Details

sample59.0ms

Algorithm

intervals

Results

28.0ms	86×	body	1280	valid
13.0ms	127×	body	80	valid
8.0ms	29×	body	640	valid
2.0ms	11×	body	320	valid
0.0ms	3×	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: 18.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.9b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 34

Calls

3 calls:

0.0ms	(hypot 1.0 x)
6.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series155.0ms

Counts

3 → 9

Calls

3 calls:

1.0ms	(hypot 1.0 x)
72.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
82.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify42.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	145	299
1	354	283
2	1416	281
3	5001	281

prune94.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 17.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
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)))))))
1.5b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`associate-*r/`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`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` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `diff-log` `div-sub` `div-exp` `pow-prod-down` `clear-num` `sqrt-prod` `div-inv`

Counts

4 → 76

Calls

4 calls:

0.0ms	(hypot 1.0 x)
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
17.0ms	(/ (- (* 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)))))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series262.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
72.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
153.0ms	(/ (- (* 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)))))))
36.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	396	1127
1	1403	1048
2	5001	1044

prune235.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 17.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
0.1b	(pow (/ 1.0 (hypot 1.0 x)) 3)
1.5b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
1.5b	(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
58×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log` `add-cbrt-cube`
13×	`unpow-prod-down` `cube-prod` `swap-sqr` `associate-r` `associate-l`
12×	`pow1` `associate-*r/`
8×	`add-log-exp`
6×	`div-inv`
5×	`cbrt-undiv` `div-exp` `frac-sub`
4×	`sub-neg` `prod-exp` `associate--l+` `cbrt-unprod` `unswap-sqr`
3×	`pow-unpow` `flip3--` `associate-*l/` `flip--`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `diff-log` `pow-exp` `sub-div` `rem-cube-cbrt`
1×	`cube-div` `pow2` `cube-mult` `pow-to-exp` `distribute-rgt-out--` `pow-pow` `pow-plus` `unpow3` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `sqr-pow`

Counts

4 → 149

Calls

4 calls:

15.0ms	(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
4.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
6.0ms	(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))

series168.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
32.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
31.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
75.0ms	(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))

simplify178.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	765	1210
1	4806	1016
2	5001	1016

prune544.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 17.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
1.5b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

0.0ms	(hypot 1.0 x)
6.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
15.0ms	(/ (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
72.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
129.0ms	(/ (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
36.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify46.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	368	1133
1	1207	1055
2	5001	1052

prune227.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 17.9b

regimes96.0ms

Accuracy

0% (0.0b remaining)

Error of 14.8b against oracle of 14.7b and baseline of 14.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	28
1	31	28

end0.0ms

sample1.6s

Algorithm

intervals

Results

950.0ms	2896×	body	1280	valid
306.0ms	4055×	body	80	valid
166.0ms	615×	body	640	valid
55.0ms	286×	body	320	valid
20.0ms	148×	body	160	valid