Details

sample78.0ms

Algorithm

intervals

Results

53.0ms	178×	body	1280	valid
7.0ms	43×	body	640	valid
6.0ms	249×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	12×	body	160	valid

simplify218.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.3b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite29.0ms

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)
24.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series68.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
55.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify97.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	211	282
1	715	269
2	3477	260
3	5001	260

prune86.0ms

Filtered

41 candidates to 29 candidates (70.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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:

3.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
11.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
7.0ms	(* 1/360 (pow x 6))
6.0ms	(* 1/12 (pow x 4))

series272.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
59.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
51.0ms	(* 1/360 (pow x 6))
35.0ms	(* 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

prune191.0ms

Filtered

87 candidates to 55 candidates (63.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 2.0)
0.0b	(+ (exp x) 2.0)
0.0b	(/ (* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
3.8b	(+ (* (exp x) (- (exp x) 2.0)) 1)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-cbrt-cube`
14×	`add-exp-log`
10×	`flip3-+` `flip-+` `add-log-exp`
8×	`*-un-lft-identity` `associate-/l/`
4×	`pow1` `cbrt-undiv` `add-sqr-sqrt` `frac-times` `add-cube-cbrt` `associate-+l+` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod`
3×	`+-commutative` `sum-log`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/` `associate-/r/` `distribute-lft-out`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

4.0ms	(+ (exp x) 2.0)
4.0ms	(+ (exp x) 2.0)
26.0ms	(/ (* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
9.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)

series169.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (exp x) 2.0)
8.0ms	(+ (exp x) 2.0)
96.0ms	(/ (* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
58.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)

simplify71.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	448	849
1	2517	617
2	5002	600

prune164.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (exp x) 2.0)
4.3b	(log (exp (+ (- (exp x) 2.0) (exp (- x)))))
4.3b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`add-sqr-sqrt`
6×	`log-pow`
5×	`add-cube-cbrt` `exp-prod`
4×	`pow1` `log-prod` `frac-add` `distribute-lft-out`
3×	`add-exp-log` `flip3--` `exp-diff` `add-cbrt-cube` `flip--` `distribute-lft-out--`
2×	`neg-sub0` `exp-neg` `associate-+l-` `sub-neg` `associate-+l+` `diff-log` `sum-log`
1×	`+-commutative` `log-div` `flip3-+` `rem-log-exp` `exp-sum` `flip-+` `difference-of-squares`

Counts

3 → 54

Calls

3 calls:

4.0ms	(- (exp x) 2.0)
64.0ms	(log (exp (+ (- (exp x) 2.0) (exp (- x)))))
24.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series126.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(- (exp x) 2.0)
56.0ms	(log (exp (+ (- (exp x) 2.0) (exp (- x)))))
57.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify95.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	243	437
1	800	405
2	3640	396
3	5002	396

prune118.0ms

Filtered

63 candidates to 41 candidates (65.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes31.0ms

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

sample2.3s

Algorithm

intervals

Results

1.7s	5703×	body	1280	valid
185.0ms	7946×	body	80	valid
182.0ms	1152×	body	640	valid
61.0ms	649×	body	320	valid
20.0ms	323×	body	160	valid