Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	195×	body	80	valid
2.0ms	25×	body	640	valid
2.0ms	14×	body	1280	valid
1.0ms	15×	body	320	valid
0.0ms	7×	body	160	valid

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	74	5
3	128	5
4	252	5
5	374	5
6	514	5
7	642	5
8	777	5
9	1010	5
10	1686	5
11	5001	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: 21.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
1.4b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
7.1b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

6.0ms	(* (- 1.0 x) y)
6.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series137.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(* (- 1.0 x) y)
66.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
40.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	338	401
1	1456	359
2	5001	359

prune128.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 0.1b

Counts

73 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 x) y)
0.0b	(/ 1 (+ y 1.0))
3.3b	(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
7.1b	(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
32×	`add-exp-log`
27×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
8×	`associate-*l/`
7×	`cbrt-unprod` `distribute-lft-out`
6×	`div-exp` `associate-l` `add-log-exp`
4×	`flip3--` `pow-prod-down` `associate-/r*` `associate-/r/` `flip--`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*`
2×	`frac-times` `flip3-+` `*-commutative` `flip-+` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-*r/` `clear-num` `un-div-inv` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

6.0ms	(* (- 1.0 x) y)
5.0ms	(/ 1 (+ y 1.0))
2.0ms	(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
15.0ms	(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (- 1.0 x) y)
21.0ms	(/ 1 (+ y 1.0))
64.0ms	(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
40.0ms	(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	509	737
1	2631	636
2	5001	599

prune179.0ms

Filtered

130 candidates to 74 candidates (56.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	130	4	134

Merged error: 0.1b

Counts

134 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 x) y)
0.1b	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
3.3b	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
16.7b	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

6.0ms	(* (- 1.0 x) y)
13.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
3.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
9.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (- 1.0 x) y)
71.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
146.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
82.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

simplify80.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	567	1027
1	3078	900
2	5001	900

prune208.0ms

Filtered

117 candidates to 82 candidates (70.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	117	4	121

Merged error: 0.1b

Counts

121 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

7.1b	(/ (* (- 1.0 x) y) (+ y 1.0))
7.1b	(/ (* (- 1.0 x) y) (+ y 1.0))
7.1b	(/ (* (- 1.0 x) y) (+ y 1.0))
12.6b	(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ (/ (* (- 1.0 x) y) (+ y 1.0)) 1.0)) (* 1.0 1.0)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

136×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
87×	`times-frac`
64×	`difference-of-squares`
48×	`unpow-prod-down` `cube-prod`
40×	`add-cube-cbrt`
32×	`sqr-pow`
28×	`associate-/l*`
21×	`add-exp-log` `add-cbrt-cube`
20×	`distribute-lft-out--`
15×	`associate-/r*`
8×	`associate-/r/` `associate-/l/`
7×	`cbrt-undiv` `div-exp`
6×	`associate-*l/` `distribute-lft-out`
4×	`pow1` `difference-cubes` `flip3--` `frac-2neg` `flip3-+` `clear-num` `flip--` `flip-+` `div-inv` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
1×	`div-sub`

Counts

4 → 201

Calls

4 calls:

8.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
8.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
11.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
40.0ms	(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ (/ (* (- 1.0 x) y) (+ y 1.0)) 1.0)) (* 1.0 1.0)))

series716.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
42.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
40.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
592.0ms	(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ (/ (* (- 1.0 x) y) (+ y 1.0)) 1.0)) (* 1.0 1.0)))

simplify117.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	660	4788
1	2954	4635
2	5002	4633

prune506.0ms

Filtered

213 candidates to 135 candidates (63.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	213	4	217

Merged error: 0.1b

Counts

217 → 4

regimes161.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 22.3b

bsearch76.0ms

Steps

Iters	Range		Point
9	584.9517338353374	10938932741.588787	126650157.27148113
10	-8893382635004147.0	-205992.06318510068	-142537258.2159406

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	11
1	31	11

end0.0ms

sample445.0ms

Algorithm

intervals

Results

157.0ms	6114×	body	80	valid
65.0ms	739×	body	640	valid
48.0ms	372×	body	1280	valid
33.0ms	482×	body	320	valid
13.0ms	293×	body	160	valid