrt (exp re))) (* (sin im) (sqrt (exp re)))) (* (sin im) (sqrt (exp re)))) (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))))
315.0ms
(* (* (* (* (sin im) (sin im)) (sin im)) (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re)))) (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))))
257.0ms
(- (+ (* 1/2 (* re im)) im) (* 1/6 (pow im 3)))

prune810.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm
rewrite-expression-head
Counts
4 → 95
Calls

4 calls. Slowest were:

49.0ms
(* (* (* (sin im) (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re))))
12.0ms
(* (* (sin im) (sqrt (exp re))) (sqrt (sqrt (exp re))))
9.0ms
(* (sin im) (sqrt (exp re)))

series342.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

141.0ms
(* (* (sin im) (sqrt (exp re))) (sqrt (sqrt (exp re))))
97.0ms
(sqrt (sqrt (exp re)))
56.0ms
(* (* (* (sin im) (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re))))
48.0ms
(* (sin im) (sqrt (exp re)))

simplify2.9s

Counts
66 → 107
Calls

66 calls. Slowest were:

596.0ms
(* (* (* (* (* (sin im) (sqrt (exp re))) (* (sin im) (sqrt (exp re)))) (* (sin im) (sqrt (exp re)))) (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re))))) (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))))
397.0ms
(* (* (* (* (* (sin im) (sqrt (exp re))) (sqrt (sqrt (exp re)))) (* (* (sin im) (sqrt (exp re))) (sqrt (sqrt (exp re))))) (* (* (sin im) (sqrt (exp re))) (sqrt (sqrt (exp re))))) (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))))
367.0ms
(* (* (* (* (sin im) (sin im)) (sin im)) (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re)))) (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))))

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/6 (pow im 3))
0.0b
(+ (* re im) im)
0.0b
(- (+ (* re im) im) (* 1/6 (pow im 3)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
3 → 52
Calls

3 calls. Slowest were:

13.0ms
(- (+ (* re im) im) (* 1/6 (pow im 3)))
2.0ms
(+ (* re im) im)
2.0ms
(* 1/6 (pow im 3))

series63.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

28.0ms
(- (+ (* re im) im) (* 1/6 (pow im 3)))
20.0ms
(* 1/6 (pow im 3))
14.0ms
(+ (* re im) im)

simplify1.6s

Counts
27 → 61
Calls

27 calls. Slowest were:

255.0ms
(fma (sqrt (+ (* re im) im)) (sqrt (+ (* re im) im)) (- (* (pow im 3) 1/6)))
235.0ms
(- (+ (* re im) im) (* 1/6 (pow im 3)))
201.0ms
(- (+ (* re im) im) (* 1/6 (pow im 3)))

prune662.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes150.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms