Details

Time bar (total: 2.5m)

sample4.3s

Algorithm
intervals
Results
3.9s925×body10240exit
72.0ms256×body80valid

simplify476.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
475.0ms
(* (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))))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize57.0ms

Local error

Found 4 expressions with local error:

29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.6b
(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)

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log sqrt-prod
4×sqrt-div insert-posit16 add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 60
Calls
4 calls:
Slowest
45.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
12.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
185.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
59.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms
(* (atan2 x.im x.re) y.im)

simplify3.6s

Counts
79 → 72
Calls
79 calls:
Slowest
358.0ms
(sqrt (+ (* (* x.re x.re) (* x.re x.re)) (- (* (* x.im x.im) (* x.im x.im)) (* (* x.re x.re) (* x.im x.im)))))
344.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
330.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
320.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
297.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))

prune1.4s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize65.0ms

Local error

Found 4 expressions with local error:

29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (atan2 x.im x.re) y.im)
0.3b
(* (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))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×*-un-lft-identity associate-*l* add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×associate-*r* add-log-exp
4×insert-posit16
3×log-pow sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sub-neg flip3-+ flip3-- diff-log flip-+ flip--
Counts
4 → 70
Calls
4 calls:
Slowest
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
8.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
6.0ms
(* (atan2 x.im x.re) y.im)

series391.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
187.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
132.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
55.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms
(* (atan2 x.im x.re) y.im)

simplify5.5s

Counts
87 → 82
Calls
87 calls:
Slowest
845.0ms
(* (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (log (sqrt (+ (* x.re x.re) (* x.im x.im))))) (* (* y.re y.re) y.re))
412.0ms
(- (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)) (* (* (atan2 x.im x.re) y.im) (* (atan2 x.im x.re) y.im)))
376.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
315.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
306.0ms
(+ (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)) (+ (* (* (atan2 x.im x.re) y.im) (* (atan2 x.im x.re) y.im)) (* (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))))

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 3 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×pow1
7×*-un-lft-identity add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r*
5×add-log-exp
3×insert-posit16
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg flip3-- diff-log log-pow flip--
Counts
3 → 52
Calls
3 calls:
Slowest
20.0ms
(* (log (- x.re)) y.re)
12.0ms
(* (atan2 x.im x.re) y.im)
9.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))

series255.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
142.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
95.0ms
(* (log (- x.re)) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)

simplify3.9s

Counts
63 → 61
Calls
63 calls:
Slowest
388.0ms
(- (* (* (log (- x.re)) y.re) (* (log (- x.re)) y.re)) (* (* (atan2 x.im x.re) y.im) (* (atan2 x.im x.re) y.im)))
351.0ms
(- (pow (* (log (- x.re)) y.re) 3) (pow (* (atan2 x.im x.re) y.im) 3))
349.0ms
(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.re y.re) y.re))
343.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
272.0ms
(+ (* (* (log (- x.re)) y.re) (* (log (- x.re)) y.re)) (+ (* (* (atan2 x.im x.re) y.im) (* (atan2 x.im x.re) y.im)) (* (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))))

prune751.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.1b

regimes184.0ms

Accuracy

98.1% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 7.1b

bsearch1.8s

end0.0ms

sample2.1m

Algorithm
intervals
Results
2.0m30363×body10240exit
3.3s8000×body80valid