Details

sample34.0ms

Algorithm

intervals

Results

14.0ms	86×	body	1280	valid
4.0ms	127×	body	80	valid
3.0ms	22×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	7×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 14.9b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(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)))))
2.8b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

0.0ms	(hypot 1.0 x)
2.0ms	(/ 1.0 (hypot 1.0 x))
8.0ms	(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))))))

series163.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
6.0ms	(/ 1.0 (hypot 1.0 x))
72.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
84.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	201	433
1	602	413
2	1998	411
3	5001	411

prune156.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
2.2b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series129.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
37.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify144.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	306	616
1	1080	568
2	4851	560
3	5001	560

prune259.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
0.0b	(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
2.2b	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
19.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
62.0ms	(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
35.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
21.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
71.0ms	(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
36.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify111.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	655	1559
1	3870	1302
2	5002	1302

prune397.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
2.2b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
2.3b	(log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
14.0ms	(log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
32.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
33.0ms	(log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))))

simplify122.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	279	682
1	983	621
2	4259	612
3	5002	612

prune305.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 14.4b

regimes78.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	15
1	21	15

end0.0ms

sample818.0ms

Algorithm

intervals

Results

464.0ms	2853×	body	1280	valid
115.0ms	4041×	body	80	valid
83.0ms	619×	body	640	valid
37.0ms	337×	body	320	valid
9.0ms	150×	body	160	valid