Details

Time bar (total: 12.6s)

sample20.0ms

Algorithm
intervals
Results
9.0ms256×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

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

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:
6.0ms
(/ (atan2 im re) (log 10.0))

series69.0ms

Counts
1 → 3
Calls
1 calls:
69.0ms
(/ (atan2 im re) (log 10.0))

simplify1.3s

Counts
36 → 36
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
054385
191368
2268344
31356344
done5000344

prune133.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.3b
(log1p (expm1 (/ (atan2 im re) (log 10.0))))
0.5b
(expm1 (/ (atan2 im re) (log 10.0)))
0.8b
(/ (atan2 im re) (log 10.0))

rewrite11.0ms

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))))
1.0ms
(expm1 (/ (atan2 im re) (log 10.0)))
7.0ms
(/ (atan2 im re) (log 10.0))

series301.0ms

Counts
3 → 9
Calls
3 calls:
135.0ms
(log1p (expm1 (/ (atan2 im re) (log 10.0))))
98.0ms
(expm1 (/ (atan2 im re) (log 10.0)))
68.0ms
(/ (atan2 im re) (log 10.0))

simplify1.3s

Counts
64 → 64
Iterations

Useful iterations: 3 (233.0ms)

IterNodesCost
074650
1124601
2359553
31664549
done5000549

prune267.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

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))))))
0.5b
(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))))

rewrite99.0ms

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)))))
77.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))

series547.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ (atan2 im re) (sqrt (log 10.0)))
153.0ms
(log1p (expm1 (* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))))
146.0ms
(expm1 (* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0)))))
86.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))

simplify4.2s

Counts
170 → 170
Iterations

Useful iterations: done (4.2s)

IterNodesCost
01822825
14852618
230291967
done50011933

prune569.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (sqrt (log 10.0)))
5.6b
(cbrt (atan2 im re))
5.6b
(cbrt (atan2 im re))
5.6b
(cbrt (atan2 im re))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
16×cbrt-prod
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log expm1-log1p-u pow1/3 sqrt-prod add-cbrt-cube log1p-expm1-u add-log-exp
1×log-pow
Counts
4 → 56
Calls
4 calls:
2.0ms
(cbrt (sqrt (log 10.0)))
1.0ms
(cbrt (atan2 im re))
1.0ms
(cbrt (atan2 im re))
1.0ms
(cbrt (atan2 im re))

series182.0ms

Counts
4 → 10
Calls
4 calls:
0.0ms
(cbrt (sqrt (log 10.0)))
48.0ms
(cbrt (atan2 im re))
60.0ms
(cbrt (atan2 im re))
74.0ms
(cbrt (atan2 im re))

simplify2.1s

Counts
66 → 66
Iterations

Useful iterations: done (2.1s)

IterNodesCost
052484
179461
2216411
31229388
done5001385

prune428.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes288.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01837
12237
done2237

end0.0ms

sample711.0ms

Algorithm
intervals
Results
385.0ms8000×body80valid