Details

sample57.0ms

Algorithm

intervals

Results

28.0ms	87×	body	1280	valid
8.0ms	130×	body	80	valid
6.0ms	24×	body	640	valid
2.0ms	12×	body	320	valid
0.0ms	3×	body	160	valid

simplify46.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(hypot 1.0 x)
1.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity` `add-log-exp`
7×	`pow1`
6×	`add-sqr-sqrt`
4×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`+-commutative` `sub-neg` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `sum-log` `sqrt-prod` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 46

Calls

4 calls:

10.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
16.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0ms	(hypot 1.0 x)
7.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series242.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
91.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms	(hypot 1.0 x)
119.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify805.0ms

Counts: 58 → 58

prune170.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 16.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(hypot 1.0 x)
0.0b	(hypot 1.0 x)
0.7b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
8×	`associate-*r/`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3--` `associate--l+` `associate-/r*` `frac-sub` `flip--` `associate-/l/` `distribute-lft-out`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 70

Calls

4 calls:

64.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0ms	(hypot 1.0 x)
0.0ms	(hypot 1.0 x)
21.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.0ms	(hypot 1.0 x)
3.0ms	(hypot 1.0 x)
37.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify868.0ms

Counts: 82 → 82

prune387.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 16.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(hypot 1.0 x)
0.1b	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
0.7b	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`pow1` `*-un-lft-identity`
6×	`add-log-exp`
5×	`cube-div` `add-cube-cbrt` `associate-*r/` `sqr-pow`
4×	`difference-of-squares`
3×	`pow-unpow` `pow-exp` `rem-cube-cbrt`
2×	`flip3--` `pow-pow` `prod-exp` `frac-sub` `flip--` `cbrt-unprod`
1×	`difference-cubes` `cbrt-undiv` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `diff-log` `unpow3` `cube-prod` `div-exp` `pow-prod-down` `distribute-lft-out--`

Counts

4 → 59

Calls

4 calls:

0.0ms	(hypot 1.0 x)
0.0ms	(hypot 1.0 x)
10.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
20.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series142.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(hypot 1.0 x)
2.0ms	(hypot 1.0 x)
45.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
93.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify878.0ms

Counts: 71 → 71

prune373.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (hypot 1.0 x))
0.2b	(cbrt (hypot 1.0 x))
0.3b	(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
0.7b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (* (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x))) (cbrt (hypot 1.0 x))))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`associate-*r/` `associate--l+` `add-cbrt-cube` `unswap-sqr`
3×	`sub-neg`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `pow-prod-down` `pow-sqr` `pow-prod-up` `frac-sub` `flip--`
1×	`pow2` `pow-plus` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 80

Calls

4 calls:

1.0ms	(cbrt (hypot 1.0 x))
1.0ms	(cbrt (hypot 1.0 x))
12.0ms	(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
31.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (* (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x))) (cbrt (hypot 1.0 x))))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (hypot 1.0 x))
135.0ms	(cbrt (hypot 1.0 x))
181.0ms	(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
47.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (* (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x))) (cbrt (hypot 1.0 x))))))

simplify661.0ms

Counts: 92 → 92

prune359.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 16.1b

regimes389.0ms

Accuracy

10.8% (0.3b remaining)

Error of 15.1b against oracle of 14.8b and baseline of 15.2b

bsearch0.0ms

simplify1.3s

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.5s	2834×	body	1280	valid
283.0ms	4045×	body	80	valid
189.0ms	617×	body	640	valid
58.0ms	345×	body	320	valid
17.0ms	159×	body	160	valid