Average Error: 0.0 → 0.0
Time: 8.2s
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 2019021 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 7.8s)Debug log

sample129.0ms

Algorithm
intervals
Results
47.0ms41×body640valid
34.0ms41×body1280valid
28.0ms221×body80valid
6.0ms17×body320valid
3.0ms12×body160valid

simplify2.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
2.0ms
(* (exp re) (sin im))

prune5.0ms

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) (sin im))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
3×add-cube-cbrt
3×associate-*l*
3×associate-*r*
3×add-cbrt-cube
3×*-un-lft-identity
3×pow1
3×add-sqr-sqrt
2×add-exp-log
1×add-log-exp
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-prod-down
Counts
1 → 17
Calls
1 calls:
Slowest
5.0ms
(* (exp re) (sin im))

series74.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
74.0ms
(* (exp re) (sin im))

simplify169.0ms

Counts
11 → 20
Calls
11 calls:
Slowest
92.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
62.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (sin im) (sin im)) (sin im)))
3.0ms
(* (exp re) (sin im))
3.0ms
(+ re (log (sin im)))
2.0ms
(* (sin im) (exp re))

prune177.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×sqrt-prod
12×associate-*l*
11×add-cube-cbrt
11×add-exp-log
11×add-cbrt-cube
11×*-un-lft-identity
11×pow1
4×add-log-exp
4×cbrt-unprod
4×prod-exp
4×pow-prod-down
4×associate-*r*
2×*-commutative
2×pow1/2
2×rem-sqrt-square
Counts
4 → 65
Calls
4 calls:
Slowest
10.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
5.0ms
(* (sqrt (exp re)) (sin im))
1.0ms
(sqrt (exp re))
0.0ms
(sqrt (exp re))

series153.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
70.0ms
(* (sqrt (exp re)) (sin im))
58.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
13.0ms
(sqrt (exp re))
11.0ms
(sqrt (exp re))

simplify1.4s

Counts
43 → 77
Calls
43 calls:
Slowest
706.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
361.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
111.0ms
(+ (* 1/8 (* (pow re 2) im)) (+ (* 1/2 (* re im)) im))
84.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
47.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im)))

prune805.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (exp re)) (cbrt (exp re)))
0.0b
(cbrt (exp re))
0.0b
(cbrt (exp re))
0.0b
(cbrt (exp re))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-cube-cbrt
11×*-un-lft-identity
11×add-sqr-sqrt
9×pow1
7×pow1/3
6×add-exp-log
6×associate-*l*
6×associate-*r*
4×add-log-exp
4×add-cbrt-cube
2×pow-prod-up
2×pow-prod-down
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-plus
1×pow2
Counts
4 → 61
Calls
4 calls:
Slowest
5.0ms
(* (cbrt (exp re)) (cbrt (exp re)))
1.0ms
(cbrt (exp re))
0.0ms
(cbrt (exp re))
0.0ms
(cbrt (exp re))

series503.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(cbrt (exp re))
136.0ms
(* (cbrt (exp re)) (cbrt (exp re)))
123.0ms
(cbrt (exp re))
107.0ms
(cbrt (exp re))

simplify210.0ms

Counts
41 → 73
Calls
41 calls:
Slowest
36.0ms
(+ (* 1/3 re) (+ (* 1/18 (pow re 2)) 1))
34.0ms
(+ (* 2/3 re) (+ (* 2/9 (pow re 2)) 1))
34.0ms
(+ (* 1/3 re) (+ (* 1/18 (pow re 2)) 1))
33.0ms
(+ (* 1/3 re) (+ (* 1/18 (pow re 2)) 1))
6.0ms
(pow (pow (exp re) 2) 1/3)

prune660.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes153.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.2s1520×body1280valid
1.1s6934×body80valid
564.0ms1241×body640valid
189.0ms629×body320valid
69.0ms326×body160valid