Details

sample48.0ms

Algorithm

intervals

Results

14.0ms

429×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	7
1	48	7
2	81	7
3	98	7
4	98	7
done	98	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x y) (* z t))
0.0b	(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))
0.0b	(+ (+ (* x y) (* z t)) (* a b))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
10×	`sum-log`
3×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`associate-+l+`

Counts

3 → 38

Calls

3 calls:

9.0ms	(+ (* x y) (* z t))
108.0ms	(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))
31.0ms	(+ (+ (* x y) (* z t)) (* a b))

series318.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (* x y) (* z t))
224.0ms	(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))
59.0ms	(+ (+ (* x y) (* z t)) (* a b))

simplify36.0ms

Counts

47 → 47

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	276	348
1	1151	333
2	5001	333
done	5001	333

prune138.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x y) (* z t)) (* a b))
0.1b	(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.1b	(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.2b	(* (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))

rewrite730.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+` `add-log-exp`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `sum-log` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `associate-+l+` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 100

Calls

4 calls:

28.0ms	(+ (+ (* x y) (* z t)) (* a b))
110.0ms	(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
112.0ms	(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
475.0ms	(* (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))

series8.1s

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (+ (* x y) (* z t)) (* a b))
3.9s	(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
3.9s	(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
231.0ms	(* (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))

simplify58.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	381	1472
1	1707	1332
2	5001	1296
done	5001	1296

prune292.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

3.4b	(+ (* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b)))) (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))))
3.7b	(* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b))))
4.9b	(+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3))
45.5b	(/ (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)) (+ (* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b)))) (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b)))))

rewrite998.0ms

Algorithm

rewrite-expression-head

Rules

42×	`associate-*r/`
32×	`frac-add`
28×	`flip3-+` `flip-+`
25×	`*-un-lft-identity`
18×	`associate-/r/`
17×	`flip3--` `flip--`
16×	`frac-times`
15×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`associate-*l/` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `sum-cubes` `distribute-lft-out` `associate-/l*`
4×	`sub-neg` `associate-+l+`
3×	`associate-r` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`+-commutative` `associate-+r+` `sum-log` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative` `div-inv`

Counts

4 → 125

Calls

4 calls:

97.0ms	(+ (* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b)))) (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))))
115.0ms	(* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b))))
204.0ms	(+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3))
575.0ms	(/ (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)) (+ (* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b)))) (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b)))))

series9.8m

Calls

1 calls:

2.6s	(/ (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)) (+ (* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b)))) (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b)))))