Average Error: 0.0 → 0.0
Time: 19.8s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{im} + \left(0.5 \cdot \sin re\right) \cdot e^{-im}\]

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 distribute-lft-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019010 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 19.3s)Debug log

sample194.0ms

Algorithm
intervals

simplify612.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
612.0ms
(* (* 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

localize39.0ms

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))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
4×add-log-exp
4×add-exp-log
4×associate-*r*
4×add-cbrt-cube
4×pow1
3×add-cube-cbrt
3×add-sqr-sqrt
2×distribute-lft-out
2×flip-+
2×associate-*r/
2×flip3-+
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-prod-down
1×associate-*l*
1×distribute-lft-in
1×sum-log
1×+-commutative
1×distribute-rgt-in
Counts
2 → 32
Calls
2 calls:
Slowest
14.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
6.0ms
(+ (exp (- 0 im)) (exp im))

series140.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
95.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
44.0ms
(+ (exp (- 0 im)) (exp im))

simplify1.7s

Counts
19 → 38
Calls
19 calls:
Slowest
362.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))
288.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))
251.0ms
(+ (* (exp (- 0 im)) (exp (- 0 im))) (- (* (exp im) (exp im)) (* (exp (- 0 im)) (exp im))))
240.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
185.0ms
(- (+ (* 1.0 re) (* 0.5 (* re (pow im 2)))) (* 0.16666666666666666 (pow re 3)))

prune370.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-*r*
7×add-cbrt-cube
7×pow1
5×add-log-exp
5×add-cube-cbrt
5×add-exp-log
5×*-un-lft-identity
5×add-sqr-sqrt
2×sub0-neg
2×cbrt-unprod
2×*-commutative
2×associate-*r/
2×prod-exp
2×pow-prod-down
2×exp-sum
2×associate-*l*
2×exp-neg
1×distribute-lft-out
1×flip-+
1×un-div-inv
1×exp-diff
1×flip3-+
1×sub-neg
1×sum-log
1×+-commutative
Counts
3 → 47
Calls
3 calls:
Slowest
18.0ms
(+ (* (* 0.5 (sin re)) (exp (- 0 im))) (* (* 0.5 (sin re)) (exp im)))
7.0ms
(* (* 0.5 (sin re)) (exp im))
6.0ms
(* (* 0.5 (sin re)) (exp (- 0 im)))

series247.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
117.0ms
(+ (* (* 0.5 (sin re)) (exp (- 0 im))) (* (* 0.5 (sin re)) (exp im)))
68.0ms
(* (* 0.5 (sin re)) (exp (- 0 im)))
61.0ms
(* (* 0.5 (sin re)) (exp im))

simplify2.6s

Counts
29 → 56
Calls
29 calls:
Slowest
381.0ms
(+ (* 0.5 (* (sin re) (exp (* -1 im)))) (* 0.5 (* (sin re) (exp im))))
347.0ms
(* (exp (* (* 0.5 (sin re)) (exp (- 0 im)))) (exp (* (* 0.5 (sin re)) (exp im))))
312.0ms
(* (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))) (* (* (exp (- 0 im)) (exp (- 0 im))) (exp (- 0 im))))
285.0ms
(- (* 0.5 re) (+ (* 0.5 (* re im)) (* 0.08333333333333333 (pow re 3))))
282.0ms
(* (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))) (* (* (exp im) (exp im)) (exp im)))

prune581.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

4.5b
(- (exp (+ im im)) 1)
0.0b
(pow (exp (- 0 im)) 3)
0.0b
(pow (exp im) 3)
0.0b
(* (exp (- im)) (exp (- im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
19×exp-prod
16×add-sqr-sqrt
15×add-cube-cbrt
15×*-un-lft-identity
11×pow1
8×cube-prod
8×add-cbrt-cube
8×unpow-prod-down
8×exp-neg
7×exp-diff
6×neg-sub0
5×pow-prod-up
5×pow-prod-down
5×exp-sum
5×pow-pow
4×add-log-exp
4×add-exp-log
4×neg-mul-1
4×frac-times
3×associate-*l*
3×associate-*r*
3×sub-neg
2×rem-cube-cbrt
2×associate-*r/
2×pow-exp
2×associate-*l/
2×difference-of-sqr-1
2×unpow3
2×pow-to-exp
2×cube-mult
2×cube-div
1×sub0-neg
1×flip--
1×cbrt-unprod
1×*-commutative
1×un-div-inv
1×prod-exp
1×flip3--
1×pow-plus
1×pow2
Counts
4 → 97
Calls
4 calls:
Slowest
8.0ms
(* (exp (- im)) (exp (- im)))
5.0ms
(- (exp (+ im im)) 1)
2.0ms
(pow (exp (- 0 im)) 3)
1.0ms
(pow (exp im) 3)

series69.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
22.0ms
(* (exp (- im)) (exp (- im)))
18.0ms
(pow (exp im) 3)
16.0ms
(pow (exp (- 0 im)) 3)
13.0ms
(- (exp (+ im im)) 1)

simplify1.4s

Counts
80 → 109
Calls
80 calls:
Slowest
266.0ms
(* (* (* (exp (- im)) (exp (- im))) (exp (- im))) (* (* (exp (- im)) (exp (- im))) (exp (- im))))
255.0ms
(+ (* 4/3 (pow im 3)) (+ (* 2 (pow im 2)) (* 2 im)))
143.0ms
(pow (* (cbrt (exp (- 0 im))) (cbrt (exp (- 0 im)))) 3)
113.0ms
(pow (* (cbrt (exp (- 0 im))) (cbrt (exp (- 0 im)))) 3)
69.0ms
(- (+ (* 9/2 (pow im 2)) 1) (* 3 im))

prune2.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes285.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample8.9s

Algorithm
intervals