Details

Time bar (total: 9.5s)

sample52.0ms

Algorithm
intervals
Results
18.0ms256×body80valid
17.0ms238×body80nan

simplify53.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01828
13122
25222
36822
48822
510022
610422
done10422

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

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))))) (fma (log base) (log base) (* 0.0 0.0)))
0.4b
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
0.6b
(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)
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 (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
0.0ms
(fma (log base) (log base) (* 0.0 0.0))

series410.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(hypot re im)
69.0ms
(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (fma (log base) (log base) (* 0.0 0.0)))
31.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
261.0ms
(fma (log base) (log base) (* 0.0 0.0))

simplify810.0ms

Counts
71 → 71
Iterations

Useful iterations: 3 (195.0ms)

IterNodesCost
01051432
11861415
24501233
317661176
done50011176

prune335.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite3.0ms

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:
2.0ms
(/ (atan2 im re) (log base))

series33.0ms

Counts
1 → 3
Calls
1 calls:
33.0ms
(/ (atan2 im re) (log base))

simplify1.0s

Counts
36 → 36
Iterations

Useful iterations: 4 (335.0ms)

IterNodesCost
064394
1105375
2223351
3623348
41416344
done5000344

prune118.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
26×times-frac
21×*-un-lft-identity
20×add-cube-cbrt
16×associate-*r*
15×add-exp-log
12×pow1
9×add-cbrt-cube
7×log-pow
4×div-exp prod-exp associate-/r*
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv expm1-log1p-u rec-exp 1-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
2 → 78
Calls
2 calls:
2.0ms
(/ 1 (log base))
9.0ms
(* (atan2 im re) (/ 1 (log base)))

series187.0ms

Counts
2 → 6
Calls
2 calls:
153.0ms
(/ 1 (log base))
33.0ms
(* (atan2 im re) (/ 1 (log base)))

simplify2.8s

Counts
84 → 84
Iterations

Useful iterations: 4 (1.4s)

IterNodesCost
0104789
1209614
2485546
31060540
43567533
done5000533

prune169.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
0.4b
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
0.4b
(* (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
0.6b
(pow (log base) 2)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
23×*-un-lft-identity
22×add-cube-cbrt
20×times-frac
18×add-exp-log
13×associate-*r*
11×add-cbrt-cube
9×pow1
4×expm1-log1p-u unpow-prod-down div-exp prod-exp log1p-expm1-u add-log-exp
3×pow-unpow associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp 1-exp cbrt-unprod div-inv
1×pow-to-exp pow-flip pow-pow frac-2neg associate-*r/ pow-prod-down pow-exp clear-num log-pow un-div-inv *-commutative fma-udef unpow2 inv-pow sqr-pow
Counts
4 → 102
Calls
4 calls:
2.0ms
(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
2.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
8.0ms
(* (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
2.0ms
(pow (log base) 2)

series471.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
36.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
67.0ms
(* (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
153.0ms
(pow (log base) 2)

simplify834.0ms

Counts
114 → 114
Iterations

Useful iterations: done (831.0ms)

IterNodesCost
01572015
13271846
29311568
done50001549

prune340.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

regimes243.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066
done66

end0.0ms

sample1.5s

Algorithm
intervals
Results
569.0ms8000×body80valid
567.0ms7982×body80nan