Details

sample81.0ms

Algorithm

intervals

Results

56.0ms	181×	body	1280	valid
6.0ms	280×	body	80	valid
6.0ms	39×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid

simplify219.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

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)
21.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series69.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
57.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify94.0ms

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

prune94.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite27.0ms

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:

11.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
3.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series272.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
127.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
50.0ms	(* 1/360 (pow x 6))
38.0ms	(* 1/12 (pow x 4))

simplify51.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (44.0ms)

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

prune197.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp x) 2.0)
0.0b	(* (- (exp x) 2.0) (- (exp x) 2.0))
0.0b	(* (exp (- x)) (exp (- x)))
3.9b	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

76×	`frac-times` `exp-prod`
72×	`frac-sub`
63×	`exp-neg`
62×	`flip3--` `flip--`
60×	`*-un-lft-identity`
54×	`neg-sub0` `exp-diff`
44×	`add-sqr-sqrt`
38×	`associate-r/` `associate-l/`
30×	`add-cube-cbrt`
24×	`distribute-rgt-neg-in`
20×	`distribute-lft-neg-in`
18×	`pow1`
16×	`pow-prod-down`
14×	`pow-sqr` `pow-prod-up`
10×	`swap-sqr`
9×	`un-div-inv`
8×	`neg-mul-1` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
7×	`distribute-lft-out--`
6×	`add-exp-log` `sub-neg` `difference-of-squares`
4×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
2×	`pow2` `pow-plus` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 220

Calls

4 calls:

4.0ms	(- (exp x) 2.0)
25.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
28.0ms	(* (exp (- x)) (exp (- x)))
19.0ms	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (exp x) 2.0)
32.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
20.0ms	(* (exp (- x)) (exp (- x)))
87.0ms	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x))))

simplify97.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	991	3327
1	3230	2922
2	5003	2897

prune323.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp x) 2.0) (+ (pow (exp x) 2) (* 2.0 (+ 2.0 (exp x)))))
0.0b	(pow (exp x) 3)
0.3b	(/ (- (* (- (* (exp x) (exp x)) (* 2.0 2.0)) (* (- (pow (exp x) 3) (pow 2.0 3)) (pow (exp x) 2))) (* (+ (exp x) 2.0) (+ (pow (exp x) 2) (* 2.0 (+ 2.0 (exp x)))))) (* (* (+ (exp x) 2.0) (+ (pow (exp x) 2) (* 2.0 (+ 2.0 (exp x))))) (pow (exp x) 2)))
4.6b	(- (* (- (* (exp x) (exp x)) (* 2.0 2.0)) (* (- (pow (exp x) 3) (pow 2.0 3)) (pow (exp x) 2))) (* (+ (exp x) 2.0) (+ (pow (exp x) 2) (* 2.0 (+ 2.0 (exp x))))))

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

172×	`associate-*l/`
136×	`frac-times`
128×	`frac-sub`
108×	`flip3-+` `flip-+`
98×	`flip3--` `flip--`
68×	`associate-*r/`
66×	`associate-/l/`
25×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`prod-exp`
8×	`associate-/r/`
7×	`pow1` `div-exp`
6×	`add-log-exp`
4×	`pow-pow` `associate-l` `cbrt-unprod`
3×	`cbrt-undiv` `pow-to-exp` `unpow-prod-down` `pow-unpow` `exp-prod` `times-frac` `cube-prod` `associate-r` `pow-exp` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
1×	`cube-mult` `sub-neg` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`

Counts

4 → 235

Calls

4 calls:

32.0ms	(* (+ (exp x) 2.0) (+ (pow (exp x) 2) (* 2.0 (+ 2.0 (exp x)))))
2.0ms	(pow (exp x) 3)
233.0ms	(/ (- (* (- (* (exp x) (exp x)) (* 2.0 2.0)) (* (- (pow (exp x) 3) (pow 2.0 3)) (pow (exp x) 2))) (* (+ (exp x) 2.0) (+ (pow (exp x) 2) (* 2.0 (+ 2.0 (exp x)))))) (* (* (+ (exp x) 2.0) (+ (pow (exp x) 2) (* 2.0 (+ 2.0 (exp x))))) (pow (exp x) 2)))
95.0ms	(- (* (- (* (exp x) (exp x)) (* 2.0 2.0)) (* (- (pow (exp x) 3) (pow 2.0 3)) (pow (exp x) 2))) (* (+ (exp x) 2.0) (+ (pow (exp x) 2) (* 2.0 (+ 2.0 (exp x))))))

series856.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (+ (exp x) 2.0) (+ (pow (exp x) 2) (* 2.0 (+ 2.0 (exp x)))))
23.0ms	(pow (exp x) 3)
477.0ms	(/ (- (* (- (* (exp x) (exp x)) (* 2.0 2.0)) (* (- (pow (exp x) 3) (pow 2.0 3)) (pow (exp x) 2))) (* (+ (exp x) 2.0) (+ (pow (exp x) 2) (* 2.0 (+ 2.0 (exp x)))))) (* (* (+ (exp x) 2.0) (+ (pow (exp x) 2) (* 2.0 (+ 2.0 (exp x))))) (pow (exp x) 2)))
295.0ms	(- (* (- (* (exp x) (exp x)) (* 2.0 2.0)) (* (- (pow (exp x) 3) (pow 2.0 3)) (pow (exp x) 2))) (* (+ (exp x) 2.0) (+ (pow (exp x) 2) (* 2.0 (+ 2.0 (exp x))))))

simplify134.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	2354	10502
1	5003	10250

prune2.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.7s	5705×	body	1280	valid
199.0ms	1217×	body	640	valid
185.0ms	8054×	body	80	valid
58.0ms	604×	body	320	valid
19.0ms	303×	body	160	valid