Details

Time bar (total: 27.0s)

sample495.0ms

Algorithm
intervals
Results
129.0ms246×body80valid
100.0ms70×body1280valid
52.0ms52×body640valid
20.0ms25×body320valid
8.0ms3×body2560valid
3.0ms7×body160valid

simplify2.3s

Counts
1 → 1
Iterations
IterNodes
done5001
51130
4249
399
263
135
019

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.4b

localize67.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
1.8b
(* (atan2 x.im x.re) y.re)
3.7b
(pow (exp y.im) (atan2 x.im x.re))
32.3b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
343×times-frac
175×add-sqr-sqrt
173×*-un-lft-identity add-cube-cbrt
153×unpow-prod-down
51×sqr-pow
29×add-exp-log
25×associate-/r*
21×div-exp
11×add-cbrt-cube
9×div-inv
8×pow-to-exp pow-exp
7×pow1 associate-/l*
4×expm1-log1p-u pow-pow log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow exp-prod associate-*r* associate-*l*
1×clear-num frac-2neg sin-sum pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 286
Calls
4 calls:
28.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
13.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(pow (exp y.im) (atan2 x.im x.re))
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series968.0ms

Counts
4 → 12
Calls
4 calls:
672.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
33.0ms
(* (atan2 x.im x.re) y.re)
61.0ms
(pow (exp y.im) (atan2 x.im x.re))
202.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify734.0ms

Counts
298 → 298
Iterations
IterNodes
done5000
11403
0526

prune2.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 6.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (cbrt y.im) (atan2 x.im x.re))
1.8b
(* (atan2 x.im x.re) y.re)
2.7b
(pow (exp (* (cbrt y.im) (cbrt y.im))) (* (cbrt y.im) (atan2 x.im x.re)))
32.3b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×pow1 associate-*l*
8×add-exp-log
7×add-cbrt-cube
6×associate-*r*
5×add-log-exp
4×cbrt-prod expm1-log1p-u log1p-expm1-u
3×unpow-prod-down pow-pow unswap-sqr
2×pow-prod-down prod-exp *-commutative cbrt-unprod
1×pow-to-exp pow-unpow exp-prod exp-to-pow sin-sum pow-exp fma-udef sqr-pow
Counts
4 → 73
Calls
4 calls:
13.0ms
(* (cbrt y.im) (atan2 x.im x.re))
11.0ms
(* (atan2 x.im x.re) y.re)
13.0ms
(pow (exp (* (cbrt y.im) (cbrt y.im))) (* (cbrt y.im) (atan2 x.im x.re)))
12.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series560.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (cbrt y.im) (atan2 x.im x.re))
21.0ms
(* (atan2 x.im x.re) y.re)
255.0ms
(pow (exp (* (cbrt y.im) (cbrt y.im))) (* (cbrt y.im) (atan2 x.im x.re)))
181.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts
85 → 85
Iterations
IterNodes
done5001
21508
1291
0134

prune1.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 6.3b

localize65.0ms

Local error

Found 4 expressions with local error:

6.9b
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
6.9b
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
6.9b
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
32.3b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3
1×sin-sum fma-udef
Counts
4 → 43
Calls
4 calls:
7.0ms
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
16.0ms
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
6.0ms
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series736.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
193.0ms
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
185.0ms
(cbrt (* (cbrt y.im) (atan2 x.im x.re)))
190.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
55 → 55
Iterations
IterNodes
done5001
41723
3483
2194
1111
066

prune799.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 6.3b

localize54.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))
1.0b
(* (atan2 x.im x.re) (cbrt y.re))
2.7b
(pow (exp (* (cbrt y.im) (cbrt y.im))) (* (cbrt y.im) (atan2 x.im x.re)))
32.3b
(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
15×add-exp-log
14×add-sqr-sqrt
12×associate-*r*
10×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube
7×cbrt-prod pow-prod-down prod-exp cbrt-unprod
5×add-log-exp
4×expm1-log1p-u associate-*l* log1p-expm1-u
3×unpow-prod-down pow-pow
2×*-commutative unswap-sqr
1×pow-to-exp pow-unpow exp-prod exp-to-pow sin-sum pow-exp fma-udef sqr-pow
Counts
4 → 79
Calls
4 calls:
66.0ms
(* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))
8.0ms
(* (atan2 x.im x.re) (cbrt y.re))
7.0ms
(pow (exp (* (cbrt y.im) (cbrt y.im))) (* (cbrt y.im) (atan2 x.im x.re)))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))))

series566.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))
102.0ms
(* (atan2 x.im x.re) (cbrt y.re))
208.0ms
(pow (exp (* (cbrt y.im) (cbrt y.im))) (* (cbrt y.im) (atan2 x.im x.re)))
214.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))))

simplify1.6s

Counts
91 → 91
Iterations
IterNodes
done5001
21846
1357
0150

prune983.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.3b

regimes1.2s

Accuracy

54.1% (2.7b remaining)

Error of 6.6b against oracle of 3.9b and baseline of 9.8b

bsearch8.0ms

simplify5.0ms

Iterations
IterNodes
done53
153
041

end0.0ms

sample9.1s

Algorithm
intervals
Results
3.5s2194×body1280valid
2.4s7935×body80valid
1.7s1386×body640valid
339.0ms537×body320valid
195.0ms49×body2560valid
92.0ms243×body160valid