Details

sample28.0ms

Algorithm

intervals

Results

7.0ms	135×	body	80	valid
7.0ms	53×	body	640	valid
3.0ms	36×	body	320	valid
3.0ms	16×	body	1280	valid
1.0ms	16×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 11.3b

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))
3.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite69.0ms

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:

6.0ms	(/ 1.0 (- x 1.0))
21.0ms	(- (/ 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)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1.0 (- x 1.0))
42.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
31.0ms	(/ 1.0 (+ x 1.0))
220.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5001	816

prune233.0ms

Filtered

126 candidates to 92 candidates (73.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	120	6	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	6	127

Merged error: 0.1b

Counts

127 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ 1.0 (+ x 1.0)))
0.0b	(sqrt (/ 1.0 (+ x 1.0)))
0.1b	(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
6.3b	(+ (- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

134×	`sqrt-prod`
116×	`*-un-lft-identity`
94×	`add-sqr-sqrt`
92×	`times-frac`
60×	`add-cube-cbrt`
29×	`swap-sqr`
25×	`distribute-lft-out`
21×	`pow1` `associate-r` `associate-l`
12×	`associate-/r/`
10×	`sqrt-pow1` `pow1/2` `sqrt-div`
9×	`add-log-exp` `unswap-sqr`
7×	`flip3-+` `flip-+`
6×	`add-exp-log` `add-cbrt-cube` `div-inv`
5×	`frac-add` `pow-prod-up`
4×	`rem-sqrt-square`
3×	`pow-prod-down` `pow-sqr` `frac-sub`
2×	`frac-times` `associate-+l+` `associate-r/` `associate-l/` `sum-log`
1×	`+-commutative` `pow2` `associate-+l-` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 189

Calls

4 calls:

6.0ms	(sqrt (/ 1.0 (+ x 1.0)))
6.0ms	(sqrt (/ 1.0 (+ x 1.0)))
22.0ms	(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
28.0ms	(+ (- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (/ 1.0 (+ x 1.0)))
94.0ms	(sqrt (/ 1.0 (+ x 1.0)))
80.0ms	(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
145.0ms	(+ (- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify99.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	601	1683
1	2878	1525
2	5001	1483

prune367.0ms

Filtered

201 candidates to 128 candidates (63.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	201	6	207

Merged error: 0.1b

Counts

207 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
17.5b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

28.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
4.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
10.0ms	(* (* (+ x 1.0) x) (- x 1.0))
12.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series238.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
37.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
102.0ms	(* (* (+ x 1.0) x) (- x 1.0))
2.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	997	2264
1	5001	2129

prune403.0ms

Filtered

136 candidates to 108 candidates (79.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	137	5	142

Merged error: 0.0b

Counts

142 → 5

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.1b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

6.0ms	(* (+ x 1.0) x)
11.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))
10.0ms	(* (* (+ x 1.0) x) (- x 1.0))

series236.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* (+ x 1.0) x)
92.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))
96.0ms	(* (* (+ x 1.0) x) (- x 1.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	430	600
1	2216	516
2	5001	515

prune132.0ms

Filtered

93 candidates to 62 candidates (66.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	93	5	98

Merged error: 0b

Counts

98 → 5

regimes21.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	4
1	9	4

end0.0ms

sample686.0ms

Algorithm

intervals

Results

237.0ms	1862×	body	640	valid
144.0ms	4140×	body	80	valid
92.0ms	582×	body	1280	valid
88.0ms	942×	body	320	valid
31.0ms	476×	body	160	valid

Details

sample28.0ms

simplify18.0ms

prune2.0ms

localize8.0ms

rewrite69.0ms

series327.0ms

simplify51.0ms

prune233.0ms

localize11.0ms

rewrite77.0ms

series414.0ms

simplify99.0ms

prune367.0ms

localize13.0ms

rewrite61.0ms

series238.0ms

simplify48.0ms

prune403.0ms

localize6.0ms

rewrite31.0ms

series236.0ms

simplify64.0ms

prune132.0ms

regimes21.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample686.0ms

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