Details

Time bar (total: 10.7s)

sample20.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01012
11112
done1112

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
28.5b
(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×log-pow
21×pow1
17×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
6×sqrt-pow1 pow1/2 associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp
4×sqrt-div associate-/r*
3×flip3-+ sqrt-prod flip-+
2×log-div div-sub
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp clear-num sum-log div-inv
Counts
3 → 74
Calls
3 calls:
8.0ms
(+ (* re re) (* im im))
29.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
7.0ms
(sqrt (+ (* re re) (* im im)))

series209.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* re re) (* im im))
142.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts
83 → 83
Iterations

Useful iterations: 3 (315.0ms)

IterNodesCost
01251357
12541281
25881165
313941163
435091163
done50011163

prune224.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
29.6b
(log (+ (* re re) (* im im)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
89×times-frac
83×add-sqr-sqrt
54×sqrt-prod
53×add-cube-cbrt *-un-lft-identity
34×pow1
32×associate-*r*
28×log-pow
25×associate-*l*
19×add-exp-log
18×add-cbrt-cube
9×unswap-sqr
7×associate-/r*
6×add-log-exp
5×cbrt-undiv div-exp
4×log-div prod-exp cbrt-unprod associate-/l*
3×log-prod flip3-+ flip-+ div-inv
2×div-sub
1×+-commutative frac-times frac-2neg associate-*r/ rem-log-exp pow-prod-down associate-*l/ clear-num sum-log *-commutative
Counts
4 → 164
Calls
4 calls:
8.0ms
(+ (* re re) (* im im))
46.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
23.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
6.0ms
(log (+ (* re re) (* im im)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ (* re re) (* im im))
151.0ms
(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
193.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
53.0ms
(log (+ (* re re) (* im im)))

simplify1.4s

Counts
176 → 176
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02143631
15503423
216513032
done50002997

prune425.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im))))
0.3b
(* (* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
29.6b
(log (+ (* re re) (* im im)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
44×add-sqr-sqrt times-frac
36×add-cube-cbrt *-un-lft-identity
30×add-cbrt-cube
29×associate-*r*
26×associate-*l*
25×sqrt-prod
22×prod-exp
19×pow1
12×cbrt-unprod
11×div-exp
9×log-prod
8×log-pow
6×cbrt-undiv add-log-exp
4×pow-prod-down associate-*l/
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp unswap-sqr
2×log-div flip3-+ *-commutative flip-+ div-inv
1×+-commutative frac-times associate-*r/ rem-log-exp sum-log un-div-inv
Counts
4 → 135
Calls
4 calls:
7.0ms
(+ (* re re) (* im im))
29.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im))))
54.0ms
(* (* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
9.0ms
(log (+ (* re re) (* im im)))

series460.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ (* re re) (* im im))
237.0ms
(* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im))))
142.0ms
(* (* (/ 1/2 (sqrt (log 10.0))) (log (+ (* re re) (* im im)))) (/ 1 (sqrt (log 10.0))))
53.0ms
(log (+ (* re re) (* im im)))

simplify1.5s

Counts
147 → 147
Iterations

Useful iterations: 2 (355.0ms)

IterNodesCost
02272987
15862699
218872139
done50002139

prune365.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(* (log (pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0))))) (/ 1 (sqrt (log 10.0))))
30.7b
(pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
46×times-frac
45×add-sqr-sqrt
35×*-un-lft-identity
33×add-cube-cbrt
26×sqrt-prod
25×pow-unpow associate-*r*
13×add-exp-log
12×pow1
8×add-cbrt-cube
7×log-pow
5×add-log-exp unswap-sqr
4×associate-*l* prod-exp
3×unpow-prod-down
2×div-exp cbrt-unprod div-inv
1×cbrt-undiv +-commutative pow-to-exp rec-exp pow-pow flip3-+ 1-exp associate-*r/ pow-prod-down pow-exp sum-log un-div-inv *-commutative flip-+ sqr-pow
Counts
3 → 101
Calls
3 calls:
8.0ms
(+ (* re re) (* im im))
26.0ms
(* (log (pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0))))) (/ 1 (sqrt (log 10.0))))
17.0ms
(pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0))))

series819.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (* re re) (* im im))
400.0ms
(* (log (pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0))))) (/ 1 (sqrt (log 10.0))))
384.0ms
(pow (+ (* re re) (* im im)) (/ 1/2 (sqrt (log 10.0))))

simplify1.2s

Counts
110 → 110
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01932223
14971977
214011716
done50001653

prune281.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.0b

regimes366.0ms

Accuracy

57.9% (10.2b remaining)

Error of 17.4b against oracle of 7.2b and baseline of 31.5b

bsearch83.0ms

Steps
ItersRangePoint
7
2396706146367806.5
3.79592842151896e+17
2.645028972296562e+17
9
-2.3499377934639055e+159
-2.508529027316973e+152
-5.224721482189338e+153

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03463
14163
done4163

end0.0ms

sample525.0ms

Algorithm
intervals
Results
342.0ms8000×body80valid