Details

sample56.0ms

Algorithm

intervals

Results

21.0ms	276×	body	80	nan
20.0ms	277×	body	80	valid

simplify140.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

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))

rewrite100.0ms

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

series167.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ y (/ 1.0 (* x 9.0)))
74.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
17.0ms	(/ 1.0 (* x 9.0))
47.0ms	(* 3.0 (sqrt x))

simplify89.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	594	1130
1	2888	878
2	5001	872

prune303.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))))

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:

3.0ms	(/ 1.0 (* x 9.0))
3.0ms	(/ 1.0 (* x 9.0))
5.0ms	(* 3.0 (sqrt x))
21.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1.0 (* x 9.0))
25.0ms	(/ 1.0 (* x 9.0))
40.0ms	(* 3.0 (sqrt x))
68.0ms	(* (sqrt (/ 1.0 (* x 9.0))) (sqrt (/ 1.0 (* x 9.0))))

simplify67.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (56.0ms)

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

prune417.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`add-cube-cbrt`
33×	`associate-r`
32×	`add-exp-log`
28×	`times-frac`
25×	`add-cbrt-cube`
18×	`prod-diff`
13×	`pow1`
12×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `cbrt-unprod`
11×	`cbrt-prod` `associate-l`
8×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `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 → 149

Calls

4 calls:

3.0ms	(+ y (* (/ (* (cbrt 1.0) (cbrt 1.0)) x) (/ (cbrt 1.0) 9.0)))
37.0ms	(* (* 3.0 (sqrt x)) (- (+ y (* (/ (* (cbrt 1.0) (cbrt 1.0)) x) (/ (cbrt 1.0) 9.0))) 1.0))
5.0ms	(* 3.0 (sqrt x))
24.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) x) (/ (cbrt 1.0) 9.0))

series571.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ y (* (/ (* (cbrt 1.0) (cbrt 1.0)) x) (/ (cbrt 1.0) 9.0)))
333.0ms	(* (* 3.0 (sqrt x)) (- (+ y (* (/ (* (cbrt 1.0) (cbrt 1.0)) x) (/ (cbrt 1.0) 9.0))) 1.0))
40.0ms	(* 3.0 (sqrt x))
117.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) x) (/ (cbrt 1.0) 9.0))

simplify133.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	888	1948
1	4703	1514
2	5001	1511

prune467.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (/ (pow (cbrt 1.0) 3) 9.0) x) y)
0.1b	(* 3.0 (- (+ (/ (/ (pow (cbrt 1.0) 3) 9.0) x) y) 1.0))
0.3b	(* (* 3.0 (- (+ (/ (/ (pow (cbrt 1.0) 3) 9.0) x) y) 1.0)) (sqrt x))
0.4b	(/ (/ (pow (cbrt 1.0) 3) 9.0) x)

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

726×	`times-frac`
397×	`*-un-lft-identity`
382×	`add-sqr-sqrt`
378×	`add-cube-cbrt`
178×	`fma-def`
126×	`cbrt-prod` `unpow-prod-down` `cube-prod`
58×	`associate-/l*`
24×	`prod-diff`
21×	`add-exp-log` `cube-mult` `unpow3` `sqr-pow`
16×	`add-cbrt-cube`
15×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-r`
11×	`pow1`
9×	`div-inv`
8×	`distribute-lft-out`
7×	`div-exp`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `sqrt-prod`
2×	`sub-neg` `flip3--` `associate-l/` `associate--l+` `-commutative` `flip--` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `sum-log` `flip-+` `associate-/l/` `difference-of-squares` `unswap-sqr`

Counts

4 → 526

Calls

4 calls:

136.0ms	(+ (/ (/ (pow (cbrt 1.0) 3) 9.0) x) y)
1.7s	(* 3.0 (- (+ (/ (/ (pow (cbrt 1.0) 3) 9.0) x) y) 1.0))
1.7s	(* (* 3.0 (- (+ (/ (/ (pow (cbrt 1.0) 3) 9.0) x) y) 1.0)) (sqrt x))
26.0ms	(/ (/ (pow (cbrt 1.0) 3) 9.0) x)

series166.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (/ (/ (pow (cbrt 1.0) 3) 9.0) x) y)
37.0ms	(* 3.0 (- (+ (/ (/ (pow (cbrt 1.0) 3) 9.0) x) y) 1.0))
69.0ms	(* (* 3.0 (- (+ (/ (/ (pow (cbrt 1.0) 3) 9.0) x) y) 1.0)) (sqrt x))
31.0ms	(/ (/ (pow (cbrt 1.0) 3) 9.0) x)

simplify80.0ms

Algorithm

egg-herbie

Counts

538 → 538

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1215	3272
1	5002	2965

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes102.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	16	7
1	16	7

end0.0ms

sample1.5s

Algorithm

intervals

Results

625.0ms	8543×	body	80	valid
570.0ms	8452×	body	80	nan