Details

Time bar (total: 10.8s)

sample59.0ms

Algorithm
intervals
Results
21.0ms283×body80nan
19.0ms256×body80valid

simplify53.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01828
13122
25222
36822
48822
510022
610422
done10422

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot re im)
0.3b
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
0.3b
(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (fma (log base) (log base) (* 0.0 0.0)))
0.5b
(fma (log base) (log base) (* 0.0 0.0))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×fma-udef
1×cbrt-undiv hypot-udef frac-2neg div-exp clear-num div-inv
Counts
4 → 59
Calls
4 calls:
0.0ms
(hypot re im)
0.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
2.0ms
(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (fma (log base) (log base) (* 0.0 0.0)))
0.0ms
(fma (log base) (log base) (* 0.0 0.0))

series424.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(hypot re im)
30.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
72.0ms
(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (fma (log base) (log base) (* 0.0 0.0)))
272.0ms
(fma (log base) (log base) (* 0.0 0.0))

simplify836.0ms

Counts
71 → 71
Iterations

Useful iterations: 3 (209.0ms)

IterNodesCost
01051432
11861415
24501233
317661176
done50001176

prune334.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ (atan2 im re) (- (log base)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×distribute-lft-neg-in distribute-rgt-neg-in
12×associate-/r*
9×pow1
8×log-pow
4×neg-mul-1
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 → 65
Calls
1 calls:
4.0ms
(/ (atan2 im re) (- (log base)))

series41.0ms

Counts
1 → 3
Calls
1 calls:
41.0ms
(/ (atan2 im re) (- (log base)))

simplify2.0s

Counts
68 → 68
Iterations

Useful iterations: 4 (878.0ms)

IterNodesCost
0108903
1186857
2438828
31361817
43250816
done5000816

prune179.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ -1 (log base))
0.4b
(* (atan2 im re) (/ -1 (log base)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt times-frac
20×add-cube-cbrt *-un-lft-identity
16×associate-*r*
11×pow1
9×add-exp-log add-cbrt-cube
7×log-pow
4×associate-/r*
3×associate-*l* associate-/l*
2×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp unswap-sqr
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
2 → 70
Calls
2 calls:
2.0ms
(/ -1 (log base))
12.0ms
(* (atan2 im re) (/ -1 (log base)))

series201.0ms

Counts
2 → 6
Calls
2 calls:
161.0ms
(/ -1 (log base))
40.0ms
(* (atan2 im re) (/ -1 (log base)))

simplify2.8s

Counts
76 → 76
Iterations

Useful iterations: 3 (1.7s)

IterNodesCost
0103741
1208670
2799612
34140551
done5000551

prune184.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
0.3b
(/ (fma 0.0 0.0 (pow (log base) 2)) (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))))
0.4b
(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))))
0.5b
(pow (log base) 2)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
56×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×add-exp-log
16×associate-/r*
11×add-cbrt-cube
8×div-exp
7×pow1
6×div-inv associate-/l*
4×cbrt-undiv expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
3×pow-unpow
2×rec-exp frac-2neg 1-exp clear-num
1×pow-to-exp pow-flip pow-pow pow-exp associate-/r/ log-pow fma-udef unpow2 inv-pow sqr-pow
Counts
4 → 138
Calls
4 calls:
0.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
2.0ms
(/ (fma 0.0 0.0 (pow (log base) 2)) (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))))
5.0ms
(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))))
2.0ms
(pow (log base) 2)

series444.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
135.0ms
(/ (fma 0.0 0.0 (pow (log base) 2)) (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))))
138.0ms
(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))))
143.0ms
(pow (log base) 2)

simplify923.0ms

Counts
150 → 150
Iterations

Useful iterations: 2 (242.0ms)

IterNodesCost
02224450
14714198
214723724
done50003724

prune425.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

regimes244.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
099
1149
2189
done189

end0.0ms

sample1.6s

Algorithm
intervals
Results
592.0ms8095×body80nan
580.0ms8000×body80valid