Average Error: 0.0 → 0.0
Time: 12.6s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \sin im\]
↓
\[\sqrt{\sqrt{e^{re}}} \cdot \left(\sqrt{\sqrt{e^{re}}} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)\right)\]

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

    \[e^{re} \cdot \sin im\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto \color{blue}{\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right)} \cdot \sin im\]

  4. Applied associate-*l*0.0

    \[\leadsto \color{blue}{\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt0.0

    \[\leadsto \sqrt{\color{blue}{\sqrt{e^{re}} \cdot \sqrt{e^{re}}}} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)\]

  7. Applied sqrt-prod0.0

    \[\leadsto \color{blue}{\left(\sqrt{\sqrt{e^{re}}} \cdot \sqrt{\sqrt{e^{re}}}\right)} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)\]

  8. Applied associate-*l*0.0

    \[\leadsto \color{blue}{\sqrt{\sqrt{e^{re}}} \cdot \left(\sqrt{\sqrt{e^{re}}} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)\right)}\]

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019016 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 12.1s)Debug log

sample87.0ms

Algorithm
intervals
Results
328×(pre true 80)
218×(body real 80)
53×(body real 1280)
31×(body real 640)
13×(body real 320)
13×(body real 160)

simplify4.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
4.0ms
(* (exp re) (sin im))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (exp re) (sin im))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
3×add-cube-cbrt
3×associate-*l*
3×associate-*r*
3×add-cbrt-cube
3×*-un-lft-identity
3×pow1
3×add-sqr-sqrt
2×add-exp-log
1×add-log-exp
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-prod-down
Counts
1 → 17
Calls
1 calls:
Slowest
4.0ms
(* (exp re) (sin im))

series43.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
43.0ms
(* (exp re) (sin im))

simplify142.0ms

Counts
11 → 20
Calls
11 calls:
Slowest
83.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
48.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (sin im) (sin im)) (sin im)))
2.0ms
(* (exp re) (sin im))
2.0ms
(+ re (log (sin im)))
2.0ms
(* (sin im) (exp re))

prune132.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
0.0b
(* (sqrt (exp re)) (sin im))
0.0b
(sqrt (exp re))
0.0b
(sqrt (exp re))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×sqrt-prod
12×associate-*l*
11×add-cube-cbrt
11×add-exp-log
11×add-cbrt-cube
11×*-un-lft-identity
11×pow1
4×add-log-exp
4×cbrt-unprod
4×prod-exp
4×pow-prod-down
4×associate-*r*
2×*-commutative
2×pow1/2
2×rem-sqrt-square
Counts
4 → 65
Calls
4 calls:
Slowest
21.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
9.0ms
(* (sqrt (exp re)) (sin im))
1.0ms
(sqrt (exp re))
1.0ms
(sqrt (exp re))

series145.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
68.0ms
(* (sqrt (exp re)) (sin im))
55.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
11.0ms
(sqrt (exp re))
11.0ms
(sqrt (exp re))

simplify1.2s

Counts
43 → 77
Calls
43 calls:
Slowest
477.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
342.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
96.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
87.0ms
(+ (* 1/8 (* (pow re 2) im)) (+ (* 1/2 (* re im)) im))
86.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im)))

prune781.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im)))
0.0b
(* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im))))
0.0b
(* (sqrt (exp re)) (sin im))
0.0b
(sqrt (exp re))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-prod
24×associate-*l*
20×add-exp-log
20×add-cbrt-cube
20×pow1
15×add-sqr-sqrt
14×add-cube-cbrt
14×*-un-lft-identity
10×cbrt-unprod
10×prod-exp
10×pow-prod-down
5×associate-*r*
4×add-log-exp
3×*-commutative
1×pow1/2
1×rem-sqrt-square
Counts
4 → 83
Calls
4 calls:
Slowest
35.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im))))
22.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im)))
4.0ms
(* (sqrt (exp re)) (sin im))
1.0ms
(sqrt (exp re))

series260.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im)))
52.0ms
(* (sqrt (exp re)) (sin im))
44.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im))))
18.0ms
(sqrt (exp re))

simplify2.0s

Counts
60 → 95
Calls
60 calls:
Slowest
460.0ms
(* (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))) (* (* (* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im))) (* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im)))) (* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im)))))
300.0ms
(* (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
265.0ms
(* (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
120.0ms
(* (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))) (* (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im)))))
118.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin im))
0.6b
(cbrt (sin im))
0.6b
(cbrt (sin im))
0.4b
(* (cbrt (sin im)) (cbrt (sin im)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-cube-cbrt
11×*-un-lft-identity
11×add-sqr-sqrt
9×pow1
7×pow1/3
6×add-exp-log
6×associate-*l*
6×associate-*r*
4×add-log-exp
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 → 61
Calls
4 calls:
Slowest
9.0ms
(* (cbrt (sin im)) (cbrt (sin im)))
1.0ms
(cbrt (sin im))
1.0ms
(cbrt (sin im))
1.0ms
(cbrt (sin im))

series647.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
187.0ms
(cbrt (sin im))
168.0ms
(cbrt (sin im))
159.0ms
(* (cbrt (sin im)) (cbrt (sin im)))
133.0ms
(cbrt (sin im))

simplify308.0ms

Counts
41 → 73
Calls
41 calls:
Slowest
87.0ms
(- (pow im 1/3) (+ (* 1/18 (pow (pow im 7) 1/3)) (* 1/3240 (pow (pow im 13) 1/3))))
86.0ms
(- (pow im 1/3) (+ (* 1/18 (pow (pow im 7) 1/3)) (* 1/3240 (pow (pow im 13) 1/3))))
51.0ms
(- (pow im 1/3) (+ (* 1/18 (pow (pow im 7) 1/3)) (* 1/3240 (pow (pow im 13) 1/3))))
34.0ms
(- (+ (* 1/405 (pow (pow im 14) 1/3)) (pow im 2/3)) (* 1/9 (pow (pow im 8) 1/3)))
3.0ms
(pow (sin im) 1/3)

prune827.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes293.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
10646×(pre true 80)
6939×(body real 80)
1533×(body real 1280)
1208×(body real 640)
660×(body real 320)
306×(body real 160)