Details

Time bar (total: 25.7s)

sample296.0ms

Algorithm
intervals
Results
101.0ms61×body1280valid
51.0ms250×body80valid
31.0ms36×body640valid
11.0ms15×body320valid
3.0ms9×body160valid

simplify2.2s

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

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.2b

localize45.0ms

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)))

rewrite41.0ms

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:
13.0ms
(* y.re (log (hypot x.re x.im)))
11.0ms
(* (atan2 x.im x.re) y.re)
9.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* y.re (log (hypot x.re x.im)))
32.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
152.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify888.0ms

Counts
93 → 93
Iterations
IterNodes
done5001
2892
1274
0142

prune782.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize97.0ms

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)))

rewrite31.0ms

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:
1.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
11.0ms
(* (atan2 x.im x.re) y.re)
12.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series384.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
18.0ms
(* (atan2 x.im x.re) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
170.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts
77 → 77
Iterations
IterNodes
done5000
2783
1221
0118

prune787.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.1b

localize123.0ms

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))))

rewrite142.0ms

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:
31.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
93.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
11.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series407.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
70.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))
29.0ms
(* (atan2 x.im x.re) y.im)
194.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify1.6s

Counts
93 → 93
Iterations
IterNodes
done5000
21435
1307
0141

prune827.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.1b

localize114.0ms

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))))))

rewrite139.0ms

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:
39.0ms
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
39.0ms
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
59.0ms
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
3.0ms
(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))))))

series390.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
73.0ms
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
92.0ms
(cbrt (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re)))
152.0ms
(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))))))

simplify1.3s

Counts
59 → 59
Iterations
IterNodes
done5001
41945
3521
2230
1131
077

prune766.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.1b

regimes934.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done21
121
017

end0.0ms

sample12.0s

Algorithm
intervals
Results
4.3s2169×body1280valid
3.3s7948×body80valid
3.1s1439×body640valid
522.0ms537×body320valid
175.0ms53×body2560valid
143.0ms248×body160valid