Details

sample161.0ms

Algorithm

intervals

Results

56.0ms	50×	body	1280	valid
46.0ms	39×	body	640	valid
27.0ms	173×	body	80	valid
11.0ms	26×	body	320	valid
4.0ms	10×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	62
6	62
5	60
4	54
3	43
2	33
1	18
0	10

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (/ x (tan B)) (- 1.0) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ x (tan B))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 69

Calls

3 calls:

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

series336.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(fma (/ x (tan B)) (- 1.0) (/ 1.0 (sin B)))
35.0ms	(/ 1.0 (sin B))
167.0ms	(/ x (tan B))

simplify977.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
3	3228
2	740
1	263
0	137

prune462.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (/ 1 (/ (tan B) x)) (- 1.0) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ (tan B) x)
0.3b	(/ 1 (/ (tan B) x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

93×	`times-frac`
62×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
19×	`associate-/r*` `add-exp-log`
13×	`add-cbrt-cube`
9×	`div-exp` `associate-/l*`
7×	`div-inv`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`rec-exp` `1-exp`
1×	`tan-quot` `associate-/r/` `fma-udef` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 147

Calls

4 calls:

0.0ms	(fma (/ 1 (/ (tan B) x)) (- 1.0) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
9.0ms	(/ (tan B) x)
12.0ms	(/ 1 (/ (tan B) x))

series321.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(fma (/ 1 (/ (tan B) x)) (- 1.0) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
53.0ms	(/ (tan B) x)
82.0ms	(/ 1 (/ (tan B) x))

simplify905.0ms

Counts

159 → 159

Iterations

Iter	Nodes
done	5001
2	2267
1	563
0	246

prune737.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (/ 1 (* (tan B) (/ 1 x))) (- 1.0) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.3b	(/ 1 (* (tan B) (/ 1 x)))
0.3b	(* (tan B) (/ 1 x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
29×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
22×	`add-cube-cbrt`
20×	`add-cbrt-cube`
19×	`div-exp`
16×	`prod-exp`
13×	`associate-r`
9×	`pow1` `rec-exp` `1-exp`
6×	`cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `tan-quot` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `div-inv` `unswap-sqr`
2×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `pow-flip`
1×	`*-commutative` `fma-udef` `inv-pow`

Counts

4 → 123

Calls

4 calls:

0.0ms	(fma (/ 1 (* (tan B) (/ 1 x))) (- 1.0) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
27.0ms	(/ 1 (* (tan B) (/ 1 x)))
27.0ms	(* (tan B) (/ 1 x))

series340.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(fma (/ 1 (* (tan B) (/ 1 x))) (- 1.0) (/ 1.0 (sin B)))
28.0ms	(/ 1.0 (sin B))
89.0ms	(/ 1 (* (tan B) (/ 1 x)))
66.0ms	(* (tan B) (/ 1 x))

simplify987.0ms

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
2	2502
1	533
0	215

prune708.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* (/ x (sin B)) (cos B)) (- 1.0) (/ 1.0 (sin B)))
0.1b	(/ x (sin B))
0.1b	(/ 1.0 (sin B))
0.1b	(* (/ x (sin B)) (cos B))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `associate-l` `add-exp-log`
6×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`pow-prod-down` `associate-l/` `-commutative` `fma-udef`

Counts

4 → 102

Calls

4 calls:

0.0ms	(fma (* (/ x (sin B)) (cos B)) (- 1.0) (/ 1.0 (sin B)))
8.0ms	(/ x (sin B))
7.0ms	(/ 1.0 (sin B))
31.0ms	(* (/ x (sin B)) (cos B))

series397.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(fma (* (/ x (sin B)) (cos B)) (- 1.0) (/ 1.0 (sin B)))
80.0ms	(/ x (sin B))
33.0ms	(/ 1.0 (sin B))
108.0ms	(* (/ x (sin B)) (cos B))

simplify696.0ms

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	1414
1	362
0	164

prune974.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes227.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	10

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.2s	1734×	body	1280	valid
1.7s	1499×	body	640	valid
1.4s	4856×	body	80	valid
346.0ms	681×	body	320	valid
186.0ms	379×	body	160	valid