Details

Time bar (total: 18.9s)

sample61.0ms

Algorithm
intervals
Results
39.0ms456×body80valid

simplify4.9s

Counts
1 → 1
Iterations

Useful iterations: 5 (324.0ms)

IterNodesCost
011362
120322
251322
3121282
4245243
5597203
61214203
73015203
done5000203

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.1b

localize20.0ms

Local error

Found 2 expressions with local error:

0.2b
(* 3 (* x.re x.re))
7.7b
(* x.im (- (* 3 (* x.re x.re)) (* x.im x.im)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
8×add-sqr-sqrt
6×associate-*l*
5×*-un-lft-identity add-cube-cbrt
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/ *-commutative add-log-exp unswap-sqr
1×flip3-- flip--
Counts
2 → 43
Calls
2 calls:
18.0ms
(* 3 (* x.re x.re))
77.0ms
(* x.im (- (* 3 (* x.re x.re)) (* x.im x.im)))

series121.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(* 3 (* x.re x.re))
75.0ms
(* x.im (- (* 3 (* x.re x.re)) (* x.im x.im)))

simplify3.8s

Counts
49 → 49
Iterations

Useful iterations: 3 (1.7s)

IterNodesCost
08011704
12329699
28099497
339889457
done50029457

prune207.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x.re x.im) (* x.im x.re))
0.2b
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.2b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
7.7b
(* (- (* x.re x.re) (* x.im x.im)) x.im)

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt associate-*l/
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
7×associate-*l*
6×associate-*r*
5×flip3-+ flip-+
4×frac-add
3×flip3-- flip--
2×+-commutative sum-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×difference-of-squares
Counts
4 → 67
Calls
4 calls:
11.0ms
(+ (* x.re x.im) (* x.im x.re))
33.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
31.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
25.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

series288.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (* x.re x.im) (* x.im x.re))
110.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
36.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
105.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

simplify2.2s

Counts
79 → 79
Iterations

Useful iterations: done (2.2s)

IterNodesCost
013529187
140621179
2171920304
done500218132

prune433.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x.re x.im) (* x.im x.re))
0.2b
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.2b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
0.2b
(* (+ x.re x.im) (* (- x.re x.im) x.im))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
42×associate-*l/
20×flip3-+ flip-+
16×frac-add
12×frac-times
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt *-un-lft-identity flip3-- flip--
8×add-log-exp
7×associate-*l* add-cube-cbrt
6×associate-*r/
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×+-commutative sum-log *-commutative
1×distribute-lft-out unswap-sqr
Counts
4 → 85
Calls
4 calls:
12.0ms
(+ (* x.re x.im) (* x.im x.re))
61.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
34.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
61.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))

series288.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (* x.re x.im) (* x.im x.re))
108.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
43.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
114.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))

simplify4.7s

Counts
97 → 97
Iterations

Useful iterations: done (4.7s)

IterNodesCost
019753116
171336595
2408634536
done500426576

prune537.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
11.9b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
11.9b
(cbrt (+ (* x.re x.im) (* x.im x.re)))
11.9b
(cbrt (+ (* x.re x.im) (* x.im x.re)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 flip-+
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
44.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
7.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
7.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
5.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

series624.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(* (cbrt (+ (* x.re x.im) (* x.im x.re))) (cbrt (+ (* x.re x.im) (* x.im x.re))))
146.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
143.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))
126.0ms
(cbrt (+ (* x.re x.im) (* x.im x.re)))

simplify104.0ms

Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
011940460