Details

Time bar (total: 22.7s)

sample411.0ms

Algorithm
intervals
Results
99.0ms52×body640valid
97.0ms67×body1280valid
52.0ms247×body80valid
18.0ms28×body320valid
4.0ms9×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
01937
13526
26325
39925
424925
5113025
done500125

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
1.8b
(* (atan2 x.im x.re) y.re)
2.6b
(* (atan2 x.im x.re) y.im)
32.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
21×times-frac
12×unpow-prod-down
10×add-cbrt-cube add-exp-log
8×pow1
7×associate-/l*
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×associate-/r* div-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×pow-to-exp cbrt-undiv cos-sum clear-num frac-2neg pow-exp fma-udef div-inv
Counts
4 → 97
Calls
4 calls:
11.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
6.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series493.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
22.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
244.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify866.0ms

Counts
109 → 109
Iterations

Useful iterations: done (861.0ms)

IterNodesCost
01851590
13541549
212421443
done50001436

prune980.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
1.8b
(* (atan2 x.im x.re) y.re)
2.6b
(* y.im (atan2 x.im x.re))
32.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

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*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
1×cos-sum
Counts
4 → 60
Calls
4 calls:
0.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
6.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* y.im (atan2 x.im x.re))
2.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series476.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
28.0ms
(* (atan2 x.im x.re) y.re)
12.0ms
(* y.im (atan2 x.im x.re))
220.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.0s

Counts
72 → 72
Iterations

Useful iterations: 3 (924.0ms)

IterNodesCost
0102729
1189720
2639636
34947630
done5000630

prune885.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3)
1.8b
(* (atan2 x.im x.re) y.re)
2.6b
(* y.im (atan2 x.im x.re))
32.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
9×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow unpow-prod-down cube-prod
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cube-mult pow-to-exp cos-sum pow-pow unpow3 pow-exp fma-udef rem-cube-cbrt sqr-pow
Counts
4 → 75
Calls
4 calls:
5.0ms
(pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3)
11.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* y.im (atan2 x.im x.re))
4.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series676.0ms

Counts
4 → 12
Calls
4 calls:
395.0ms
(pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3)
26.0ms
(* (atan2 x.im x.re) y.re)
12.0ms
(* y.im (atan2 x.im x.re))
244.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify844.0ms

Counts
87 → 87
Iterations

Useful iterations: done (840.0ms)

IterNodesCost
01181100
12881018
21161912
done5000906

prune867.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize69.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))) 3)
1.8b
(* (atan2 x.im x.re) y.re)
2.6b
(* y.im (atan2 x.im x.re))
32.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
11×pow1
9×add-cbrt-cube add-exp-log
8×log-pow
7×unpow-prod-down cube-prod
6×exp-prod associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cube-mult pow-to-exp cos-sum pow-pow unpow3 pow-exp fma-udef rem-cube-cbrt sqr-pow
Counts
4 → 83
Calls
4 calls:
5.0ms
(pow (log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))) 3)
6.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* y.im (atan2 x.im x.re))
2.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series690.0ms

Counts
4 → 12
Calls
4 calls:
422.0ms
(pow (log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))) 3)
25.0ms
(* (atan2 x.im x.re) y.re)
12.0ms
(* y.im (atan2 x.im x.re))
231.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify904.0ms

Counts
95 → 95
Iterations

Useful iterations: done (900.0ms)

IterNodesCost
01361402
13621212
214881084
done50011078

prune782.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.2b

regimes780.0ms

Accuracy

0% (0.6b remaining)

Error of 3.4b against oracle of 2.8b and baseline of 3.4b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02031
12731
22931
done2931

end0.0ms

sample8.1s

Algorithm
intervals
Results
2.8s2027×body1280valid
2.2s7967×body80valid
1.6s1404×body640valid
519.0ms647×body320valid
139.0ms299×body160valid