Average Error: 0.0 → 0.0
Time: 1.2m
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 2019016 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 1.2m)Debug log

sample311.0ms

Algorithm
intervals
Results
520×(pre true 80)
274×(body real 80)
108×(body real 1280)
69×(body real 640)
51×(body real 320)
18×(body real 160)

simplify269.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
269.0ms
(* (* 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

localize19.0ms

Local error

Found 1 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
4×associate-*r*
4×*-un-lft-identity
3×add-exp-log
3×add-cbrt-cube
3×pow1
2×add-cube-cbrt
2×associate-*r/
2×add-sqr-sqrt
1×add-log-exp
1×distribute-lft-out
1×flip-+
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-prod-down
1×associate-*l*
1×flip3-+
1×distribute-lft-in
1×distribute-rgt-in
Counts
1 → 20
Calls
1 calls:
Slowest
31.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

series96.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
96.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

simplify2.0s

Counts
14 → 23
Calls
14 calls:
Slowest
540.0ms
(- (+ (* 1.0 re) (* 0.5 (* re (pow im 2)))) (* 0.16666666666666666 (pow re 3)))
349.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))
295.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))
284.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
199.0ms
(* (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))) (* (* (+ (exp (- 0 im)) (exp im)) (+ (exp (- 0 im)) (exp im))) (+ (exp (- 0 im)) (exp im))))

prune228.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-*r*
6×add-cbrt-cube
6×pow1
4×add-cube-cbrt
4×add-exp-log
4×*-un-lft-identity
4×add-sqr-sqrt
2×sub0-neg
2×add-log-exp
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×un-div-inv
1×exp-diff
1×sub-neg
Counts
2 → 35
Calls
2 calls:
Slowest
13.0ms
(* (* 0.5 (sin re)) (exp (- 0 im)))
6.0ms
(* (* 0.5 (sin re)) (exp im))

series128.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
65.0ms
(* (* 0.5 (sin re)) (exp (- 0 im)))
63.0ms
(* (* 0.5 (sin re)) (exp im))

simplify1.4s

Counts
23 → 41
Calls
23 calls:
Slowest
272.0ms
(- (* 0.5 re) (+ (* 0.5 (* re im)) (* 0.08333333333333333 (pow re 3))))
254.0ms
(* (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))) (* (* (exp im) (exp im)) (exp im)))
246.0ms
(* (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))) (* (* (exp (- 0 im)) (exp (- 0 im))) (exp (- 0 im))))
243.0ms
(- (+ (* 0.5 re) (* 0.5 (* re im))) (* 0.08333333333333333 (pow re 3)))
128.0ms
(+ (log (* 0.5 (sin re))) (- 0 im))

prune428.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im))))
0.4b
(* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im))))
0.0b
(sqrt (+ (exp (- im)) (exp im)))
0.0b
(sqrt (+ (exp (- 0 im)) (exp im)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-div
18×*-un-lft-identity
16×sqrt-prod
14×associate-*r*
12×add-sqr-sqrt
11×add-exp-log
11×add-cbrt-cube
11×pow1
10×add-cube-cbrt
10×associate-*r/
9×flip-+
9×flip3-+
4×add-log-exp
4×distribute-lft-out
4×cbrt-unprod
4×prod-exp
4×pow-prod-down
4×frac-times
2×*-commutative
2×associate-*l/
2×associate-*l*
2×pow1/2
2×rem-sqrt-square
Counts
4 → 81
Calls
4 calls:
Slowest
39.0ms
(* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im))))
16.0ms
(sqrt (+ (exp (- im)) (exp im)))
13.0ms
(sqrt (+ (exp (- 0 im)) (exp im)))
12.0ms
(* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im))))
88.0ms
(* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im))))
63.0ms
(sqrt (+ (exp (- im)) (exp im)))
41.0ms
(sqrt (+ (exp (- 0 im)) (exp im)))

