Details

sample27.0ms

Algorithm

intervals

Results

9.0ms	247×	body	80	valid
1.0ms	8×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	10×	body	160	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	2560	valid

simplify118.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 12.6b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.5b	(- (+ x y) (/ (* (- z t) y) (- a t)))
10.0b	(/ (* (- z t) y) (- a t))

rewrite31.0ms

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)
14.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
9.0ms	(/ (* (- z t) y) (- a t))

series195.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(* (- z t) y)
110.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
58.0ms	(/ (* (- z t) y) (- a t))

simplify46.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (11.0ms)

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

prune215.0ms

Filtered

79 candidates to 56 candidates (70.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	64	15	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	15	80

Merged error: 4.0b

Counts

80 → 15

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
4.6b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
5.7b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
29.0ms	(* (/ (- 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)))))

series477.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt (- a t))
139.0ms	(cbrt (- a t))
93.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
109.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	785	1736
1	3321	1577
2	5002	1498

prune400.0ms

Filtered

139 candidates to 104 candidates (74.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	134	5	139
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	140	14	154

Merged error: 4.0b

Counts

154 → 14

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.9b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t))))))
5.9b	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
39×	`add-cbrt-cube`
36×	`cbrt-div`
32×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
19×	`frac-times`
17×	`add-sqr-sqrt` `associate-l`
16×	`associate-/r/`
15×	`associate-*l/`
14×	`frac-sub`
13×	`flip3--` `associate-r` `flip--`
11×	`-un-lft-identity` `associate-r/`
10×	`times-frac`
9×	`add-cube-cbrt` `add-log-exp`
7×	`flip3-+` `flip-+`
6×	`pow1` `cbrt-prod`
4×	`unswap-sqr`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 126

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
34.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t))))))
7.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

series786.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt y)
175.0ms	(cbrt y)
271.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t))))))
159.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1077	3236
1	5001	2555

prune569.0ms

Filtered

138 candidates to 104 candidates (75.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	137	15	152

Merged error: 4.0b

Counts

152 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

1.5b	(cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))
1.8b	(* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))
2.2b	(* (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))) (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t)))))
5.5b	(- (+ x y) (* (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))) (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

101×	`cbrt-div`
60×	`frac-times`
58×	`cbrt-prod` `add-sqr-sqrt`
43×	`times-frac`
38×	`associate-r/` `associate-l/`
34×	`*-un-lft-identity`
31×	`associate-r`
30×	`add-exp-log` `frac-sub`
24×	`add-cube-cbrt`
21×	`associate-l`
18×	`pow1` `associate-/r/`
15×	`flip3-+` `prod-exp` `add-cbrt-cube` `cbrt-unprod` `flip-+`
14×	`flip3--` `flip--`
9×	`pow-prod-down` `add-log-exp` `unswap-sqr`
5×	`distribute-lft-out--` `difference-of-squares`
3×	`cbrt-undiv` `div-exp` `div-inv`
2×	`diff-log` `*-commutative`
1×	`sub-neg` `pow1/3` `associate--l+` `sum-log`

Counts

4 → 186

Calls

4 calls:

12.0ms	(cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))
31.0ms	(* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))
42.0ms	(* (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))) (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t)))))
9.0ms	(- (+ x y) (* (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))) (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))))

series2.0s

Counts

4 → 12

Calls

4 calls:

349.0ms	(cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))
1.4s	(* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))
96.0ms	(* (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))) (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t)))))
114.0ms	(- (+ x y) (* (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))) (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))))

simplify158.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (122.0ms)

Iter	Nodes	Cost
0	1185	5216
1	4455	4527
2	5002	4344

prune611.0ms

Filtered

198 candidates to 135 candidates (68.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	195	3	198
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	198	15	213

Merged error: 4.0b

Counts

213 → 15

regimes455.0ms

Accuracy

41.6% (4.4b remaining)

Error of 8.2b against oracle of 3.9b and baseline of 11.3b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	78
1	47	78

end0.0ms

sample712.0ms

Algorithm

intervals

Results

283.0ms	7408×	body	80	valid
62.0ms	461×	body	640	valid
43.0ms	253×	body	1280	valid
42.0ms	376×	body	320	valid
18.0ms	255×	body	160	valid
3.0ms	13×	body	2560	valid