Details

sample37.0ms

Algorithm

intervals

Results

16.0ms	92×	body	1280	valid
6.0ms	182×	body	80	valid
4.0ms	38×	body	640	valid
1.0ms	23×	body	320	valid
1.0ms	12×	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: 28.7b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

4.0ms

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

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

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

simplify39.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	103	100
1	300	92
2	1055	90
3	5001	90

prune48.0ms

Filtered

17 candidates to 12 candidates (70.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 9.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
87×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
9×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`add-exp-log`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `pow-pow` `associate-/r*`
2×	`associate-+l+` `flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `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-exp` `clear-num` `sum-log` `div-inv` `rem-cube-cbrt`

Counts

4 → 192

Calls

4 calls:

8.0ms	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
24.0ms	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
3.0ms	(pow (exp (* a x)) 3)
11.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

series243.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
113.0ms	(/ (- (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)
57.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

simplify99.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	629	3765
1	2526	3671
2	5001	3592

prune418.0ms

Filtered

204 candidates to 108 candidates (52.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
0.0b	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
0.2b	(* (* a x) 3)
3.5b	(- (exp (* (* a x) 3)) (pow 1.0 3))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

7.0ms	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
15.0ms	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
5.0ms	(* (* a x) 3)
6.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

series216.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))
103.0ms	(/ (- (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)
44.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

simplify72.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	542	2111
1	2213	1992
2	5001	1987

prune349.0ms

Filtered

127 candidates to 85 candidates (66.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a x) 3)
3.5b	(- (exp (* (* a x) 3)) (pow 1.0 3))
3.5b	(- (exp (* (* a x) 3)) (pow 1.0 3))
3.5b	(- (exp (* (* a x) 3)) (pow 1.0 3))

rewrite27.0ms

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:

5.0ms	(* (* a x) 3)
6.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))
6.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))
7.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

series160.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* a x) 3)
48.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))
44.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))
48.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

simplify40.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (31.0ms)

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

prune340.0ms

Filtered

90 candidates to 59 candidates (65.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.9b

regimes165.0ms

Accuracy

95% (1.1b remaining)

Error of 9.3b against oracle of 8.2b and baseline of 29.6b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	68
1	58	68

end0.0ms

sample957.0ms

Algorithm

intervals

Results

438.0ms	2696×	body	1280	valid
142.0ms	1324×	body	640	valid
110.0ms	5496×	body	80	valid
50.0ms	736×	body	320	valid
20.0ms	438×	body	160	valid