Average Error: 0.0 → 0.0
Time: 28.4s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(\sin re \cdot e^{\log \left(e^{im} + e^{-im}\right)}\right) \cdot 0.5\]

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied add-exp-log0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \color{blue}{e^{\log \left(e^{0 - im} + e^{im}\right)}}\]
  4. Using strategy rm

  5. Applied associate-*l*0.0

    \[\leadsto \color{blue}{0.5 \cdot \left(\sin re \cdot e^{\log \left(e^{0 - im} + e^{im}\right)}\right)}\]

  6. Final simplification0.0

    \[\leadsto \left(\sin re \cdot e^{\log \left(e^{im} + e^{-im}\right)}\right) \cdot 0.5\]

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 27.9s)Debug log

sample299.0ms

Algorithm
intervals

simplify781.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

780.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
0.0b
(+ (exp (- 0 im)) (exp im))

rewrite28.0ms

Algorithm
rewrite-expression-head
Counts
2 → 41
Calls

2 calls. Slowest were:

21.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
6.0ms
(+ (exp (- 0 im)) (exp im))

series109.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

84.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
25.0ms
(+ (exp (- 0 im)) (exp im))

simplify2.3s

Counts
23 → 47
Calls

23 calls. Slowest were:

476.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))
442.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
373.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))

prune370.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (* 0.5 (sin re)) (exp (log (+ (exp (- 0 im)) (exp im)))))
0.0b
(+ (exp (- 0 im)) (exp im))
0.0b
(log (+ (exp (- 0 im)) (exp im)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Counts
3 → 59
Calls

3 calls. Slowest were:

37.0ms
(* (* 0.5 (sin re)) (exp (log (+ (exp (- 0 im)) (exp im)))))
13.0ms
(+ (exp (- 0 im)) (exp im))
8.0ms
(log (+ (exp (- 0 im)) (exp im)))

series198.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

96.0ms
(log (+ (exp (- 0 im)) (exp im)))
76.0ms
(* (* 0.5 (sin re)) (exp (log (+ (exp (- 0 im)) (exp im)))))
27.0ms
(+ (exp (- 0 im)) (exp im))

simplify3.0s

Counts
34 → 68
Calls

34 calls. Slowest were:

527.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))
496.0ms
(log (- (* (exp (- 0 im)) (exp (- 0 im))) (* (exp im) (exp im))))
447.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))

prune900.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (sin re) (exp (log (+ (exp (- 0 im)) (exp im)))))
0.0b
(+ (exp (- 0 im)) (exp im))
0.0b
(log (+ (exp (- 0 im)) (exp im)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Counts
3 → 61
Calls

3 calls. Slowest were:

16.0ms
(* (sin re) (exp (log (+ (exp (- 0 im)) (exp im)))))
6.0ms
(+ (exp (- 0 im)) (exp im))
5.0ms
(log (+ (exp (- 0 im)) (exp im)))

series276.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

135.0ms
(log (+ (exp (- 0 im)) (exp im)))
100.0ms
(* (sin re) (exp (log (+ (exp (- 0 im)) (exp im)))))
41.0ms
(+ (exp (- 0 im)) (exp im))

simplify2.4s

Counts
36 → 70
Calls

36 calls. Slowest were:

600.0ms
(log (- (* (exp (- 0 im)) (exp (- 0 im))) (* (exp im) (exp im))))
540.0ms
(* (* (* (sin re) (sin re)) (sin re)) (* (* (exp (log (+ (exp (- 0 im)) (exp im)))) (exp (log (+ (exp (- 0 im)) (exp im))))) (exp (log (+ (exp (- 0 im)) (exp im))))))
321.0ms
(exp (log (+ (* (exp (- 0 im)) (exp (- 0 im))) (- (* (exp im) (exp im)) (* (exp (- 0 im)) (exp im))))))

prune873.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b
(log (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3)))
0.2b
(/ (* (sin re) (exp (log (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3))))) (fma (exp (- im)) (exp (- im)) (expm1 (+ im im))))
0.0b
(pow (exp (- 0 im)) 3)
0.0b
(pow (exp im) 3)

rewrite34.0ms

Algorithm
rewrite-expression-head
Counts
4 → 98
Calls

4 calls. Slowest were:

18.0ms
(/ (* (sin re) (exp (log (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3))))) (fma (exp (- im)) (exp (- im)) (expm1 (+ im im))))
8.0ms
(log (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3)))
4.0ms
(pow (exp (- 0 im)) 3)

series435.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

242.0ms
(/ (* (sin re) (exp (log (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3))))) (fma (exp (- im)) (exp (- im)) (expm1 (+ im im))))
158.0ms
(log (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3)))
19.0ms
(pow (exp im) 3)
15.0ms
(pow (exp (- 0 im)) 3)

simplify4.1s

Counts
67 → 110
Calls

67 calls. Slowest were:

323.0ms
(log (- (* (pow (exp (- 0 im)) 3) (pow (exp (- 0 im)) 3)) (* (pow (exp im) 3) (pow (exp im) 3))))
300.0ms
(/ (* (sin re) (+ (pow (exp im) 3) (pow (exp (- im)) 3))) (- (+ (exp (* 2 im)) (pow (exp (- im)) 2)) 1))
290.0ms
(- (+ (* 2 re) (* re (pow im 2))) (* 1/3 (pow re 3)))

prune2.3s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes118.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample9.1s

Algorithm
intervals