Details

Time bar (total: 17.0s)

sample38.0ms

Algorithm
intervals
Results
24.0ms256×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01012
11112
done1112

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
29.1b
(sqrt (+ (* re re) (* im im)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
21×pow1
17×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
6×sqrt-pow1 pow1/2 associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp
4×sqrt-div associate-/r*
3×flip3-+ sqrt-prod flip-+
2×log-div div-sub
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp clear-num sum-log div-inv
Counts
3 → 74
Calls
3 calls:
18.0ms
(+ (* re re) (* im im))
62.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
16.0ms
(sqrt (+ (* re re) (* im im)))

series304.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (* re re) (* im im))
206.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
62.0ms
(sqrt (+ (* re re) (* im im)))

simplify3.4s

Counts
83 → 83
Iterations

Useful iterations: 3 (421.0ms)

IterNodesCost
01251357
12541281
25881165
313941163
435091163
done50011163

prune446.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(/ (/ 1 2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
0.6b
(/ (log 10.0) (log (+ (* re re) (* im im))))
30.2b
(log (+ (* re re) (* im im)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
689×times-frac
288×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
127×pow1
123×log-pow
37×div-inv
29×add-exp-log
24×associate-/r*
18×add-cbrt-cube
17×div-exp associate-/l*
9×cbrt-undiv
6×add-log-exp
3×log-prod
2×log-div rec-exp frac-2neg flip3-+ 1-exp clear-num flip-+
1×+-commutative rem-log-exp sum-log associate-/r/ associate-/l/
Counts
4 → 378
Calls
4 calls:
9.0ms
(+ (* re re) (* im im))
28.0ms
(/ (/ 1 2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
8.0ms
(/ (log 10.0) (log (+ (* re re) (* im im))))
8.0ms
(log (+ (* re re) (* im im)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(+ (* re re) (* im im))
208.0ms
(/ (/ 1 2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
173.0ms
(/ (log 10.0) (log (+ (* re re) (* im im))))
67.0ms
(log (+ (* re re) (* im im)))

simplify2.1s

Counts
390 → 390
Iterations

Useful iterations: done (2.1s)

IterNodesCost
047511187
112919527
227409096
done50008954

prune746.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.2b

localize56.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (log 10.0))
1.0b
(cbrt (log 10.0))
1.6b
(* (cbrt (log 10.0)) (cbrt (log 10.0)))
30.2b
(log (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod
23×add-sqr-sqrt
20×pow1
17×*-un-lft-identity
15×add-cube-cbrt
9×swap-sqr log-pow
8×pow1/3
7×add-exp-log associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
3×log-prod
2×log-div pow-prod-down pow-sqr pow-prod-up
1×pow2 flip3-+ pow-plus rem-log-exp prod-exp *-commutative cbrt-unprod flip-+
Counts
4 → 83
Calls
4 calls:
1.0ms
(cbrt (log 10.0))
1.0ms
(cbrt (log 10.0))
16.0ms
(* (cbrt (log 10.0)) (cbrt (log 10.0)))
14.0ms
(log (+ (* re re) (* im im)))

series61.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt (log 10.0))
0.0ms
(cbrt (log 10.0))
0.0ms
(* (cbrt (log 10.0)) (cbrt (log 10.0)))
61.0ms
(log (+ (* re re) (* im im)))

simplify5.1s

Counts
89 → 89
Iterations

Useful iterations: done (5.1s)

IterNodesCost
098910
1199823
2489751
31364679
44851662
done5001632

prune404.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt 1/2) (log (+ (* re re) (* im im))))
0.5b
(/ (sqrt (/ 1 2)) (/ (log 10.0) (* (sqrt 1/2) (log (+ (* re re) (* im im))))))
0.6b
(/ (log 10.0) (* (sqrt 1/2) (log (+ (* re re) (* im im)))))
30.2b
(log (+ (* re re) (* im im)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
281×times-frac
122×add-sqr-sqrt
121×sqrt-prod
118×add-cube-cbrt *-un-lft-identity
28×div-inv
27×pow1
21×add-exp-log log-pow
20×add-cbrt-cube associate-/l*
9×log-prod associate-/r*
7×cbrt-undiv div-exp
6×associate-*l*
4×associate-*r* add-log-exp
3×distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod
2×log-div frac-2neg clear-num unswap-sqr
1×flip3-+ sqrt-div rem-log-exp pow-prod-down associate-/r/ *-commutative flip-+ associate-/l/
Counts
4 → 236
Calls
4 calls:
40.0ms
(* (sqrt 1/2) (log (+ (* re re) (* im im))))
55.0ms
(/ (sqrt (/ 1 2)) (/ (log 10.0) (* (sqrt 1/2) (log (+ (* re re) (* im im))))))
13.0ms
(/ (log 10.0) (* (sqrt 1/2) (log (+ (* re re) (* im im)))))
7.0ms
(log (+ (* re re) (* im im)))

series822.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(* (sqrt 1/2) (log (+ (* re re) (* im im))))
329.0ms
(/ (sqrt (/ 1 2)) (/ (log 10.0) (* (sqrt 1/2) (log (+ (* re re) (* im im))))))
285.0ms
(/ (log 10.0) (* (sqrt 1/2) (log (+ (* re re) (* im im)))))
77.0ms
(log (+ (* re re) (* im im)))

simplify1.8s

Counts
248 → 248
Iterations

Useful iterations: done (1.8s)

IterNodesCost
04006748
18375890
221425351
done50005345

prune725.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.1b

regimes6.0ms