simplify6.9s

Counts
64 → 93
Calls
64 calls:
Slowest
819.0ms
(* (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))) (* (* (sqrt (+ (exp (- 0 im)) (exp im))) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- 0 im)) (exp im)))))
367.0ms
(- (+ (sqrt 2) (+ (* 1/2 (/ (pow im 2) (sqrt 2))) (* 1/24 (/ (pow im 4) (sqrt 2))))) (* 1/8 (/ (pow im 4) (pow (sqrt 2) 3))))
332.0ms
(* (sqrt (+ (* (exp (- 0 im)) (exp (- 0 im))) (- (* (exp im) (exp im)) (* (exp (- 0 im)) (exp im))))) (sqrt (- (exp (- im)) (exp im))))
323.0ms
(- (+ (sqrt 2) (+ (* 1/2 (/ (pow im 2) (sqrt 2))) (* 1/24 (/ (pow im 4) (sqrt 2))))) (* 1/8 (/ (pow im 4) (pow (sqrt 2) 3))))
307.0ms
(* (* (* 0.5 (sin re)) (sqrt (- (* (exp (- 0 im)) (exp (- 0 im))) (* (exp im) (exp im))))) (sqrt (+ (exp (- im)) (exp im))))

prune1.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
252×sqrt-div
176×associate-*r/
168×cbrt-div
148×frac-times
126×flip-+
126×flip3-+
50×associate-*l/
9×pow1
7×pow1/3
6×add-cube-cbrt
6×add-exp-log
6×*-un-lft-identity
6×add-sqr-sqrt
5×cbrt-prod
4×add-log-exp
4×associate-*l*
4×associate-*r*
4×add-cbrt-cube
2×pow-prod-up
2×pow-prod-down
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-plus
1×pow2
Counts
4 → 155
Calls
4 calls:
Slowest
61.0ms
(* (cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im))))) (cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im))))))
35.0ms
(cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im)))))
34.0ms
(cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im)))))
30.0ms
(cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im)))))

series913.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
284.0ms
(* (cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im))))) (cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im))))))
222.0ms
(cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im)))))
211.0ms
(cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im)))))
196.0ms
(cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im)))))

simplify41.7s

Counts
199 → 167
Calls
199 calls:
Slowest
538.0ms
(* (cbrt (* (sqrt (- (exp (- 0 im)) (exp im))) (sqrt (- (exp (- im)) (exp im))))) (cbrt (* (sqrt (+ (* (exp (- 0 im)) (exp (- 0 im))) (- (* (exp im) (exp im)) (* (exp (- 0 im)) (exp im))))) (sqrt (+ (* (exp (- im)) (exp (- im))) (- (* (exp im) (exp im)) (* (exp (- im)) (exp im))))))))
448.0ms
(* (cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3)))) (sqrt (- (* (exp (- im)) (exp (- im))) (* (exp im) (exp im)))))) (cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (- (* (exp (- im)) (exp (- im))) (* (exp im) (exp im)))))))
427.0ms
(* (cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3)))) (sqrt (+ (exp (- im)) (exp im))))) (cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (- (* (exp (- im)) (exp (- im))) (* (exp im) (exp im)))))))
419.0ms
(* (cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (+ (pow (exp (- im)) 3) (pow (exp im) 3))))) (cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3)))) (sqrt (- (* (exp (- im)) (exp (- im))) (* (exp im) (exp im)))))))
379.0ms
(* (cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (exp (- 0 im)) (exp im)))) (sqrt (- (* (exp (- im)) (exp (- im))) (* (exp im) (exp im)))))) (cbrt (* (* (* 0.5 (sin re)) (sqrt (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3)))) (sqrt (+ (exp (- im)) (exp im))))))

prune4.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes143.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
15926×(pre true 80)
8577×(body real 80)
3045×(body real 1280)
2474×(body real 640)
1214×(body real 320)
616×(body real 160)