Details

sample24.0ms

Algorithm

intervals

Results

10.0ms

301×

body

valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	4
1	29	4
2	56	4
3	86	4
4	118	4
5	145	4
6	156	4
7	166	4
8	167	4
9	171	4
10	175	4
11	286	4
12	324	4
13	350	4
14	448	4
15	517	4
16	599	4
17	705	4
18	799	4
19	808	4
20	808	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (- y z))
9.0b	(/ (* x (- y z)) (- t z))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 77

Calls

2 calls:

26.0ms	(* x (- y z))
28.0ms	(/ (* x (- y z)) (- t z))

series115.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(* x (- y z))
72.0ms	(/ (* x (- y z)) (- t z))

simplify50.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	346	543
1	1624	380
2	5001	380

prune147.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- y z))
2.4b	(/ x (/ (- t z) (- y z)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
194×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
11×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l*`
6×	`flip3--` `flip--` `div-inv`
4×	`cbrt-undiv` `div-exp`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`div-sub`

Counts

2 → 198

Calls

2 calls:

24.0ms	(/ (- t z) (- y z))
28.0ms	(/ x (/ (- t z) (- y z)))

series442.0ms

Counts

2 → 6

Calls

2 calls:

283.0ms	(/ (- t z) (- y z))
159.0ms	(/ x (/ (- t z) (- y z)))

simplify79.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	642	1801
1	2887	1748
2	5001	1745

prune452.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (* (cbrt x) (cbrt x)) (* (cbrt (/ (- t z) (- y z))) (cbrt (/ (- t z) (- y z)))))
3.1b	(cbrt (/ (- t z) (- y z)))
3.1b	(cbrt (/ (- t z) (- y z)))
3.1b	(cbrt (/ (- t z) (- y z)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
76×	`times-frac`
37×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
9×	`associate-/r/`
8×	`add-cbrt-cube`
7×	`cbrt-div`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 152

Calls

4 calls:

37.0ms	(/ (* (cbrt x) (cbrt x)) (* (cbrt (/ (- t z) (- y z))) (cbrt (/ (- t z) (- y z)))))
9.0ms	(cbrt (/ (- t z) (- y z)))
10.0ms	(cbrt (/ (- t z) (- y z)))
12.0ms	(cbrt (/ (- t z) (- y z)))

series1.3s

Counts

4 → 12

Calls

4 calls:

344.0ms	(/ (* (cbrt x) (cbrt x)) (* (cbrt (/ (- t z) (- y z))) (cbrt (/ (- t z) (- y z)))))
337.0ms	(cbrt (/ (- t z) (- y z)))
331.0ms	(cbrt (/ (- t z) (- y z)))
332.0ms	(cbrt (/ (- t z) (- y z)))

simplify56.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	522	1804
1	1447	1672
2	5001	1645

prune595.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

1.3b	(+ (* x y) (* x (- z)))
9.0b	(/ (+ (* x y) (* x (- z))) (- t z))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`times-frac`
13×	`add-cube-cbrt`
7×	`distribute-lft-out`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `distribute-rgt-neg-out` `add-cbrt-cube` `associate-/l*` `add-log-exp`
2×	`pow1` `expm1-log1p-u` `flip3-+` `div-sub` `unsub-neg` `associate-/r/` `flip-+` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `flip3--` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 66

Calls

2 calls:

11.0ms	(+ (* x y) (* x (- z)))
32.0ms	(/ (+ (* x y) (* x (- z))) (- t z))

series117.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(+ (* x y) (* x (- z)))
72.0ms	(/ (+ (* x y) (* x (- z))) (- t z))

simplify43.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	269	589
1	1062	522
2	5001	515

prune171.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes127.0ms

Accuracy

-3.1% (2.2b remaining)

Error of 2.2b against oracle of 0.0b and baseline of 2.1b

bsearch42.0ms

Steps

Iters	Range		Point
7	3.963744232080374e-98	2.6474833247400647e-96	6.64621136584563e-98
3	-3.178892914518939e-19	-2.4145172411293186e-19	-2.4622907207161703e-19

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	10
1	31	10
2	32	10
3	32	10

end0.0ms

sample525.0ms

Algorithm

intervals

Results

222.0ms

8727×

body

valid

Iter	Nodes	Cost
0	14	4
1	29	4
2	56	4
3	86	4
4	118	4
5	145	4
6	156	4
7	166	4
8	167	4
9	171	4
10	175	4
11	286	4
12	324	4
13	350	4
14	448	4
15	517	4
16	599	4
17	705	4
18	799	4
19	808	4
20	808	4

Iter	Nodes	Cost
0	14	4
1	29	4
2	56	4
3	86	4
4	118	4
5	145	4
6	156	4
7	166	4
8	167	4
9	171	4
10	175	4
11	286	4
12	324	4
13	350	4
14	448	4
15	517	4
16	599	4
17	705	4
18	799	4
19	808	4
20	808	4

Iter	Nodes	Cost
0	14	4
1	29	4
2	56	4
3	86	4
4	118	4
5	145	4
6	156	4
7	166	4
8	167	4
9	171	4
10	175	4
11	286	4
12	324	4
13	350	4
14	448	4
15	517	4
16	599	4
17	705	4
18	799	4
19	808	4
20	808	4