Details

sample32.0ms

Algorithm

intervals

Results

16.0ms	98×	body	1280	valid
4.0ms	118×	body	80	valid
3.0ms	21×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	8×	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: 18.9b

localize8.0ms

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)))))
2.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
2.0ms	(/ 1.0 (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))))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms	(/ 1.0 (hypot 1.0 x))
78.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
89.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2323	463
3	5001	463

prune165.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 18.4b

localize13.0ms

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	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite14.0ms

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:

2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(+ 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))))

series132.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
83.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
38.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify141.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (30.0ms)

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

prune258.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (hypot 1.0 x)))
0.1b	(sqrt (/ 1.0 (hypot 1.0 x)))
0.3b	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
2.0b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

92×	`sqrt-prod`
84×	`add-sqr-sqrt`
62×	`times-frac`
50×	`add-cube-cbrt` `*-un-lft-identity`
21×	`pow1`
18×	`swap-sqr`
16×	`associate-r` `associate-l`
15×	`associate-*r/`
14×	`sqrt-div`
10×	`sqrt-pow1` `pow1/2`
9×	`unswap-sqr`
6×	`add-exp-log` `frac-sub` `add-cbrt-cube` `div-inv` `add-log-exp`
5×	`pow-prod-up`
4×	`rem-sqrt-square` `flip3--` `associate--l+` `flip--`
3×	`frac-times` `sub-neg` `pow-prod-down` `associate-*l/` `pow-sqr`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`pow2` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 159

Calls

4 calls:

2.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
6.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
19.0ms	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
9.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
46.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
65.0ms	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
111.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))))

simplify74.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	413	1304
1	1998	1163
2	5002	1134

prune493.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (hypot 1.0 x)))
0.1b	(exp (log (- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))))))
0.3b	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
2.0b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

79×	`sqrt-prod`
76×	`add-sqr-sqrt`
52×	`times-frac`
45×	`add-cube-cbrt` `*-un-lft-identity`
29×	`associate-*r/`
21×	`pow1` `sqrt-div`
18×	`swap-sqr`
16×	`associate-r` `associate-l`
12×	`frac-sub`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
8×	`log-div` `flip3--` `exp-diff` `flip--`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`frac-times` `associate-*l/` `pow-prod-up` `div-inv`
4×	`exp-prod` `associate--l+`
3×	`sub-neg` `log-prod` `exp-sum` `pow-prod-down` `pow-sqr`
2×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in`
1×	`pow2` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `log-pow` `*-commutative` `cbrt-unprod` `rem-exp-log`

Counts

4 → 157

Calls

4 calls:

2.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
15.0ms	(exp (log (- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))))))
19.0ms	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
12.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
114.0ms	(exp (log (- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))))))
65.0ms	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
110.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))))

simplify78.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	478	1580
1	2132	1401
2	5001	1345

prune508.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

regimes91.0ms

Accuracy

0% (0.0b remaining)

Error of 14.4b against oracle of 14.4b and baseline of 14.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	20
1	28	20
2	28	20

end0.0ms

sample991.0ms

Algorithm

intervals

Results

645.0ms	2796×	body	1280	valid
121.0ms	4124×	body	80	valid
77.0ms	610×	body	640	valid
30.0ms	309×	body	320	valid
9.0ms	161×	body	160	valid