Details

Time bar (total: 16.7s)

sample369.0ms

Algorithm
intervals
Results
46.0ms71×body1280valid
22.0ms254×body80valid
21.0ms50×body640valid
7.0ms19×body320valid
3.0ms2×body2560valid
1.0ms8×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
01937
13526
26325
39825
421525
585925
done500025

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (atan2 x.im x.re) y.re)
0.5b
(/ (* (pow (hypot x.re x.im) y.re) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
1.7b
(* (atan2 x.im x.re) y.im)
34.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt
13×add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l*
5×prod-exp
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×times-frac associate-/r* cbrt-unprod
2×cbrt-undiv pow-prod-down *-commutative unswap-sqr
1×pow-to-exp frac-2neg sin-sum pow-exp clear-num fma-udef div-inv associate-/l*
Counts
4 → 75
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(/ (* (pow (hypot x.re x.im) y.re) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series616.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
407.0ms
(/ (* (pow (hypot x.re x.im) y.re) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
17.0ms
(* (atan2 x.im x.re) y.im)
175.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts
87 → 87
Iterations

Useful iterations: 3 (933.0ms)

IterNodesCost
01531462
13321430
210271222
345151213
done50001213

prune413.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.6b

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
1.7b
(* (atan2 x.im x.re) y.im)
1.7b
(* (atan2 x.im x.re) y.im)
34.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum fma-udef
Counts
4 → 70
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(* (atan2 x.im x.re) y.im)
164.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts
82 → 82
Iterations

Useful iterations: 3 (124.0ms)

IterNodesCost
070721
1122710
2260626
3475624
4675624
51166624
62187624
done5000624

prune435.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (atan2 x.im x.re) y.re)
0.6b
(/ (pow (hypot x.re x.im) y.re) (/ (exp (* (atan2 x.im x.re) y.im)) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
1.7b
(* (atan2 x.im x.re) y.im)
34.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
163×times-frac
96×add-sqr-sqrt
92×add-cube-cbrt *-un-lft-identity
42×unpow-prod-down
18×add-exp-log
14×sqr-pow
13×associate-/r* add-cbrt-cube
9×div-exp div-inv
8×pow1
7×associate-/l*
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv
2×pow-to-exp pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod unswap-sqr
1×frac-2neg sin-sum clear-num associate-/r/ fma-udef
Counts
4 → 182
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.re)
8.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (exp (* (atan2 x.im x.re) y.im)) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series582.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
392.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (exp (* (atan2 x.im x.re) y.im)) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
16.0ms
(* (atan2 x.im x.re) y.im)
159.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify903.0ms

Counts
194 → 194
Iterations

Useful iterations: 2 (424.0ms)

IterNodesCost
03466873
17406688
224066460
done50006460

prune917.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
0.6b
(/ (pow (hypot x.re x.im) y.re) (/ (exp (* (atan2 x.im x.re) y.im)) (sin (fma (log (hypot x.re x.im)) y.im (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))))
1.7b
(* (atan2 x.im x.re) y.im)
34.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
163×times-frac
93×add-sqr-sqrt
91×add-cube-cbrt *-un-lft-identity
42×unpow-prod-down
16×add-exp-log
14×sqr-pow
13×associate-/r*
11×add-cbrt-cube
9×div-exp div-inv
7×associate-/l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv cbrt-prod associate-*r* associate-*l*
2×pow-to-exp pow-exp
1×frac-2neg sin-sum pow1/3 pow-prod-down prod-exp clear-num associate-/r/ *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 175
Calls
4 calls:
1.0ms
(cbrt y.re)
8.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (exp (* (atan2 x.im x.re) y.im)) (sin (fma (log (hypot x.re x.im)) y.im (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))))
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series792.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(cbrt y.re)
419.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (exp (* (atan2 x.im x.re) y.im)) (sin (fma (log (hypot x.re x.im)) y.im (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))))
16.0ms
(* (atan2 x.im x.re) y.im)
180.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify903.0ms

Counts
187 → 187
Iterations

Useful iterations: 2 (427.0ms)

IterNodesCost
03498422
17408236
223797058
done50007058

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.1b

regimes345.0ms

Accuracy

48.5% (2.9b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 8.7b

bsearch280.0ms

Steps
ItersRangePoint
10
3.1829129060004216e-05
3771905773154.8457
20.400440132882025
11
-1.710852101153785e+75
-1.0452457700408589e+52
-2.368427375727665e+74

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02585
13160
done3160

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.4s2248×body1280valid
708.0ms7995×body80valid
611.0ms1483×body640valid
172.0ms582×body320valid
66.0ms41×body2560valid
46.0ms233×body160valid