Details

Time bar (total: 21.7s)

sample26.0ms

Algorithm
intervals
Results
12.0ms256×body80valid

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066
done66

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize8.0ms

Local error

Found 1 expressions with local error:

0.8b
(/ (atan2 im re) (log 10.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×times-frac
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1
4×associate-/r* log-pow
3×add-exp-log add-cbrt-cube associate-/l*
1×cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 33
Calls
1 calls:
9.0ms
(/ (atan2 im re) (log 10.0))

series83.0ms

Counts
1 → 3
Calls
1 calls:
83.0ms
(/ (atan2 im re) (log 10.0))

simplify3.3s

Counts
36 → 36
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
054385
186368
2175344
3325344
4545344
5860344
61993344
done5000344

prune159.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.4b
(log1p (expm1 (/ (atan2 im re) (log 10.0))))
0.6b
(expm1 (/ (atan2 im re) (log 10.0)))
0.8b
(/ (atan2 im re) (log 10.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
7×pow1
5×add-exp-log add-cbrt-cube
4×associate-/r* log-pow log1p-expm1-u
3×expm1-log1p-u associate-/l* add-log-exp
1×cbrt-undiv log1p-udef expm1-log1p frac-2neg log1p-expm1 div-exp clear-num div-inv expm1-udef
Counts
3 → 55
Calls
3 calls:
0.0ms
(log1p (expm1 (/ (atan2 im re) (log 10.0))))
0.0ms
(expm1 (/ (atan2 im re) (log 10.0)))
6.0ms
(/ (atan2 im re) (log 10.0))

series390.0ms

Counts
3 → 9
Calls
3 calls:
159.0ms
(log1p (expm1 (/ (atan2 im re) (log 10.0))))
130.0ms
(expm1 (/ (atan2 im re) (log 10.0)))
101.0ms
(/ (atan2 im re) (log 10.0))

simplify4.0s

Counts
64 → 64
Iterations

Useful iterations: 3 (151.0ms)

IterNodesCost
074650
1111601
2225551
3445549
4985549
53360549
done5000549

prune205.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (atan2 im re) (sqrt (log 10.0)))
0.4b
(log1p (expm1 (* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))))
0.6b
(expm1 (* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0)))))
0.8b
(* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
94×add-sqr-sqrt
85×times-frac
54×*-un-lft-identity
51×sqrt-prod
48×add-cube-cbrt
28×add-exp-log
25×associate-*r* associate-*l*
18×add-cbrt-cube
16×pow1
15×unswap-sqr
10×log-pow
9×div-exp
8×prod-exp
7×associate-/r*
5×cbrt-undiv log1p-expm1-u
4×expm1-log1p-u cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rec-exp 1-exp
1×frac-times log1p-udef expm1-log1p frac-2neg log1p-expm1 associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative expm1-udef
Counts
4 → 158
Calls
4 calls:
8.0ms
(/ (atan2 im re) (sqrt (log 10.0)))
0.0ms
(log1p (expm1 (* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))))
0.0ms
(expm1 (* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0)))))
82.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))

series482.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(/ (atan2 im re) (sqrt (log 10.0)))
148.0ms
(log1p (expm1 (* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))))
101.0ms
(expm1 (* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0)))))
77.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))

simplify3.7s

Counts
170 → 170
Iterations

Useful iterations: done (3.7s)

IterNodesCost
01822825
14122464
211681933
330631933
done50001837

prune571.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(log1p (expm1 (* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0)))))))
0.6b
(expm1 (* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0))))))
0.8b
(* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0)))))
1.0b
(/ 1 (log 10.0))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
33×times-frac
30×add-exp-log
27×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
25×associate-*l*
18×add-cbrt-cube
17×pow1
12×prod-exp sqrt-prod
7×log-pow
6×div-exp cbrt-unprod
5×log1p-expm1-u
4×expm1-log1p-u associate-/r* add-log-exp
3×cbrt-undiv rec-exp 1-exp associate-*r/ pow-prod-down associate-/l*
2×sqrt-div div-inv
1×frac-times log1p-udef expm1-log1p pow-flip frac-2neg log1p-expm1 associate-*r* associate-*l/ clear-num *-commutative inv-pow expm1-udef
Counts
4 → 112
Calls
4 calls:
0.0ms
(log1p (expm1 (* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0)))))))
0.0ms
(expm1 (* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0))))))
77.0ms
(* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0)))))
18.0ms
(/ 1 (log 10.0))

series381.0ms

Counts
4 → 10
Calls
4 calls:
170.0ms
(log1p (expm1 (* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0)))))))
137.0ms
(expm1 (* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0))))))
74.0ms
(* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0)))))
0.0ms
(/ 1 (log 10.0))

simplify6.8s

Counts
122 → 122
Iterations

Useful iterations: 2 (266.0ms)

IterNodesCost
01511806
13171477
28341303
324401303
done50001303

prune443.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes171.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
11817
done1817

end0.0ms

sample668.0ms

Algorithm
intervals
Results
366.0ms8000×body80valid