Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	289×	body	80	nan
8.0ms	277×	body	80	valid

simplify117.0ms

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: 0.4b

localize12.0ms

Local error

Found 3 expressions with local error:

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))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 102

Calls

3 calls:

83.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
4.0ms	(* 3.0 (sqrt x))
3.0ms	(/ 1.0 (* x 9.0))

series119.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
37.0ms	(* 3.0 (sqrt x))
16.0ms	(/ 1.0 (* x 9.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	539	1055
1	2716	802
2	5001	796

prune201.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

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)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
75×	`distribute-rgt-in` `distribute-lft-in`
72×	`prod-diff`
57×	`add-sqr-sqrt`
51×	`add-cube-cbrt`
19×	`distribute-lft-out`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
7×	`associate-r`
6×	`sub-neg` `associate-*r/` `associate--l+`
5×	`prod-exp` `cbrt-unprod`
4×	`pow-prod-down` `sqrt-prod`
3×	`expm1-log1p-u` `times-frac` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`cbrt-undiv` `flip3--` `div-exp` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `difference-of-squares`

Counts

3 → 164

Calls

3 calls:

94.0ms	(* (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)))

series140.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
16.0ms	(/ 1.0 (* x 9.0))
67.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	578	2329
1	2493	1678
2	5001	1672

prune224.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (sqrt x))
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))))

rewrite36.0ms

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` `expm1-log1p-u` `sqrt-div` `div-exp` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 136

Calls

4 calls:

5.0ms	(* 3.0 (sqrt x))
3.0ms	(/ 1.0 (* x 9.0))
3.0ms	(/ 1.0 (* x 9.0))
20.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 3.0 (sqrt x))
15.0ms	(/ 1.0 (* x 9.0))
15.0ms	(/ 1.0 (* x 9.0))
56.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

simplify58.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	384	624
1	1873	540
2	5001	527

prune364.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* (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	(/ 1.0 (* x 9.0))
0.4b	(* (cbrt 3.0) (sqrt x))

rewrite178.0ms

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:

143.0ms	(* (* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
19.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x)))
3.0ms	(/ 1.0 (* x 9.0))
6.0ms	(* (cbrt 3.0) (sqrt x))

series271.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
82.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (sqrt x)))
16.0ms	(/ 1.0 (* x 9.0))
71.0ms	(* (cbrt 3.0) (sqrt x))

simplify110.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	714	1970
1	3790	1353
2	5001	1284

prune297.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes89.0ms

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

sample787.0ms

Algorithm

intervals

Results

266.0ms	8540×	body	80	valid
259.0ms	8532×	body	80	nan