Details

Time bar (total: 2.8s)

sample17.0ms

Algorithm
intervals
Results
7.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
063
163
done63

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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:
5.0ms
(/ (atan2 im re) (log 10.0))

series57.0ms

Counts
1 → 3
Calls
1 calls:
56.0ms
(/ (atan2 im re) (log 10.0))

simplify87.0ms

Counts
36 → 36
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
086210
1234196
2597196
31533196
44399196
55001196
done5001196

prune81.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b
(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))

rewrite7.0ms

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)))
5.0ms
(/ (atan2 im re) (log 10.0))

series246.0ms

Counts
3 → 9
Calls
3 calls:
105.0ms
(log1p (expm1 (/ (atan2 im re) (log 10.0))))
87.0ms
(expm1 (/ (atan2 im re) (log 10.0)))
55.0ms
(/ (atan2 im re) (log 10.0))

simplify90.0ms

Counts
64 → 64
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
0111346
1297316
2759315
32692315
45001315
done5001315

prune142.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (atan2 im re) (sqrt (log 10.0)))
0.3b
(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)))))
0.7b
(* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))

rewrite59.0ms

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:
7.0ms
(/ (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)))))
45.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))

series358.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (atan2 im re) (sqrt (log 10.0)))
106.0ms
(log1p (expm1 (* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))))
88.0ms
(expm1 (* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0)))))
58.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))

simplify58.0ms

Counts
170 → 170
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04371720
119291461
250011337
done50011337

prune379.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(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))))))
0.7b
(* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0)))))
1.0b
(/ 1 (log 10.0))

rewrite63.0ms

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))))))
52.0ms
(* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0)))))
6.0ms
(/ 1 (log 10.0))

series264.0ms

Counts
4 → 10
Calls
4 calls:
115.0ms
(log1p (expm1 (* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0)))))))
91.0ms
(expm1 (* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0))))))
57.0ms
(* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0)))))
0.0ms
(/ 1 (log 10.0))

simplify41.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03361014
11482878
25001843
done5001843

prune276.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes161.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01911
12111
22111
done2111

end0.0ms

sample406.0ms

Algorithm
intervals
Results
223.0ms8000×body80valid