Average Error: 0.0 → 0.0
Time: 10.3s
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 2019018 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 9.8s)Debug log

sample87.0ms

Algorithm
intervals
Results
26.0ms34×body1280valid
22.0ms221×body80valid
18.0ms36×body640valid
8.0ms22×body320valid
3.0ms13×body160valid

simplify2.0ms

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

prune17.0ms

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

series51.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
51.0ms
(* (exp re) (sin im))

simplify178.0ms

Counts
11 → 20
Calls
11 calls:
Slowest
109.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
58.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (sin im) (sin im)) (sin im)))
2.0ms
(* (sin im) (exp re))
2.0ms
(* (exp re) (sin im))
2.0ms
(+ re (log (sin im)))

prune183.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

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
13.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
4.0ms
(* (sqrt (exp re)) (sin im))
1.0ms
(sqrt (exp re))
1.0ms
(sqrt (exp re))

series170.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
70.0ms
(* (sqrt (exp re)) (sin im))
59.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
21.0ms
(sqrt (exp re))
20.0ms
(sqrt (exp re))

simplify1.3s

Counts
43 → 77
Calls
43 calls:
Slowest
490.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
311.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
142.0ms
(+ (* 1/8 (* (pow re 2) im)) (+ (* 1/2 (* re im)) im))
107.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
71.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im)))

prune690.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
18×add-cbrt-cube
18×pow1
9×cbrt-unprod
9×add-cube-cbrt
9×prod-exp
9×pow-prod-down
9×*-un-lft-identity
9×add-sqr-sqrt
7×associate-*l*
6×cbrt-prod
4×add-log-exp
4×associate-*r*
3×sqrt-prod
2×*-commutative
2×pow1/3
Counts
4 → 64
Calls
4 calls:
Slowest
22.0ms
(* (* (fabs (cbrt (exp re))) (sqrt (cbrt (exp re)))) (* (sqrt (exp re)) (sin im)))
7.0ms
(* (sqrt (exp re)) (sin im))
1.0ms
(cbrt (exp re))
1.0ms
(cbrt (exp re))

series495.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(* (* (fabs (cbrt (exp re))) (sqrt (cbrt (exp re)))) (* (sqrt (exp re)) (sin im)))
146.0ms
(cbrt (exp re))
126.0ms
(cbrt (exp re))
69.0ms
(* (sqrt (exp re)) (sin im))

simplify2.0s

Counts
43 → 76
Calls
43 calls:
Slowest
681.0ms
(* (* (* (* (fabs (cbrt (exp re))) (sqrt (cbrt (exp re)))) (* (fabs (cbrt (exp re))) (sqrt (cbrt (exp re))))) (* (fabs (cbrt (exp re))) (sqrt (cbrt (exp re))))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
363.0ms
(+ (* 2/9 (* (pow re 2) (* (fabs (pow (exp re) 1/3)) im))) (+ (* 2/3 (* re (* (fabs (pow (exp re) 1/3)) im))) (* (fabs (pow (exp re) 1/3)) im)))
124.0ms
(* (* (* (* (fabs (cbrt (exp re))) (fabs (cbrt (exp re)))) (fabs (cbrt (exp re)))) (* (* (sqrt (cbrt (exp re))) (sqrt (cbrt (exp re)))) (sqrt (cbrt (exp re))))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
111.0ms
(* (* (* (* (fabs (cbrt (exp re))) (sqrt (cbrt (exp re)))) (* (fabs (cbrt (exp re))) (sqrt (cbrt (exp re))))) (* (fabs (cbrt (exp re))) (sqrt (cbrt (exp re))))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
107.0ms
(+ (* 1/8 (* (pow re 2) im)) (+ (* 1/2 (* re im)) im))

prune992.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes180.0ms

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
1.5s1493×body1280valid
725.0ms6967×body80valid
596.0ms1208×body640valid
222.0ms621×body320valid
93.0ms297×body160valid