Details

sample78.0ms

Algorithm

intervals

Results

31.0ms	56×	body	1280	valid
16.0ms	47×	body	640	valid
14.0ms	141×	body	80	valid
5.0ms	21×	body	320	valid
2.0ms	13×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 69

Calls

3 calls:

0.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))

series145.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
39.0ms	(/ 1.0 (tan B))

simplify54.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	246	416
1	694	382
2	2127	382
3	5002	377

prune219.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (cos B) (sin B))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`fma-udef`

Counts

3 → 68

Calls

3 calls:

0.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
9.0ms	(/ (cos B) (sin B))

series122.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(fma (- x) (* 1.0 (/ (cos B) (sin B))) (/ 1.0 (sin B)))
17.0ms	(/ 1.0 (sin B))
18.0ms	(/ (cos B) (sin B))

simplify57.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	241	480
1	721	438
2	2196	438
3	5001	433

prune208.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.2b	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))
0.2b	(* x (cos B))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-l`
12×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-r` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
3×	`expm1-log1p-u` `prod-exp` `associate-/r` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `sub-neg` `flip3--` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv`
1×	`frac-2neg` `associate-*l/` `clear-num`

Counts

3 → 97

Calls

3 calls:

5.0ms	(/ 1.0 (sin B))
30.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))
8.0ms	(* x (cos B))

series115.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(/ 1.0 (sin B))
66.0ms	(* (/ 1.0 (sin B)) (- 1 (* x (cos B))))
31.0ms	(* x (cos B))

simplify52.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	415	714
1	2094	633
2	5002	629

prune348.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1 (* x (cos B))))
0.2b	(cbrt (- 1 (* x (cos B))))
0.2b	(cbrt (- 1 (* x (cos B))))
0.2b	(* (cbrt (- 1 (* x (cos B)))) (cbrt (- 1 (* x (cos B)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

3.0ms	(cbrt (- 1 (* x (cos B))))
3.0ms	(cbrt (- 1 (* x (cos B))))
3.0ms	(cbrt (- 1 (* x (cos B))))
30.0ms	(* (cbrt (- 1 (* x (cos B)))) (cbrt (- 1 (* x (cos B)))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(cbrt (- 1 (* x (cos B))))
51.0ms	(cbrt (- 1 (* x (cos B))))
55.0ms	(cbrt (- 1 (* x (cos B))))
61.0ms	(* (cbrt (- 1 (* x (cos B)))) (cbrt (- 1 (* x (cos B)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	311	1261
1	1405	1184
2	5002	1121

prune323.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	6
1	14	6

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1736×	body	1280	valid
474.0ms	1396×	body	640	valid
387.0ms	4937×	body	80	valid
178.0ms	743×	body	320	valid
68.0ms	392×	body	160	valid