Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify109.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	10
1	71	10
2	184	10
3	381	10
4	682	10
5	1102	10
6	2122	10
7	4337	10
8	5001	10

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 26.0b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.4b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
1.5b	(+ (* (+ x y) z) (* (+ t y) a))
24.4b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

684×	`*-un-lft-identity`
304×	`distribute-lft-out`
254×	`associate-l`
140×	`distribute-lft-out--`
125×	`times-frac`
75×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
25×	`associate-/l*`
14×	`difference-of-squares`
11×	`add-log-exp`
10×	`associate-*l/`
8×	`add-exp-log` `add-cbrt-cube` `unswap-sqr`
7×	`flip3-+` `flip-+`
6×	`pow1`
5×	`associate-/r*`
4×	`frac-add`
3×	`associate-r`
2×	`+-commutative` `flip3--` `diff-log` `associate--l+` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 254

Calls

4 calls:

9.0ms	(* (+ x y) z)
30.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
19.0ms	(+ (* (+ x y) z) (* (+ t y) a))
48.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series860.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (+ x y) z)
108.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
49.0ms	(+ (* (+ x y) z) (* (+ t y) a))
673.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify93.0ms

Algorithm

egg-herbie

Counts

266 → 266

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	559	3069
1	2328	3005
2	5001	3005

prune296.0ms

Filtered

266 candidates to 85 candidates (68.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	256	10	266
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	257	10	267

Merged error: 5.8b

Counts

267 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))))
1.4b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
1.5b	(+ (* (+ x y) z) (* (+ t y) a))
24.4b	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

2919×	`*-un-lft-identity`
1239×	`distribute-lft-out`
1018×	`times-frac`
964×	`associate-l`
560×	`distribute-lft-out--`
434×	`add-sqr-sqrt`
294×	`add-cube-cbrt`
181×	`associate-/r*`
56×	`difference-of-squares`
45×	`associate-/r/`
28×	`unswap-sqr`
17×	`add-exp-log`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-log-exp`
8×	`div-exp` `associate-*l/`
7×	`flip3-+` `flip-+`
6×	`flip3--` `flip--` `div-inv`
5×	`pow1`
4×	`cbrt-undiv` `frac-add` `clear-num` `associate-/l/` `remove-double-div`
3×	`frac-2neg`
2×	`+-commutative` `rec-exp` `diff-log` `1-exp` `associate--l+` `sum-log`
1×	`sub-neg` `pow-flip` `inv-pow`

Counts

4 → 818

Calls

4 calls:

66.0ms	(/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))))
33.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
19.0ms	(+ (* (+ x y) z) (* (+ t y) a))
41.0ms	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

series946.0ms

Counts

4 → 12

Calls

4 calls:

662.0ms	(/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))))
111.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
50.0ms	(+ (* (+ x y) z) (* (+ t y) a))
123.0ms	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

simplify201.0ms

Algorithm

egg-herbie

Counts

830 → 830

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	829	11087
1	4058	10434
2	5001	9772

prune402.0ms

Filtered

830 candidates to 125 candidates (84.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	827	3	830
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	830	10	840

Merged error: 3.6b

Counts

840 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
1.4b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
1.5b	(+ (* (+ x y) z) (* (+ t y) a))
24.4b	(* (/ 1 (+ (+ x t) y)) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

245×	`*-un-lft-identity`
105×	`distribute-lft-out`
101×	`associate-l`
47×	`add-sqr-sqrt`
40×	`distribute-lft-out--`
32×	`times-frac`
30×	`add-cube-cbrt`
25×	`associate-r`
22×	`frac-times`
20×	`associate-/r*`
19×	`associate-*l/`
17×	`add-exp-log`
13×	`flip3--` `flip--`
12×	`associate-/l*`
11×	`add-cbrt-cube` `add-log-exp`
7×	`pow1` `flip3-+` `flip-+`
6×	`associate--l+`
5×	`unswap-sqr`
4×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `frac-add` `prod-exp` `clear-num` `associate-/r/` `difference-of-squares`
3×	`sub-neg`
2×	`cbrt-undiv` `rec-exp` `diff-log` `1-exp` `associate-*r/` `sum-log` `cbrt-unprod` `div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 209

Calls

4 calls:

7.0ms	(/ 1 (+ (+ x t) y))
33.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
18.0ms	(+ (* (+ x y) z) (* (+ t y) a))
56.0ms	(* (/ 1 (+ (+ x t) y)) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

series865.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1 (+ (+ x t) y))
113.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
48.0ms	(+ (* (+ x y) z) (* (+ t y) a))
647.0ms	(* (/ 1 (+ (+ x t) y)) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

simplify124.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	797	2430
1	4041	2281
2	5001	2227

prune313.0ms

Filtered

221 candidates to 98 candidates (55.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	221	10	231

Merged error: 3.6b

Counts

231 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
0.4b	(- (* (+ x y) z) (* y b))
14.3b	(/ (* a (+ t y)) (+ (+ x t) y))
16.4b	(/ (- (* (+ x y) z) (* y b)) (+ (+ x t) y))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

310×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
130×	`times-frac`
105×	`distribute-lft-out`
71×	`associate-l`
58×	`add-cube-cbrt`
42×	`distribute-lft-out--`
35×	`unswap-sqr`
28×	`difference-of-squares`
27×	`associate-r`
26×	`associate-/l*`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
7×	`*-commutative`
6×	`pow1` `add-log-exp`
4×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
3×	`cbrt-undiv` `div-exp`
2×	`flip3--` `frac-2neg` `associate-r/` `associate-l/` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv`
1×	`sub-neg` `diff-log` `div-sub` `pow-prod-down`

Counts

4 → 244

Calls

4 calls:

6.0ms	(* (+ x y) z)
16.0ms	(- (* (+ x y) z) (* y b))
21.0ms	(/ (* a (+ t y)) (+ (+ x t) y))
25.0ms	(/ (- (* (+ x y) z) (* y b)) (+ (+ x t) y))

series337.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (+ x y) z)
33.0ms	(- (* (+ x y) z) (* y b))
65.0ms	(/ (* a (+ t y)) (+ (+ x t) y))
209.0ms	(/ (- (* (+ x y) z) (* y b)) (+ (+ x t) y))

simplify104.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	702	2388
1	2991	2307
2	5003	2307

prune410.0ms

Filtered

256 candidates to 131 candidates (48.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	251	5	256
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	254	12	266

Merged error: 2.1b

Counts

266 → 12

regimes477.0ms

Accuracy

41.5% (9.2b remaining)

Error of 12.6b against oracle of 3.3b and baseline of 19.1b

bsearch122.0ms

Steps

Iters	Range		Point
9	3.637078954097819e+62	2.970289645651054e+69	2.6574689117362167e+63
9	-2.3839202753352175e+214	-1.8812003113546087e+207	-1.9701480721904167e+207

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	16
1	45	16
2	45	16

end0.0ms

sample654.0ms

Algorithm

intervals

Results

373.0ms	7997×	body	80	valid
0.0ms	2×	body	640	valid
0.0ms	1×	body	1280	valid