Details

sample56.0ms

Algorithm

intervals

Results

23.0ms	277×	body	80	valid
19.0ms	276×	body	80	nan

simplify107.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	7
1	65	7
2	182	7
3	338	7
4	488	7
5	757	7
6	1166	7
7	1729	7
8	2793	7
9	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (/ 1.0 (* x 9.0)))
0.2b	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.3b	(/ 1.0 (* x 9.0))
0.3b	(* 3.0 (sqrt x))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

5.0ms	(+ y (/ 1.0 (* x 9.0)))
70.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
3.0ms	(/ 1.0 (* x 9.0))
4.0ms	(* 3.0 (sqrt x))

series149.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ y (/ 1.0 (* x 9.0)))
63.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
18.0ms	(/ 1.0 (* x 9.0))
39.0ms	(* 3.0 (sqrt x))

simplify54.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	456	548
1	2172	486
2	5002	484

prune206.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (* x 9.0))
0.3b	(/ 1.0 (* x 9.0))
0.3b	(* 3.0 (sqrt x))
0.5b	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
21×	`pow1`
18×	`add-exp-log` `times-frac` `add-cbrt-cube`
16×	`associate-r`
13×	`associate-l`
12×	`swap-sqr`
8×	`sqrt-pow1` `pow1/2`
6×	`div-inv` `associate-/l*` `unswap-sqr`
5×	`pow-prod-up`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`pow-sqr`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `rem-square-sqrt`

Counts

4 → 128

Calls

4 calls:

3.0ms	(/ 1.0 (* x 9.0))
3.0ms	(/ 1.0 (* x 9.0))
4.0ms	(* 3.0 (sqrt x))
20.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1.0 (* x 9.0))
19.0ms	(/ 1.0 (* x 9.0))
38.0ms	(* 3.0 (sqrt x))
57.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

simplify56.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	372	604
1	1934	516
2	5001	505

prune328.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* (/ (sqrt 1.0) x) (/ (sqrt 1.0) 9.0)))
0.2b	(* (* 3.0 (sqrt x)) (- (+ y (* (/ (sqrt 1.0) x) (/ (sqrt 1.0) 9.0))) 1.0))
0.3b	(* 3.0 (sqrt x))
0.4b	(* (/ (sqrt 1.0) x) (/ (sqrt 1.0) 9.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
48×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
33×	`associate-r`
28×	`sqrt-prod`
26×	`associate-l`
23×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
11×	`unswap-sqr`
8×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`pow-prod-down`
4×	`cbrt-undiv` `div-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `-commutative`
2×	`sub-neg` `associate--l+` `div-inv`
1×	`+-commutative` `frac-times` `flip3--` `flip3-+` `associate-*l/` `sum-log` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 134

Calls

4 calls:

2.0ms	(+ y (* (/ (sqrt 1.0) x) (/ (sqrt 1.0) 9.0)))
28.0ms	(* (* 3.0 (sqrt x)) (- (+ y (* (/ (sqrt 1.0) x) (/ (sqrt 1.0) 9.0))) 1.0))
4.0ms	(* 3.0 (sqrt x))
25.0ms	(* (/ (sqrt 1.0) x) (/ (sqrt 1.0) 9.0))

series409.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ y (* (/ (sqrt 1.0) x) (/ (sqrt 1.0) 9.0)))
175.0ms	(* (* 3.0 (sqrt x)) (- (+ y (* (/ (sqrt 1.0) x) (/ (sqrt 1.0) 9.0))) 1.0))
40.0ms	(* 3.0 (sqrt x))
91.0ms	(* (/ (sqrt 1.0) x) (/ (sqrt 1.0) 9.0))

simplify93.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	760	1177
1	3827	996
2	5002	936

prune357.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (/ 1.0 9.0) x) y)
0.1b	(* 3.0 (- (+ (/ (/ 1.0 9.0) x) y) 1.0))
0.3b	(* (* 3.0 (- (+ (/ (/ 1.0 9.0) x) y) 1.0)) (sqrt x))
0.4b	(/ (/ 1.0 9.0) x)

rewrite808.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
57×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
12×	`associate-r`
11×	`pow1`
6×	`add-log-exp`
5×	`div-inv`
4×	`associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-/r*` `sqrt-prod`
2×	`sub-neg` `flip3--` `associate-l/` `associate--l+` `-commutative` `flip--` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `associate-/l/` `difference-of-squares` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

27.0ms	(+ (/ (/ 1.0 9.0) x) y)
362.0ms	(* 3.0 (- (+ (/ (/ 1.0 9.0) x) y) 1.0))
409.0ms	(* (* 3.0 (- (+ (/ (/ 1.0 9.0) x) y) 1.0)) (sqrt x))
6.0ms	(/ (/ 1.0 9.0) x)

series137.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (/ (/ 1.0 9.0) x) y)
29.0ms	(* 3.0 (- (+ (/ (/ 1.0 9.0) x) y) 1.0))
65.0ms	(* (* 3.0 (- (+ (/ (/ 1.0 9.0) x) y) 1.0)) (sqrt x))
17.0ms	(/ (/ 1.0 9.0) x)

simplify65.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	642	971
1	2784	894
2	5001	894

prune339.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes128.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	9
1	29	9
2	30	9
3	30	9

end0.0ms

sample1.5s

Algorithm

intervals

Results

624.0ms	8543×	body	80	valid
573.0ms	8452×	body	80	nan