Details

sample176.0ms

Algorithm

intervals

Results

80.0ms	256×	body	80	valid
58.0ms	305×	body	80	nan

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	28
1	23	28
done	23	28

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
93.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
17.0ms	(* (log base) (log base))
10.0ms	(sqrt (+ (* re re) (* im im)))

series570.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
149.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
217.0ms	(* (log base) (log base))
68.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.6s

Counts

122 → 122

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	200	2451
1	442	2259
2	1344	2035
3	4400	1998
done	5000	1992

prune803.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
0.5b	(/ (+ (pow (* (log base) (log (sqrt (+ (* re re) (* im im))))) 1) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
23×	`pow1`
18×	`log-prod`
10×	`add-exp-log` `associate-r` `log-pow` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `sqrt-prod`
8×	`associate-l`
6×	`swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 116

Calls

4 calls:

24.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
72.0ms	(/ (+ (pow (* (log base) (log (sqrt (+ (* re re) (* im im))))) 1) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
19.0ms	(* (log base) (log base))
16.0ms	(sqrt (+ (* re re) (* im im)))

series705.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
177.0ms	(/ (+ (pow (* (log base) (log (sqrt (+ (* re re) (* im im))))) 1) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
284.0ms	(* (log base) (log base))
73.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.3s

Counts

128 → 128

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	213	2682
1	456	2354
2	1425	2134
3	4866	2109
done	5001	2103

prune738.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.9b

localize71.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
58×	`times-frac`
41×	`*-un-lft-identity`
35×	`add-cube-cbrt`
32×	`sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
11×	`pow1`
8×	`unpow-prod-down` `div-exp` `prod-exp`
6×	`pow-unpow` `sqrt-div`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `rec-exp` `pow-pow` `1-exp` `pow-exp` `log-pow` `div-inv` `unpow2` `sqr-pow`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 140

Calls

4 calls:

167.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
6.0ms	(pow (log base) 2)
6.0ms	(pow (log base) 2)
17.0ms	(sqrt (+ (* re re) (* im im)))

series799.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
268.0ms	(pow (log base) 2)
262.0ms	(pow (log base) 2)
49.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

152 → 152

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	235	5236
1	624	4886
2	2107	4095
done	5001	4080

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.9b

localize65.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
30.6b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `unpow-prod-down`
11×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`pow-unpow`
7×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `sqrt-prod` `log-pow` `unpow2` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 72

Calls

4 calls:

3.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 2)
9.0ms	(sqrt (+ (* re re) (* im im)))

series806.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(pow (log base) 2)
231.0ms	(pow (log base) 2)
280.0ms	(pow (log base) 2)
65.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.7s

Counts

84 → 84

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	74	660
1	165	561
2	360	494
3	981	479
4	4546	467
done	5001	467

prune623.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.9b

Details

sample176.0ms

simplify16.0ms

prune7.0ms

localize26.0ms

rewrite139.0ms

series570.0ms

simplify3.6s

prune803.0ms

localize34.0ms

rewrite138.0ms

series705.0ms

simplify4.3s

prune738.0ms

localize71.0ms

rewrite206.0ms

series799.0ms

simplify2.2s

prune1.0s

localize65.0ms

rewrite20.0ms

series806.0ms

simplify4.7s

prune623.0ms

regimes23.0ms