Details

sample37.0ms

Algorithm

intervals

Results

15.0ms	84×	body	1280	valid
6.0ms	188×	body	80	valid
4.0ms	40×	body	640	valid
2.0ms	23×	body	320	valid
1.0ms	16×	body	160	valid

simplify61.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.1b	(- (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:

15.0ms	(exp (* a x))
33.0ms	(- (exp (* a x)) 1.0)

simplify40.0ms

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

prune66.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 9.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (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)))
0.0b	(pow (exp (* a x)) 3)
4.0b	(- (pow (exp (* a x)) 3) (pow 1.0 3))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-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×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 191

Calls

4 calls:

3.0ms	(+ (exp (* a x)) 1.0)
56.0ms	(/ (- (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))

series206.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (exp (* a x)) 1.0)
112.0ms	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
23.0ms	(pow (exp (* a x)) 3)
55.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

simplify99.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	629	3662
1	2568	3579
2	5003	3500

prune412.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 9.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (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)
4.0b	(- (exp (* (* a x) 3)) (pow 1.0 3))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `times-frac`
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×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-l` `clear-num` `sum-log` `*-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 114

Calls

4 calls:

3.0ms	(+ (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))

series182.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify77.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	548	1994
1	2362	1891
2	5001	1886

prune337.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (exp (* (* a x) 3)) (pow 1.0 3))))
0.0b	(/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (exp (* (* a x) 3)) (pow 1.0 3)))
0.3b	(* (* a x) 3)
4.0b	(- (exp (* (* a x) 3)) (pow 1.0 3))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

282×	`times-frac`
240×	`add-sqr-sqrt`
155×	`*-un-lft-identity`
121×	`add-cube-cbrt`
68×	`difference-of-squares`
51×	`difference-cubes`
50×	`associate-/r*`
23×	`add-log-exp`
22×	`add-exp-log`
17×	`unpow-prod-down` `exp-lft-cube` `exp-prod` `exp-to-pow` `cube-prod` `distribute-lft-out--` `sqr-pow`
16×	`add-cbrt-cube`
11×	`associate-/r/`
10×	`pow1`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
4×	`cbrt-undiv`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `pow-flip` `flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+` `inv-pow`

Counts

4 → 281

Calls

4 calls:

29.0ms	(/ 1 (/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (exp (* (* a x) 3)) (pow 1.0 3))))
32.0ms	(/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (exp (* (* a x) 3)) (pow 1.0 3)))
6.0ms	(* (* a x) 3)
7.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

series266.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1 (/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (exp (* (* a x) 3)) (pow 1.0 3))))
99.0ms	(/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (exp (* (* a x) 3)) (pow 1.0 3)))
19.0ms	(* (* a x) 3)
48.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

simplify147.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	882	7104
1	4693	6679
2	5003	6676

prune687.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes94.0ms

Accuracy

96.8% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 21.7b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	23
1	36	23

end0.0ms

sample1.1s

Algorithm

intervals

Results

477.0ms	2696×	body	1280	valid
181.0ms	5580×	body	80	valid
155.0ms	1303×	body	640	valid
59.0ms	728×	body	320	valid
22.0ms	375×	body	160	valid