Details

sample104.0ms

Algorithm

intervals

Results

41.0ms	797×	body	80	nan
11.0ms	196×	body	80	valid
8.0ms	26×	body	640	valid
5.0ms	7×	body	1280	valid
2.0ms	11×	body	320	valid
2.0ms	18×	body	160	valid

simplify127.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	9
1	49	9
2	118	9
3	256	9
4	533	9
5	1250	9
6	2637	9
7	4297	9
8	4573	9
9	4588	9
10	4588	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.1b	(* (- x 1.0) (log y))
5.4b	(log (- 1.0 y))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

9.0ms	(* (- z 1.0) (log (- 1.0 y)))
11.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
7.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series303.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (- z 1.0) (log (- 1.0 y)))
157.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
54.0ms	(* (- x 1.0) (log y))
45.0ms	(log (- 1.0 y))

simplify48.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	498	803
1	1805	714
2	5001	701

prune304.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.1b	(* (- x 1.0) (log y))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

13.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
13.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
11.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
7.0ms	(* (- x 1.0) (log y))

series521.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
240.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
152.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
61.0ms	(* (- x 1.0) (log y))

simplify120.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	888	2535
1	4674	2460
2	5001	2448

prune656.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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)

rewrite11.0ms

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:

6.0ms	(* (cbrt y) (cbrt y))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series738.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (cbrt y) (cbrt y))
175.0ms	(cbrt y)
180.0ms	(cbrt y)
177.0ms	(cbrt y)

simplify91.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (86.0ms)

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

prune429.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (- x 1.0) (log y))) (cbrt (* (- x 1.0) (log y))))
0.5b	(cbrt (* (- x 1.0) (log y)))
0.5b	(cbrt (* (- x 1.0) (log y)))
0.5b	(cbrt (* (- x 1.0) (log y)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*l/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3--` `pow1/3` `flip--`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`associate-*r/` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

7.0ms	(* (cbrt (* (- x 1.0) (log y))) (cbrt (* (- x 1.0) (log y))))
5.0ms	(cbrt (* (- x 1.0) (log y)))
5.0ms	(cbrt (* (- x 1.0) (log y)))
5.0ms	(cbrt (* (- x 1.0) (log y)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (cbrt (* (- x 1.0) (log y))) (cbrt (* (- x 1.0) (log y))))
104.0ms	(cbrt (* (- x 1.0) (log y)))
104.0ms	(cbrt (* (- x 1.0) (log y)))
105.0ms	(cbrt (* (- x 1.0) (log y)))

simplify40.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	350	996
1	1130	931
2	5002	893

prune459.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes251.0ms

Accuracy

0% (0.3b 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	35	23
1	35	23

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	24371×	body	80	nan
327.0ms	5863×	body	80	valid
235.0ms	765×	body	640	valid
167.0ms	274×	body	1280	valid
133.0ms	702×	body	320	valid
48.0ms	419×	body	160	valid