Details

Time bar (total: 20.6s)

sample394.0ms

Algorithm
intervals
Results
114.0ms67×body1280valid
43.0ms250×body80valid
19.0ms25×body640valid
8.0ms16×body320valid
2.0ms6×body160valid
2.0ms1×body2560valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
01937
13526
26325
39925
423225
5103425
done500025

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.9b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
1.1b
(* (atan2 x.im x.re) y.re)
3.3b
(* (atan2 x.im x.re) y.im)
32.0b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
21×times-frac
12×unpow-prod-down
10×add-exp-log add-cbrt-cube
8×pow1
7×associate-/l*
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×div-exp associate-/r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cbrt-undiv pow-to-exp frac-2neg sin-sum pow-exp clear-num fma-udef div-inv
Counts
4 → 97
Calls
4 calls:
13.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
18.0ms
(* (atan2 x.im x.re) y.re)
14.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series548.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
23.0ms
(* (atan2 x.im x.re) y.re)
33.0ms
(* (atan2 x.im x.re) y.im)
301.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts
109 → 109
Iterations

Useful iterations: done (998.0ms)

IterNodesCost
01851599
13531557
212281451
done50001444

prune705.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (hypot x.re x.im)) y.re)
1.1b
(* (atan2 x.im x.re) y.re)
3.3b
(* (atan2 x.im x.re) y.im)
32.0b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×pow1
10×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
9×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow fma-udef
Counts
4 → 71
Calls
4 calls:
12.0ms
(* (log (hypot x.re x.im)) y.re)
8.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (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)))

series521.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(* (log (hypot x.re x.im)) y.re)
34.0ms
(* (atan2 x.im x.re) y.re)
34.0ms
(* (atan2 x.im x.re) y.im)
294.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify730.0ms

Counts
83 → 83
Iterations

Useful iterations: done (728.0ms)

IterNodesCost
0120757
1241741
2828655
done5001649

prune510.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (hypot x.re x.im)) y.re)
1.1b
(* (atan2 x.im x.re) y.re)
3.3b
(* (atan2 x.im x.re) y.im)
32.0b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×pow1
10×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
9×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow fma-udef
Counts
4 → 71
Calls
4 calls:
17.0ms
(* (log (hypot x.re x.im)) y.re)
14.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(* (log (hypot x.re x.im)) y.re)
19.0ms
(* (atan2 x.im x.re) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)
250.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify821.0ms

Counts
83 → 83
Iterations

Useful iterations: done (817.0ms)

IterNodesCost
0120757
1241741
2828655
done5001649

prune614.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize75.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))
0.9b
(* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re))
3.3b
(* (atan2 x.im x.re) y.im)
32.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt associate-*r*
10×pow-prod-down prod-exp cbrt-unprod
9×add-cube-cbrt *-un-lft-identity
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod *-commutative
2×unswap-sqr
1×sin-sum fma-udef
Counts
4 → 77
Calls
4 calls:
140.0ms
(* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))
30.0ms
(* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re))
7.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))))

series519.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))
133.0ms
(* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re))
22.0ms
(* (atan2 x.im x.re) y.im)
319.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))))

simplify1.5s

Counts
89 → 89
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01371193
13151169
218071006
done5001782

prune558.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.5b

regimes499.0ms

Accuracy

0% (0.3b remaining)

Error of 3.7b against oracle of 3.5b and baseline of 3.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02035
12535
done2535

end0.0ms

sample9.0s

Algorithm
intervals
Results
4.0s2178×body1280valid
1.8s7942×body80valid
1.4s1451×body640valid
498.0ms229×body160valid
397.0ms568×body320valid
114.0ms47×body2560valid