Details

Time bar (total: 21.5s)

sample44.0ms

Algorithm
intervals
Results
26.0ms443×body80valid

simplify5.2s

Counts
1 → 1
Iterations

Useful iterations: 5 (241.0ms)

IterNodesCost
01119
12019
24517
310817
424513
562311
6134611
7374011
done500111

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* 3 (* x.re x.re)) (* x.im x.im))
0.2b
(* 3 (* x.re x.re))
7.4b
(* (- (* 3 (* x.re x.re)) (* x.im x.im)) x.im)

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity associate-*l*
5×add-log-exp
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×flip3-- associate-*l/ *-commutative flip-- unswap-sqr
1×sub-neg diff-log
Counts
3 → 51
Calls
3 calls:
23.0ms
(- (* 3 (* x.re x.re)) (* x.im x.im))
17.0ms
(* 3 (* x.re x.re))
111.0ms
(* (- (* 3 (* x.re x.re)) (* x.im x.im)) x.im)

series179.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(- (* 3 (* x.re x.re)) (* x.im x.im))
44.0ms
(* 3 (* x.re x.re))
88.0ms
(* (- (* 3 (* x.re x.re)) (* x.im x.im)) x.im)

simplify2.0s

Counts
60 → 60
Iterations

Useful iterations: 3 (740.0ms)

IterNodesCost
086725
1208688
2625592
32055582
done5000582

prune193.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.8b

localize35.0ms

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)
7.4b
(* (- (* x.re x.re) (* x.im x.im)) x.im)

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt associate-*l/
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
7×associate-*l*
6×associate-*r*
5×flip3-+ flip-+
4×frac-add
3×flip3-- flip--
2×+-commutative pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
1×difference-of-squares
Counts
4 → 67
Calls
4 calls:
8.0ms
(+ (* x.re x.im) (* x.im x.re))
50.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
49.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
57.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

series231.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* x.re x.im) (* x.im x.re))
88.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
30.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
85.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

simplify1.4s

Counts
79 → 79
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01351507
13991393
216981127
done50011029

prune332.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- x.re x.im) x.im)
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)
0.3b
(* (+ x.re x.im) (* (- x.re x.im) x.im))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
44×associate-*l/
19×flip3-+ flip-+
16×frac-add
15×add-sqr-sqrt
13×pow1 add-exp-log *-un-lft-identity add-cbrt-cube
12×frac-times associate-*l*
10×flip3-- flip--
9×add-cube-cbrt
7×associate-*r*
6×associate-*r/ add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
3×*-commutative
2×unswap-sqr
1×+-commutative sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 96
Calls
4 calls:
44.0ms
(* (- x.re x.im) x.im)
70.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
29.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
62.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))

series331.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (- x.re x.im) x.im)
108.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
41.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
117.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))

simplify4.4s

Counts
108 → 108
Iterations

Useful iterations: done (4.4s)

IterNodesCost
02102695
17262477
238592007
done50001585

prune399.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im))))
12.7b
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))
12.7b
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))
12.7b
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))

rewrite259.0ms

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×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×swap-sqr associate-*r* associate-*l* add-cbrt-cube 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:
116.0ms
(* (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im))))
30.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))
55.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))
32.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))

series861.0ms

Counts
4 → 12
Calls
4 calls:
245.0ms
(* (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im))))
195.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))
203.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))
218.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))

simplify1.5s

Counts
174 → 174
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02706030
14525687
212335538
done50005410

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes123.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01442
12142
done2142

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.8s14404×body80valid