Details

sample2.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.531006%

Guaranteed chance to sample good point: 40.633245%

Results

8.0ms	205×	body	80	valid
3.0ms	19×	body	640	valid
2.0ms	11×	body	1280	valid
1.0ms	34×	body	80	invalid
1.0ms	12×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	2560	valid

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1498	6
6	3410	6
7	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: 26.2b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
1.7b	(+ x (/ (* (- y z) (- t x)) (- a z)))
20.4b	(/ (* (- y z) (- t x)) (- a z))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

8.0ms	(* (- y z) (- t x))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
11.0ms	(/ (* (- y z) (- t x)) (- a z))

series94.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
50.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
34.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	466	583
1	2158	534
2	5001	534

prune139.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	10	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 5.6b

Counts

91 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.8b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
37.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a z))
26.0ms	(cbrt (- a z))
57.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
54.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	752	1839
1	3320	1671
2	5001	1580

prune377.0ms

Filtered

104 candidates to 146 candidates (-40.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	138	8	146
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	139	17	156

Merged error: 5.5b

Counts

156 → 17

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
10.2b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

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

series131.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a z))
27.0ms	(cbrt (- a z))
26.0ms	(cbrt (- a z))
53.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify35.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	272	837
1	850	765
2	5001	735

prune166.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	14	15
Picked	0	1	1
Done	0	1	1
Total	68	17	85

Merged error: 5.5b

Counts

85 → 17

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.8b	(* (/ (- y z) (* (cbrt (- a z)) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))) (/ (- t x) (cbrt (- a z))))
8.8b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))) (/ (- t x) (cbrt (- a z)))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

384×	`cbrt-div`
137×	`frac-times`
111×	`flip3--` `flip--`
89×	`associate-l`
82×	`associate-/r/`
67×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
51×	`associate-*r/`
49×	`add-exp-log`
47×	`times-frac`
46×	`associate-r`
45×	`associate-*l/`
36×	`cbrt-prod`
30×	`add-cbrt-cube`
27×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
16×	`distribute-lft-out--` `difference-of-squares`
13×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
3×	`unswap-sqr`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 211

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
92.0ms	(* (/ (- y z) (* (cbrt (- a z)) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))) (/ (- t x) (cbrt (- a z)))))

series165.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a z))
28.0ms	(cbrt (- a z))
56.0ms	(* (/ (- y z) (* (cbrt (- a z)) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))) (/ (- t x) (cbrt (- a z))))
55.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))) (/ (- t x) (cbrt (- a z)))))

simplify148.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1148	4504
1	4995	3581
2	5002	3581

prune358.0ms

Filtered

189 candidates to 223 candidates (-18.0%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	14	14
Picked	0	1	1
Done	0	2	2
Total	223	17	240

Merged error: 5.5b

Counts

240 → 17

regimes831.0ms

Accuracy

6.9% (7.6b remaining)

Error of 12.0b against oracle of 4.4b and baseline of 12.5b

bsearch144.0ms

Steps

Iters	Range		Point
10	4.46830498014735e-98	5.053839626649171e-86	1.3001505304057336e-97
10	3.1365059177324255e-215	9.490614439504917e-197	3.206105607853923e-215
7	4.063852638501255e-265	8.470277452457338e-263	8.279345736877767e-263
10	-3.517169278918287e-115	-1.33535267852067e-130	-4.81935027695448e-119

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	63
1	56	63

end0.0ms

sample3.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.531006%

Guaranteed chance to sample good point: 40.633245%

Results

273.0ms	6524×	body	80	valid
81.0ms	529×	body	640	valid
55.0ms	276×	body	1280	valid
50.0ms	1170×	body	80	invalid
44.0ms	395×	body	320	valid
24.0ms	255×	body	160	valid
5.0ms	21×	body	2560	valid

Details

sample2.7s

simplify65.0ms

prune4.0ms

localize9.0ms

rewrite32.0ms

series94.0ms

simplify52.0ms

prune139.0ms

localize14.0ms

rewrite52.0ms

series164.0ms

simplify88.0ms

prune377.0ms

localize23.0ms

rewrite13.0ms

series131.0ms

simplify35.0ms

prune166.0ms

localize25.0ms

rewrite123.0ms

series165.0ms

simplify148.0ms

prune358.0ms

regimes831.0ms

bsearch144.0ms

simplify2.0ms

end0.0ms

sample3.7s

Profiling