Details

sample32.0ms

Algorithm

intervals

Results

8.0ms	280×	body	80	nan
8.0ms	271×	body	80	valid

simplify100.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

localize12.0ms

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

rewrite169.0ms

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:

12.0ms	(+ y (/ 1.0 (* x 9.0)))
140.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
9.0ms	(* 3.0 (sqrt x))
7.0ms	(/ 1.0 (* x 9.0))

series132.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ y (/ 1.0 (* x 9.0)))
58.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
35.0ms	(* 3.0 (sqrt x))
15.0ms	(/ 1.0 (* x 9.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (46.0ms)

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

prune202.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

10.0ms	(+ y (/ 1.0 (* x 9.0)))
161.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
149.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
7.0ms	(/ 1.0 (* x 9.0))

series150.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ y (/ 1.0 (* x 9.0)))
53.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
59.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
15.0ms	(/ 1.0 (* x 9.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	427	770
1	1858	694
2	5002	694

prune205.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
33×	`add-sqr-sqrt`
24×	`pow1`
21×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
18×	`times-frac`
13×	`associate-l`
12×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
11×	`associate-r`
8×	`sqrt-pow1` `pow1/2`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`
5×	`associate-*r/` `pow-prod-up`
4×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate--l+` `add-log-exp` `unswap-sqr`
3×	`pow-sqr`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative`
1×	`pow2` `frac-times` `flip3--` `pow-plus` `sqrt-unprod` `associate-*l/` `rem-square-sqrt` `flip--`

Counts

4 → 138

Calls

4 calls:

62.0ms	(* 3.0 (* (sqrt x) (- (+ y (* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))) 1.0)))
7.0ms	(/ 1.0 (* x 9.0))
7.0ms	(/ 1.0 (* x 9.0))
42.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* 3.0 (* (sqrt x) (- (+ y (* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))) 1.0)))
15.0ms	(/ 1.0 (* x 9.0))
15.0ms	(/ 1.0 (* x 9.0))
53.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	518	1027
1	2522	790
2	5001	747

prune332.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite523.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

18.0ms	(+ (/ 1.0 (* x 9.0)) y)
226.0ms	(* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0))
269.0ms	(* (* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0)) (sqrt x))
7.0ms	(/ 1.0 (* x 9.0))

series120.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (/ 1.0 (* x 9.0)) y)
27.0ms	(* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0))
54.0ms	(* (* 3.0 (- (+ (/ 1.0 (* x 9.0)) y) 1.0)) (sqrt x))
17.0ms	(/ 1.0 (* x 9.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	418	605
1	1918	533
2	5003	531

prune202.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

regimes82.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	7
1	22	7
2	22	7

end0.0ms

sample901.0ms

Algorithm

intervals

Results

261.0ms	8522×	body	80	nan
259.0ms	8511×	body	80	valid