Details

sample32.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify24.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
2	22	14
3	24	14
done	24	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.1b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`sqrt-prod`
11×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`sum-log`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`+-commutative` `rem-sqrt-square` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `associate-+l+` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 78

Calls

4 calls:

10.0ms	(+ (* x x) (* y y))
62.0ms	(+ (+ (* x x) (* y y)) (* z z))
120.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
61.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series353.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* x x) (* y y))
58.0ms	(+ (+ (* x x) (* y y)) (* z z))
69.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
192.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.8s

Counts

90 → 90

Iterations

Useful iterations: 3 (845.0ms)

Iter	Nodes	Cost
0	139	1707
1	319	1620
2	948	1477
3	3245	1461
done	5000	1461

prune398.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
34.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.1b	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
28×	`sqrt-prod`
21×	`cbrt-prod`
9×	`pow1` `sqrt-div`
6×	`add-exp-log` `associate-/r` `associate-/l`
5×	`add-cbrt-cube`
4×	`sqrt-pow1` `add-log-exp`
3×	`flip3-+` `pow1/2` `flip-+`
2×	`rem-sqrt-square` `associate-/l/`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `clear-num` `div-inv`

Counts

4 → 106

Calls

4 calls:

78.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
61.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
56.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
96.0ms	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

341.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
175.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
161.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
400.0ms	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

simplify3.5s

Counts

118 → 118

Iterations

Useful iterations: 3 (421.0ms)

Iter	Nodes	Cost
0	145	2892
1	250	2456
2	562	2347
3	1458	2289
4	4472	2289
done	5001	2289

prune572.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
0.4b	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
34.1b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite435.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
75×	`times-frac` `sqrt-prod`
53×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`cbrt-prod`
25×	`associate-r`
16×	`unswap-sqr`
10×	`associate-l`
9×	`pow1` `add-log-exp`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r*`
5×	`sqrt-div`
4×	`div-inv`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `sum-log` `associate-/l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+l+` `frac-2neg` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 157

Calls

4 calls:

32.0ms	(+ (+ (* x x) (* y y)) (* z z))
145.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
191.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
60.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ (+ (* x x) (* y y)) (* z z))
209.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
548.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
577.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify3.0s

Counts

169 → 169

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	223	4498
1	426	4299
2	1180	4070
3	3926	4054
done	5000	4032

prune988.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0))))
0.4b	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0)))))
1.0b	(/ 1 (cbrt 3.0))
34.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite472.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
51×	`sqrt-prod`
47×	`times-frac`
43×	`*-un-lft-identity`
39×	`add-cube-cbrt`
29×	`sqrt-div`
26×	`associate-r`
25×	`cbrt-prod`
18×	`pow1`
16×	`associate-l`
15×	`add-exp-log`
12×	`add-cbrt-cube` `unswap-sqr`
11×	`frac-times`
10×	`pow-prod-down`
8×	`associate-*r/`
7×	`flip3-+` `associate-*l/` `flip-+`
6×	`sqrt-pow1` `pow1/2` `associate-/r*`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`sqrt-unprod` `div-inv` `associate-/l*`
2×	`pow-flip` `div-exp` `*-commutative`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `frac-2neg` `pow1/3` `1-exp` `clear-num` `inv-pow`

Counts

4 → 160

Calls

4 calls:

116.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0))))
275.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0)))))
13.0ms	(/ 1 (cbrt 3.0))
53.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series1.3s

Counts

4 → 10

Calls

4 calls:

566.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0))))
505.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 (cbrt 3.0)))))
0.0ms	(/ 1 (cbrt 3.0))
202.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify4.1s

Counts

170 → 170

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	230	3710
1	455	3312
2	1139	3090
3	4395	2960
done	5000	2942

prune715.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 20.2b

Details

sample32.0ms

simplify24.0ms

prune5.0ms

localize24.0ms

rewrite255.0ms

series353.0ms

simplify1.8s

prune398.0ms

localize41.0ms

rewrite295.0ms

series1.1s

simplify3.5s

prune572.0ms

localize18.0ms

rewrite435.0ms

series1.4s

simplify3.0s

prune988.0ms

localize30.0ms

rewrite472.0ms

series1.3s

simplify4.1s

prune715.0ms

regimes5.0ms