Details

sample33.0ms

Algorithm

intervals

Results

17.0ms	99×	body	1280	valid
4.0ms	130×	body	80	valid
1.0ms	16×	body	320	valid
1.0ms	9×	body	640	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.6b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite29.0ms

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:

0.0ms	(hypot 1.0 x)
10.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
25.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
74.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
83.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	167	381
1	423	355
2	1736	353
3	5002	352

prune136.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.1b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
11.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
15.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series117.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
74.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
31.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify40.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	299	576
1	1026	547
2	5001	544

prune276.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.1b	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

10.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms	(/ 1.0 (hypot 1.0 x))
11.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
28.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series143.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms	(/ 1.0 (hypot 1.0 x))
74.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
30.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	417	649
1	1680	608
2	5001	608

prune506.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.1b

localize20.0ms

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)))
1.1b	(- (* 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)))))

rewrite32.0ms

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))
13.0ms	(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
15.0ms	(- (* 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)))))

series366.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (hypot 1.0 x))
104.0ms	(cbrt (hypot 1.0 x))
122.0ms	(* (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)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	250	746
1	1101	640
2	5001	581

prune279.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 13.1b

regimes45.0ms

Accuracy

0% (0.1b remaining)

Error of 15.0b against oracle of 14.9b and baseline of 15.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	20
1	23	20

end0.0ms

sample888.0ms

Algorithm

intervals

Results

501.0ms	2927×	body	1280	valid
124.0ms	4026×	body	80	valid
80.0ms	580×	body	640	valid
31.0ms	307×	body	320	valid
9.0ms	160×	body	160	valid