Details

sample100.0ms

Algorithm

intervals

Results

65.0ms	171×	body	1280	valid
11.0ms	47×	body	640	valid
10.0ms	234×	body	80	valid
2.0ms	15×	body	320	valid
2.0ms	16×	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: 31.9b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.9b	(+ (- (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)))

series65.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify89.0ms

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

prune95.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

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))

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:

3.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
14.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(* 1/360 (pow x 6))
6.0ms	(* 1/12 (pow x 4))

series258.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
50.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
48.0ms	(* 1/360 (pow x 6))
35.0ms	(* 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

prune196.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
25.9b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
25.9b	(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)))))
22.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 1/12 (pow x 4))
34.0ms	(* 1/12 (pow x 4))
99.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
96.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify197.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (30.0ms)

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

prune288.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))
0.1b	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
21.9b	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
16×	`add-cube-cbrt` `unpow-prod-down`
15×	`add-exp-log`
14×	`cbrt-prod` `associate-r`
9×	`add-cbrt-cube`
8×	`cube-prod`
6×	`associate-l` `prod-exp` `unswap-sqr` `sqr-pow`
5×	`pow1`
4×	`cube-div` `distribute-lft-out` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `pow-exp`
2×	`cube-mult` `cbrt-div` `flip3-+` `unpow3` `*-commutative` `cbrt-unprod` `flip-+`
1×	`pow-pow` `pow1/3` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))
21.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
23.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

series210.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* 1/360 (pow x 6))
36.0ms	(* 1/12 (pow x 4))
71.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
55.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

simplify61.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	419	910
1	1865	843
2	5003	830

prune232.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b 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

sample3.2s

Algorithm

intervals

Results

2.2s	5720×	body	1280	valid
340.0ms	8012×	body	80	valid
289.0ms	1218×	body	640	valid
95.0ms	611×	body	320	valid
30.0ms	286×	body	160	valid