Details

Time bar (total: 26.1s)

sample31.0ms

Algorithm
intervals
Results
16.0ms477×body80valid

simplify5.1s

Counts
1 → 1
Iterations

Useful iterations: 5 (249.0ms)

IterNodesCost
01119
12019
24517
310817
424513
562311
6134611
7374011
done500111

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* x.re x.re) (* x.im x.im))
0.1b
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
5.8b
(* (- (* x.re x.re) (* x.im x.im)) x.im)

rewrite100.0ms

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*
4×flip3-- flip3-+ frac-add flip-- flip-+
2×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
1×+-commutative sub-neg diff-log sum-log
Counts
4 → 69
Calls
4 calls:
10.0ms
(- (* x.re x.re) (* x.im x.im))
24.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
25.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
37.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

series241.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* x.re x.re) (* x.im x.im))
91.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
28.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
85.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

simplify1.5s

Counts
81 → 81
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01381527
14021415
216971163
done50001081

prune331.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- x.re x.im) x.im)
0.1b
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.1b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
0.2b
(* (+ x.re x.im) (* (- x.re x.im) x.im))

rewrite242.0ms

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:
42.0ms
(* (- x.re x.im) x.im)
58.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
45.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
93.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))

series291.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (- x.re x.im) x.im)
90.0ms
(+ (* (+ x.re x.im) (* (- x.re 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)
102.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))

simplify4.2s

Counts
108 → 108
Iterations

Useful iterations: done (4.2s)

IterNodesCost
02102695
17262477
238592007
done50001585

prune418.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

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)))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im))))
16.1b
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))
16.1b
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))
16.1b
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))

rewrite775.0ms

Algorithm
rewrite-expression-head
Rules
2200×frac-times
2120×associate-*l/
1968×cbrt-div
738×flip3-- flip3-+ flip-- flip-+
572×associate-*r/
23×pow1
12×pow1/3
9×add-exp-log pow-prod-up
6×add-sqr-sqrt pow-plus
5×add-cube-cbrt *-un-lft-identity pow-prod-down add-cbrt-cube
4×cbrt-prod associate-*r* add-log-exp
3×prod-exp pow-sqr cbrt-unprod
2×pow2
1×associate-*l* pow3 *-commutative unswap-sqr
Counts
4 → 811
Calls
4 calls:
363.0ms
(* (* (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im))))
31.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))
63.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))
60.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))

series721.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (* (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))) (cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im))))
209.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))
232.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))
187.0ms
(cbrt (* (+ x.re x.im) (* (- x.re x.im) x.im)))

simplify3.2s

Counts
823 → 823
Iterations

Useful iterations: done (3.1s)

IterNodesCost
0150359632
1292556837
2370955992
done500055856

prune2.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt (+ x.re x.im)) (cbrt (+ x.re x.im)))
0.6b
(cbrt (+ x.re x.im))
0.6b
(cbrt (+ x.re x.im))
0.6b
(cbrt (+ x.re x.im))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
79.0ms
(* (cbrt (+ x.re x.im)) (cbrt (+ x.re x.im)))
8.0ms
(cbrt (+ x.re x.im))
8.0ms
(cbrt (+ x.re x.im))
8.0ms
(cbrt (+ x.re x.im))

series694.0ms

Counts
4 → 12
Calls
4 calls:
206.0ms
(* (cbrt (+ x.re x.im)) (cbrt (+ x.re x.im)))
150.0ms
(cbrt (+ x.re x.im))
165.0ms
(cbrt (+ x.re x.im))
173.0ms
(cbrt (+ x.re x.im))

simplify3.4s

Counts
107 → 107
Iterations

Useful iterations: done (3.4s)

IterNodesCost
01161266
12491147
25911089
314131012
440781006
done5000967

prune396.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes80.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01119
11719
done1719

end0.0ms

sample1.2s

Algorithm
intervals
Results
756.0ms14481×body80valid