Details

sample75.0ms

Algorithm

intervals

Results

51.0ms	178×	body	1280	valid
6.0ms	38×	body	640	valid
6.0ms	245×	body	80	valid
2.0ms	27×	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	1452	5
9	5002	5

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 31.7b

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)))

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)))

series75.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
62.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	279	506
1	980	381
2	5002	367

prune131.0ms

Filtered

71 candidates to 51 candidates (28.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	69	3	72

Merged error: 0.0b

Counts

72 → 3

localize9.0ms

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))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

1.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
6.0ms	(* 1/12 (pow x 4))

series170.0ms

Counts

2 → 6

Calls

2 calls:

130.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
40.0ms	(* 1/12 (pow x 4))

simplify85.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	123	179
1	469	165
2	2154	162
3	5002	162

prune85.0ms

Filtered

44 candidates to 29 candidates (34.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	44	3	47

Merged error: 0.0b

Counts

47 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3))
0.0b	(pow (exp x) 3)
0.0b	(pow (exp x) 3)
4.3b	(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`pow-pow`
6×	`pow1` `add-exp-log` `unpow-prod-down` `pow-unpow` `exp-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow3` `fma-udef` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

1.0ms	(fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3))
3.0ms	(pow (exp x) 3)
3.0ms	(pow (exp x) 3)
1.0ms	(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

series259.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3))
24.0ms	(pow (exp x) 3)
24.0ms	(pow (exp x) 3)
131.0ms	(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

simplify176.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (170.0ms)

Iter	Nodes	Cost
0	220	430
1	812	380
2	4337	373
3	5001	372

prune240.0ms

Filtered

82 candidates to 58 candidates (29.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	82	3	85

Merged error: 0.0b

Counts

85 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 3)
0.0b	(* (sqrt (fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))) (sqrt (fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))))
4.3b	(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))
4.3b	(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
20×	`pow1`
18×	`sqrt-prod`
15×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`unpow-prod-down` `pow-unpow` `exp-prod` `pow-prod-down` `pow-sqr`
2×	`pow-exp` `fma-udef`
1×	`pow2` `pow-to-exp` `pow-plus` `sqrt-unprod` `unpow3` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

3.0ms	(pow (exp x) 3)
6.0ms	(* (sqrt (fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))) (sqrt (fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))))
1.0ms	(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))
1.0ms	(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow (exp x) 3)
132.0ms	(* (sqrt (fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))) (sqrt (fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))))
136.0ms	(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))
131.0ms	(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

simplify50.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	256	1315
1	1074	1140
2	5001	1064

prune306.0ms

Filtered

108 candidates to 66 candidates (38.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	108	3	111

Merged error: 0.0b

Counts

111 → 3

regimes37.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

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	5570×	body	1280	valid
200.0ms	1274×	body	640	valid
177.0ms	7959×	body	80	valid
68.0ms	643×	body	320	valid
21.0ms	353×	body	160	valid