Details

Time bar (total: 23.3s)

sample70.0ms

Algorithm
intervals
Results
42.0ms452×body80valid

simplify5.1s

Counts
1 → 1
Iterations

Useful iterations: 5 (221.0ms)

IterNodesCost
01119
12019
24517
310817
424513
562311
6134611
7374011
done500111

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.6b

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.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)
8.1b
(* (- (* x.re x.re) (* x.im x.im)) x.im)

rewrite120.0ms

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))
26.0ms
(+ (* (- (* 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)
56.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

series260.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ (* x.re x.im) (* x.im x.re))
84.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
40.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
99.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

simplify1.5s

Counts
79 → 79
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01351507
13991393
216981127
done50011029

prune359.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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

rewrite204.0ms

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:
47.0ms
(* (- x.re x.im) x.im)
63.0ms
(+ (* (+ x.re x.im) (* (- x.re 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)
57.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))

series254.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (- x.re x.im) x.im)
104.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
27.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
82.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))

simplify4.6s

Counts
108 → 108
Iterations

Useful iterations: done (4.6s)

IterNodesCost
02102695
17262477
238592007
done50001585

prune784.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (* x.re (* x.re (+ x.im x.im)))) (cbrt (* x.re (* x.re (+ x.im x.im)))))
22.8b
(cbrt (* x.re (* x.re (+ x.im x.im))))
22.8b
(cbrt (* x.re (* x.re (+ x.im x.im))))
22.8b
(cbrt (* x.re (* x.re (+ x.im x.im))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
38×associate-*r/
18×cbrt-div
11×pow1
10×add-sqr-sqrt
9×flip3-+ pow1/3 flip-+
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×frac-times swap-sqr associate-*r* associate-*l* add-cbrt-cube add-log-exp
2×pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 72
Calls
4 calls:
41.0ms
(* (cbrt (* x.re (* x.re (+ x.im x.im)))) (cbrt (* x.re (* x.re (+ x.im x.im)))))
25.0ms
(cbrt (* x.re (* x.re (+ x.im x.im))))
42.0ms
(cbrt (* x.re (* x.re (+ x.im x.im))))
37.0ms
(cbrt (* x.re (* x.re (+ x.im x.im))))

series668.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(* (cbrt (* x.re (* x.re (+ x.im x.im)))) (cbrt (* x.re (* x.re (+ x.im x.im)))))
139.0ms
(cbrt (* x.re (* x.re (+ x.im x.im))))
153.0ms
(cbrt (* x.re (* x.re (+ x.im x.im))))
152.0ms
(cbrt (* x.re (* x.re (+ x.im x.im))))

simplify1.9s

Counts
84 → 84
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01211434
12731200
26771004
31858837
done5001810

prune378.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x.re)
13.5b
(cbrt (* x.re (+ x.im x.im)))
22.8b
(cbrt (* x.re (* x.re (+ x.im x.im))))
22.8b
(cbrt (* x.re (* x.re (+ x.im x.im))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-*r/
6×cbrt-prod cbrt-div
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log pow1/3 add-cbrt-cube add-log-exp
3×flip3-+ flip-+
Counts
4 → 44
Calls
4 calls:
2.0ms
(cbrt x.re)
15.0ms
(cbrt (* x.re (+ x.im x.im)))
40.0ms
(cbrt (* x.re (* x.re (+ x.im x.im))))
35.0ms
(cbrt (* x.re (* x.re (+ x.im x.im))))

series813.0ms

Counts
4 → 12
Calls
4 calls:
339.0ms
(cbrt x.re)
147.0ms
(cbrt (* x.re (+ x.im x.im)))
176.0ms
(cbrt (* x.re (* x.re (+ x.im x.im))))
151.0ms
(cbrt (* x.re (* x.re (+ x.im x.im))))

simplify3.2s

Counts
56 → 56
Iterations

Useful iterations: done (3.2s)

IterNodesCost
0102588
1223527
2463455
31157414
43427404
done5001401

prune286.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes96.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01119
11719
done1719

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.7s14469×body80valid