Details

Time bar (total: 10.9s)

sample40.0ms

Algorithm
intervals
Results
19.0ms265×body80valid

simplify69.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11915
23615
34815
46615
57215
done7215

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* x.im y.re) (* x.re y.im))
23.4b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Counts
2 → 44
Calls
2 calls:
11.0ms
(- (* x.im y.re) (* x.re y.im))
49.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series194.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(- (* x.im y.re) (* x.re y.im))
140.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify710.0ms

Counts
50 → 50
Iterations

Useful iterations: done (708.0ms)

IterNodesCost
089954
1258936
21073856
done5000854

prune266.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.1b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×*-un-lft-identity add-cube-cbrt
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×flip3-+ add-cbrt-cube add-exp-log flip-+
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×flip3-- flip--
Counts
4 → 266
Calls
4 calls:
36.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
22.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
11.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series375.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
172.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
50.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
58.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts
278 → 278
Iterations

Useful iterations: done (1.1s)

IterNodesCost
030711144
176410034
232059469
done50009101

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.1b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* x.im y.re) (* x.re y.im))
0.4b
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
23.1b
(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
55×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×associate-/r*
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp
6×flip3-- div-inv flip-- associate-/l*
5×add-log-exp
4×pow1 cbrt-undiv
2×rec-exp clear-num frac-2neg 1-exp associate-/l/
1×sub-neg flip3-+ diff-log flip-+ pow-flip inv-pow
Counts
3 → 127
Calls
3 calls:
14.0ms
(- (* x.im y.re) (* x.re y.im))
30.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
30.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

series321.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(- (* x.im y.re) (* x.re y.im))
187.0ms
(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
77.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

simplify1.7s

Counts
136 → 136
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01953518
15363269
227513060
done50022964

prune558.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.1b

localize51.0ms

Local error

Found 4 expressions with local error:

16.1b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b
(cbrt (+ (* y.re y.re) (* y.im y.im)))
27.1b
(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
6×cbrt-prod associate-/r* add-cbrt-cube add-exp-log
5×pow1
4×cbrt-div flip3-+ sqrt-div flip-+ add-log-exp
3×associate-/l*
2×pow1/3 associate-/r/ associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 div-sub div-exp div-inv flip--
Counts
4 → 85
Calls
4 calls:
23.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
18.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

series506.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
50.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
144.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))
134.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify637.0ms

Counts
97 → 97
Iterations

Useful iterations: done (634.0ms)

IterNodesCost
01351897
13351785
212921635
done50001627

prune719.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 20.1b

regimes506.0ms

Accuracy

3.7% (3.0b remaining)

Error of 25.8b against oracle of 22.8b and baseline of 25.9b

bsearch46.0ms

Steps
ItersRangePoint
7
2.779174960643886e+83
1.7372164856765643e+85
1.0110714407946299e+85

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01840
12340
done2340

end0.0ms

sample1.3s

Algorithm
intervals
Results
805.0ms8456×body80valid