Details

analyze956.0ms

Algorithm: search

sample27.0ms

Algorithm

intervals

Results

8.0ms	219×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	9×	body	640	valid
1.0ms	18×	body	80	invalid
1.0ms	4×	body	1280	valid
1.0ms	8×	body	160	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: 13.1b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.7b	(- (+ x y) (/ (* (- z t) y) (- a t)))
8.0b	(/ (* (- 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)))
8.0ms	(/ (* (- z t) y) (- a t))

series59.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- z t) y)
34.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
15.0ms	(/ (* (- z t) y) (- a t))

simplify47.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (10.0ms)

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

prune139.0ms

Filtered

56 candidates to 79 candidates (-41.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	68	11	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	11	80

Merged error: 2.9b

Counts

80 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
3.5b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.1b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite48.0ms

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))
31.0ms	(* (/ (- 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)))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt (- a t))
26.0ms	(cbrt (- a t))
25.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
35.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify89.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (74.0ms)

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

prune191.0ms

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	3	7	10
Picked	1	0	1
Done	0	0	0
Total	139	11	150

Merged error: 2.9b

Counts

150 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
2.5b	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
3.4b	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

3.0ms	(cbrt (- z t))
3.0ms	(cbrt (- z t))
34.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
7.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

series112.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- z t))
29.0ms	(cbrt (- z t))
22.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))
36.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t))))))

simplify88.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	804	2507
1	3114	2079
2	5001	1921

prune161.0ms

Filtered

75 candidates to 132 candidates (-76.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	128	4	132
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	131	12	143

Merged error: 2.9b

Counts

143 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
7.0b	(- (+ x y) (* (- z t) (/ (/ (/ y (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t)))))
9.3b	(* (- z t) (/ (/ (/ y (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t))))

rewrite842.0ms

Algorithm

rewrite-expression-head

Rules

5458×	`times-frac`
3417×	`cbrt-prod`
3374×	`add-sqr-sqrt`
3310×	`*-un-lft-identity`
1974×	`associate-r`
1948×	`add-cube-cbrt`
681×	`distribute-lft-out--` `difference-of-squares`
150×	`cbrt-div`
146×	`associate-/r/`
82×	`flip3--` `flip--`
73×	`div-inv`
18×	`add-exp-log`
15×	`unswap-sqr`
12×	`add-cbrt-cube`
10×	`frac-sub`
9×	`add-log-exp`
6×	`pow1` `cbrt-undiv` `frac-times` `div-exp` `associate-*l/`
5×	`flip3-+` `associate-l` `flip-+`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-*r/`
2×	`pow1/3` `diff-log`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 2070

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
7.0ms	(- (+ x y) (* (- z t) (/ (/ (/ y (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t)))))
495.0ms	(* (- z t) (/ (/ (/ y (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t))))

series109.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- a t))
26.0ms	(cbrt (- a t))
41.0ms	(- (+ x y) (* (- z t) (/ (/ (/ y (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t)))))
16.0ms	(* (- z t) (/ (/ (/ y (cbrt (- a t))) (cbrt (- a t))) (cbrt (- a t))))

simplify319.0ms

Algorithm

egg-herbie

Counts

2082 → 2082

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5001	31189

prune1.9s

Filtered

1358 candidates to 2082 candidates (-53.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	2082	0	2082
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	2082	12	2094

Merged error: 2.9b

Counts

2094 → 12

regimes620.0ms

Accuracy

29.6% (5.6b remaining)

Error of 9.5b against oracle of 3.9b and baseline of 11.8b

bsearch3.3s

Steps

Iters	Range		Point
11	1.4046899159835096e-69	2.0685299388887008e-48	6.929415103858996e-69
10	-1.6459093104401388e-142	-1.0747978019208856e-154	-6.308714194995097e-146

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	32
1	38	32

end0.0ms

analyze1.2s

Algorithm: search

sample759.0ms

Algorithm

intervals

Results

273.0ms	6672×	body	80	valid
73.0ms	450×	body	640	valid
45.0ms	248×	body	1280	valid
45.0ms	370×	body	320	valid
32.0ms	707×	body	80	invalid
18.0ms	248×	body	160	valid
3.0ms	12×	body	2560	valid

Details

analyze956.0ms

sample27.0ms

simplify121.0ms

prune4.0ms

localize14.0ms

rewrite26.0ms

series59.0ms

simplify47.0ms

prune139.0ms

localize13.0ms

rewrite48.0ms

series113.0ms

simplify89.0ms

prune191.0ms

localize18.0ms

rewrite54.0ms

series112.0ms

simplify88.0ms

prune161.0ms

localize13.0ms

rewrite842.0ms

series109.0ms

simplify319.0ms

prune1.9s

regimes620.0ms

bsearch3.3s

simplify2.0ms

end0.0ms

analyze1.2s

sample759.0ms

Profiling