Details

sample8.0ms

Algorithm

intervals

Results

3.0ms

256×

body

valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	5
1	6	5
done	6	5

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize3.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ x (/ 1.0 3.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity`
3×	`fma-def` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`

Counts

1 → 17

Calls

1 calls:

6.0ms

(+ x (/ 1.0 3.0))

series16.0ms

Counts

1 → 3

Calls

1 calls:

16.0ms

(+ x (/ 1.0 3.0))

simplify1.3s

Counts

20 → 20

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	30	135
1	83	129
2	191	119
3	448	119
4	1170	119
5	3417	119
done	5000	119

prune39.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x (/ 1.0 3.0)))
0.0b	(+ x (/ 1.0 3.0))
0.0b	(+ x (/ 1.0 3.0))
0.2b	(* (sqrt (+ x (/ 1.0 3.0))) (sqrt (+ x (/ 1.0 3.0))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
30×	`sqrt-prod`
20×	`pow1`
15×	`add-cube-cbrt`
14×	`sqrt-div`
11×	`swap-sqr`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out`
8×	`add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `fma-def` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`+-commutative` `associate-r/` `associate-l/` `sum-log` `hypot-def`
1×	`pow2` `rem-sqrt-square` `times-frac` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 118

Calls

4 calls:

12.0ms	(sqrt (+ x (/ 1.0 3.0)))
9.0ms	(+ x (/ 1.0 3.0))
6.0ms	(+ x (/ 1.0 3.0))
48.0ms	(* (sqrt (+ x (/ 1.0 3.0))) (sqrt (+ x (/ 1.0 3.0))))

series87.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ x (/ 1.0 3.0)))
17.0ms	(+ x (/ 1.0 3.0))
17.0ms	(+ x (/ 1.0 3.0))
18.0ms	(* (sqrt (+ x (/ 1.0 3.0))) (sqrt (+ x (/ 1.0 3.0))))

simplify1.1s

Counts

130 → 130

Iterations

Useful iterations: 3 (234.0ms)

Iter	Nodes	Cost
0	115	1700
1	237	1163
2	699	1068
3	2211	1038
done	5000	1038

prune225.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fabs (cbrt (+ (/ 1.0 3.0) x))) (sqrt (cbrt (+ (/ 1.0 3.0) x))))
0.2b	(* (sqrt (+ x (/ 1.0 3.0))) (* (fabs (cbrt (+ (/ 1.0 3.0) x))) (sqrt (cbrt (+ (/ 1.0 3.0) x)))))
0.3b	(cbrt (+ (/ 1.0 3.0) x))
0.3b	(cbrt (+ (/ 1.0 3.0) x))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
14×	`sqrt-div`
13×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `cbrt-div`
11×	`pow1` `add-exp-log` `associate-r` `add-cbrt-cube`
10×	`associate-r/` `associate-l*`
9×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`unswap-sqr`
2×	`pow1/3` `associate-l/` `-commutative`

Counts

4 → 95

Calls

4 calls:

32.0ms	(* (fabs (cbrt (+ (/ 1.0 3.0) x))) (sqrt (cbrt (+ (/ 1.0 3.0) x))))
56.0ms	(* (sqrt (+ x (/ 1.0 3.0))) (* (fabs (cbrt (+ (/ 1.0 3.0) x))) (sqrt (cbrt (+ (/ 1.0 3.0) x)))))
7.0ms	(cbrt (+ (/ 1.0 3.0) x))
7.0ms	(cbrt (+ (/ 1.0 3.0) x))

series403.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (fabs (cbrt (+ (/ 1.0 3.0) x))) (sqrt (cbrt (+ (/ 1.0 3.0) x))))
134.0ms	(* (sqrt (+ x (/ 1.0 3.0))) (* (fabs (cbrt (+ (/ 1.0 3.0) x))) (sqrt (cbrt (+ (/ 1.0 3.0) x)))))
85.0ms	(cbrt (+ (/ 1.0 3.0) x))
88.0ms	(cbrt (+ (/ 1.0 3.0) x))

simplify601.0ms

Counts

107 → 107

Iterations

Useful iterations: done (597.0ms)

Iter	Nodes	Cost
0	263	2530
1	659	2364
2	2110	2178
done	5000	2177

prune360.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ x (/ 1.0 3.0))))
0.0b	(sqrt (sqrt (+ x (/ 1.0 3.0))))
0.1b	(* (pow (sqrt (sqrt (+ x (/ 1.0 3.0)))) 3) (sqrt (sqrt (+ x (/ 1.0 3.0)))))
0.2b	(pow (sqrt (sqrt (+ x (/ 1.0 3.0)))) 3)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

121×	`sqrt-prod`
74×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
36×	`sqrt-div`
29×	`unpow-prod-down` `cube-prod`
26×	`associate-l`
25×	`add-cube-cbrt`
24×	`unswap-sqr`
12×	`pow1` `sqrt-pow1`
10×	`add-exp-log` `associate-r`
9×	`flip3-+` `flip-+`
8×	`cube-div`
7×	`add-cbrt-cube` `distribute-lft-out`
6×	`pow1/2`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`cube-mult` `pow-to-exp` `unpow3` `associate-r/` `associate-l/` `pow-exp`
1×	`pow-plus` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 178

Calls

4 calls:

13.0ms	(sqrt (sqrt (+ x (/ 1.0 3.0))))
12.0ms	(sqrt (sqrt (+ x (/ 1.0 3.0))))
86.0ms	(* (pow (sqrt (sqrt (+ x (/ 1.0 3.0)))) 3) (sqrt (sqrt (+ x (/ 1.0 3.0)))))
14.0ms	(pow (sqrt (sqrt (+ x (/ 1.0 3.0)))) 3)

series339.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sqrt (sqrt (+ x (/ 1.0 3.0))))
87.0ms	(sqrt (sqrt (+ x (/ 1.0 3.0))))
23.0ms	(* (pow (sqrt (sqrt (+ x (/ 1.0 3.0)))) 3) (sqrt (sqrt (+ x (/ 1.0 3.0)))))
142.0ms	(pow (sqrt (sqrt (+ x (/ 1.0 3.0)))) 3)

simplify54.0ms

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	216	3768