Details

Time bar (total: 16.4s)

sample38.0ms

Algorithm
intervals
Results
25.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
27
17
06

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* re re) (* im im))
26.6b
(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-log-exp
3×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
2×flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ insert-posit16
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
2 → 28
Calls
2 calls:
28.0ms
(+ (* re re) (* im im))
13.0ms
(sqrt (+ (* re re) (* im im)))

series108.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(+ (* re re) (* im im))
67.0ms
(sqrt (+ (* re re) (* im im)))

simplify5.2s

Counts
34 → 34
Iterations
IterNodes
48265
31605
2411
1129
050

prune341.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.7b

localize23.0ms

Local error

Found 4 expressions with local error:

16.8b
(sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
27.7b
(cbrt (+ (* re re) (* im im)))
27.7b
(cbrt (+ (* re re) (* im im)))
27.7b
(cbrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
12×pow1
9×cbrt-prod sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×frac-times add-cbrt-cube add-exp-log insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 70
Calls
4 calls:
20.0ms
(sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
114.0ms
(cbrt (+ (* re re) (* im im)))
128.0ms
(cbrt (+ (* re re) (* im im)))
130.0ms
(cbrt (+ (* re re) (* im im)))

simplify1.2s

Counts
82 → 82
Iterations
IterNodes
42678
3990
2382
1180
098

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (cbrt (+ (* re re) (* im im))))
0.3b
(* (pow (+ (* re re) (* im im)) 1/3) (sqrt (cbrt (+ (* re re) (* im im)))))
27.7b
(cbrt (+ (* re re) (* im im)))
30.2b
(pow (+ (* re re) (* im im)) 1/3)

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
18×sqrt-prod
14×*-un-lft-identity add-cube-cbrt
13×cbrt-prod
10×add-exp-log
9×unpow-prod-down associate-*r* unswap-sqr
7×add-cbrt-cube associate-*l*
6×pow1 cbrt-div
5×sqr-pow
4×sqrt-div insert-posit16 add-log-exp
3×pow-unpow sqrt-pow1 flip3-+ pow1/3 prod-exp flip-+
2×pow-to-exp rem-sqrt-square unpow1/3 pow-exp associate-*r/ cbrt-unprod
1×pow-pow pow1/2 *-commutative pow-prod-up
Counts
4 → 96
Calls
4 calls:
6.0ms
(sqrt (cbrt (+ (* re re) (* im im))))
53.0ms
(* (pow (+ (* re re) (* im im)) 1/3) (sqrt (cbrt (+ (* re re) (* im im)))))
4.0ms
(cbrt (+ (* re re) (* im im)))
14.0ms
(pow (+ (* re re) (* im im)) 1/3)

series428.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(sqrt (cbrt (+ (* re re) (* im im))))
44.0ms
(* (pow (+ (* re re) (* im im)) 1/3) (sqrt (cbrt (+ (* re re) (* im im)))))
149.0ms
(cbrt (+ (* re re) (* im im)))
117.0ms
(pow (+ (* re re) (* im im)) 1/3)

simplify1.1s

Counts
108 → 108
Iterations
IterNodes
32467
2839
1321
0143

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.7b

localize42.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (cbrt 1/3) (cbrt 1/3))
6.2b
(pow (pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
27.7b
(cbrt (+ (* re re) (* im im)))
29.0b
(pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×cbrt-prod
18×*-un-lft-identity add-cube-cbrt
13×unpow-prod-down
12×pow1
9×add-exp-log
7×pow-unpow pow1/3
6×swap-sqr associate-*r* associate-*l*
5×pow-exp
4×add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
3×pow-to-exp sqr-pow
2×cbrt-div pow-pow pow-prod-down pow-sqr pow-prod-up
1×pow2 flip3-+ pow-plus prod-exp *-commutative cbrt-unprod flip-+
Counts
4 → 98
Calls
4 calls:
7.0ms
(* (cbrt 1/3) (cbrt 1/3))
17.0ms
(pow (pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
8.0ms
(cbrt (+ (* re re) (* im im)))
9.0ms
(pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3)))

series834.0ms

Counts
4 → 10
Calls
4 calls:
0.0ms
(* (cbrt 1/3) (cbrt 1/3))
393.0ms
(pow (pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
128.0ms
(cbrt (+ (* re re) (* im im)))
312.0ms
(pow (+ (* re re) (* im im)) (* (cbrt 1/3) (cbrt 1/3)))

simplify1.4s

Counts
108 → 108
Iterations
IterNodes
32986
21049
1411
0152

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.7b

regimes404.0ms

Accuracy

59.4% (8.9b remaining)

Error of 16.4b against oracle of 7.5b and baseline of 29.5b

bsearch48.0ms

Steps
ItersRangePoint
4
5.963630453679508e+152
8.36129926162593e+152
7.2373920079010435e+152
9
-1.353228999018124e+158
-1.2306742943533307e+151
-1.114939147891607e+154

simplify2.0ms

Iterations
IterNodes
214
114
013

end0.0ms

sample881.0ms

Algorithm
intervals
Results
691.0ms8000×body80valid