Details

sample83.0ms

Algorithm

intervals

Results

55.0ms	173×	body	1280	valid
7.0ms	42×	body	640	valid
7.0ms	251×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	14×	body	160	valid

simplify216.0ms

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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.5b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.8b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite15.0ms

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)))

series68.0ms

Counts

2 → 6

Calls

2 calls:

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

prune144.0ms

Filtered

71 candidates to 51 candidates (71.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	3	72

Merged error: 0.0b

Counts

72 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

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

series152.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
34.0ms	(* 1/12 (pow x 4))

simplify86.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	123	177
1	469	163
2	2175	160
3	5002	160

prune87.0ms

Filtered

43 candidates to 29 candidates (67.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	43	3	46

Merged error: 0.0b

Counts

46 → 3

localize11.0ms

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)))
4.4b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite21.0ms

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)))
10.0ms	(/ (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))

series354.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (+ (exp x) 2.0) (exp x))
36.0ms	(fma (- 2.0) 2.0 (exp (+ x x)))
207.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
89.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (33.0ms)

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

prune184.0ms

Filtered

80 candidates to 66 candidates (82.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	80	3	83

Merged error: 0.0b

Counts

83 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (exp x) 2.0))
0.0b	(cbrt (- (exp x) 2.0))
0.0b	(cbrt (- (exp x) 2.0))
6.0b	(fma (* (cbrt (- (exp x) 2.0)) (cbrt (- (exp x) 2.0))) (cbrt (- (exp x) 2.0)) (exp (- x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

4.0ms	(cbrt (- (exp x) 2.0))
4.0ms	(cbrt (- (exp x) 2.0))
4.0ms	(cbrt (- (exp x) 2.0))
1.0ms	(fma (* (cbrt (- (exp x) 2.0)) (cbrt (- (exp x) 2.0))) (cbrt (- (exp x) 2.0)) (exp (- x)))

series734.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(cbrt (- (exp x) 2.0))
137.0ms	(cbrt (- (exp x) 2.0))
131.0ms	(cbrt (- (exp x) 2.0))
336.0ms	(fma (* (cbrt (- (exp x) 2.0)) (cbrt (- (exp x) 2.0))) (cbrt (- (exp x) 2.0)) (exp (- x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	228	609
1	691	551
2	2839	527
3	5001	507

prune187.0ms

Filtered

73 candidates to 60 candidates (82.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	72	4	76

Merged error: 0.0b

Counts

76 → 4

regimes21.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.8s	5590×	body	1280	valid
215.0ms	1269×	body	640	valid
212.0ms	7927×	body	80	valid
64.0ms	609×	body	320	valid
23.0ms	337×	body	160	valid