Details

sample76.0ms

Algorithm

intervals

Results

52.0ms	185×	body	1280	valid
6.0ms	41×	body	640	valid
6.0ms	251×	body	80	valid
1.0ms	16×	body	320	valid
0.0ms	8×	body	160	valid

simplify212.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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: 29.5b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.0b	(+ (- (exp x) 2.0) (exp (- 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 (- x)))

series73.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(- (exp x) 2.0)
54.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify91.0ms

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

prune90.0ms

Filtered

41 candidates to 29 candidates (70.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	3	42

Merged error: 0.0b

Counts

42 → 3

localize14.0ms

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))

rewrite23.0ms

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))

series274.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
58.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
52.0ms	(* 1/360 (pow x 6))
35.0ms	(* 1/12 (pow x 4))

simplify51.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (43.0ms)

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

prune206.0ms

Filtered

87 candidates to 55 candidates (63.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))
2.9b	(exp (log (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
30.0b	(log (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-exp-log`
14×	`associate-r`
13×	`add-cube-cbrt`
8×	`unpow-prod-down` `log-prod` `add-cbrt-cube`
6×	`pow1` `associate-l` `prod-exp` `unswap-sqr`
4×	`log-div` `exp-prod` `exp-sum` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `exp-diff` `pow-exp` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 83

Calls

4 calls:

5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))
8.0ms	(exp (log (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
11.0ms	(log (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series241.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 1/360 (pow x 6))
35.0ms	(* 1/12 (pow x 4))
58.0ms	(exp (log (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
95.0ms	(log (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	355	681
1	1365	618
2	5002	592

prune248.0ms

Filtered

95 candidates to 60 candidates (63.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	95	4	99

Merged error: 0.0b

Counts

99 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))
3.2b	(pow E (log (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
30.0b	(log (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-exp-log`
14×	`add-cube-cbrt` `associate-r`
11×	`unpow-prod-down`
8×	`log-prod` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l` `prod-exp` `unswap-sqr`
5×	`sqr-pow`
4×	`unpow-prod-up` `log-div` `pow-unpow` `pow-exp` `add-log-exp`
3×	`pow-to-exp`
2×	`flip3-+` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `pow-sub`
1×	`e-exp-1` `pow-pow` `rem-log-exp`

Counts

4 → 90

Calls

4 calls:

5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))
8.0ms	(pow E (log (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
7.0ms	(log (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series361.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 1/360 (pow x 6))
35.0ms	(* 1/12 (pow x 4))
170.0ms	(pow E (log (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
103.0ms	(log (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	460	859
1	1786	786
2	5002	765

prune283.0ms

Filtered

102 candidates to 67 candidates (65.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	102	4	106

Merged error: 0.0b

Counts

106 → 4

regimes17.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.7s	5678×	body	1280	valid
193.0ms	1238×	body	640	valid
184.0ms	8156×	body	80	valid
58.0ms	602×	body	320	valid
21.0ms	336×	body	160	valid