Details

Time bar (total: 22.1s)

sample494.0ms

Algorithm
intervals
Results
147.0ms256×body80valid
126.0ms56×body1280valid
45.0ms20×body320valid
29.0ms41×body640valid
1.0ms4×body160valid

simplify1.5s

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

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
0.7b
(* (atan2 x.im x.re) y.re)
2.7b
(pow (exp y.im) (atan2 x.im x.re))
34.5b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
343×times-frac
175×add-sqr-sqrt
173×*-un-lft-identity add-cube-cbrt
153×unpow-prod-down
51×sqr-pow
29×add-exp-log
25×associate-/r*
21×div-exp
11×add-cbrt-cube
9×div-inv
8×pow-to-exp pow-exp
7×pow1 associate-/l*
4×expm1-log1p-u pow-pow log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow exp-prod associate-*r* associate-*l*
1×cos-sum clear-num frac-2neg pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 286
Calls
4 calls:
30.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
5.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(pow (exp y.im) (atan2 x.im x.re))
7.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series788.0ms

Counts
4 → 12
Calls
4 calls:
500.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
19.0ms
(* (atan2 x.im x.re) y.re)
37.0ms
(pow (exp y.im) (atan2 x.im x.re))
232.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify767.0ms

Counts
298 → 298
Iterations
IterNodes
done5000
11415
0529

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize64.0ms

Local error

Found 4 expressions with local error:

5.5b
(cbrt (atan2 x.im x.re))
5.5b
(cbrt (atan2 x.im x.re))
5.5b
(cbrt (atan2 x.im x.re))
34.5b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3
1×cos-sum fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(cbrt (atan2 x.im x.re))
59.0ms
(cbrt (atan2 x.im x.re))
66.0ms
(cbrt (atan2 x.im x.re))
158.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify867.0ms

Counts
61 → 61
Iterations
IterNodes
done5001
31255
2313
1119
066

prune690.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize167.0ms

Local error

Found 4 expressions with local error:

5.5b
(cbrt (atan2 x.im x.re))
5.5b
(cbrt (atan2 x.im x.re))
5.5b
(cbrt (atan2 x.im x.re))
34.5b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3
1×cos-sum fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series366.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(cbrt (atan2 x.im x.re))
67.0ms
(cbrt (atan2 x.im x.re))
50.0ms
(cbrt (atan2 x.im x.re))
190.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify951.0ms

Counts
61 → 61
Iterations
IterNodes
done5001
31255
2313
1119
066

prune774.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

localize122.0ms

Local error

Found 4 expressions with local error:

2.7b
(pow (exp y.im) (atan2 x.im x.re))
34.5b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
34.5b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
34.5b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u pow-pow add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow-unpow cos-sum exp-prod unpow-prod-down fma-udef
1×pow-to-exp pow-exp sqr-pow
Counts
4 → 52
Calls
4 calls:
4.0ms
(pow (exp y.im) (atan2 x.im x.re))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
3.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series647.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(pow (exp y.im) (atan2 x.im x.re))
188.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
226.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
189.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify532.0ms

Counts
64 → 64
Iterations
IterNodes
done5000
2730
1204
090

prune952.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.2b

regimes694.0ms

Accuracy

20% (4.0b remaining)

Error of 8.0b against oracle of 4.0b and baseline of 9.0b

bsearch190.0ms

Steps
ItersRangePoint
9
-9.713669503619017e+174
-4.437896097689987e+169
-2.3377545237864465e+171

simplify5.0ms

Iterations
IterNodes
done39
139
034

end0.0ms

sample8.3s

Algorithm
intervals
Results
2.6s8005×body80valid
2.6s2015×body1280valid
1.6s1389×body640valid
383.0ms648×body320valid
167.0ms319×body160valid