Details

sample75.0ms

Algorithm

intervals

Results

52.0ms	186×	body	1280	valid
6.0ms	261×	body	80	valid
6.0ms	41×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	6×	body	160	valid

simplify223.0ms

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	104	5
6	161	5
7	344	5
8	1454	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: 27.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
2.8b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `expm1-log1p-u` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

2 → 65

Calls

2 calls:

4.0ms	(- (exp x) 2.0)
9.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series74.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
61.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify33.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	282	506
1	1008	381
2	5001	367

prune163.0ms

Filtered

71 candidates to 51 candidates (71.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`add-exp-log`
7×	`associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 47

Calls

3 calls:

4.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
1.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
5.0ms	(* 1/12 (pow x 4))

series226.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
132.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
38.0ms	(* 1/12 (pow x 4))

simplify97.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	143	265
1	544	240
2	2626	237
3	5001	237

prune147.0ms

Filtered

56 candidates to 39 candidates (69.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp x) 2.0) (exp x))
0.0b	(fma (- 2.0) 2.0 (exp (+ x x)))
0.0b	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
3.3b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-exp-log`
8×	`add-cube-cbrt`
6×	`pow1`
4×	`expm1-log1p-u` `associate-l` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `associate-/l*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `fma-udef`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

7.0ms	(* (+ (exp x) 2.0) (exp x))
1.0ms	(fma (- 2.0) 2.0 (exp (+ x x)))
11.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
1.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series387.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (+ (exp x) 2.0) (exp x))
43.0ms	(fma (- 2.0) 2.0 (exp (+ x x)))
223.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
97.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	309	842
1	1272	718
2	5002	714

prune235.0ms

Filtered

80 candidates to 66 candidates (82.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp x) 2.0) (exp x))
0.0b	(/ 1 (/ (* (+ (exp x) 2.0) (exp x)) (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))))
0.0b	(/ (* (+ (exp x) 2.0) (exp x)) (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)))
3.3b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
27×	`add-exp-log`
26×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`add-cube-cbrt`
20×	`add-cbrt-cube`
14×	`div-exp`
10×	`associate-/r*`
7×	`pow1` `cbrt-undiv`
6×	`div-inv`
5×	`prod-exp`
4×	`expm1-log1p-u` `associate-l` `associate-l/` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-r` `cbrt-unprod`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
1×	`pow-flip` `pow-prod-down` `associate-/r/` `*-commutative` `fma-udef` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

8.0ms	(* (+ (exp x) 2.0) (exp x))
9.0ms	(/ 1 (/ (* (+ (exp x) 2.0) (exp x)) (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))))
9.0ms	(/ (* (+ (exp x) 2.0) (exp x)) (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)))
1.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series592.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (+ (exp x) 2.0) (exp x))
231.0ms	(/ 1 (/ (* (+ (exp x) 2.0) (exp x)) (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))))
240.0ms	(/ (* (+ (exp x) 2.0) (exp x)) (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)))
99.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	493	1989
1	2442	1742
2	5001	1686

prune283.0ms

Filtered

128 candidates to 80 candidates (62.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes25.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.6s	5633×	body	1280	valid
186.0ms	1233×	body	640	valid
176.0ms	8092×	body	80	valid
58.0ms	657×	body	320	valid
16.0ms	285×	body	160	valid