Average Error: 0.0 → 0.0
Time: 10.4s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \sin im\]
↓
\[e^{re} \cdot \sin im\]

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

    \[e^{re} \cdot \sin im\]

  2. Initial simplification0.0

    \[\leadsto \sin im \cdot e^{re}\]

  3. Final simplification0.0

    \[\leadsto e^{re} \cdot \sin im\]

Reproduce

herbie shell --seed 2018362 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 5.1s)Debug log

start114.0ms

Algorithm
intervals

setup10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 19
Calls

1 calls. Slowest were:

4.0ms
(* (sin im) (exp re))

series35.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

35.0ms
(* (sin im) (exp re))

simplify349.0ms

Counts
11 → 22
Calls

11 calls. Slowest were:

281.0ms
(- (+ (* re im) im) (* 1/6 (pow im 3)))
53.0ms
(* (* (* (sin im) (sin im)) (sin im)) (* (* (exp re) (exp re)) (exp re)))
4.0ms
(* (sin im) (exp re))

prune211.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (* (sin im) (exp re)))
0.7b
(cbrt (* (sin im) (exp re)))
0.7b
(cbrt (* (sin im) (exp re)))
0.3b
(* (cbrt (* (sin im) (exp re))) (cbrt (* (sin im) (exp re))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Counts
4 → 59
Calls

4 calls. Slowest were:

20.0ms
(* (cbrt (* (sin im) (exp re))) (cbrt (* (sin im) (exp re))))
5.0ms
(cbrt (* (sin im) (exp re)))
5.0ms
(cbrt (* (sin im) (exp re)))

series416.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

114.0ms
(cbrt (* (sin im) (exp re)))
108.0ms
(cbrt (* (sin im) (exp re)))
106.0ms
(* (cbrt (* (sin im) (exp re))) (cbrt (* (sin im) (exp re))))
88.0ms
(cbrt (* (sin im) (exp re)))

simplify663.0ms

Counts
31 → 71
Calls

31 calls. Slowest were:

148.0ms
(- (+ (* 1/3 (* re (pow im 1/3))) (pow im 1/3)) (* 1/18 (pow (pow im 7) 1/3)))
145.0ms
(- (+ (* 1/3 (* re (pow im 1/3))) (pow im 1/3)) (* 1/18 (pow (pow im 7) 1/3)))
125.0ms
(- (+ (* 1/3 (* re (pow im 1/3))) (pow im 1/3)) (* 1/18 (pow (pow im 7) 1/3)))

prune877.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (* (sin im) (exp re)))
0.7b
(cbrt (* (sin im) (exp re)))
0.6b
(cbrt (sin im))
0.3b
(* (cbrt (* (sin im) (exp re))) (cbrt (* (sin im) (exp re))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Counts
4 → 61
Calls

4 calls. Slowest were:

23.0ms
(* (cbrt (* (sin im) (exp re))) (cbrt (* (sin im) (exp re))))
4.0ms
(cbrt (* (sin im) (exp re)))
4.0ms
(cbrt (* (sin im) (exp re)))

series454.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

190.0ms
(cbrt (sin im))
101.0ms
(* (cbrt (* (sin im) (exp re))) (cbrt (* (sin im) (exp re))))
85.0ms
(cbrt (* (sin im) (exp re)))
79.0ms
(cbrt (* (sin im) (exp re)))

simplify696.0ms

Counts
33 → 73
Calls

33 calls. Slowest were:

151.0ms
(- (+ (* 1/3 (* re (pow im 1/3))) (pow im 1/3)) (* 1/18 (pow (pow im 7) 1/3)))
134.0ms
(- (+ (* 1/3 (* re (pow im 1/3))) (pow im 1/3)) (* 1/18 (pow (pow im 7) 1/3)))
126.0ms
(- (pow im 1/3) (+ (* 1/18 (pow (pow im 7) 1/3)) (* 1/3240 (pow (pow im 13) 1/3))))

prune957.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes156.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms