Details

sample105.0ms

Algorithm

intervals

Results

68.0ms	178×	body	1280	valid
14.0ms	239×	body	80	valid
8.0ms	33×	body	640	valid
4.0ms	26×	body	320	valid
1.0ms	11×	body	160	valid

simplify213.0ms

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	67	5
5	100	5
6	144	5
7	296	5
8	1321	5
9	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
5.3b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite30.0ms

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)
25.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series65.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
53.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify93.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	211	282
1	715	269
2	3477	260
3	5001	260

prune85.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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))

rewrite30.0ms

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:

3.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
12.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
8.0ms	(* 1/360 (pow x 6))
6.0ms	(* 1/12 (pow x 4))

series256.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
52.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
47.0ms	(* 1/360 (pow x 6))
35.0ms	(* 1/12 (pow x 4))

simplify48.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	327	476
1	1399	444
2	5001	426

prune184.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (exp x) (exp x)) (* 2.0 2.0))
0.0b	(/ (- (* (exp x) (exp x)) (* 2.0 2.0)) (+ (exp x) 2.0))
0.0b	(* (exp x) (exp x))
5.6b	(+ (/ (- (* (exp x) (exp x)) (* 2.0 2.0)) (+ (exp x) 2.0)) (exp (- x)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-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`
6×	`add-exp-log` `distribute-lft-out` `difference-of-squares`
4×	`pow-prod-down` `associate-/r` `pow-sqr` `pow-prod-up` `associate-/l`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`flip3--` `flip3-+` `div-sub` `frac-add` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `neg-sub0` `exp-neg` `associate-+l-` `sub-neg` `frac-2neg` `pow-plus` `exp-diff` `diff-log` `div-exp` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 103

Calls

4 calls:

7.0ms	(- (* (exp x) (exp x)) (* 2.0 2.0))
26.0ms	(/ (- (* (exp x) (exp x)) (* 2.0 2.0)) (+ (exp x) 2.0))
8.0ms	(* (exp x) (exp x))
71.0ms	(+ (/ (- (* (exp x) (exp x)) (* 2.0 2.0)) (+ (exp x) 2.0)) (exp (- x)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(- (* (exp x) (exp x)) (* 2.0 2.0))
42.0ms	(/ (- (* (exp x) (exp x)) (* 2.0 2.0)) (+ (exp x) 2.0))
15.0ms	(* (exp x) (exp x))
126.0ms	(+ (/ (- (* (exp x) (exp x)) (* 2.0 2.0)) (+ (exp x) 2.0)) (exp (- x)))

simplify71.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	474	1032
1	2302	948
2	5002	943

prune230.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
44.2b	(/ (+ (pow x 4) (- (* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (- (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
32×	`times-frac`
27×	`add-cube-cbrt`
21×	`add-exp-log` `associate-r`
20×	`difference-of-squares`
17×	`unpow-prod-down`
12×	`add-cbrt-cube`
11×	`sqr-pow`
9×	`associate-l` `prod-exp` `distribute-lft-out` `unswap-sqr`
8×	`associate-/r*`
5×	`distribute-lft-out--` `unpow2`
4×	`pow1` `associate-/l*` `add-log-exp`
3×	`pow-to-exp` `div-sub` `pow-exp` `*-commutative` `cbrt-unprod`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `neg-sub0` `associate-+r-` `flip3--` `frac-2neg` `flip3-+` `div-exp` `unsub-neg` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 138

Calls

4 calls:

5.0ms	(* 1/12 (pow x 4))
5.0ms	(* 1/12 (pow x 4))
5.0ms	(* 1/12 (pow x 4))
41.0ms	(/ (+ (pow x 4) (- (* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (- (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series247.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* 1/12 (pow x 4))
36.0ms	(* 1/12 (pow x 4))
34.0ms	(* 1/12 (pow x 4))
143.0ms	(/ (+ (pow x 4) (- (* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (- (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	359	2510
1	1638	2337
2	5003	2205

prune324.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes20.0ms

Accuracy

44.5% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.7b

bsearch35.0ms

Steps

Iters	Range		Point
8	0.00035723662727133143	3.9715340067303715	0.027742406259524545

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	18
1	32	18

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.2s	5660×	body	1280	valid
441.0ms	7756×	body	80	valid
295.0ms	1244×	body	640	valid
99.0ms	621×	body	320	valid
35.0ms	307×	body	160	valid