Details

Time bar (total: 21.7s)

sample57.0ms

Algorithm
intervals
Results
35.0ms451×body80valid

simplify4.4s

Counts
1 → 1
Iterations

Useful iterations: 6 (1.3s)

IterNodesCost
011362
121322
258322
3156322
4340282
5833242
61970203
done5000203

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x.re x.im) (* x.im x.re))
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
0.1b
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
8.6b
(* (- (* x.re x.re) (* x.im x.im)) x.re)

rewrite107.0ms

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*
4×flip3-+ flip3-- frac-sub flip-+ flip--
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative sum-log sub-neg diff-log difference-of-squares
Counts
4 → 68
Calls
4 calls:
6.0ms
(+ (* x.re x.im) (* x.im x.re))
34.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
44.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
20.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)

series273.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ (* x.re x.im) (* x.im x.re))
61.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
99.0ms
(- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
77.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.re)

simplify2.4s

Counts
80 → 80
Iterations

Useful iterations: done (2.4s)

IterNodesCost
013629591
140021503
2171921063
done501119626

prune478.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x.re x.im) (* x.im x.re))
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
0.1b
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
0.1b
(* (+ x.re x.im) (* (- x.re x.im) x.re))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
42×associate-*l/
19×flip3-+ flip-+
16×frac-sub
12×frac-times
11×pow1 add-cbrt-cube add-exp-log
10×flip3-- flip--
9×add-sqr-sqrt *-un-lft-identity
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
1×+-commutative sum-log sub-neg diff-log distribute-lft-out unswap-sqr
Counts
4 → 86
Calls
4 calls:
8.0ms
(+ (* x.re x.im) (* x.im x.re))
19.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
79.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
79.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))

series249.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(+ (* x.re x.im) (* x.im x.re))
47.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.im)
63.0ms
(- (* (+ x.re x.im) (* (- x.re x.im) x.re)) (* (+ (* x.re x.im) (* x.im x.re)) x.im))
97.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.re))

simplify11.6s

Counts
98 → 98
Iterations

Useful iterations: done (11.6s)

IterNodesCost
019853520
172136919
2421834897
done500027100

prune503.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re))))
13.8b
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))
13.8b
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))
13.8b
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))

rewrite230.0ms

Algorithm
rewrite-expression-head
Rules
176×associate-*l/
168×cbrt-div
148×frac-times
63×flip3-+ flip3-- flip-+ flip--
50×associate-*r/
11×pow1
10×add-sqr-sqrt
9×pow1/3
8×*-un-lft-identity add-cube-cbrt
7×cbrt-prod
6×add-exp-log
4×add-cbrt-cube swap-sqr associate-*r* associate-*l* add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 162
Calls
4 calls:
100.0ms
(* (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re))))
29.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))
27.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))
49.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))

series795.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(* (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re))))
213.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))
213.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))
219.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.re)))

simplify322.0ms

Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
0251139352