Details

Time bar (total: 14.6s)

sample137.0ms

Algorithm
intervals
Results
11.0ms197×body80valid
5.0ms19×body2560valid
5.0ms14×body5120valid
3.0ms15×body1280valid
1.0ms5×body640valid
0.0ms3×body320valid
0.0ms3×body160valid

simplify44.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01215
11715
22415
33015
43515
done3515

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.0b
(+ (* re re) (* im im))
0.8b
(- (sqrt (+ (* re re) (* im im))) re)
29.1b
(sqrt (+ (* re re) (* im im)))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×pow1 add-log-exp
7×*-un-lft-identity
5×add-cube-cbrt sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×sqrt-pow1
2×flip3-- flip3-+ pow1/2 associate-*r/ flip-- flip-+ difference-of-squares
1×+-commutative sub-neg rem-sqrt-square diff-log pow-prod-down sum-log distribute-lft-out--
Counts
4 → 54
Calls
4 calls:
45.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
9.0ms
(+ (* re re) (* im im))
52.0ms
(- (sqrt (+ (* re re) (* im im))) re)
11.0ms
(sqrt (+ (* re re) (* im im)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
285.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
53.0ms
(+ (* re re) (* im im))
82.0ms
(- (sqrt (+ (* re re) (* im im))) re)
68.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.3s

Counts
66 → 66
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0114942
1255828
2709752
32136727
done5000721

prune348.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.8b
(- (sqrt (+ (* re re) (* im im))) re)
4.6b
(exp (log (- (sqrt (+ (* re re) (* im im))) re)))
29.1b
(sqrt (+ (* re re) (* im im)))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×*-un-lft-identity
8×add-log-exp
7×add-cube-cbrt
6×pow1 log-prod exp-sum
5×sqrt-prod
4×add-exp-log exp-prod add-cbrt-cube difference-of-squares
2×log-div flip3-- flip3-+ exp-diff sqrt-div flip-- flip-+ distribute-lft-out--
1×+-commutative sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log sum-log log-pow rem-exp-log
Counts
4 → 61
Calls
4 calls:
9.0ms
(+ (* re re) (* im im))
71.0ms
(- (sqrt (+ (* re re) (* im im))) re)
42.0ms
(exp (log (- (sqrt (+ (* re re) (* im im))) re)))
21.0ms
(sqrt (+ (* re re) (* im im)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(+ (* re re) (* im im))
63.0ms
(- (sqrt (+ (* re re) (* im im))) re)
73.0ms
(exp (log (- (sqrt (+ (* re re) (* im im))) re)))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify3.5s

Counts
73 → 73
Iterations

Useful iterations: 4 (1.6s)

IterNodesCost
01081062
1209917
2504815
31320799
43761789
done5000789

prune349.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b
(+ (sqrt (+ (* re re) (* im im))) re)
27.6b
(sqrt (* 2.0 (* im im)))
29.1b
(sqrt (+ (* re re) (* im im)))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
32×sqrt-prod
28×times-frac
24×add-sqr-sqrt
23×add-cube-cbrt
11×pow1
7×associate-/r*
6×add-exp-log add-cbrt-cube distribute-lft-out add-log-exp
4×sqrt-pow1 sqrt-div associate-/l*
3×flip3-+ pow-prod-down flip-+
2×pow1/2 associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square sqrt-undiv frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 93
Calls
4 calls:
111.0ms
(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
66.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
23.0ms
(sqrt (* 2.0 (* im im)))
17.0ms
(sqrt (+ (* re re) (* im im)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
282.0ms
(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
73.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
68.0ms
(sqrt (* 2.0 (* im im)))
42.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts
105 → 105
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01812231
13871998
210671907
331811877
done50001871

prune446.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b
(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
0.7b
(+ (sqrt (+ (* re re) (* im im))) re)
29.1b
(sqrt (+ (* re re) (* im im)))

rewrite316.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
53×*-un-lft-identity
46×times-frac
39×sqrt-prod
37×add-cube-cbrt
27×associate-*r*
11×add-exp-log add-cbrt-cube
8×distribute-lft-out
7×pow1 associate-/r*
6×sqrt-div associate-*l* add-log-exp unswap-sqr
4×flip3-+ associate-/r/ flip-+
3×associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
4 → 125
Calls
4 calls:
70.0ms
(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
178.0ms
(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
47.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
14.0ms
(sqrt (+ (* re re) (* im im)))

series495.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
201.0ms
(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
77.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
53.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts
137 → 137
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02482920
15982628
220092460
done50002407

prune633.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.7b

regimes6.0ms