Details

sample70.0ms

Algorithm

intervals

Results

30.0ms	98×	body	1280	valid
15.0ms	80×	body	640	valid
8.0ms	258×	body	80	valid
5.0ms	45×	body	320	valid
1.0ms	17×	body	160	valid

simplify219.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	23	5
2	31	5
3	36	5
4	41	5
5	65	5
6	108	5
7	267	5
8	1342	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: 56.8b

Counts

2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

5.9b	(- (exp x) (exp (- x)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

5.0ms

(- (exp x) (exp (- x)))

series39.0ms

Counts

1 → 3

Calls

1 calls:

39.0ms

(- (exp x) (exp (- x)))

simplify112.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	158	354
1	416	228
2	2421	226
3	5002	203

prune59.0ms

Filtered

31 candidates to 18 candidates (58.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	2	32

Merged error: 0.0b

Counts

32 → 2

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))

series56.0ms

Counts

1 → 3

Calls

1 calls:

56.0ms

(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))

simplify30.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	49	89
1	150	78
2	862	78
3	5001	78

prune30.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	13	2	15

Merged error: 0.0b

Counts

15 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(/ (fma (- 1) (pow (exp x) -2) (exp (+ x x))) (+ (exp x) (exp (- x))))
0.1b	(pow (exp x) -2)
5.8b	(fma (- 1) (pow (exp x) -2) (exp (+ x x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow1` `distribute-lft-out`
4×	`expm1-log1p-u` `pow-pow` `associate-/r*` `log1p-expm1-u`
3×	`unpow-prod-down` `pow-unpow` `exp-prod` `fma-def` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `div-exp` `pow-exp` `clear-num` `sum-log` `fma-udef` `div-inv` `sqr-pow`

Counts

4 → 84

Calls

4 calls:

5.0ms	(+ (exp x) (exp (- x)))
6.0ms	(/ (fma (- 1) (pow (exp x) -2) (exp (+ x x))) (+ (exp x) (exp (- x))))
3.0ms	(pow (exp x) -2)
1.0ms	(fma (- 1) (pow (exp x) -2) (exp (+ x x)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (exp x) (exp (- x)))
110.0ms	(/ (fma (- 1) (pow (exp x) -2) (exp (+ x x))) (+ (exp x) (exp (- x))))
22.0ms	(pow (exp x) -2)
69.0ms	(fma (- 1) (pow (exp x) -2) (exp (+ x x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	328	934
1	1277	846
2	5002	813

prune240.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	96	2	98

Merged error: 0.0b

Counts

98 → 2

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(/ (fma (- 1) (exp (* x -2)) (exp (+ x x))) (+ (exp x) (exp (- x))))
5.8b	(fma (- 1) (exp (* x -2)) (exp (+ x x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
4×	`associate-/r*`
3×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `fma-udef` `div-inv`

Counts

3 → 62

Calls

3 calls:

5.0ms	(+ (exp x) (exp (- x)))
6.0ms	(/ (fma (- 1) (exp (* x -2)) (exp (+ x x))) (+ (exp x) (exp (- x))))
1.0ms	(fma (- 1) (exp (* x -2)) (exp (+ x x)))

series168.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (exp x) (exp (- x)))
91.0ms	(/ (fma (- 1) (exp (* x -2)) (exp (+ x x))) (+ (exp x) (exp (- x))))
55.0ms	(fma (- 1) (exp (* x -2)) (exp (+ x x)))

simplify218.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	257	851
1	829	770
2	4655	745
3	5001	745

prune191.0ms

Filtered

71 candidates to 58 candidates (81.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	70	3	73

Merged error: 0b

Counts

73 → 3

regimes20.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	6
1	14	6

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.0s	3317×	body	1280	valid
471.0ms	2482×	body	640	valid
245.0ms	8030×	body	80	valid
151.0ms	1251×	body	320	valid
52.0ms	652×	body	160	valid