Details

sample33.0ms

Algorithm

intervals

Results

11.0ms	286×	body	80	nan
8.0ms	272×	body	80	valid

simplify125.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	7
1	65	7
2	190	7
3	412	7
4	644	7
5	1083	7
6	1628	7
7	2273	7
8	3723	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)))
0.3b	(/ 1.0 (* x 9.0))
0.3b	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.3b	(* 3.0 (sqrt x))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
24×	`prod-diff`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-r`
11×	`pow1`
8×	`distribute-lft-out`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `associate-r/` `div-exp` `associate--l+` `-commutative` `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 → 119

Calls

4 calls:

5.0ms	(+ y (/ 1.0 (* x 9.0)))
3.0ms	(/ 1.0 (* x 9.0))
83.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
5.0ms	(* 3.0 (sqrt x))

series147.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ 1.0 (* x 9.0)))
19.0ms	(/ 1.0 (* x 9.0))
62.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
41.0ms	(* 3.0 (sqrt x))

simplify79.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	594	1130
1	2890	878
2	5001	872

prune249.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
75×	`distribute-rgt-in` `distribute-lft-in`
72×	`prod-diff`
59×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
20×	`distribute-lft-out`
16×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
9×	`associate-l`
7×	`associate-r`
6×	`sub-neg` `associate-*r/` `associate--l+` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `associate-/r*` `sum-log` `flip-+` `div-inv` `difference-of-squares`

Counts

4 → 181

Calls

4 calls:

5.0ms	(+ y (/ 1.0 (* x 9.0)))
3.0ms	(/ 1.0 (* x 9.0))
94.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
99.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ 1.0 (* x 9.0)))
16.0ms	(/ 1.0 (* x 9.0))
58.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
65.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

simplify86.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	633	2404
1	2665	1754
2	5002	1748

prune270.0ms

Pruning

9 alts after pruning (9 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))
0.3b	(* (* 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))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

84×	`*-un-lft-identity`
75×	`times-frac`
71×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
24×	`prod-diff`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-rgt-in` `distribute-lft-in`
13×	`associate-/l*`
12×	`associate-r`
11×	`pow1`
8×	`distribute-lft-out`
6×	`add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-def` `div-exp` `associate-/r*`
2×	`sub-neg` `associate-r/` `associate--l+` `-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3--` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip--` `flip-+` `associate-/l/` `difference-of-squares`

Counts

4 → 168

Calls

4 calls:

17.0ms	(+ y (/ (/ 1.0 x) 9.0))
278.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
6.0ms	(/ (/ 1.0 x) 9.0)
5.0ms	(* 3.0 (sqrt x))

series144.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ y (/ (/ 1.0 x) 9.0))
65.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
16.0ms	(/ (/ 1.0 x) 9.0)
38.0ms	(* 3.0 (sqrt x))

simplify105.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	818	1496
1	3749	1238
2	5001	1234

prune392.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1.0 (sqrt x)) 9.0)
0.3b	(* (* 3.0 (sqrt x)) (- (+ y (* (/ 1 (sqrt x)) (/ (/ 1.0 (sqrt x)) 9.0))) 1.0))
0.3b	(* 3.0 (sqrt x))
0.3b	(* (/ 1 (sqrt x)) (/ (/ 1.0 (sqrt x)) 9.0))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

317×	`times-frac`
249×	`add-sqr-sqrt`
180×	`*-un-lft-identity`
170×	`add-cube-cbrt`
89×	`sqrt-prod`
81×	`associate-r`
55×	`add-exp-log`
37×	`add-cbrt-cube`
26×	`associate-l`
22×	`associate-/l*` `unswap-sqr`
21×	`div-exp`
18×	`prod-diff`
16×	`prod-exp`
13×	`pow1`
12×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in`
10×	`cbrt-unprod` `div-inv`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-r/` `associate-/r` `*-commutative`
2×	`sub-neg` `associate--l+`
1×	`frac-times` `flip3--` `frac-2neg` `associate-*l/` `clear-num` `flip--` `associate-/l/` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 324

Calls

4 calls:

9.0ms	(/ (/ 1.0 (sqrt x)) 9.0)
33.0ms	(* (* 3.0 (sqrt x)) (- (+ y (* (/ 1 (sqrt x)) (/ (/ 1.0 (sqrt x)) 9.0))) 1.0))
5.0ms	(* 3.0 (sqrt x))
55.0ms	(* (/ 1 (sqrt x)) (/ (/ 1.0 (sqrt x)) 9.0))

series186.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (/ 1.0 (sqrt x)) 9.0)
83.0ms	(* (* 3.0 (sqrt x)) (- (+ y (* (/ 1 (sqrt x)) (/ (/ 1.0 (sqrt x)) 9.0))) 1.0))
36.0ms	(* 3.0 (sqrt x))
27.0ms	(* (/ 1 (sqrt x)) (/ (/ 1.0 (sqrt x)) 9.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1442	3500
1	5001	3048

prune742.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes63.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	10
1	17	10

end0.0ms

sample759.0ms

Algorithm

intervals

Results

254.0ms	8497×	body	80	nan
251.0ms	8539×	body	80	valid