Details

Time bar (total: 2.5m)

sample4.1s

Algorithm
intervals
Results
3.9s881×body10240exit
78.0ms256×body80valid

simplify389.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
388.0ms
(* (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))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize56.0ms

Local error

Found 4 expressions with local error:

30.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
24.6b
(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)

rewrite61.0ms

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
26.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(* (atan2 x.im x.re) y.im)

series367.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
227.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(* (atan2 x.im x.re) y.im)

simplify1.6s

Counts
36 → 72
Calls
36 calls:
Slowest
346.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
275.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
246.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
212.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
183.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.4s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize29.0ms

Local error

Found 4 expressions with local error:

30.4b
(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))

rewrite56.0ms

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
18.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
11.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
191.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
127.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms
(* (atan2 x.im x.re) y.im)

simplify2.1s

Counts
39 → 82
Calls
39 calls:
Slowest
426.0ms
(* (* (* (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))
312.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
262.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
227.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
200.0ms
(/ (exp (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)) (exp (* (atan2 x.im x.re) y.im)))

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

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))

rewrite31.0ms

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
13.0ms
(* (log (- x.re)) y.re)
11.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))

series305.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
181.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
101.0ms
(* (log (- x.re)) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)

simplify1.5s

Counts
28 → 61
Calls
28 calls:
Slowest
324.0ms
(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.re y.re) y.re))
323.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
200.0ms
(/ (exp (* (log (- x.re)) y.re)) (exp (* (atan2 x.im x.re) y.im)))
128.0ms
(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))
119.0ms
(- (* y.re (log -1)) (+ (* y.im (atan2 x.im x.re)) (* y.re (log (/ 1 x.re)))))

prune799.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×log-prod
11×*-un-lft-identity add-cube-cbrt
8×pow1
7×add-cbrt-cube associate-*r* add-exp-log
6×distribute-rgt-in distribute-lft-in associate-*l* associate--l+
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 → 64
Calls
3 calls:
Slowest
12.0ms
(- (* y.re (log x.im)) (* (atan2 x.im x.re) y.im))
6.0ms
(* y.re (log x.im))
5.0ms
(* (atan2 x.im x.re) y.im)

series189.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
115.0ms
(- (* y.re (log x.im)) (* (atan2 x.im x.re) y.im))
52.0ms
(* y.re (log x.im))
22.0ms
(* (atan2 x.im x.re) y.im)

simplify1.6s

Counts
42 → 73
Calls
42 calls:
Slowest
345.0ms
(* (* (* y.re y.re) y.re) (* (* (log x.im) (log x.im)) (log x.im)))
311.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
246.0ms
(- (* y.re (log -1)) (+ (* y.re (log (/ -1 x.im))) (* y.im (atan2 x.im x.re))))
182.0ms
(* y.re (- (log -1) (log (/ -1 x.im))))
134.0ms
(/ (exp (* y.re (log x.im))) (exp (* (atan2 x.im x.re) y.im)))

prune889.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.1b

regimes210.0ms

Accuracy

95.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 7.3b

bsearch1.9s

end0.0ms

sample2.2m

Algorithm
intervals
Results
2.0m30304×body10240exit
4.3s8000×body80valid