Details

sample55.0ms

Algorithm

intervals

Results

29.0ms	82×	body	1280	valid
8.0ms	129×	body	80	valid
6.0ms	26×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	5×	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: 17.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.5b	(- 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)))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 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))))))

series188.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
72.0ms	(sqrt (* 0.5 (+ 1.0 (/ 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))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2325	463
3	5001	463

prune156.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 16.5b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
18.0ms	(/ (- (* 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))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
78.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
157.0ms	(/ (- (* 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)))))))
32.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify53.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	423	1277
1	1641	1179
2	5001	1174

prune279.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.5b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
23×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-r`
15×	`add-exp-log`
13×	`associate-*r/`
11×	`add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `flip3--` `frac-sub` `flip--`
4×	`frac-times` `associate-*l/` `prod-exp` `associate--l+` `distribute-lft-out`
3×	`sub-neg` `div-exp` `associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate-/r/` `cbrt-unprod` `flip-+` `div-inv`
1×	`+-commutative` `rec-exp` `frac-2neg` `diff-log` `1-exp` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `*-commutative`

Counts

4 → 106

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(+ 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)))) (/ 1 (+ 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))))

series274.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
77.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
157.0ms	(* (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
33.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify67.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	526	1403
1	2281	1261
2	5002	1244

prune307.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 16.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
0.0b	(* (/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))))) (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.1b	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
1.0b	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite310.0ms

Algorithm

rewrite-expression-head

Rules

534×	`associate-*r/`
208×	`frac-add`
150×	`associate-/r/`
144×	`flip3--` `flip--`
137×	`frac-times`
105×	`associate-l`
89×	`add-sqr-sqrt`
73×	`times-frac`
64×	`*-un-lft-identity`
53×	`associate-*l/`
40×	`add-cube-cbrt`
35×	`flip3-+` `flip-+`
34×	`add-exp-log`
33×	`sqr-pow`
32×	`difference-of-squares`
24×	`add-cbrt-cube`
18×	`associate-r`
10×	`div-exp` `prod-exp`
9×	`pow1` `cube-div` `associate-/l*`
8×	`difference-cubes` `distribute-lft-out--`
6×	`cbrt-undiv` `cbrt-unprod` `add-log-exp` `unswap-sqr`
4×	`frac-sub` `associate-/l/`
3×	`pow-unpow` `pow-exp` `associate-/r*` `div-inv` `distribute-lft-out` `rem-cube-cbrt`
2×	`rec-exp` `pow-pow` `1-exp` `pow-prod-down`
1×	`cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `frac-2neg` `diff-log` `unpow3` `div-sub` `cube-prod` `clear-num` `un-div-inv` `*-commutative`

Counts

4 → 329

Calls

4 calls:

66.0ms	(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
190.0ms	(* (/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))))) (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
4.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
10.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series625.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
338.0ms	(* (/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))))) (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
32.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
75.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify157.0ms

Algorithm

egg-herbie

Counts

341 → 341

Iterations

Useful iterations: 1 (54.0ms)

Iter	Nodes	Cost
0	2885	11165
1	5002	10749

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.2b

regimes127.0ms

Accuracy

0% (0.3b remaining)

Error of 14.7b against oracle of 14.4b and baseline of 14.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	48
1	34	48

end0.0ms

sample1.5s

Algorithm

intervals

Results

921.0ms	2892×	body	1280	valid
242.0ms	4011×	body	80	valid
167.0ms	650×	body	640	valid
54.0ms	304×	body	320	valid
17.0ms	143×	body	160	valid