Details

sample13.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	25	5
3	26	5
4	26	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 0.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
6.4b	(/ y (+ 1.0 (/ (* x y) 2.0)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
13×	`times-frac`
11×	`add-cube-cbrt`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `associate-/r/` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out--`

Counts

2 → 48

Calls

2 calls:

9.0ms	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
6.0ms	(/ y (+ 1.0 (/ (* x y) 2.0)))

series99.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
62.0ms	(/ y (+ 1.0 (/ (* x y) 2.0)))

simplify165.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	268	432
1	956	411
2	4742	403
3	5001	403

prune102.0ms

Filtered

54 candidates to 40 candidates (74.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	3	55

Merged error: 0.0b

Counts

55 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0))))
0.2b	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
3.3b	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
16.2b	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log` `add-cbrt-cube`
39×	`add-sqr-sqrt`
37×	`times-frac`
32×	`*-un-lft-identity`
30×	`add-cube-cbrt`
25×	`associate-l`
17×	`prod-exp` `cbrt-unprod`
14×	`cbrt-undiv` `div-exp`
13×	`pow1`
12×	`associate-r`
8×	`difference-of-squares`
7×	`swap-sqr`
6×	`div-inv` `add-log-exp`
5×	`sub-neg` `flip3--` `flip--`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*` `associate-/r/` `associate--r+`
3×	`frac-times` `associate-r/` `associate-/l` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `-commutative`
1×	`pow2` `frac-2neg` `pow-plus` `diff-log` `clear-num` `pow-sqr` `pow-prod-up` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

3.0ms	(- x (* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0))))
10.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
5.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
13.0ms	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- x (* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0))))
36.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
53.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
118.0ms	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

simplify106.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	760	1884
1	4240	1661
2	5001	1651

prune314.0ms

Filtered

164 candidates to 111 candidates (67.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	163	4	167

Merged error: 0b

Counts

167 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (+ 1.0 (/ (* x y) 2.0))) (/ y (- 1.0 (/ (* x y) 2.0))))
0.3b	(/ 1 (+ 1.0 (/ (* x y) 2.0)))
6.4b	(/ y (- 1.0 (/ (* x y) 2.0)))
16.2b	(* (* (/ 1 (+ 1.0 (/ (* x y) 2.0))) (/ y (- 1.0 (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
64×	`add-exp-log`
61×	`times-frac`
41×	`add-cube-cbrt`
38×	`add-cbrt-cube`
26×	`associate-r`
25×	`prod-exp`
19×	`div-exp` `associate-l`
13×	`cbrt-unprod`
12×	`pow1`
10×	`cbrt-undiv` `frac-times`
9×	`associate-/r*`
8×	`associate-/r/` `distribute-lft-out--` `difference-of-squares`
7×	`associate-*l/` `distribute-lft-out`
6×	`flip3--` `associate-r/` `flip--` `associate-/l` `unswap-sqr`
5×	`rec-exp` `1-exp`
4×	`pow-prod-down` `div-inv` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`pow-flip` `inv-pow`

Counts

4 → 188

Calls

4 calls:

23.0ms	(* (/ 1 (+ 1.0 (/ (* x y) 2.0))) (/ y (- 1.0 (/ (* x y) 2.0))))
6.0ms	(/ 1 (+ 1.0 (/ (* x y) 2.0)))
6.0ms	(/ y (- 1.0 (/ (* x y) 2.0)))
19.0ms	(* (* (/ 1 (+ 1.0 (/ (* x y) 2.0))) (/ y (- 1.0 (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (/ 1 (+ 1.0 (/ (* x y) 2.0))) (/ y (- 1.0 (/ (* x y) 2.0))))
49.0ms	(/ 1 (+ 1.0 (/ (* x y) 2.0)))
67.0ms	(/ y (- 1.0 (/ (* x y) 2.0)))
57.0ms	(* (* (/ 1 (+ 1.0 (/ (* x y) 2.0))) (/ y (- 1.0 (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

simplify108.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	827	2328
1	4375	1983
2	5001	1957

prune362.0ms

Filtered

200 candidates to 125 candidates (62.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	200	4	204

Merged error: 0b

Counts

204 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ (* x y) 2.0) 3)
1.5b	(/ y (* (+ (* (pow 1.0 3) 1.0) (- (* (pow (/ (* x y) 2.0) 3) (/ (* x y) 2.0)))) 1))
16.2b	(* (* (/ y (* (+ (* (pow 1.0 3) 1.0) (- (* (pow (/ (* x y) 2.0) 3) (/ (* x y) 2.0)))) 1)) (+ (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))
21.2b	(* (/ y (* (+ (* (pow 1.0 3) 1.0) (- (* (pow (/ (* x y) 2.0) 3) (/ (* x y) 2.0)))) 1)) (+ (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log`
38×	`add-cbrt-cube`
20×	`prod-exp`
19×	`add-sqr-sqrt`
18×	`frac-times`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
14×	`cbrt-unprod`
13×	`associate-*l/`
12×	`pow1` `times-frac`
11×	`div-exp`
10×	`flip3-+` `associate-r/` `associate-l*` `flip-+`
8×	`cbrt-undiv` `associate-r`
7×	`unpow-prod-down` `cube-prod`
6×	`flip3--` `flip--`
4×	`pow-prod-down` `associate-/r/` `div-inv` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `1-exp` `pow-exp` `associate-/l*` `rem-cube-cbrt`
2×	`sub-neg` `*-commutative`
1×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `unpow3` `clear-num` `associate-/r*` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 142

Calls

4 calls:

5.0ms	(pow (/ (* x y) 2.0) 3)
9.0ms	(/ y (* (+ (* (pow 1.0 3) 1.0) (- (* (pow (/ (* x y) 2.0) 3) (/ (* x y) 2.0)))) 1))
18.0ms	(* (* (/ y (* (+ (* (pow 1.0 3) 1.0) (- (* (pow (/ (* x y) 2.0) 3) (/ (* x y) 2.0)))) 1)) (+ (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))
14.0ms	(* (/ y (* (+ (* (pow 1.0 3) 1.0) (- (* (pow (/ (* x y) 2.0) 3) (/ (* x y) 2.0)))) 1)) (+ (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(pow (/ (* x y) 2.0) 3)
62.0ms	(/ y (* (+ (* (pow 1.0 3) 1.0) (- (* (pow (/ (* x y) 2.0) 3) (/ (* x y) 2.0)))) 1))
173.0ms	(* (* (/ y (* (+ (* (pow 1.0 3) 1.0) (- (* (pow (/ (* x y) 2.0) 3) (/ (* x y) 2.0)))) 1)) (+ (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))
110.0ms	(* (/ y (* (+ (* (pow 1.0 3) 1.0) (- (* (pow (/ (* x y) 2.0) 3) (/ (* x y) 2.0)))) 1)) (+ (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))

simplify52.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	999	3004
1	5002	2219

prune469.0ms

Filtered

154 candidates to 108 candidates (70.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	154	4	158

Merged error: 0b

Counts

158 → 4

regimes80.0ms

Accuracy

91.1% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 8.3b

bsearch61.0ms

Steps

Iters	Range		Point
7	0.0014765281187882199	0.09117784756913819	0.08972597238176828
8	-2.9148937725967404e-17	-3.1158541889032954e-21	-2.843277202027643e-17

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	16
1	31	16

end0.0ms

sample348.0ms

Algorithm

intervals

Results

218.0ms	7998×	body	80	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	320	valid