Details

sample33.0ms

Algorithm

intervals

Results

15.0ms	88×	body	1280	valid
4.0ms	39×	body	640	valid
4.0ms	175×	body	80	valid
1.0ms	20×	body	320	valid
1.0ms	13×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	26	3
3	48	3
4	110	3
5	318	3
6	1623	3
7	5001	3

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.4b	(- (exp (* a x)) 1.0)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

1.0ms	(exp (* a x))
4.0ms	(- (exp (* a x)) 1.0)

series48.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
36.0ms	(- (exp (* a x)) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	115	135
1	333	127
2	1116	125
3	5001	125

prune68.0ms

Filtered

30 candidates to 20 candidates (66.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.6b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(cbrt (pow (- (exp (* a x)) 1.0) 3))
0.1b	(pow (- (exp (* a x)) 1.0) 3)
3.4b	(- (exp (* a x)) 1.0)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`cbrt-prod`
10×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`cube-div`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 80

Calls

4 calls:

1.0ms	(exp (* a x))
6.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
6.0ms	(pow (- (exp (* a x)) 1.0) 3)
4.0ms	(- (exp (* a x)) 1.0)

series129.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* a x))
35.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
47.0ms	(pow (- (exp (* a x)) 1.0) 3)
35.0ms	(- (exp (* a x)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	269	550
1	1076	527
2	5001	516

prune156.0ms

Filtered

92 candidates to 48 candidates (52.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3)
0.0b	(pow (+ (exp (* a x)) 1.0) 3)
0.0b	(cbrt (/ (pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
3.3b	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

202×	`cbrt-prod`
196×	`times-frac`
155×	`*-un-lft-identity`
120×	`unpow-prod-down` `cube-prod`
95×	`add-sqr-sqrt` `add-cube-cbrt`
31×	`difference-of-squares`
30×	`cube-mult` `unpow3` `distribute-lft-out` `sqr-pow`
6×	`pow1` `add-exp-log` `cube-div` `pow-unpow` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `flip3--` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip--` `flip-+` `rem-cube-cbrt`
1×	`sub-neg` `cbrt-div` `pow1/3` `diff-log` `div-inv`

Counts

4 → 278

Calls

4 calls:

9.0ms	(pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3)
6.0ms	(pow (+ (exp (* a x)) 1.0) 3)
25.0ms	(cbrt (/ (pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
5.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))

series206.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3)
32.0ms	(pow (+ (exp (* a x)) 1.0) 3)
65.0ms	(cbrt (/ (pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
48.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))

simplify165.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	808	6330
1	4264	6122
2	5001	5986

prune368.0ms

Filtered

290 candidates to 92 candidates (31.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3)
0.0b	(/ (pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3) (pow (+ (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (exp (* a x)) 2))) (* (pow (exp (* a x)) 2) (pow (exp (* a x)) 2))) 3))
0.0b	(cbrt (/ (/ (pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3) (pow (+ (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (exp (* a x)) 2))) (* (pow (exp (* a x)) 2) (pow (exp (* a x)) 2))) 3)) (pow (+ (exp (* a x)) 1.0) 3)))
3.3b	(- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

16788×	`times-frac`
11233×	`unpow-prod-down` `cube-prod`
8154×	`cbrt-prod`
7532×	`*-un-lft-identity`
7394×	`add-sqr-sqrt`
5840×	`difference-of-squares`
4474×	`add-cube-cbrt`
4405×	`sqr-pow`
1485×	`cube-mult` `unpow3`
1164×	`distribute-lft-out`
365×	`difference-cubes` `distribute-lft-out--`
48×	`associate-/l*`
36×	`cube-div`
32×	`associate-/r/`
17×	`add-exp-log`
16×	`flip3-+` `flip-+` `div-inv`
12×	`associate-/r*`
9×	`div-exp`
7×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1`
3×	`pow-unpow` `flip3--` `flip--`
2×	`associate-/l/`
1×	`cbrt-undiv` `sub-neg` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `clear-num` `rem-cube-cbrt`

Counts

4 → 8914

Calls

4 calls:

16.0ms	(pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3)
111.0ms	(/ (pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3) (pow (+ (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (exp (* a x)) 2))) (* (pow (exp (* a x)) 2) (pow (exp (* a x)) 2))) 3))
530.0ms	(cbrt (/ (/ (pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3) (pow (+ (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (exp (* a x)) 2))) (* (pow (exp (* a x)) 2) (pow (exp (* a x)) 2))) 3)) (pow (+ (exp (* a x)) 1.0) 3)))
9.0ms	(- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3))

series520.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3)
200.0ms	(/ (pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3) (pow (+ (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (exp (* a x)) 2))) (* (pow (exp (* a x)) 2) (pow (exp (* a x)) 2))) 3))
177.0ms	(cbrt (/ (/ (pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3) (pow (+ (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (exp (* a x)) 2))) (* (pow (exp (* a x)) 2) (pow (exp (* a x)) 2))) 3)) (pow (+ (exp (* a x)) 1.0) 3)))
62.0ms	(- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3))

simplify5.2s

Algorithm

egg-herbie

Counts

8926 → 8926

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5877	601334

prune10.3s

Filtered

8926 candidates to 1449 candidates (16.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.6b

regimes316.0ms

Accuracy

92.7% (1.6b remaining)

Error of 10.2b against oracle of 8.6b and baseline of 30.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	39
1	57	39

end0.0ms

sample988.0ms

Algorithm

intervals

Results

450.0ms	2708×	body	1280	valid
144.0ms	1360×	body	640	valid
114.0ms	5445×	body	80	valid
54.0ms	788×	body	320	valid
19.0ms	394×	body	160	valid