Details

sample32.0ms

Algorithm

intervals

Results

15.0ms	80×	body	1280	valid
4.0ms	128×	body	80	valid
3.0ms	26×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid

simplify10.0ms

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: 17.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(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))))))

rewrite13.0ms

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:

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

series167.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(hypot 1.0 x)
75.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
86.0ms	(- 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

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.5b

localize13.0ms

Local error

Found 4 expressions with local error:

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)))))))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.3b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

9.0ms	(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)))))))
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))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
163.0ms	(/ (- (* 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)))))))
79.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
32.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify51.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	403	1245
1	1428	1156
2	5001	1151

prune237.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 16.5b

localize26.0ms

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)
2.3b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
2.3b	(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))

rewrite33.0ms

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:

12.0ms	(* (/ 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))))

series170.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
33.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
37.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
76.0ms	(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))

simplify179.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 1 (22.0ms)

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

prune720.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 16.5b

localize18.0ms

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 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.2b	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.3b	(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `associate-/r/`
5×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `times-frac` `div-exp` `associate-/r*` `distribute-lft-out`
3×	`distribute-rgt-out--` `div-inv`
2×	`+-commutative` `prod-exp` `sum-log` `cbrt-unprod`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `associate-r/` `clear-num` `frac-sub` `flip--` `associate-/l/` `associate-/l` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 71

Calls

4 calls:

2.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
8.0ms	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
38.0ms	(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

series633.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
77.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
152.0ms	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
324.0ms	(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	373	1324
1	1536	1171
2	5002	1142

prune207.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 16.2b

regimes70.0ms

Accuracy

0% (0.2b remaining)

Error of 14.8b against oracle of 14.6b 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

sample796.0ms

Algorithm

intervals

Results

452.0ms	2850×	body	1280	valid
118.0ms	4115×	body	80	valid
80.0ms	600×	body	640	valid
25.0ms	273×	body	320	valid
12.0ms	162×	body	160	valid