Average Error: 0.0 → 0.0
Time: 15.7s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[e^{im} \cdot \left(0.5 \cdot \cos re\right) + \left(0.5 \cdot \cos re\right) \cdot e^{-im}\]

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

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

  3. Applied distribute-lft-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019016 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

Details

Time bar (total: 15.4s)Debug log

sample216.0ms

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

simplify379.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
378.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

rewrite13.0ms

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
13.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

series76.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
76.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

simplify1.2s

Counts
14 → 23
Calls
14 calls:
Slowest
367.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
241.0ms
(* 0.5 (* (cos re) (+ (exp (- im)) (exp im))))
178.0ms
(* (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))) (* (* (+ (exp (- im)) (exp im)) (+ (exp (- im)) (exp im))) (+ (exp (- im)) (exp im))))
161.0ms
(+ (* (exp (- im)) (exp (- im))) (- (* (exp im) (exp im)) (* (exp (- im)) (exp im))))
118.0ms
(* 0.5 (* (+ (exp im) (exp (* -1 im))) (cos re)))

prune304.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* (* 0.5 (cos re)) (exp (- im))) (* (* 0.5 (cos re)) (exp im)))
0.0b
(* (* 0.5 (cos re)) (exp (- im)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
4×add-log-exp
4×add-cbrt-cube
4×pow1
3×add-cube-cbrt
3×add-exp-log
3×associate-*r*
3×*-un-lft-identity
3×add-sqr-sqrt
2×associate-*r/
2×exp-neg
1×distribute-lft-out
1×flip-+
1×cbrt-unprod
1×*-commutative
1×un-div-inv
1×prod-exp
1×pow-prod-down
1×associate-*l*
1×exp-diff
1×flip3-+
1×sum-log
1×+-commutative
1×neg-sub0
Counts
2 → 30
Calls
2 calls:
Slowest
11.0ms
(+ (* (* 0.5 (cos re)) (exp (- im))) (* (* 0.5 (cos re)) (exp im)))
7.0ms
(* (* 0.5 (cos re)) (exp (- im)))

series161.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
99.0ms
(+ (* (* 0.5 (cos re)) (exp (- im))) (* (* 0.5 (cos re)) (exp im)))
61.0ms
(* (* 0.5 (cos re)) (exp (- im)))

simplify1.4s

Counts
18 → 36
Calls
18 calls:
Slowest
348.0ms
(* (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))) (* (* (exp (- im)) (exp (- im))) (exp (- im))))
329.0ms
(+ (* 0.5 (* (exp (- im)) (cos re))) (* 0.5 (* (exp im) (cos re))))
270.0ms
(+ (* 0.5 (* (exp im) (cos re))) (* 0.5 (* (exp (* -1 im)) (cos re))))
210.0ms
(* (exp (* (* 0.5 (cos re)) (exp (- im)))) (exp (* (* 0.5 (cos re)) (exp im))))
64.0ms
(* 0.5 (* (exp (- im)) (cos re)))

prune344.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

4.1b
(+ (* (exp im) (exp im)) -1)
0.0b
(pow (exp im) 3)
0.0b
(pow (exp (- im)) 3)
0.0b
(* (exp im) (exp im))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
11×add-cube-cbrt
11×*-un-lft-identity
11×pow1
11×add-sqr-sqrt
8×add-cbrt-cube
6×cube-prod
6×pow-pow
6×unpow-prod-down
4×add-log-exp
4×add-exp-log
4×exp-prod
3×associate-*l*
3×associate-*r*
2×rem-cube-cbrt
2×pow-exp
2×unpow3
2×pow-to-exp
2×cube-mult
2×cube-div
1×flip-+
1×cbrt-unprod
1×pow-prod-up
1×*-commutative
1×prod-exp
1×pow-prod-down
1×exp-diff
1×pow-plus
1×flip3-+
1×neg-mul-1
1×difference-of-sqr--1
1×+-commutative
1×exp-neg
1×neg-sub0
1×pow2
Counts
4 → 75
Calls
4 calls:
Slowest
7.0ms
(+ (* (exp im) (exp im)) -1)
4.0ms
(* (exp im) (exp im))
2.0ms
(pow (exp (- im)) 3)
1.0ms
(pow (exp im) 3)

series75.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
26.0ms
(pow (exp (- im)) 3)
17.0ms
(* (exp im) (exp im))
16.0ms
(+ (* (exp im) (exp im)) -1)
16.0ms
(pow (exp im) 3)

simplify755.0ms

Counts
48 → 87
Calls
48 calls:
Slowest
206.0ms
(+ (* 4/3 (pow im 3)) (+ (* 2 (pow im 2)) (* 2 im)))
76.0ms
(pow (* (cbrt (exp (- im))) (cbrt (exp (- im)))) 3)
75.0ms
(pow (* (cbrt (exp (- im))) (cbrt (exp (- im)))) 3)
61.0ms
(- (+ (* 9/2 (pow im 2)) 1) (* 3 im))
58.0ms
(+ (* 2 (pow im 2)) (+ (* 2 im) 1))

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes170.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
15930×(pre true 80)
8580×(body real 80)
3042×(body real 1280)
2476×(body real 640)
1220×(body real 320)
612×(body real 160)