Details

analyze4.0ms

Algorithm: search

sample72.0ms

Algorithm

intervals

Results

56.0ms	179×	body	1280	valid
6.0ms	37×	body	640	valid
2.0ms	21×	body	320	valid
1.0ms	16×	body	160	valid
0.0ms	3×	body	80	valid

simplify137.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	65	5
5	96	5
6	140	5
7	285	5
8	1642	5
9	5001	5

prune3.0ms

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: 29.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
6.2b	(+ (- (exp x) 2.0) (exp (neg x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `associate-+l+` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

4.0ms	(- (exp x) 2.0)
7.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

series9.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(- (exp x) 2.0)
7.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

simplify89.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	209	282
1	694	269
2	3196	260
3	5001	260

prune60.0ms

Filtered

29 candidates to 41 candidates (-41.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	2	42

Merged error: 0.0b

Counts

42 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
12×	`*-un-lft-identity`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`pow1` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 75

Calls

4 calls:

4.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
7.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series27.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
6.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
4.0ms	(* 1/360 (pow x 6))
4.0ms	(* 1/12 (pow x 4))

simplify50.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	327	476
1	1399	443
2	5001	425

prune145.0ms

Filtered

55 candidates to 87 candidates (-58.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	85	4	89

Merged error: 0b

Counts

89 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
30.6b	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
30.6b	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
30.6b	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

16.0ms	(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
6.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
8.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
6.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
15.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
15.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
16.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	354	2145
1	1202	2017
2	5002	1805

prune529.0ms

Filtered

75 candidates to 107 candidates (-42.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	107	4	111

Merged error: 0b

Counts

111 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 2.0)
0.0b	(/ (- (* (exp x) (exp x)) (* 2.0 2.0)) (+ (exp x) 2.0))
0.0b	(* (exp x) (exp x))
6.0b	(+ (/ (- (* (exp x) (exp x)) (* 2.0 2.0)) (+ (exp x) 2.0)) (exp (neg x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
18×	`exp-prod`
16×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-log-exp`
7×	`distribute-lft-out`
6×	`add-exp-log`
5×	`difference-of-squares`
4×	`pow-prod-down` `associate-/r` `pow-sqr` `pow-prod-up` `associate-/l`
3×	`flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+`
2×	`+-commutative` `div-sub` `frac-add` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `neg-sub0` `exp-neg` `associate-+l-` `flip3--` `frac-2neg` `pow-plus` `exp-diff` `div-exp` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

4.0ms	(+ (exp x) 2.0)
11.0ms	(/ (- (* (exp x) (exp x)) (* 2.0 2.0)) (+ (exp x) 2.0))
6.0ms	(* (exp x) (exp x))
16.0ms	(+ (/ (- (* (exp x) (exp x)) (* 2.0 2.0)) (+ (exp x) 2.0)) (exp (neg x)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ (exp x) 2.0)
9.0ms	(/ (- (* (exp x) (exp x)) (* 2.0 2.0)) (+ (exp x) 2.0))
3.0ms	(* (exp x) (exp x))
21.0ms	(+ (/ (- (* (exp x) (exp x)) (* 2.0 2.0)) (+ (exp x) 2.0)) (exp (neg x)))

simplify68.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	464	982
1	2248	906
2	5001	899

prune118.0ms

Filtered

80 candidates to 114 candidates (-42.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	114	4	118

Merged error: 0b

Counts

118 → 4

regimes38.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

analyze4.0ms

Algorithm: search

sample2.2s

Algorithm

intervals

Results

1.8s	5651×	body	1280	valid
217.0ms	1257×	body	640	valid
65.0ms	608×	body	320	valid
22.0ms	315×	body	160	valid
6.0ms	169×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze4.0ms

sample72.0ms

simplify137.0ms

prune3.0ms

localize6.0ms

rewrite12.0ms

series9.0ms

simplify89.0ms

prune60.0ms

localize10.0ms

rewrite22.0ms

series27.0ms

simplify50.0ms

prune145.0ms

localize16.0ms

rewrite40.0ms

series65.0ms

simplify54.0ms

prune529.0ms

localize10.0ms

rewrite39.0ms

series34.0ms

simplify68.0ms

prune118.0ms

regimes38.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze4.0ms

sample2.2s

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