Details

Time bar (total: 16.5s)

sample4.1s

Algorithm
intervals
Results
3.9s988×body10240exit
93.0ms256×body80valid

simplify446.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
445.0ms
(* (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))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize47.0ms

Local error

Found 4 expressions with local error:

31.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1
8×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube associate-*l* add-exp-log sqrt-prod
4×sqrt-div insert-posit16 add-log-exp
3×sqrt-pow1 pow1/2 associate-*r* log-pow
2×rem-sqrt-square flip3-+ flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 63
Calls
4 calls:
Slowest
40.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
19.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
207.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
99.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
71.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.4s

Counts
37 → 75
Calls
37 calls:
Slowest
450.0ms
(* (* (* (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))
383.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
299.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
290.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
232.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))

prune1.5s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.0b

localize51.0ms

Local error

Found 4 expressions with local error:

31.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.2b
(* (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))

rewrite33.0ms

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
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
9.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(* (atan2 x.im x.re) y.im)

series406.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
184.0ms
(- (* (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)
71.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms
(* (atan2 x.im x.re) y.im)

simplify2.5s

Counts
39 → 82
Calls
39 calls:
Slowest
489.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
475.0ms
(* (* (* (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))
305.0ms
(sqrt (+ (pow (* x.re x.re) 3) (pow (* x.im x.im) 3)))
279.0ms
(sqrt (- (* (* x.re x.re) (* x.re x.re)) (* (* x.im x.im) (* x.im x.im))))
234.0ms
(/ (exp (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)) (exp (* (atan2 x.im x.re) y.im)))

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (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))

rewrite20.0ms

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
7.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
7.0ms
(* (log (- x.re)) y.re)
5.0ms
(* (atan2 x.im x.re) y.im)

series702.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
531.0ms
(* (log (- x.re)) y.re)
147.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
24.0ms
(* (atan2 x.im x.re) y.im)

simplify1.6s

Counts
28 → 61
Calls
28 calls:
Slowest
379.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
372.0ms
(* (* (* (log (- x.re)) (log (- x.re))) (log (- x.re))) (* (* y.re y.re) y.re))
177.0ms
(- (* y.re (log -1)) (+ (* y.im (atan2 x.im x.re)) (* y.re (log (/ 1 x.re)))))
165.0ms
(/ (exp (* (log (- x.re)) y.re)) (exp (* (atan2 x.im x.re) y.im)))
124.0ms
(- (+ (* y.re (log (/ -1 x.re))) (* y.im (atan2 x.im x.re))))

prune789.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes233.0ms