Details

sample92.0ms

Algorithm

intervals

Results

59.0ms	181×	body	1280	valid
12.0ms	278×	body	80	valid
8.0ms	47×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	7×	body	160	valid

simplify217.0ms

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: 29.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.0b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite31.0ms

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:

7.0ms	(- (exp x) 2.0)
23.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series68.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
56.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify94.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (20.0ms)

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

prune92.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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:

12.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
6.0ms	(* 1/360 (pow x 6))
6.0ms	(* 1/12 (pow x 4))

series271.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
131.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
50.0ms	(* 1/360 (pow x 6))
37.0ms	(* 1/12 (pow x 4))

simplify50.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	329	464
1	1456	439
2	5001	423

prune194.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
29.3b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
29.3b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-exp-log` `associate-r`
12×	`add-cube-cbrt`
8×	`unpow-prod-down` `sqrt-prod` `add-cbrt-cube`
6×	`pow1` `associate-l` `prod-exp` `unswap-sqr`
4×	`sqrt-div` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* 1/12 (pow x 4))
5.0ms	(* 1/12 (pow x 4))
19.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
21.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 1/12 (pow x 4))
37.0ms	(* 1/12 (pow x 4))
102.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
101.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify203.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	259	662
1	1019	626
2	4841	616
3	5001	616

prune289.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (log (exp (* 1/360 (pow x 6)))) (* 1/12 (pow x 4)))
0.0b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))
0.7b	(log (exp (* 1/360 (pow x 6))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

5.0ms	(+ (log (exp (* 1/360 (pow x 6)))) (* 1/12 (pow x 4)))
6.0ms	(* 1/360 (pow x 6))
6.0ms	(* 1/12 (pow x 4))
1.0ms	(log (exp (* 1/360 (pow x 6))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(+ (log (exp (* 1/360 (pow x 6)))) (* 1/12 (pow x 4)))
48.0ms	(* 1/360 (pow x 6))
41.0ms	(* 1/12 (pow x 4))
52.0ms	(log (exp (* 1/360 (pow x 6))))

simplify44.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	275	419
1	1084	372
2	5002	358

prune234.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes21.0ms

Accuracy

0% (0.5b 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

sample2.8s

Algorithm

intervals

Results

1.8s	5650×	body	1280	valid
364.0ms	8202×	body	80	valid
238.0ms	1280×	body	640	valid
75.0ms	625×	body	320	valid
27.0ms	306×	body	160	valid