Average Error: 0.0 → 0.0
Time: 44.6s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)\]

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019002 +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: 43.5s)Debug log

sample247.0ms

Algorithm
intervals

simplify564.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

564.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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))

rewrite39.0ms

Algorithm
rewrite-expression-head
Counts
2 → 41
Calls

2 calls. Slowest were:

26.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
13.0ms
(+ (exp (- 0 im)) (exp im))

series138.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

114.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
24.0ms
(+ (exp (- 0 im)) (exp im))

simplify2.6s

Counts
23 → 47
Calls

23 calls. Slowest were:

638.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))
519.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))
438.0ms
(+ (* (exp (- 0 im)) (exp (- 0 im))) (- (* (exp im) (exp im)) (* (exp (- 0 im)) (exp im))))

prune606.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
0.6b
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
0.6b
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
0.5b
(* (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))) (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

39.0ms
(* (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))) (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))))
13.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
13.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

series813.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

234.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
219.0ms
(* (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))) (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))))
182.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
179.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

simplify13.4s

Counts
49 → 85
Calls

49 calls. Slowest were:

881.0ms
(* (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))) (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
872.0ms
(* (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))) (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
643.0ms
(+ (log (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))) (log (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))))

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
0.6b
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
0.6b
(cbrt (* (* 0.5 (sin re)) (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3))))
0.5b
(* (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))) (cbrt (* (* 0.5 (sin re)) (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3)))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Counts
4 → 69
Calls

4 calls. Slowest were:

21.0ms
(* (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))) (cbrt (* (* 0.5 (sin re)) (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3)))))
19.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
17.0ms
(cbrt (* (* 0.5 (sin re)) (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3))))

series887.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

293.0ms
(* (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))) (cbrt (* (* 0.5 (sin re)) (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3)))))
221.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
191.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
181.0ms
(cbrt (* (* 0.5 (sin re)) (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3))))

simplify11.5s

Counts
44 → 81
Calls

44 calls. Slowest were:

693.0ms
(* (pow (* (pow (sin re) 2) (* (+ (pow (exp im) 3) (pow (exp (- im)) 3)) (+ (exp (- im)) (exp im)))) 1/3) (pow (cbrt 0.5) 2))
646.0ms
(cbrt (cbrt (* (* 0.5 (sin re)) (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3)))))
574.0ms
(cbrt (* (* 0.5 (sin re)) (+ (pow (pow (exp (- 0 im)) 3) 3) (pow (pow (exp im) 3) 3))))

prune2.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes323.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample8.9s

Algorithm
intervals