Details

analyze6.0ms

Algorithm: search

sample26.0ms

Algorithm

intervals

Results

9.0ms	65×	body	640	valid
5.0ms	128×	body	80	valid
4.0ms	37×	body	320	valid
3.0ms	16×	body	1280	valid
1.0ms	10×	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: 7.9b

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))
2.1b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite67.0ms

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))
35.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series22.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1.0 (- x 1.0))
3.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms	(/ 1.0 (+ x 1.0))
11.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (37.0ms)

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

prune199.0ms

Filtered

92 candidates to 126 candidates (-37.0%)

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

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
0.2b	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
2.1b	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
13.3b	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

340×	`*-un-lft-identity`
225×	`times-frac`
176×	`add-sqr-sqrt`
150×	`frac-sub`
101×	`distribute-lft-out--`
94×	`frac-times`
65×	`add-cube-cbrt`
64×	`flip3--` `flip--`
52×	`associate-r/` `associate-l/`
51×	`difference-of-squares`
47×	`associate-/l/`
41×	`swap-sqr`
31×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
18×	`pow1`
16×	`distribute-lft-out`
13×	`associate-/r/`
11×	`associate-/r*`
6×	`add-log-exp`
5×	`cbrt-undiv` `sub-neg` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 352

Calls

4 calls:

19.0ms	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
38.0ms	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
42.0ms	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
78.0ms	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
4.0ms	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
12.0ms	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
26.0ms	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

simplify105.0ms

Algorithm

egg-herbie

Counts

364 → 364

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1780	7719
1	5001	7418

prune1.3s

Filtered

222 candidates to 364 candidates (-64.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	363	1	364
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	363	4	367

Merged error: 0.1b

Counts

367 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(* (+ x 1.0) x)
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
20.5b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

6.0ms	(* (+ x 1.0) x)
6.0ms	(* (+ x 1.0) x)
10.0ms	(* (* (+ 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))

series18.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ x 1.0) x)
4.0ms	(* (+ x 1.0) x)
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))

simplify120.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	751	1323
1	4427	1240
2	5003	1240

prune231.0ms

Filtered

82 candidates to 117 candidates (-42.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	117	4	121

Merged error: 0.1b

Counts

121 → 4

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

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

series19.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(* (+ x 1.0) x)
8.0ms	(* (* (+ x 1.0) x) (- x 1.0))
6.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	430	600
1	2219	516
2	5002	515

prune102.0ms

Filtered

62 candidates to 93 candidates (-50.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	94	3	97

Merged error: 0b

Counts

97 → 3

regimes30.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

end0.0ms

analyze6.0ms

Algorithm: search

sample730.0ms

Algorithm

intervals

Results

262.0ms	1900×	body	640	valid
152.0ms	4129×	body	80	valid
99.0ms	576×	body	1280	valid
95.0ms	922×	body	320	valid
32.0ms	473×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze6.0ms

sample26.0ms

simplify15.0ms

prune2.0ms

localize8.0ms

rewrite67.0ms

series22.0ms

simplify48.0ms

prune199.0ms

localize13.0ms

rewrite209.0ms

series45.0ms

simplify105.0ms

prune1.3s

localize15.0ms

rewrite38.0ms

series18.0ms

simplify120.0ms

prune231.0ms

localize6.0ms

rewrite30.0ms

series19.0ms

simplify58.0ms

prune102.0ms

regimes30.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze6.0ms

sample730.0ms

Profiling