Details

sample30.0ms

Algorithm

intervals

Results

12.0ms	75×	body	1280	valid
3.0ms	183×	body	80	valid
3.0ms	36×	body	640	valid
2.0ms	28×	body	320	valid
1.0ms	18×	body	160	valid

simplify62.0ms

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: 28.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
5.0b	(- (exp (* a x)) 1.0)

rewrite6.0ms

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)

series45.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
33.0ms	(- (exp (* a x)) 1.0)

simplify45.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (11.0ms)

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

prune70.0ms

Filtered

30 candidates to 20 candidates (66.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp (* a x)) (+ (exp (* a x)) 1.0))
0.0b	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
0.1b	(pow (exp (* a x)) 3)
4.8b	(- (pow (exp (* a x)) 3) (pow 1.0 3))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

161×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
39×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
9×	`add-cbrt-cube`
7×	`pow1` `add-exp-log` `add-log-exp`
5×	`difference-cubes`
4×	`associate-r`
3×	`pow-unpow` `pow-pow` `associate-l` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-*r/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 202

Calls

4 calls:

14.0ms	(* (exp (* a x)) (+ (exp (* a x)) 1.0))
57.0ms	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
2.0ms	(pow (exp (* a x)) 3)
17.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

series226.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (exp (* a x)) (+ (exp (* a x)) 1.0))
114.0ms	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
24.0ms	(pow (exp (* a x)) 3)
55.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

simplify123.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	677	3771
1	3048	3688
2	5002	3611

prune450.0ms

Filtered

214 candidates to 112 candidates (52.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp (* a x)) (+ (exp (* a x)) 1.0))
0.0b	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
0.3b	(* (* a x) 3)
5.1b	(- (exp (* (* a x) 3)) (pow 1.0 3))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`times-frac`
23×	`add-cube-cbrt`
20×	`difference-of-squares`
15×	`difference-cubes`
13×	`add-cbrt-cube`
12×	`add-exp-log`
11×	`pow1` `associate-/l*` `add-log-exp`
7×	`associate-r`
5×	`unpow-prod-down` `exp-lft-cube` `exp-prod` `exp-to-pow` `cube-prod` `distribute-lft-out--` `sqr-pow`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`associate-/r*`
2×	`flip3--` `flip3-+` `associate-r/` `associate-/r/` `-commutative` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 125

Calls

4 calls:

14.0ms	(* (exp (* a x)) (+ (exp (* a x)) 1.0))
29.0ms	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
6.0ms	(* (* a x) 3)
7.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

series197.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (exp (* a x)) (+ (exp (* a x)) 1.0))
100.0ms	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
19.0ms	(* (* a x) 3)
43.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

simplify86.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	599	2118
1	2643	2009
2	5001	2004

prune368.0ms

Filtered

137 candidates to 89 candidates (65.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* a x) 3)
5.1b	(- (exp (* (* a x) 3)) (pow 1.0 3))
5.1b	(- (exp (* (* a x) 3)) (pow 1.0 3))
5.1b	(- (exp (* (* a x) 3)) (pow 1.0 3))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
13×	`add-log-exp`
12×	`difference-of-squares`
11×	`*-un-lft-identity`
9×	`pow1` `difference-cubes` `add-exp-log` `add-cbrt-cube`
5×	`add-cube-cbrt`
3×	`sub-neg` `unpow-prod-down` `exp-lft-cube` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `cube-prod` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `distribute-lft-out--` `sqr-pow`
1×	`associate-l` `*-commutative`

Counts

4 → 78

Calls

4 calls:

6.0ms	(* (* a x) 3)
7.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))
7.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))
7.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

series151.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (* a x) 3)
42.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))
45.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))
45.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

simplify40.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	240	725
1	1014	663
2	5001	651

prune340.0ms

Filtered

90 candidates to 59 candidates (65.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

regimes316.0ms

Accuracy

96.6% (0.7b remaining)

Error of 8.7b against oracle of 8.0b and baseline of 29.0b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	124
1	71	124

end0.0ms

sample893.0ms

Algorithm

intervals

Results

409.0ms	2707×	body	1280	valid
126.0ms	1275×	body	640	valid
104.0ms	5449×	body	80	valid
51.0ms	812×	body	320	valid
15.0ms	359×	body	160	valid