Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	276×	body	80	valid
8.0ms	272×	body	80	nan

simplify116.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 0.5b

localize195.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (/ 1.0 (* x 9.0)))
0.2b	(/ 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))

rewrite99.0ms

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))
81.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
6.0ms	(* 3.0 (sqrt x))

series143.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ y (/ 1.0 (* x 9.0)))
16.0ms	(/ 1.0 (* x 9.0))
63.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
37.0ms	(* 3.0 (sqrt x))

simplify73.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (62.0ms)

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

prune239.0ms

Pruning

11 alts after pruning (11 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))
0.2b	(/ 1.0 (* x 9.0))
0.3b	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

rewrite203.0ms

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)))
90.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
3.0ms	(/ 1.0 (* x 9.0))
97.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ 1.0 (* x 9.0)))
59.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
16.0ms	(/ 1.0 (* x 9.0))
64.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

simplify81.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (61.0ms)

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

prune265.0ms

Pruning

11 alts after pruning (10 fresh and 1 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	(/ (/ 1.0 x) 9.0)
0.3b	(* 3.0 (* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0)))

rewrite647.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 230

Calls

4 calls:

17.0ms	(+ y (/ (/ 1.0 x) 9.0))
317.0ms	(* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
6.0ms	(/ (/ 1.0 x) 9.0)
296.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0)))

series165.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ y (/ (/ 1.0 x) 9.0))
58.0ms	(* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
16.0ms	(/ (/ 1.0 x) 9.0)
66.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0)))

simplify105.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	856	2770
1	3565	2116
2	5002	2110

prune391.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
41×	`add-exp-log`
36×	`pow1`
35×	`add-sqr-sqrt`
28×	`add-cbrt-cube`
25×	`add-cube-cbrt`
24×	`prod-diff`
23×	`prod-exp` `cbrt-unprod`
22×	`pow-prod-down`
15×	`distribute-rgt-in` `distribute-lft-in`
13×	`associate-r`
8×	`associate-l`
7×	`distribute-lft-out`
5×	`cbrt-prod` `sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`times-frac` `-commutative` `associate-/l`
2×	`cbrt-undiv` `sub-neg` `associate-*r/` `div-exp` `associate--l+` `distribute-lft-out--`
1×	`flip3--` `frac-2neg` `clear-num` `associate-/r*` `flip--` `div-inv` `difference-of-squares`

Counts

4 → 140

Calls

4 calls:

3.0ms	(/ 1.0 (* x 9.0))
137.0ms	(* (* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
21.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x)))
6.0ms	(* (cbrt 3.0) (sqrt x))

series253.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1.0 (* x 9.0))
97.0ms	(* (* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
77.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x)))
63.0ms	(* (cbrt 3.0) (sqrt x))

simplify106.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	714	1970
1	3792	1353
2	5002	1284

prune259.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes68.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	7
1	16	7

end0.0ms

sample816.0ms

Algorithm

intervals

Results

274.0ms	8626×	body	80	nan
271.0ms	8568×	body	80	valid