Details

Time bar (total: 24.7s)

sample20.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify1.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066
done66

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite13.0ms

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:
11.0ms
(/ (atan2 im re) (log 10.0))

series89.0ms

Counts
1 → 3
Calls
1 calls:
89.0ms
(/ (atan2 im re) (log 10.0))

simplify3.2s

Counts
36 → 36
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
054385
186368
2175344
3325344
4545344
5860344
61993344
done5000344

prune110.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (atan2 im re) (sqrt (log 10.0)))
0.8b
(* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
85×times-frac
52×*-un-lft-identity
51×sqrt-prod
46×add-cube-cbrt
26×add-exp-log
25×associate-*r* associate-*l*
16×add-cbrt-cube
15×unswap-sqr
14×pow1
10×log-pow
9×div-exp
8×prod-exp
7×associate-/r*
5×cbrt-undiv
4×cbrt-unprod
3×div-inv associate-/l*
2×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
2 → 136
Calls
2 calls:
7.0ms
(/ (atan2 im re) (sqrt (log 10.0)))
95.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))

series263.0ms

Counts
2 → 6
Calls
2 calls:
180.0ms
(/ (atan2 im re) (sqrt (log 10.0)))
83.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))

simplify4.1s

Counts
142 → 142
Iterations

Useful iterations: done (4.1s)

IterNodesCost
01612378
13852101
211451726
330201726
done50001630

prune311.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (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))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
47×times-frac
45×add-sqr-sqrt
37×*-un-lft-identity
36×add-cube-cbrt
31×add-exp-log sqrt-prod
28×associate-*l*
21×pow1
20×associate-*r*
19×add-cbrt-cube
13×prod-exp
10×log-pow
7×cbrt-unprod
6×div-exp
4×associate-*r/ pow-prod-down associate-/r* unswap-sqr
3×cbrt-undiv expm1-log1p-u rec-exp sqrt-div 1-exp log1p-expm1-u div-inv associate-/l* add-log-exp
2×*-commutative
1×frac-times pow-flip frac-2neg associate-*l/ clear-num inv-pow
Counts
3 → 130
Calls
3 calls:
34.0ms
(* (atan2 im re) (sqrt (/ 1 (log 10.0))))
105.0ms
(* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0)))))
12.0ms
(/ 1 (log 10.0))

series256.0ms

Counts
3 → 7
Calls
3 calls:
161.0ms
(* (atan2 im re) (sqrt (/ 1 (log 10.0))))
95.0ms
(* (/ 1 (sqrt (log 10.0))) (* (atan2 im re) (sqrt (/ 1 (log 10.0)))))
0.0ms
(/ 1 (log 10.0))

simplify7.2s

Counts
137 → 137
Iterations

Useful iterations: 2 (251.0ms)

IterNodesCost
01681838
13501506
29261355
325641355
done50001355

prune398.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (expm1 (/ (atan2 im re) (sqrt (log 10.0)))))
0.1b
(/ (atan2 im re) (sqrt (log 10.0)))
0.5b
(expm1 (/ (atan2 im re) (sqrt (log 10.0))))
0.8b
(* (/ 1 (sqrt (log 10.0))) (log1p (expm1 (/ (atan2 im re) (sqrt (log 10.0))))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
46×times-frac
37×*-un-lft-identity
35×add-cube-cbrt
30×sqrt-prod
25×associate-*l*
15×add-exp-log
13×pow1
11×add-cbrt-cube
7×associate-/r* log-pow
5×log1p-expm1-u unswap-sqr
4×expm1-log1p-u prod-exp add-log-exp
3×div-exp associate-*r* associate-/l*
2×cbrt-undiv cbrt-unprod div-inv
1×rec-exp log1p-udef expm1-log1p frac-2neg 1-exp log1p-expm1 pow-prod-down associate-*l/ clear-num *-commutative expm1-udef
Counts
4 → 118
Calls
4 calls:
0.0ms
(log1p (expm1 (/ (atan2 im re) (sqrt (log 10.0)))))
21.0ms
(/ (atan2 im re) (sqrt (log 10.0)))
1.0ms
(expm1 (/ (atan2 im re) (sqrt (log 10.0))))
36.0ms
(* (/ 1 (sqrt (log 10.0))) (log1p (expm1 (/ (atan2 im re) (sqrt (log 10.0))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
262.0ms
(log1p (expm1 (/ (atan2 im re) (sqrt (log 10.0)))))
148.0ms
(/ (atan2 im re) (sqrt (log 10.0)))
249.0ms
(expm1 (/ (atan2 im re) (sqrt (log 10.0))))
413.0ms
(* (/ 1 (sqrt (log 10.0))) (log1p (expm1 (/ (atan2 im re) (sqrt (log 10.0))))))

simplify6.0s

Counts
130 → 130
Iterations

Useful iterations: 2 (163.0ms)

IterNodesCost
01561972
12791645
26801365
315731365
435951365
done50011365

prune341.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes228.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01215
11615
done1615

end0.0ms

sample611.0ms

Algorithm
intervals
Results
395.0ms8000×body80valid