Details

sample46.0ms

Algorithm

intervals

Results

15.0ms	65×	body	1280	valid
10.0ms	62×	body	640	valid
7.0ms	178×	body	80	valid
5.0ms	20×	body	320	valid
1.0ms	13×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.7b	(- (exp x) 1.0)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

11.0ms	(/ (- (exp x) 1.0) x)
5.0ms	(- (exp x) 1.0)

series58.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

simplify75.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	222	329
1	625	311
2	2739	309
3	5001	309

prune122.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
0.2b	(* 1/6 (pow x 2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log` `add-log-exp`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp` `sum-log`
2×	`pow1` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 40

Calls

2 calls:

9.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
6.0ms	(* 1/6 (pow x 2))

series48.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
28.0ms	(* 1/6 (pow x 2))

simplify35.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	201	222
1	825	201
2	5001	198

prune93.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/6 (pow x 2))
0.2b	(* 1/6 (pow x 2))
11.2b	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
15.8b	(/ (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)) (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
20×	`add-cube-cbrt`
16×	`add-exp-log` `associate-r`
15×	`times-frac`
10×	`add-cbrt-cube`
8×	`unpow-prod-down` `unswap-sqr`
6×	`associate-l` `prod-exp` `add-log-exp`
5×	`sum-cubes` `distribute-lft-out` `associate-/l*`
4×	`pow1` `unpow2` `sqr-pow`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`pow-to-exp` `pow-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 106

Calls

4 calls:

6.0ms	(* 1/6 (pow x 2))
6.0ms	(* 1/6 (pow x 2))
20.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
95.0ms	(/ (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)) (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))

series185.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 1/6 (pow x 2))
25.0ms	(* 1/6 (pow x 2))
53.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
77.0ms	(/ (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)) (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	406	1692
1	2139	1561
2	5002	1555

prune365.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

11.2b	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
11.2b	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
11.2b	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
13.7b	(/ (* (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))) (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)))) (* (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2))))) (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-div`
16×	`add-exp-log`
15×	`flip3-+` `flip-+`
10×	`*-un-lft-identity` `add-log-exp`
8×	`frac-times` `associate-/r/` `add-cbrt-cube` `associate-/l/`
4×	`pow1` `cbrt-undiv` `add-sqr-sqrt` `add-cube-cbrt` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod`
3×	`+-commutative` `sum-log` `sum-cubes` `distribute-lft-out`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

23.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
21.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
21.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
117.0ms	(/ (* (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))) (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)))) (* (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2))))) (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
50.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
54.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
126.0ms	(/ (* (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))) (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)))) (* (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2))))) (cbrt (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))))

simplify80.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	507	2673
1	2053	2286
2	5003	2270

prune459.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes49.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.6b

bsearch39.0ms

Steps

Iters	Range		Point
8	-0.0019174381104543623	-3.774608270569166e-06	-0.00015819896650017998

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

end0.0ms

sample1.3s

Algorithm

intervals

Results

518.0ms	2216×	body	1280	valid
273.0ms	1661×	body	640	valid
221.0ms	5446×	body	80	valid
95.0ms	828×	body	320	valid
38.0ms	447×	body	160	valid