Average Error: 0.0 → 0.0
Time: 13.7s
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 2019010 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 13.2s)Debug log

sample123.0ms

Algorithm
intervals

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

localize11.0ms

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))

series54.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
54.0ms
(* (exp re) (sin im))

simplify153.0ms

Counts
11 → 20
Calls
11 calls:
Slowest
82.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
60.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (sin im) (sin im)) (sin im)))
2.0ms
(* (exp re) (sin im))
2.0ms
(* (sin im) (exp re))
2.0ms
(* (sin im) (exp re))

prune140.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

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))
1.0ms
(sqrt (exp re))
1.0ms
(sqrt (exp re))

series133.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
62.0ms
(* (sqrt (exp re)) (sin im))
48.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
12.0ms
(sqrt (exp re))
11.0ms
(sqrt (exp re))

simplify1.3s

Counts
43 → 77
Calls
43 calls:
Slowest
464.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
345.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
149.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
99.0ms
(+ (* 1/8 (* (pow re 2) im)) (+ (* 1/2 (* re im)) im))
47.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im)))

prune793.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-prod
18×add-exp-log
18×add-cbrt-cube
18×pow1
15×associate-*l*
13×add-sqr-sqrt
11×add-cube-cbrt
11×*-un-lft-identity
9×cbrt-unprod
9×prod-exp
9×pow-prod-down
4×add-log-exp
2×*-commutative
2×associate-*r*
2×pow1/2
2×rem-sqrt-square
Counts
4 → 72
Calls
4 calls:
Slowest
37.0ms
(* (sqrt (exp re)) (* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (sin im))))
18.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (sin im)))
1.0ms
(sqrt (exp re))
1.0ms
(sqrt (exp re))

series137.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
64.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (sin im)))
47.0ms
(* (sqrt (exp re)) (* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (sin im))))
14.0ms
(sqrt (exp re))
12.0ms
(sqrt (exp re))

simplify2.5s

Counts
50 → 84
Calls
50 calls:
Slowest
573.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (sin im))) (* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (sin im)))) (* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (sin im)))))
568.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (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)))) (* (* (sin im) (sin im)) (sin im)))))
358.0ms
(* (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))) (* (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))) (* (* (sin im) (sin im)) (sin im))))
331.0ms
(* (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))) (* (* (* (sqrt (sqrt (exp re))) (sin im)) (* (sqrt (sqrt (exp re))) (sin im))) (* (sqrt (sqrt (exp re))) (sin im))))
147.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))

prune736.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log
15×add-cbrt-cube
15×pow1
10×add-cube-cbrt
10×*-un-lft-identity
10×add-sqr-sqrt
9×associate-*l*
7×cbrt-unprod
7×prod-exp
7×pow-prod-down
6×cbrt-prod
4×add-log-exp
4×associate-*r*
3×sqrt-prod
2×*-commutative
2×pow1/3
Counts
4 → 63
Calls
4 calls:
Slowest
24.0ms
(* (fabs (cbrt (exp re))) (* (sqrt (cbrt (exp re))) (* (sqrt (exp re)) (sin im))))
4.0ms
(* (sqrt (exp re)) (sin im))
1.0ms
(cbrt (exp re))
0.0ms
(cbrt (exp re))

series461.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(cbrt (exp re))
136.0ms
(cbrt (exp re))
118.0ms
(* (fabs (cbrt (exp re))) (* (sqrt (cbrt (exp re))) (* (sqrt (exp re)) (sin im))))
71.0ms
(* (sqrt (exp re)) (sin im))

simplify1.2s

Counts
41 → 75
Calls
41 calls:
Slowest
358.0ms
(+ (* 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)))
117.0ms
(+ (* 1/8 (* (pow re 2) im)) (+ (* 1/2 (* re im)) im))
85.0ms
(* (* (* (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)))))
84.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im)))
74.0ms
(* (* (* (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)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im)))))

prune1.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes195.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample4.0s

Algorithm
intervals