Details

Time bar (total: 2.3m)

sample4.1s

Algorithm
intervals
Results
3.8s869×body10240exit
103.0ms256×body80valid

simplify171.0ms

Calls
1 calls:
Slowest
171.0ms
(* (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))))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize58.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0b
(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.im)

rewrite37.0ms

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
18.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series207.0ms

Calls
4 calls:
Slowest
127.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
45.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms
(* (atan2 x.im x.re) y.im)

simplify960.0ms

Calls
27 calls:
Slowest
218.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
194.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
147.0ms
(cos (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
108.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
106.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))

prune1.0s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize4.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (atan2 x.im x.re) y.im)
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))

rewrite26.0ms

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
12.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
8.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series279.0ms

Calls
4 calls:
Slowest
119.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
108.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
29.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms
(* (atan2 x.im x.re) y.im)

simplify938.0ms

Calls
23 calls:
Slowest
238.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
142.0ms
(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))
122.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
97.0ms
(* -1 (* y.re (log (/ -1 x.re))))
95.0ms
(* -1 (* y.re (log (/ 1 x.re))))

prune896.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (atan2 x.im x.re) y.im)
0.2b
(* (log (- x.re)) y.re)
0.0b
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))

rewrite12.0ms

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
5.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
3.0ms
(* (log (- x.re)) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)

series222.0ms

Calls
3 calls:
Slowest
119.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
86.0ms
(* (log (- x.re)) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)

simplify727.0ms

Calls
14 calls:
Slowest
150.0ms
(- (* y.re (log -1)) (+ (* y.im (atan2 x.im x.re)) (* y.re (log (/ 1 x.re)))))
119.0ms
(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))
107.0ms
(* -1 (* y.re (log (/ -1 x.re))))
95.0ms
(- (+ (* y.re (log -1)) (* y.re (log x.re))) (* y.im (atan2 x.im x.re)))
88.0ms
(/ (exp (* (log (- x.re)) y.re)) (exp (* (atan2 x.im x.re) y.im)))

prune684.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (atan2 x.im x.re) y.im)
0.1b
(* (log x.im) y.re)
0.0b
(- (* (log x.im) y.re) (* (atan2 x.im x.re) y.im))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
6×associate-*l*
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
3×pow1 add-cbrt-cube add-exp-log insert-posit16
2×*-commutative
1×sub-neg flip3-- diff-log flip--
Calls
3 calls:
Slowest
11.0ms
(- (* (log x.im) y.re) (* (atan2 x.im x.re) y.im))
6.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(* (log x.im) y.re)

series201.0ms

Calls
3 calls:
Slowest
127.0ms
(- (* (log x.im) y.re) (* (atan2 x.im x.re) y.im))
61.0ms
(* (log x.im) y.re)
14.0ms
(* (atan2 x.im x.re) y.im)

simplify755.0ms

Calls
14 calls:
Slowest
296.0ms
(- (* y.re (log -1)) (+ (* y.re (log (/ -1 x.im))) (* y.im (atan2 x.im x.re))))
132.0ms
(* y.re (- (log -1) (log (/ -1 x.im))))
94.0ms
(- (+ (* y.re (log (/ 1 x.im))) (* y.im (atan2 x.im x.re))))
92.0ms
(* -1 (* y.re (log (/ 1 x.im))))
79.0ms
(/ (exp (* (log x.im) y.re)) (exp (* (atan2 x.im x.re) y.im)))

prune542.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes264.0ms

Accuracy

92.9% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 7.0b

bsearch2.2s

end0.0ms

sample2.1m

Algorithm
intervals
Results
2.0m30286×body10240exit
2.7s8000×body80valid