Details

Time bar (total: 19.5s)

sample118.0ms

Algorithm
intervals
Results
57.0ms256×body80valid
39.0ms265×body80nan

simplify2.6s

Counts
1 → 1
Iterations
IterNodes
done5174
71116
6232
578
453
339
224
122
018

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.9b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.4b
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
26.7b
(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
21×pow1
17×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
6×sqrt-pow1 pow1/2 associate-/l*
5×add-cbrt-cube add-exp-log add-log-exp
4×associate-/r* sqrt-div
3×flip3-+ sqrt-prod flip-+ insert-posit16
2×log-div div-sub
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg div-exp div-inv
Counts
3 → 77
Calls
3 calls:
7.0ms
(+ (* re re) (* im im))
22.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
6.0ms
(sqrt (+ (* re re) (* im im)))

series240.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(+ (* re re) (* im im))
137.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
55.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.9s

Counts
86 → 86
Iterations
IterNodes
done5003
32220
2686
1269
0133

prune517.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sqrt (+ (* re re) (* im im))))
26.7b
(sqrt (+ (* re re) (* im im)))
26.7b
(sqrt (+ (* re re) (* im im)))
26.7b
(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
8×sqrt-div
7×pow1
6×cbrt-prod
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 65
Calls
4 calls:
4.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
6.0ms
(sqrt (+ (* re re) (* im im)))
6.0ms
(sqrt (+ (* re re) (* im im)))
6.0ms
(sqrt (+ (* re re) (* im im)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(cbrt (sqrt (+ (* re re) (* im im))))
44.0ms
(sqrt (+ (* re re) (* im im)))
41.0ms
(sqrt (+ (* re re) (* im im)))
38.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts
77 → 77
Iterations
IterNodes
done5001
43626
31040
2341
1149
072

prune552.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.9b

localize60.0ms

Local error

Found 4 expressions with local error:

26.7b
(sqrt (+ (* re re) (* im im)))
26.7b
(sqrt (+ (* re re) (* im im)))
26.7b
(sqrt (+ (* re re) (* im im)))
26.7b
(sqrt (+ (* re re) (* im im)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 64
Calls
4 calls:
12.0ms
(sqrt (+ (* re re) (* im im)))
13.0ms
(sqrt (+ (* re re) (* im im)))
12.0ms
(sqrt (+ (* re re) (* im im)))
11.0ms
(sqrt (+ (* re re) (* im im)))

series208.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(sqrt (+ (* re re) (* im im)))
56.0ms
(sqrt (+ (* re re) (* im im)))
49.0ms
(sqrt (+ (* re re) (* im im)))
56.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.3s

Counts
76 → 76
Iterations
IterNodes
done5001
53254
4995
3435
2196
192
039

prune610.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.9b

localize58.0ms

Local error

Found 4 expressions with local error:

26.7b
(sqrt (+ (* re re) (* im im)))
26.7b
(sqrt (+ (* re re) (* im im)))
26.7b
(sqrt (+ (* re re) (* im im)))
26.7b
(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 64
Calls
4 calls:
9.0ms
(sqrt (+ (* re re) (* im im)))
10.0ms
(sqrt (+ (* re re) (* im im)))
9.0ms
(sqrt (+ (* re re) (* im im)))
9.0ms
(sqrt (+ (* re re) (* im im)))

series193.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (+ (* re re) (* im im)))
49.0ms
(sqrt (+ (* re re) (* im im)))
47.0ms
(sqrt (+ (* re re) (* im im)))
55.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts
76 → 76
Iterations
IterNodes
done5001
53254
4995
3435
2196
192
039

prune483.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 5.9b

regimes630.0ms

Accuracy

56% (10.3b remaining)

Error of 17.3b against oracle of 7.0b and baseline of 30.4b

bsearch419.0ms

Steps
ItersRangePoint
9
3.5627589106734345e+99
6.741762871954432e+106
2.1214141144086502e+101
6
-9.98405984174964e-304
-1.146206375811988e-304
-4.64950550008063e-304
7
-2.1551503804424012e-194
-1.00806654500884e-195
-1.610831336314797e-195
8
-1.0537521384392173e+77
-2.9102656186225933e+72
-3.912111704121843e+74

simplify22.0ms

Iterations
IterNodes
done51
151
045

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.9s7972×body80nan
1.2s8000×body80valid