Details

Time bar (total: 12.5s)

sample24.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
178
done78

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* re re) (* im im))
28.5b
(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
2 → 26
Calls
2 calls:
14.0ms
(+ (* re re) (* im im))
14.0ms
(sqrt (+ (* re re) (* im im)))

series102.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(+ (* re re) (* im im))
55.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts
32 → 32
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
048379
1124347
2343295
3968295
42668295
done5000295

prune126.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sqrt (+ (* re re) (* im im))))
28.5b
(sqrt (+ (* re re) (* im im)))
28.5b
(sqrt (+ (* re re) (* im im)))
28.5b
(sqrt (+ (* re re) (* im im)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×cbrt-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 61
Calls
4 calls:
10.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
13.0ms
(sqrt (+ (* re re) (* im im)))
13.0ms
(sqrt (+ (* re re) (* im im)))
13.0ms
(sqrt (+ (* re re) (* im im)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
62.0ms
(sqrt (+ (* re re) (* im im)))
57.0ms
(sqrt (+ (* re re) (* im im)))
63.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts
73 → 73
Iterations

Useful iterations: 3 (155.0ms)

IterNodesCost
070952
1149853
2323761
3693750
41884750
done5000750

prune317.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.3b

localize19.0ms

Local error

Found 4 expressions with local error:

28.5b
(sqrt (+ (* re re) (* im im)))
28.5b
(sqrt (+ (* re re) (* im im)))
28.5b
(sqrt (+ (* re re) (* im im)))
28.5b
(sqrt (+ (* re re) (* im im)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
9.0ms
(sqrt (+ (* re re) (* im im)))
17.0ms
(sqrt (+ (* re re) (* im im)))
13.0ms
(sqrt (+ (* re re) (* im im)))
9.0ms
(sqrt (+ (* re re) (* im im)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(sqrt (+ (* re re) (* im im)))
63.0ms
(sqrt (+ (* re re) (* im im)))
62.0ms
(sqrt (+ (* re re) (* im im)))
63.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts
72 → 72
Iterations

Useful iterations: 3 (102.0ms)

IterNodesCost
038852
191744
2205680
3444656
41114656
53182656
done5001656

prune330.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.3b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
5.7b
(exp (log (sqrt (+ (* re re) (* im im)))))
28.5b
(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 log-prod exp-prod exp-sum sqrt-prod
5×add-log-exp
4×sqrt-div
3×add-exp-log flip3-+ log-pow add-cbrt-cube flip-+
2×log-div sqrt-pow1 pow1/2 exp-diff
1×+-commutative rem-sqrt-square sum-log rem-exp-log
Counts
3 → 48
Calls
3 calls:
8.0ms
(+ (* re re) (* im im))
16.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
17.0ms
(sqrt (+ (* re re) (* im im)))

series165.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(+ (* re re) (* im im))
51.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
63.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts
57 → 57
Iterations

Useful iterations: 4 (1.1s)

IterNodesCost
087739
1169626
2398534
31056534
42807528
done5001528

prune149.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.3b

regimes447.0ms

Accuracy

58.9% (9.9b remaining)

Error of 17.7b against oracle of 7.8b and baseline of 31.9b

bsearch64.0ms

Steps
ItersRangePoint
10
1.2073698495971617e+61
3.217811591970086e+74
2.7153468834491098e+73
5
-1.7457635943519997e+137
-5.665103565004941e+136
-1.2876568362185878e+137

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01319
11419
done1419

end0.0ms

sample910.0ms

Algorithm
intervals
Results
683.0ms8000×body80valid