Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	60×	body	640	valid
4.0ms	136×	body	80	valid
3.0ms	33×	body	320	valid
2.0ms	15×	body	1280	valid
1.0ms	12×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7

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: 12.3b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b	(/ 1.0 (+ x 1.0))
3.5b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
16.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms	(/ 1.0 (+ x 1.0))
33.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1.0 (- x 1.0))
47.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
25.0ms	(/ 1.0 (+ x 1.0))
222.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5002	816

prune232.0ms

Filtered

126 candidates to 92 candidates (73.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	3	127

Merged error: 0.1b

Counts

127 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
3.0b	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
12.8b	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
18×	`times-frac`
16×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`associate-/r` `associate-/l`
4×	`pow1` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
2×	`frac-2neg` `flip3-+` `div-sub` `associate-*l/` `clear-num` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `associate-+l-` `sub-neg` `diff-log` `frac-add` `prod-exp` `sum-log` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 89

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
3.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
23.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
9.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

series608.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1.0 (- x 1.0))
41.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
476.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
64.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

simplify60.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	542	844
1	2119	764
2	5001	758

prune172.0ms

Filtered

101 candidates to 77 candidates (76.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	101	3	104

Merged error: 0.1b

Counts

104 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.1b	(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
6.4b	(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
14.6b	(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
13×	`flip3-+` `flip-+`
12×	`frac-times`
11×	`associate-/r/` `associate-/l/`
10×	`add-log-exp`
9×	`times-frac`
8×	`frac-add` `distribute-lft-out`
6×	`associate-*l/`
4×	`pow1` `cbrt-undiv` `add-sqr-sqrt` `add-cube-cbrt` `associate-+r+` `flip3--` `associate-*r/` `div-exp` `prod-exp` `flip--` `cbrt-unprod`
3×	`+-commutative` `sum-log`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`frac-2neg` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 88

Calls

4 calls:

16.0ms	(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
16.0ms	(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
10.0ms	(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
42.0ms	(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
40.0ms	(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
130.0ms	(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
323.0ms	(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	627	1549
1	3230	1162
2	5002	1152

prune212.0ms

Filtered

100 candidates to 78 candidates (78.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	99	4	103

Merged error: 0.0b

Counts

103 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
0.1b	(/ 1 (pow x 3))
0.3b	(/ 1 (pow x 5))
0.5b	(/ 1 (pow x 7))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
73×	`*-un-lft-identity`
63×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`unpow-prod-down`
31×	`add-exp-log`
26×	`associate-/r*`
18×	`div-exp`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
7×	`div-inv` `distribute-lft-out`
6×	`add-log-exp`
4×	`pow1` `cube-mult` `unpow3`
3×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `inv-pow`
1×	`+-commutative` `flip3-+` `frac-add` `sum-log` `flip-+`

Counts

4 → 198

Calls

4 calls:

45.0ms	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
5.0ms	(/ 1 (pow x 3))
5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 7))

series222.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
35.0ms	(/ 1 (pow x 3))
41.0ms	(/ 1 (pow x 5))
58.0ms	(/ 1 (pow x 7))

simplify59.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	469	961
1	2563	767
2	5001	767

prune247.0ms

Filtered

210 candidates to 82 candidates (39.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	211	3	214

Merged error: 0b

Counts

214 → 3

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 26.1b

bsearch107.0ms

Steps

Iters	Range		Point
9	2.1846438371975785e-05	719.5386143167987	114.93123855267724
10	-43540924890.08803	-0.0051836583041924315	-113.48504878618368

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	19
1	44	19

end0.0ms

sample637.0ms

Algorithm

intervals

Results

212.0ms	1894×	body	640	valid
132.0ms	4157×	body	80	valid
82.0ms	951×	body	320	valid
82.0ms	544×	body	1280	valid
32.0ms	458×	body	160	valid