Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	58×	body	640	valid
5.0ms	145×	body	80	valid
3.0ms	19×	body	1280	valid
2.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid

simplify15.0ms

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

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: 8.6b

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

rewrite63.0ms

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

series17.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1.0 (+ x 1.0))
2.0ms	(/ 1.0 (- x 1.0))
3.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
10.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (36.0ms)

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

prune190.0ms

Filtered

92 candidates to 126 candidates (-37.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	121	5	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	5	127

Merged error: 0.1b

Counts

127 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))))
2.0b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
2.0b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
2.0b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

435×	`*-un-lft-identity`
156×	`times-frac`
100×	`distribute-lft-out`
89×	`distribute-lft-out--`
76×	`cbrt-prod`
60×	`cbrt-div`
45×	`frac-add`
30×	`swap-sqr`
25×	`frac-times`
20×	`add-sqr-sqrt`
19×	`add-log-exp`
15×	`flip3--` `flip3-+` `frac-sub` `flip--` `flip-+`
12×	`add-cube-cbrt` `associate-r` `associate-l`
11×	`pow1`
6×	`add-exp-log` `associate-+l+` `pow1/3` `sum-log`
5×	`associate-r/` `associate-l/`
4×	`add-cbrt-cube` `unswap-sqr`
3×	`+-commutative` `associate-+l-` `sub-neg` `diff-log`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 183

Calls

4 calls:

70.0ms	(* (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))))
33.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
29.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
31.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))))
15.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
10.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
10.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify80.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	529	4153
1	1751	4023
2	5001	3553

prune526.0ms

Filtered

103 candidates to 195 candidates (-89.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	195	5	200

Merged error: 0.1b

Counts

200 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- x 1.0))
0.2b	(cbrt (- x 1.0))
0.2b	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
14.3b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
38×	`cbrt-prod`
34×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1` `distribute-lft-out--`
10×	`swap-sqr`
9×	`flip3--` `flip--` `add-log-exp`
8×	`pow1/3` `associate-r` `associate-l`
6×	`add-exp-log` `times-frac` `difference-of-squares`
5×	`distribute-lft-out`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`frac-add`
2×	`associate-+l+` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `pow-sqr` `pow-prod-up`
1×	`+-commutative` `pow2` `associate-+l-` `sub-neg` `flip3-+` `pow-plus` `diff-log` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+`

Counts

4 → 108

Calls

4 calls:

3.0ms	(cbrt (- x 1.0))
3.0ms	(cbrt (- x 1.0))
10.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
86.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

series38.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(cbrt (- x 1.0))
7.0ms	(cbrt (- x 1.0))
10.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
14.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

simplify61.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	597	1292
1	2169	1173
2	5001	1110

prune259.0ms

Filtered

84 candidates to 120 candidates (-42.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	120	5	125

Merged error: 0.1b

Counts

125 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
16.0b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

46×	`associate-*l/`
16×	`flip3--` `frac-add` `flip--`
13×	`flip3-+` `flip-+`
12×	`frac-times`
11×	`pow1` `add-exp-log` `add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
8×	`associate-r` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-*r/`
5×	`sub-neg` `associate-l`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`*-commutative`
1×	`+-commutative` `diff-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

8.0ms	(* (+ x 1.0) x)
4.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
9.0ms	(* (* (+ x 1.0) x) (- x 1.0))
11.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series17.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ x 1.0) x)
4.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
8.0ms	(* (* (+ x 1.0) x) (- x 1.0))
1.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify122.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	771	1337
1	4470	1257
2	5001	1257

prune207.0ms

Filtered

78 candidates to 108 candidates (-38.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	2	2
Picked	1	0	1
Done	1	1	2
Total	109	4	113

Merged error: 0.1b

Counts

113 → 4

regimes67.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample865.0ms

Algorithm

intervals

Results

288.0ms	1858×	body	640	valid
167.0ms	4177×	body	80	valid
113.0ms	586×	body	1280	valid
106.0ms	911×	body	320	valid
38.0ms	469×	body	160	valid

Details

sample27.0ms

simplify15.0ms

prune2.0ms

localize8.0ms

rewrite63.0ms

series17.0ms

simplify47.0ms

prune190.0ms

localize12.0ms

rewrite179.0ms

series59.0ms

simplify80.0ms

prune526.0ms

localize12.0ms

rewrite106.0ms

series38.0ms

simplify61.0ms

prune259.0ms

localize12.0ms

rewrite36.0ms

series17.0ms

simplify122.0ms

prune207.0ms

regimes67.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample865.0ms

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