Details

Time bar (total: 2.2m)

sample3.8s

Algorithm
intervals
Results
3.7s953×body10240exit
69.0ms256×body80valid

simplify196.0ms

Calls
1 calls:
Slowest
195.0ms
(* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize84.0ms

Local error

Found 4 expressions with local error:

30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.8b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
0.3b
(* (atan2 x.im x.re) y.re)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×sqrt-prod
4×pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16 add-log-exp
3×associate-*l*
2×rem-sqrt-square flip3-+ pow1/2 flip-+
1×cos-sum *-commutative
Calls
4 calls:
Slowest
10.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(* (atan2 x.im x.re) y.re)
2.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series356.0ms

Calls
4 calls:
Slowest
206.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
81.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms
(* (atan2 x.im x.re) y.re)

simplify889.0ms

Calls
27 calls:
Slowest
244.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
228.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
104.0ms
(cos (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
88.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
83.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))

prune1.2s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize8.0ms

Local error

Found 4 expressions with local error:

30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.3b
(* (atan2 x.im x.re) y.im)
0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt associate-*l*
7×*-un-lft-identity add-cube-cbrt
6×add-log-exp
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16
3×sqrt-prod
2×pow1/2 sqrt-div log-pow *-commutative
1×rem-sqrt-square sub-neg flip3-+ flip3-- diff-log flip-+ flip--
Calls
4 calls:
Slowest
5.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
4.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(* (atan2 x.im x.re) y.im)

series390.0ms

Calls
4 calls:
Slowest
185.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
139.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
48.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms
(* (atan2 x.im x.re) y.im)

simplify981.0ms

Calls
23 calls:
Slowest
237.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
148.0ms
(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))
99.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
97.0ms
(* -1 (* y.re (log (/ -1 x.re))))
95.0ms
(/ (exp (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)) (exp (* (atan2 x.im x.re) y.im)))

prune914.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (log (- x.re)) y.re)
0.3b
(* (atan2 x.im x.re) y.im)
0.0b
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
7×associate-*l*
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
4×pow1
3×add-cbrt-cube add-exp-log insert-posit16
2×*-commutative
1×sub-neg flip3-- diff-log log-pow flip--
Calls
3 calls:
Slowest
7.0ms
(* (log (- x.re)) y.re)
6.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
5.0ms
(* (atan2 x.im x.re) y.im)

series306.0ms

Calls
3 calls:
Slowest
176.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
99.0ms
(* (log (- x.re)) y.re)
30.0ms
(* (atan2 x.im x.re) y.im)

simplify730.0ms

Calls
14 calls:
Slowest
189.0ms
(- (* y.re (log -1)) (+ (* y.im (atan2 x.im x.re)) (* y.re (log (/ 1 x.re)))))
156.0ms
(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))
105.0ms
(/ (exp (* (log (- x.re)) y.re)) (exp (* (atan2 x.im x.re) y.im)))
86.0ms
(* -1 (* y.re (log (/ -1 x.re))))
80.0ms
(- (+ (* y.re (log -1)) (* y.re (log x.re))) (* y.im (atan2 x.im x.re)))

prune577.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes229.0ms

Accuracy

93.8% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 7.3b

bsearch1.6s

end0.0ms

sample2.0m

Algorithm
intervals
Results
2.0m30138×body10240exit
2.6s8000×body80valid