Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	53×	body	640	valid
5.0ms	144×	body	80	valid
3.0ms	20×	body	1280	valid
3.0ms	27×	body	320	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: 7.9b

Counts

2 → 1

localize11.0ms

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))
1.9b	(+ (- (/ 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))
17.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms	(/ 1.0 (+ x 1.0))
30.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1.0 (- x 1.0))
41.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
27.0ms	(/ 1.0 (+ x 1.0))
210.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (42.0ms)

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

prune210.0ms

Filtered

126 candidates to 92 candidates (73.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	125	2	127

Merged error: 0.0b

Counts

127 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ 2.0 x))
0.5b	(/ 1.0 (- (* x x) (* 1.0 1.0)))
5.9b	(+ (- (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
13.8b	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 128

Calls

4 calls:

13.0ms	(- (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ 2.0 x))
5.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
24.0ms	(+ (- (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
13.0ms	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0))

series446.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ 2.0 x))
48.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
274.0ms	(+ (- (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
51.0ms	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0))

simplify91.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	732	1554
1	3294	1469
2	5001	1467

prune265.0ms

Filtered

140 candidates to 109 candidates (77.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	140	2	142

Merged error: 0.0b

Counts

142 → 2

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 5))
0.1b	(/ 1 (pow x 3))
0.1b	(/ 1 (pow x 7))

rewrite68.0ms

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 5))
6.0ms	(/ 1 (pow x 3))
5.0ms	(/ 1 (pow x 7))

series220.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
45.0ms	(/ 1 (pow x 5))
30.0ms	(/ 1 (pow x 3))
56.0ms	(/ 1 (pow x 7))

simplify61.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	469	982
1	2563	788
2	5001	788

prune276.0ms

Filtered

210 candidates to 82 candidates (39.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	210	2	212

Merged error: 0b

Counts

212 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac`
38×	`*-un-lft-identity`
35×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down`
21×	`add-exp-log`
14×	`associate-/r*`
12×	`div-exp`
8×	`sqr-pow`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `div-inv`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `frac-add` `clear-num` `distribute-lft-out` `inv-pow`
1×	`+-commutative` `neg-sub0` `pow-neg` `flip3-+` `sum-log` `flip-+` `pow-sub`

Counts

3 → 121

Calls

3 calls:

15.0ms	(+ (/ 1 (pow x 5)) (pow x (- 3)))
5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 7))

series205.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(+ (/ 1 (pow x 5)) (pow x (- 3)))
40.0ms	(/ 1 (pow x 5))
56.0ms	(/ 1 (pow x 7))

simplify42.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	349	640
1	1615	527
2	5001	527

prune179.0ms

Filtered

130 candidates to 56 candidates (43.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	130	2	132

Merged error: 0b

Counts

132 → 2

regimes19.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 26.9b

bsearch123.0ms

Steps

Iters	Range		Point
10	0.0002141056345597589	3206628.0142593775	113.2115835016841
11	-4.816760182774211e+16	-0.0014803844373699059	-115.21870918376057

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	20
1	42	20

end0.0ms

sample710.0ms

Algorithm

intervals

Results

253.0ms	1954×	body	640	valid
154.0ms	4139×	body	80	valid
92.0ms	927×	body	320	valid
83.0ms	511×	body	1280	valid
31.0ms	473×	body	160	valid