Details

sample190.0ms

Algorithm

intervals

Results

51.0ms	62×	body	1280	valid
24.0ms	50×	body	640	valid
15.0ms	134×	body	80	valid
8.0ms	21×	body	320	valid
3.0ms	11×	body	160	valid

simplify113.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	56
6	56
5	54
4	48
3	41
2	33
1	18
0	10

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (* x 1.0) (tan B))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

133×	`times-frac`
107×	`add-sqr-sqrt`
104×	`*-un-lft-identity` `prod-diff`
102×	`add-cube-cbrt`
24×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `distribute-lft-out--`

Counts

3 → 188

Calls

3 calls:

53.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
5.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (tan B))

series445.0ms

Counts

3 → 9

Calls

3 calls:

197.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
29.0ms	(/ 1.0 (sin B))
219.0ms	(/ (* x 1.0) (tan B))

simplify1.9s

Counts

197 → 197

Iterations

Iter	Nodes
done	5000
2	1836
1	680
0	285

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ (* x 1.0) (sin B))
0.2b	(* (/ (* x 1.0) (sin B)) (cos B))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt` `times-frac`
31×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
13×	`fma-neg` `prod-diff`
7×	`associate-l`
6×	`pow1` `associate-/r*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-r` `associate-*l/`
2×	`clear-num` `frac-2neg`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

53.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
9.0ms	(/ 1.0 (sin B))
17.0ms	(/ (* x 1.0) (sin B))
41.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series499.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
45.0ms	(/ 1.0 (sin B))
111.0ms	(/ (* x 1.0) (sin B))
180.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify2.0s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1878
1	485
0	186

prune884.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize412.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (tan B))
0.2b	(* (/ 1 (tan B)) (* x 1.0))
0.2b	(* (/ 1 (tan B)) (* x 1.0))
61.2b	(fma (- (/ 1 (tan B))) (* x 1.0) (* (/ 1 (tan B)) (* x 1.0)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
30×	`add-cbrt-cube`
28×	`associate-l`
27×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
24×	`prod-exp`
15×	`pow1`
12×	`cbrt-unprod`
10×	`div-exp`
6×	`pow-prod-down`
5×	`cbrt-undiv` `rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `tan-quot` `associate-/r/` `div-inv` `associate-/l`
2×	`associate-r` `associate-l/` `-commutative`
1×	`clear-num` `frac-2neg` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 124

Calls

4 calls:

9.0ms	(/ 1 (tan B))
31.0ms	(* (/ 1 (tan B)) (* x 1.0))
46.0ms	(* (/ 1 (tan B)) (* x 1.0))
1.0ms	(fma (- (/ 1 (tan B))) (* x 1.0) (* (/ 1 (tan B)) (* x 1.0)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1 (tan B))
137.0ms	(* (/ 1 (tan B)) (* x 1.0))
138.0ms	(* (/ 1 (tan B)) (* x 1.0))
92.0ms	(fma (- (/ 1 (tan B))) (* x 1.0) (* (/ 1 (tan B)) (* x 1.0)))

simplify2.4s

Counts

136 → 136

Iterations

Iter	Nodes
done	5017
3	3395
2	925
1	318
0	133

prune932.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1 (tan B)))
0.5b	(cbrt (/ 1 (tan B)))
0.5b	(cbrt (/ 1 (tan B)))
61.2b	(fma (- (/ 1 (tan B))) (* x 1.0) (* (/ 1 (tan B)) (* x 1.0)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

42×	`cbrt-prod`
27×	`times-frac`
25×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `tan-quot` `associate-/r/` `div-inv`
1×	`fma-udef`

Counts

4 → 85

Calls

4 calls:

3.0ms	(cbrt (/ 1 (tan B)))
3.0ms	(cbrt (/ 1 (tan B)))
3.0ms	(cbrt (/ 1 (tan B)))
0.0ms	(fma (- (/ 1 (tan B))) (* x 1.0) (* (/ 1 (tan B)) (* x 1.0)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt (/ 1 (tan B)))
212.0ms	(cbrt (/ 1 (tan B)))
179.0ms	(cbrt (/ 1 (tan B)))
111.0ms	(fma (- (/ 1 (tan B))) (* x 1.0) (* (/ 1 (tan B)) (* x 1.0)))

simplify4.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
4	2719
3	838
2	327
1	153
0	92

prune767.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes173.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.1s	1746×	body	1280	valid
1.6s	1449×	body	640	valid
892.0ms	4902×	body	80	valid
770.0ms	688×	body	320	valid
257.0ms	353×	body	160	valid