Details

Time bar (total: 10.0s)

sample60.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
20.0ms283×body80nan

simplify54.0ms

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

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)))))
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))

series421.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(hypot re im)
31.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
73.0ms
(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (fma (log base) (log base) (* 0.0 0.0)))
271.0ms
(fma (log base) (log base) (* 0.0 0.0))

simplify845.0ms

Counts
71 → 71
Iterations

Useful iterations: 3 (188.0ms)

IterNodesCost
01051432
11891415
25041233
319691176
done50011176

prune327.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

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))

series37.0ms

Counts
1 → 3
Calls
1 calls:
37.0ms
(/ (atan2 im re) (log base))

simplify1.8s

Counts
36 → 36
Iterations

Useful iterations: 4 (395.0ms)

IterNodesCost
064394
1108375
2273351
3726348
41830344
done5000344

prune117.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
43×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
32×add-exp-log
20×add-cbrt-cube
13×associate-*r* associate-*l*
11×div-exp
8×prod-exp
7×pow1
6×cbrt-undiv associate-/r* associate-/l* unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×rec-exp 1-exp
2×frac-2neg clear-num
1×frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef inv-pow
Counts
4 → 130
Calls
4 calls:
2.0ms
(/ 1 (hypot (log base) 0.0))
2.0ms
(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (hypot (log base) 0.0))
0.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
13.0ms
(* (/ 1 (hypot (log base) 0.0)) (/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (hypot (log base) 0.0)))

series668.0ms

Counts
4 → 12
Calls
4 calls:
351.0ms
(/ 1 (hypot (log base) 0.0))
82.0ms
(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (hypot (log base) 0.0))
35.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
199.0ms
(* (/ 1 (hypot (log base) 0.0)) (/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (hypot (log base) 0.0)))

simplify852.0ms

Counts
142 → 142
Iterations

Useful iterations: 2 (162.0ms)

IterNodesCost
01823421
14533254
217782842
done50012842

prune485.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
32×add-exp-log
28×times-frac
26×add-cbrt-cube
23×add-cube-cbrt *-un-lft-identity
13×associate-*r*
10×cbrt-undiv div-exp
9×prod-exp cbrt-unprod
7×associate-*l*
6×pow1 associate-/r*
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp unswap-sqr
2×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef
Counts
4 → 112
Calls
4 calls:
4.0ms
(/ (* (cbrt 1) (cbrt 1)) (hypot (log base) 0.0))
2.0ms
(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (hypot (log base) 0.0))
0.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
204.0ms
(* (/ (* (cbrt 1) (cbrt 1)) (hypot (log base) 0.0)) (/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (hypot (log base) 0.0)))

series654.0ms

Counts
4 → 12
Calls
4 calls:
345.0ms
(/ (* (cbrt 1) (cbrt 1)) (hypot (log base) 0.0))
81.0ms
(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (hypot (log base) 0.0))
30.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
197.0ms
(* (/ (* (cbrt 1) (cbrt 1)) (hypot (log base) 0.0)) (/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (hypot (log base) 0.0)))

simplify1.2s

Counts
124 → 124
Iterations

Useful iterations: 2 (157.0ms)

IterNodesCost
01733457
14623231
218622526
done50002526

prune460.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes215.0ms

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
566.0ms8095×body80nan
550.0ms8000×body80valid