Details

Time bar (total: 5.3s)

sample12.0ms

Algorithm
intervals
Results
5.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
068
178
done78

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize5.0ms

Local error

Found 1 expressions with local error:

27.4b
(sqrt (+ (* re re) (* im im)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt sqrt-prod
2×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
1×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
1 → 15
Calls
1 calls:
4.0ms
(sqrt (+ (* re re) (* im im)))

series37.0ms

Counts
1 → 3
Calls
1 calls:
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts
18 → 18
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
038213
191186
2207170
3459164
41009164
52575164
done5001164

prune50.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.7b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (+ (* re re) (* im im))))
0.5b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
27.4b
(sqrt (+ (* re re) (* im im)))
27.4b
(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
32×sqrt-div
31×pow1
20×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
2×associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 134
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ (* re re) (* im im))))
29.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series196.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(sqrt (sqrt (+ (* re re) (* im im))))
36.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
39.0ms
(sqrt (+ (* re re) (* im im)))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts
146 → 146
Iterations

Useful iterations: 3 (438.0ms)

IterNodesCost
01272962
12491876
26701671
321871616
done50011616

prune254.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3))
0.7b
(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
27.4b
(sqrt (+ (* re re) (* im im)))
27.4b
(sqrt (+ (* re re) (* im im)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
204×sqrt-prod
106×add-sqr-sqrt
46×sqrt-div
40×unpow-prod-down cube-prod unswap-sqr
30×associate-*r*
28×add-cube-cbrt *-un-lft-identity
12×associate-*l*
11×pow1 sqrt-pow1
10×add-exp-log
9×flip3-+ flip-+
8×cube-div
7×pow-pow add-cbrt-cube
6×sqr-pow
5×pow1/2
4×frac-times add-log-exp
3×pow-unpow prod-exp
2×cube-mult pow-to-exp rem-sqrt-square unpow3 associate-*r/ associate-*l/ pow-exp
1×*-commutative pow-prod-up sqrt-pow2 cbrt-unprod rem-cube-cbrt
Counts
4 → 183
Calls
4 calls:
51.0ms
(* (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3))
7.0ms
(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3))
107.0ms
(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
39.0ms
(sqrt (+ (* re re) (* im im)))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify623.0ms

Counts
195 → 195
Iterations

Useful iterations: 2 (195.0ms)

IterNodesCost
01755314
14264689
214673337
done50003337

prune389.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 7.7b

localize1.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 7.7b

regimes253.0ms

Accuracy

58.8% (9.6b remaining)

Error of 17.3b against oracle of 7.8b and baseline of 31.0b

bsearch53.0ms

Steps
ItersRangePoint
9
6.3129433769575865e+100
1.1419719569126802e+107
1.158407537644574e+105
10
-2.7283838574175814e+156
-2.4047927607493394e+144
-6.523076260268755e+150

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01319
11419
done1419

end0.0ms

sample298.0ms

Algorithm
intervals
Results
170.0ms8000×body80valid