Details

sample17.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.537109%

Guaranteed chance to sample good point: 39.865611%

Results

9.0ms	215×	body	80	valid
2.0ms	16×	body	640	valid
2.0ms	9×	body	1280	valid
1.0ms	11×	body	320	valid
1.0ms	17×	body	80	invalid
0.0ms	5×	body	160	valid

simplify125.0ms

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

prune6.0ms

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: 15.5b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
1.5b	(- (+ x y) (/ (* (- z t) y) (- a t)))
10.5b	(/ (* (- z t) y) (- a t))

rewrite26.0ms

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))

series58.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(* (- z t) y)
36.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
16.0ms	(/ (* (- z t) y) (- a t))

simplify44.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (9.0ms)

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

prune120.0ms

Filtered

56 candidates to 79 candidates (-41.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	8	80

Merged error: 4.1b

Counts

80 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
4.4b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.2b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite50.0ms

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))
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)))))

series116.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a t))
29.0ms	(cbrt (- a t))
23.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
37.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	793	1744
1	3353	1585
2	5001	1502

prune187.0ms

Filtered

104 candidates to 139 candidates (-33.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	133	6	139
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	136	11	147

Merged error: 4.1b

Counts

147 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

7.1b	(- (+ x y) (* (* (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))))
7.5b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
7.5b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
7.5b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

297×	`cbrt-div`
261×	`frac-times`
153×	`associate-*l/`
129×	`associate-*r/`
126×	`frac-sub`
63×	`flip3-+` `flip-+`
9×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `pow1/3`
2×	`diff-log`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

4 → 176

Calls

4 calls:

18.0ms	(- (+ x y) (* (* (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))))
19.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
18.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
17.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (+ x y) (* (* (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))))
82.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
81.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
84.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify150.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	1758	9997
1	4205	9460
2	5001	9279

prune200.0ms

Filtered

95 candidates to 188 candidates (-97.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	187	12	199

Merged error: 4.1b

Counts

199 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

6.2b	(cbrt (/ y (cbrt (- a t))))
6.2b	(cbrt (/ y (cbrt (- a t))))
6.2b	(cbrt (/ y (cbrt (- a t))))
8.6b	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (/ y (cbrt (- a t))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

135×	`cbrt-prod`
72×	`times-frac`
67×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`cbrt-div`
49×	`add-cube-cbrt`
34×	`frac-times`
30×	`frac-sub`
26×	`associate-*l/`
22×	`associate-*r/`
15×	`flip3-+` `flip-+`
9×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`pow1/3` `div-inv`
2×	`diff-log`
1×	`sub-neg` `associate--l+` `sum-log`

Counts

4 → 161

Calls

4 calls:

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

series188.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(cbrt (/ y (cbrt (- a t))))
47.0ms	(cbrt (/ y (cbrt (- a t))))
50.0ms	(cbrt (/ y (cbrt (- a t))))
43.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (/ y (cbrt (- a t))))))

simplify87.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	850	3223
1	2739	3016
2	5001	2967

prune189.0ms

Filtered

137 candidates to 173 candidates (-26.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	173	12	185

Merged error: 4.1b

Counts

185 → 12

regimes547.0ms

Accuracy

19.1% (6.0b remaining)

Error of 10.4b against oracle of 4.4b and baseline of 11.8b

bsearch114.0ms

Steps

Iters	Range		Point
9	1.0754297813140411e+213	2.87351243641981e+219	8.78196241788829e+213
8	-6.856807993447167e+200	-1.7575969443267336e+197	-5.398458761476919e+199

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	43
1	34	43

end0.0ms

sample19.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.537109%

Guaranteed chance to sample good point: 39.865611%

Results

278.0ms	6604×	body	80	valid
73.0ms	482×	body	640	valid
49.0ms	253×	body	1280	valid
43.0ms	387×	body	320	valid
30.0ms	702×	body	80	invalid
20.0ms	258×	body	160	valid
4.0ms	16×	body	2560	valid

Details

sample17.6s

simplify125.0ms

prune6.0ms

localize9.0ms

rewrite26.0ms

series58.0ms

simplify44.0ms

prune120.0ms

localize13.0ms

rewrite50.0ms

series116.0ms

simplify91.0ms

prune187.0ms

localize21.0ms

rewrite89.0ms

series292.0ms

simplify150.0ms

prune200.0ms

localize18.0ms

rewrite38.0ms

series188.0ms

simplify87.0ms

prune189.0ms

regimes547.0ms

bsearch114.0ms

simplify2.0ms

end0.0ms

sample19.1s

Profiling