Details

sample104.0ms

Algorithm

intervals

Results

35.0ms	832×	body	80	nan
8.0ms	184×	body	80	valid
8.0ms	29×	body	640	valid
5.0ms	8×	body	1280	valid
4.0ms	20×	body	320	valid
2.0ms	16×	body	160	valid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	7
1	30	7
2	39	7
3	45	7
4	60	7
5	88	7
6	125	7
7	176	7
8	208	7
9	225	7
10	293	7
11	293	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
0.0b	(* z (log (- 1.0 y)))
0.3b	(* x (log y))
7.0b	(log (- 1.0 y))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
21×	`log-prod` `*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`pow1`
9×	`add-exp-log` `add-log-exp`
8×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `add-cbrt-cube`
6×	`associate-l`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`log-pow`
2×	`log-div` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-log-exp` `associate--l+` `sum-log`

Counts

4 → 86

Calls

4 calls:

38.0ms	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
16.0ms	(* z (log (- 1.0 y)))
8.0ms	(* x (log y))
5.0ms	(log (- 1.0 y))

series245.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
70.0ms	(* z (log (- 1.0 y)))
38.0ms	(* x (log y))
45.0ms	(log (- 1.0 y))

simplify44.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	436	628
1	1539	553
2	5002	530

prune248.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.0b	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.3b	(* x (log y))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `log-prod`
21×	`*-un-lft-identity`
16×	`distribute-rgt-in` `add-cube-cbrt` `distribute-lft-in`
13×	`associate--l+`
11×	`add-log-exp`
10×	`pow1` `associate-+r+` `associate-r`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-+l+` `associate-l`
5×	`sub-neg`
3×	`distribute-lft-out--`
2×	`flip3--` `diff-log` `associate-r/` `pow-prod-down` `prod-exp` `sum-log` `log-pow` `-commutative` `flip--` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `flip3-+` `flip-+`

Counts

4 → 101

Calls

4 calls:

40.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
16.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
60.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
8.0ms	(* x (log y))

series474.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
131.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
115.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
39.0ms	(* x (log y))

simplify56.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	435	1202
1	1650	1138
2	5002	1111

prune397.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt y) (cbrt y))
0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

10.0ms	(* (cbrt y) (cbrt y))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series747.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(* (cbrt y) (cbrt y))
175.0ms	(cbrt y)
183.0ms	(cbrt y)
190.0ms	(cbrt y)

simplify93.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	115	288
1	472	261
2	2959	238
3	5003	235

prune423.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (cbrt y)) x)
0.3b	(* x (log (* 1 (pow y 2/3))))
0.6b	(cbrt y)
5.9b	(pow y 2/3)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log`
8×	`associate-l` `add-cbrt-cube`
7×	`associate-r`
4×	`add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow` `log-pow`
2×	`log-prod` `pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `pow-to-exp` `pow-pow` `distribute-lft-in` `pow-exp` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

8.0ms	(* (log (cbrt y)) x)
21.0ms	(* x (log (* 1 (pow y 2/3))))
1.0ms	(cbrt y)
3.0ms	(pow y 2/3)

series562.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (log (cbrt y)) x)
87.0ms	(* x (log (* 1 (pow y 2/3))))
181.0ms	(cbrt y)
181.0ms	(pow y 2/3)

simplify41.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	248	327
1	1097	273
2	5001	260

prune412.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes217.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	19
1	41	19
2	41	19

end0.0ms

sample3.0s

Algorithm

intervals

Results

961.0ms	23996×	body	80	nan
254.0ms	5517×	body	80	valid
243.0ms	886×	body	640	valid
239.0ms	425×	body	1280	valid
124.0ms	754×	body	320	valid
47.0ms	448×	body	160	valid