Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	10	12
1	11	12
done	11	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
27.4b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
20×	`pow1`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
4×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube`
3×	`sqrt-prod`
2×	`log-div` `flip3-+` `div-sub` `flip-+` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

2 → 63

Calls

2 calls:

11.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series167.0ms

Counts

2 → 6

Calls

2 calls:

132.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.2s

Counts

69 → 69

Iterations

Useful iterations: 3 (151.0ms)

Iter	Nodes	Cost
0	116	1191
1	225	1120
2	492	1046
3	1059	1032
4	2367	1032
done	5000	1032

prune199.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.4b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
28.5b	(log (+ (* re re) (* im im)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
82×	`add-sqr-sqrt`
54×	`sqrt-prod`
52×	`add-cube-cbrt` `*-un-lft-identity`
33×	`pow1`
32×	`associate-r`
28×	`log-pow`
25×	`associate-l`
18×	`add-exp-log`
17×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-/r*`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`log-prod` `div-inv` `add-log-exp`
2×	`flip3-+` `div-sub` `flip-+`
1×	`frac-times` `frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 153

Calls

3 calls:

31.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
12.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
3.0ms	(log (+ (* re re) (* im im)))

series377.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
185.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
50.0ms	(log (+ (* re re) (* im im)))

simplify642.0ms

Counts

162 → 162

Iterations

Useful iterations: done (637.0ms)

Iter	Nodes	Cost
0	205	3465
1	535	3302
2	1802	2921
done	5000	2886

prune386.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.3b	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
28.5b	(log (+ (* re re) (* im im)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
46×	`times-frac`
45×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`add-cube-cbrt`
29×	`associate-l` `add-cbrt-cube`
26×	`associate-r` `sqrt-prod`
22×	`prod-exp`
18×	`pow1`
12×	`cbrt-unprod`
11×	`div-exp`
8×	`log-pow`
6×	`cbrt-undiv`
5×	`associate-*r/` `unswap-sqr`
4×	`pow-prod-down`
3×	`rec-exp` `log-prod` `1-exp` `un-div-inv` `add-log-exp`
2×	`frac-times` `log-div` `*-commutative` `div-inv`
1×	`flip3-+` `rem-log-exp` `associate-*l/` `flip-+`

Counts

3 → 122

Calls

3 calls:

29.0ms	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
15.0ms	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
3.0ms	(log (+ (* re re) (* im im)))

series386.0ms

Counts

3 → 9

Calls

3 calls:

144.0ms	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
191.0ms	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
51.0ms	(log (+ (* re re) (* im im)))

simplify1.3s

Counts

131 → 131

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	212	2728
1	567	2406
2	2173	1986
done	5001	1804

prune312.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.3b

localize20.0ms

Local error

Found 3 expressions with local error:

0.2b

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* im im) (* re re)) (/ 1 (sqrt (log 10.0))))))

14.3b

(pow (+ (* im im) (* re re)) (/ 1 (sqrt (log 10.0))))

15.6b

(log (pow (+ (* im im) (* re re)) (/ 1 (sqrt (log 10.0)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
44×	`times-frac`
39×	`add-cube-cbrt` `*-un-lft-identity`
25×	`pow-unpow` `associate-l` `sqrt-prod`
21×	`log-prod`
12×	`pow1` `unpow-prod-down`
11×	`add-exp-log`
8×	`log-pow` `add-cbrt-cube`
7×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `sqr-pow`
3×	`rem-log-exp` `add-log-exp` `unswap-sqr`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `pow-pow` `div-exp` `pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 117

Calls

3 calls:

24.0ms

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* im im) (* re re)) (/ 1 (sqrt (log 10.0))))))

7.0ms

(pow (+ (* im im) (* re re)) (/ 1 (sqrt (log 10.0))))

5.0ms

(log (pow (+ (* im im) (* re re)) (/ 1 (sqrt (log 10.0)))))

series974.0ms

Counts

3 → 9

Calls

3 calls:

367.0ms

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* im im) (* re re)) (/ 1 (sqrt (log 10.0))))))

320.0ms

(pow (+ (* im im) (* re re)) (/ 1 (sqrt (log 10.0))))

287.0ms

(log (pow (+ (* im im) (* re re)) (/ 1 (sqrt (log 10.0)))))

simplify49.0ms

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	196	2895