Average Error: 0.0 → 0.0
Time: 7.0s
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 2019022 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 6.7s)Debug log

sample93.0ms

Algorithm
intervals
Results
37.0ms49×body1280valid
24.0ms240×body80valid
14.0ms32×body640valid
5.0ms15×body320valid
1.0ms6×body160valid

simplify4.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
4.0ms
(* (exp re) (sin im))

prune9.0ms

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
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
3.0ms
(* (exp re) (sin im))

series71.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
71.0ms
(* (exp re) (sin im))

simplify206.0ms

Counts
11 → 20
Calls
11 calls:
Slowest
131.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
58.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (sin im) (sin im)) (sin im)))
3.0ms
(* (sin im) (exp re))
3.0ms
(* (sin im) (exp re))
2.0ms
(* (exp re) (sin im))

prune186.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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
21.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
9.0ms
(* (sqrt (exp re)) (sin im))
2.0ms
(sqrt (exp re))
1.0ms
(sqrt (exp re))

series165.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
81.0ms
(* (sqrt (exp re)) (sin im))
58.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
15.0ms
(sqrt (exp re))
12.0ms
(sqrt (exp re))

simplify1.2s

Counts
43 → 77
Calls
43 calls:
Slowest
450.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
392.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
110.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
89.0ms
(+ (* 1/8 (* (pow re 2) im)) (+ (* 1/2 (* re im)) im))
60.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im)))

prune654.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes191.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.2s1483×body1280valid
1.1s1290×body640valid
880.0ms6924×body80valid
296.0ms612×body320valid
109.0ms301×body160valid