Details

Time bar (total: 14.5s)

sample397.0ms

Algorithm
intervals
Results
122.0ms54×body1280valid
49.0ms255×body80valid
48.0ms40×body640valid
9.0ms14×body320valid
3.0ms8×body160valid

simplify1.0s

Counts
1 → 1

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (atan2 x.im x.re) y.im)
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
200.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
68 → 68

prune599.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.5b

localize52.0ms

Local error

Found 4 expressions with local error:

29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×sin-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 39
Calls
4 calls:
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
47.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series732.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
225.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
224.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
227.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.0s

Counts
51 → 51

prune603.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.5b

localize107.0ms

Local error

Found 4 expressions with local error:

31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube add-log-exp
Counts
4 → 32
Calls
4 calls:
39.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
24.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series931.0ms

Counts
4 → 12
Calls
4 calls:
239.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
227.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
235.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
230.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify697.0ms

Counts
44 → 44

prune543.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.5b

localize49.0ms

Local error

Found 4 expressions with local error:

29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
39.3b
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
13×add-sqr-sqrt
12×sqrt-prod
11×add-cube-cbrt *-un-lft-identity
6×pow1 unpow-prod-down sqrt-div cube-prod
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ flip-+
2×cube-div rem-sqrt-square cbrt-div sqrt-pow1 pow1/2
1×cube-mult sin-sum pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 67
Calls
4 calls:
23.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
11.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series368.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
209.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
68.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify969.0ms

Counts
79 → 79

prune561.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 18.5b

regimes475.0ms

bsearch332.0ms

Steps
ItersRangePoint
11
-1.8064072260362412e-290
5.147296625674691e-303
-8.7495601278646e-311

simplify1.1s