Details

analyze935.0ms

Algorithm: search

sample29.0ms

Algorithm

intervals

Results

8.0ms	202×	body	80	valid
3.0ms	22×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	26×	body	80	invalid
1.0ms	9×	body	160	valid
0.0ms	1×	body	2560	valid

simplify121.0ms

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

prune4.0ms

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: 18.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.8b	(- (+ x y) (/ (* (- z t) y) (- a t)))
11.1b	(/ (* (- z t) y) (- a t))

rewrite29.0ms

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:

9.0ms	(* (- z t) y)
9.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
8.0ms	(/ (* (- z t) y) (- a t))

series55.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(* (- z t) y)
33.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
16.0ms	(/ (* (- z t) y) (- a t))

simplify46.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (10.0ms)

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

prune122.0ms

Filtered

56 candidates to 79 candidates (-41.1%)

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: 4.0b

Counts

80 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
3.7b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
9.6b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite45.0ms

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))
28.0ms	(* (/ (- 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)))))

series110.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt (- a t))
25.0ms	(cbrt (- a t))
21.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
36.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (70.0ms)

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

prune182.0ms

Filtered

104 candidates to 139 candidates (-33.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	137	11	148

Merged error: 4.0b

Counts

148 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

6.0b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
6.0b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
6.0b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
10.6b	(- (+ 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)))))))

rewrite90.0ms

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	(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)))))
17.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
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)))))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
79.0ms	(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)))))
42.0ms	(- (+ 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)))))))

simplify152.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (80.0ms)

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

prune202.0ms

Filtered

95 candidates to 188 candidates (-97.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	186	13	199

Merged error: 4.0b

Counts

199 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

4.5b	(cbrt (/ y (cbrt (- a t))))
4.5b	(cbrt (/ y (cbrt (- a t))))
4.5b	(cbrt (/ y (cbrt (- a t))))
10.3b	(- (+ 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))))))

rewrite35.0ms

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))))))

series190.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(cbrt (/ y (cbrt (- a t))))
50.0ms	(cbrt (/ y (cbrt (- a t))))
48.0ms	(cbrt (/ y (cbrt (- a t))))
45.0ms	(- (+ 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))))))

simplify93.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (62.0ms)

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

prune196.0ms

Filtered

137 candidates to 173 candidates (-26.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	171	15	186

Merged error: 4.0b

Counts

186 → 15

regimes732.0ms

Accuracy

4.5% (7.5b remaining)

Error of 11.3b against oracle of 3.8b and baseline of 11.7b

bsearch6.1s

Steps

Iters	Range		Point
8	4.144950304121691e+57	3.672231635540882e+60	4.2051587456830085e+57
9	3.7108087093817167e-69	1.16390569274791e-63	2.0626164423737537e-64
6	2.0809958058644447e-175	1.115334185111597e-174	3.138337039432787e-175
10	-4.6010237129477126e-188	-3.684905956547746e-204	-1.307643700899874e-192
8	-9.539627097232579e+29	-2.026524974383915e+25	-4.6223666241838157e+27

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	34
1	44	34

end0.0ms

analyze923.0ms

Algorithm: search

sample749.0ms

Algorithm

intervals

Results

266.0ms	6624×	body	80	valid
72.0ms	489×	body	640	valid
46.0ms	401×	body	320	valid
43.0ms	244×	body	1280	valid
29.0ms	698×	body	80	invalid
16.0ms	231×	body	160	valid
2.0ms	11×	body	2560	valid

Details

analyze935.0ms

sample29.0ms

simplify121.0ms

prune4.0ms

localize9.0ms

rewrite29.0ms

series55.0ms

simplify46.0ms

prune122.0ms

localize12.0ms

rewrite45.0ms

series110.0ms

simplify85.0ms

prune182.0ms

localize23.0ms

rewrite90.0ms

series285.0ms

simplify152.0ms

prune202.0ms

localize20.0ms

rewrite35.0ms

series190.0ms

simplify93.0ms

prune196.0ms

regimes732.0ms

bsearch6.1s

simplify2.0ms

end0.0ms

analyze923.0ms

sample749.0ms

Profiling