Details

Time bar (total: 59.8s)

sample369.0ms

Algorithm
intervals
Results
136.0ms61×body1280valid
55.0ms250×body80valid
33.0ms36×body640valid
10.0ms15×body320valid
4.0ms9×body160valid

simplify3.8s

Counts
1 → 1
Iterations
IterNodes
done5000
5823
4210
395
262
135
019

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize200.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (log (hypot x.re x.im)))
1.4b
(* (atan2 x.im x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.im)
35.0b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×pow1
10×add-cbrt-cube associate-*r* add-exp-log
9×associate-*l*
6×log-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow fma-udef
Counts
4 → 81
Calls
4 calls:
21.0ms
(* y.re (log (hypot x.re x.im)))
31.0ms
(* (atan2 x.im x.re) y.re)
33.0ms
(* (atan2 x.im x.re) y.im)
23.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series699.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(* y.re (log (hypot x.re x.im)))
45.0ms
(* (atan2 x.im x.re) y.re)
47.0ms
(* (atan2 x.im x.re) y.im)
415.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify7.4s

Counts
93 → 93
Iterations
IterNodes
done5001
43517
31403
2583
1267
0142

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize241.0ms

Local error

Found 4 expressions with local error:

0.4b
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
1.4b
(* (atan2 x.im x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.im)
35.0b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×log1p-udef sin-sum log1p-expm1 fma-udef
Counts
4 → 65
Calls
4 calls:
2.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
16.0ms
(* (atan2 x.im x.re) y.re)
24.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series1.1s

Counts
4 → 12
Calls
4 calls:
590.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
57.0ms
(* (atan2 x.im x.re) y.re)
69.0ms
(* (atan2 x.im x.re) y.im)
345.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify9.5s

Counts
77 → 77
Iterations
IterNodes
done5003
44122
31322
2498
1221
0118

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.1b

localize395.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
0.9b
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
1.8b
(* (atan2 x.im x.re) y.im)
35.0b
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt
10×associate-*r* pow-prod-down prod-exp cbrt-unprod
9×*-un-lft-identity add-cube-cbrt
7×associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod *-commutative
2×unswap-sqr
1×sin-sum fma-udef
Counts
4 → 81
Calls
4 calls:
52.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
180.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
17.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series796.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
77.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
40.0ms
(* (atan2 x.im x.re) y.im)
457.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify6.9s

Counts
93 → 93
Iterations
IterNodes
done5000
32312
2815
1306
0141

prune1.7s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 3.1b

localize606.0ms

Local error

Found 4 expressions with local error:

6.4b
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
6.4b
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
6.4b
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
35.1b
(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))) (cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))) (cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))))

rewrite565.0ms

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 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3
1×sin-sum fma-udef
Counts
4 → 47
Calls
4 calls:
178.0ms
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
161.0ms
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
218.0ms
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
6.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))) (cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))) (cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))))

series900.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
138.0ms
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
189.0ms
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
368.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))) (cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))) (cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))))

simplify8.2s

Counts
59 → 59
Iterations
IterNodes
done5000
64819
51983
4823
3393
2215
1131
077

prune1.3s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.1b

regimes2.0s

Accuracy

0% (0.2b remaining)

Error of 3.5b against oracle of 3.3b and baseline of 3.5b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done20
120
017

end0.0ms

sample9.3s

Algorithm
intervals
Results
4.2s2169×body1280valid
1.9s7948×body80valid
1.9s1439×body640valid
399.0ms537×body320valid
143.0ms53×body2560valid
135.0ms248×body160valid