Details

Time bar (total: 14.2s)

sample422.0ms

Algorithm
intervals
Results
35.0ms57×body1280valid
25.0ms18×body320valid
21.0ms257×body80valid
18.0ms40×body640valid
2.0ms10×body160valid
2.0msbody2560valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01937
13526
26325
39625
421525
584325
done500025

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (atan2 x.im x.re) y.im)
0.7b
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
1.2b
(* (atan2 x.im x.re) y.re)
28.9b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite39.0ms

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
pow1
associate-/l*
associate-*r* associate-*l*
expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
div-exp associate-/r*
pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
cbrt-undiv pow-to-exp frac-2neg sin-sum pow-exp clear-num fma-udef div-inv
Counts
4 → 97
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
7.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
132.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
21.0ms
(* (atan2 x.im x.re) y.re)
178.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts
109 → 109
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01851599
13381557
28411449
324051444
done50001443

prune477.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (hypot x.re x.im)) y.re)
0.7b
(* (atan2 x.im x.re) y.im)
1.2b
(* (atan2 x.im x.re) y.re)
28.9b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite29.0ms

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
associate-*r*
expm1-log1p-u log1p-expm1-u add-log-exp
pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
sin-sum log-pow fma-udef
Counts
4 → 71
Calls
4 calls:
8.0ms
(* (log (hypot x.re x.im)) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (log (hypot x.re x.im)) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
21.0ms
(* (atan2 x.im x.re) y.re)
164.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts
83 → 83
Iterations

Useful iterations: 3 (338.0ms)

IterNodesCost
0120757
1232741
2572653
31000649
41430649
52734649
done5001649

prune342.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.4b

localize27.0ms

Local error

Found 4 expressions with local error:

7.6b
(cbrt (* (atan2 x.im x.re) y.im))
7.6b
(cbrt (* (atan2 x.im x.re) y.im))
7.6b
(cbrt (* (atan2 x.im x.re) y.im))
28.9b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
cbrt-prod pow1/3
sin-sum fma-udef
Counts
4 → 43
Calls
4 calls:
3.0ms
(cbrt (* (atan2 x.im x.re) y.im))
4.0ms
(cbrt (* (atan2 x.im x.re) y.im))
3.0ms
(cbrt (* (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)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(cbrt (* (atan2 x.im x.re) y.im))
66.0ms
(cbrt (* (atan2 x.im x.re) y.im))
66.0ms
(cbrt (* (atan2 x.im x.re) y.im))
165.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
55 → 55
Iterations

Useful iterations: done (1.2s)

IterNodesCost
072601
1121596
2184533
3315513
4608486
51453486
done5000483

prune299.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.4b

localize29.0ms

Local error

Found 4 expressions with local error:

7.6b
(cbrt (* (atan2 x.im x.re) y.im))
7.6b
(cbrt (* (atan2 x.im x.re) y.im))
7.6b
(cbrt (* (atan2 x.im x.re) y.im))
28.9b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
cbrt-prod pow1/3
sin-sum fma-udef
Counts
4 → 43
Calls
4 calls:
3.0ms
(cbrt (* (atan2 x.im x.re) y.im))
6.0ms
(cbrt (* (atan2 x.im x.re) y.im))
3.0ms
(cbrt (* (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)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(cbrt (* (atan2 x.im x.re) y.im))
62.0ms
(cbrt (* (atan2 x.im x.re) y.im))
66.0ms
(cbrt (* (atan2 x.im x.re) y.im))
168.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts
55 → 55
Iterations

Useful iterations: done (1.1s)

IterNodesCost
072601
1121596
2184533
3315513
4608486
51453486
done5000483

prune291.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.4b

regimes235.0ms

Accuracy

0% (0.1b remaining)

Error of 3.4b against oracle of 3.3b and baseline of 3.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
02360
12960
done2960

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.4s2268×body1280valid
671.0ms7982×body80valid
511.0ms1328×body640valid
151.0ms547×body320valid
69.0ms46×body2560valid
48.0ms271×body160valid