Details

sample110.0ms

Algorithm: halfpoints

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	7
1	47	7
2	84	7
3	131	7
4	223	7
5	466	7
6	1123	7
7	2244	7
8	5002	7

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(+ (exp x) (exp (- x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`associate-l`
13×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `distribute-lft-out` `add-log-exp`
3×	`fma-def` `associate-r`
2×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `div-exp` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 54

Calls

2 calls:

10.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
5.0ms	(+ (exp x) (exp (- x)))

series82.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
24.0ms	(+ (exp x) (exp (- x)))

simplify174.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	286	487
1	1053	428
2	4913	426
3	5001	426

prune135.0ms

Filtered

60 candidates to 47 candidates (78.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	2	61

Merged error: 0b

Counts

61 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(+ (exp x) (exp (- x)))
0.2b	(log1p (expm1 (* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))))
0.6b	(expm1 (* (/ (+ (exp x) (exp (- x))) 2.0) (cos y)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
16×	`associate-l`
14×	`add-cube-cbrt`
13×	`times-frac`
9×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `distribute-lft-out`
3×	`fma-def` `associate-r`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `log1p-udef` `expm1-log1p` `flip3-+` `log1p-expm1` `div-exp` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `div-inv` `expm1-udef`

Counts

4 → 76

Calls

4 calls:

10.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
5.0ms	(+ (exp x) (exp (- x)))
1.0ms	(log1p (expm1 (* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))))
1.0ms	(expm1 (* (/ (+ (exp x) (exp (- x))) 2.0) (cos y)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
22.0ms	(+ (exp x) (exp (- x)))
94.0ms	(log1p (expm1 (* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))))
94.0ms	(expm1 (* (/ (+ (exp x) (exp (- x))) 2.0) (cos y)))

simplify39.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	343	754
1	1197	661
2	5001	657

prune215.0ms

Filtered

88 candidates to 69 candidates (78.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	88	2	90

Merged error: 0b

Counts

90 → 2

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (fma 1/12 (pow x 4) 2))
0.0b	(fma 1/12 (pow x 4) 2)
0.0b	(* (/ (fma x x (fma 1/12 (pow x 4) 2)) 2.0) (cos y))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`associate-l`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

3 → 54

Calls

3 calls:

1.0ms	(fma x x (fma 1/12 (pow x 4) 2))
1.0ms	(fma 1/12 (pow x 4) 2)
6.0ms	(* (/ (fma x x (fma 1/12 (pow x 4) 2)) 2.0) (cos y))

series192.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(fma x x (fma 1/12 (pow x 4) 2))
81.0ms	(fma 1/12 (pow x 4) 2)
71.0ms	(* (/ (fma x x (fma 1/12 (pow x 4) 2)) 2.0) (cos y))

simplify119.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	224	417
1	879	363
2	4402	360
3	5001	359

prune141.0ms

Filtered

63 candidates to 49 candidates (77.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	63	2	65

Merged error: 0b

Counts

65 → 2

regimes29.0ms

Accuracy

0% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	9
1	14	9

end0.0ms

sample1.8s

Algorithm: halfpoints