Details

Time bar (total: 10.8s)

sample36.0ms

Algorithm
intervals
Results
17.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066
done66

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×times-frac
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1
4×associate-/r* log-pow
3×add-cbrt-cube add-exp-log associate-/l*
1×expm1-log1p-u cbrt-undiv clear-num frac-2neg div-exp log1p-expm1-u div-inv add-log-exp
Counts
1 → 33
Calls
1 calls:
7.0ms
(/ (atan2 im re) (log 10.0))

series86.0ms

Counts
1 → 3
Calls
1 calls:
86.0ms
(/ (atan2 im re) (log 10.0))

simplify1.2s

Counts
36 → 36
Iterations

Useful iterations: 3 (221.0ms)

IterNodesCost
054385
191368
2265346
31224344
done5001344

prune149.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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))

rewrite12.0ms

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

series362.0ms

Counts
3 → 9
Calls
3 calls:
168.0ms
(log1p (expm1 (/ (atan2 im re) (log 10.0))))
118.0ms
(expm1 (/ (atan2 im re) (log 10.0)))
76.0ms
(/ (atan2 im re) (log 10.0))

simplify950.0ms

Counts
64 → 64
Iterations

Useful iterations: 3 (204.0ms)

IterNodesCost
074650
1124601
2356553
31601549
done5000549

prune313.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

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))))

rewrite77.0ms

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 clear-num frac-2neg pow-prod-down associate-*l/ log1p-expm1 associate-*r/ *-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)))))
58.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))

series562.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (atan2 im re) (sqrt (log 10.0)))
159.0ms
(log1p (expm1 (* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))))
110.0ms
(expm1 (* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0)))))
109.0ms
(* (/ 1 (sqrt (log 10.0))) (/ (atan2 im re) (sqrt (log 10.0))))

simplify2.7s

Counts
170 → 170
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01832825
14872618
230502227
done50011933

prune720.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (atan2 im re) (sqrt (log 10.0)))
0.4b
(log1p (expm1 (* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (atan2 im re) (sqrt (log 10.0)))))))
0.6b
(expm1 (* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (atan2 im re) (sqrt (log 10.0))))))
0.7b
(* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (atan2 im re) (sqrt (log 10.0)))))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
53×sqrt-prod
42×times-frac
35×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
28×associate-*l*
16×pow1
15×add-cbrt-cube add-exp-log
8×sqrt-div
7×associate-/r* log-pow
5×frac-times prod-exp associate-*r/ cbrt-unprod log1p-expm1-u
4×expm1-log1p-u add-log-exp
3×pow-prod-down associate-*l/ associate-/l*
2×cbrt-undiv div-exp div-inv
1×log1p-udef expm1-log1p clear-num frac-2neg associate-*r* log1p-expm1 *-commutative expm1-udef
Counts
4 → 121
Calls
4 calls:
11.0ms
(/ (atan2 im re) (sqrt (log 10.0)))
0.0ms
(log1p (expm1 (* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (atan2 im re) (sqrt (log 10.0)))))))
1.0ms
(expm1 (* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (atan2 im re) (sqrt (log 10.0))))))
100.0ms
(* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (atan2 im re) (sqrt (log 10.0)))))

series520.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ (atan2 im re) (sqrt (log 10.0)))
159.0ms
(log1p (expm1 (* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (atan2 im re) (sqrt (log 10.0)))))))
122.0ms
(expm1 (* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (atan2 im re) (sqrt (log 10.0))))))
82.0ms
(* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (atan2 im re) (sqrt (log 10.0)))))

simplify958.0ms

Counts
133 → 133
Iterations

Useful iterations: done (951.0ms)

IterNodesCost
01782644
13602009
216281802
done50011680

prune616.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes352.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02238
12737
done2737

end0.0ms

sample843.0ms

Algorithm
intervals
Results
480.0ms8000×body80valid