Details

sample28.0ms

Algorithm

intervals

Results

9.0ms	242×	body	80	valid
2.0ms	13×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	2560	valid

simplify122.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	109	6
3	195	6
4	445	6
5	828	6
6	1434	6
7	2520	6
8	4830	6
9	5001	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 15.8b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.1b	(- (+ x y) (/ (* (- z t) y) (- a t)))
9.7b	(/ (* (- z t) y) (- a t))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-l` `associate-/r*` `distribute-lft-out--`
4×	`flip3--` `associate-*l/` `flip--` `difference-of-squares`
3×	`associate-r`
2×	`cbrt-undiv` `diff-log` `div-exp` `prod-exp` `associate-/r/` `frac-sub` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 70

Calls

3 calls:

6.0ms	(* (- z t) y)
10.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
9.0ms	(/ (* (- z t) y) (- a t))

series203.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(* (- z t) y)
110.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
62.0ms	(/ (* (- z t) y) (- a t))

simplify49.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	383	461
1	1704	422
2	5001	422

prune178.0ms

Filtered

79 candidates to 56 candidates (70.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	70	9	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	9	80

Merged error: 3.8b

Counts

80 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.6b	(* (cbrt (- a t)) (cbrt (- a t)))
3.4b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.7b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
50×	`cbrt-prod`
38×	`associate-r`
36×	`times-frac`
30×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
18×	`add-cbrt-cube`
15×	`flip3--` `flip--`
13×	`pow1`
11×	`frac-times` `distribute-lft-out--`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`prod-exp` `cbrt-unprod` `add-log-exp` `difference-of-squares`
7×	`cbrt-undiv` `pow1/3` `associate-r/` `div-exp` `associate-l/`
6×	`frac-sub`
3×	`flip3-+` `pow-prod-down` `flip-+`
2×	`diff-log` `pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`pow2` `sub-neg` `pow-plus` `associate--l+` `sum-log`

Counts

4 → 168

Calls

4 calls:

3.0ms	(cbrt (- a t))
10.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
32.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (- a t))
121.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
94.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
111.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify125.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	886	2068
1	4326	1890
2	5001	1779

prune455.0ms

Filtered

180 candidates to 125 candidates (69.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	174	6	180
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	175	14	189

Merged error: 3.7b

Counts

189 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.6b	(* (cbrt (- a t)) (cbrt (- a t)))
3.4b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
13.4b	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
50×	`cbrt-prod`
38×	`associate-r`
36×	`times-frac`
30×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
18×	`add-cbrt-cube`
15×	`flip3--` `flip--`
13×	`pow1`
11×	`distribute-lft-out--`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`frac-times` `prod-exp` `cbrt-unprod` `difference-of-squares`
7×	`cbrt-undiv` `pow1/3` `div-exp`
6×	`add-log-exp`
5×	`associate-r/` `associate-l/`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`pow2` `sub-neg` `pow-plus` `diff-log`

Counts

4 → 160

Calls

4 calls:

3.0ms	(cbrt (- a t))
11.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
29.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
3.0ms	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (- a t))
118.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
94.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
81.0ms	(- y (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify106.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	758	1856
1	3690	1686
2	5001	1571

prune499.0ms

Filtered

172 candidates to 118 candidates (68.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	173	13	186

Merged error: 3.7b

Counts

186 → 13

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
5.2b	(- y (pow (* (/ y (- a t)) (- z t)) 1))
11.4b	(* (/ y (- a t)) (- z t))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`distribute-lft-out--`
5×	`pow1` `flip3--` `associate-r` `associate-/r*` `flip--` `add-log-exp`
4×	`associate-/r/`
3×	`sub-neg` `associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-2neg` `diff-log` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `sqr-pow`

Counts

3 → 102

Calls

3 calls:

5.0ms	(/ y (- a t))
4.0ms	(- y (pow (* (/ y (- a t)) (- z t)) 1))
12.0ms	(* (/ y (- a t)) (- z t))

series289.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ y (- a t))
122.0ms	(- y (pow (* (/ y (- a t)) (- z t)) 1))
140.0ms	(* (/ y (- a t)) (- z t))

simplify48.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	404	653
1	1689	606
2	5001	605

prune232.0ms

Filtered

111 candidates to 81 candidates (73.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	111	13	124

Merged error: 3.7b

Counts

124 → 13

regimes306.0ms

Accuracy

3.1% (5.0b remaining)

Error of 8.9b against oracle of 3.9b and baseline of 9.0b

bsearch82.0ms

Steps

Iters	Range		Point
6	1.5217784360643389e-114	1.1322275647380475e-113	3.448929507451353e-114
10	-4.5953435074748267e+24	-13078662382.933744	-6.517989351601534e+19

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	19
1	34	19

end0.0ms

sample743.0ms

Algorithm

intervals

Results

286.0ms	7387×	body	80	valid
72.0ms	468×	body	640	valid
48.0ms	252×	body	1280	valid
46.0ms	374×	body	320	valid
17.0ms	240×	body	160	valid
3.0ms	16×	body	2560	valid