Details

sample351.0ms

Algorithm

intervals

Results

127.0ms	95×	body	1280	valid
109.0ms	48×	body	640	valid
13.0ms	68×	body	80	valid
11.0ms	27×	body	320	valid
6.0ms	18×	body	160	valid

simplify117.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
4	20
3	19
2	16
1	12
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.1b	(cos (+ a b))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `times-frac` `associate-r` `associate-l*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 56

Calls

3 calls:

9.0ms	(* r (sin b))
12.0ms	(/ (* r (sin b)) (cos (+ a b)))
9.0ms	(cos (+ a b))

series226.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(* r (sin b))
131.0ms	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify1.1s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
2	894
1	223
0	101

prune352.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `div-inv` `flip--` `associate-/l*` `sub-div`

Counts

4 → 93

Calls

4 calls:

19.0ms	(* (cos a) (cos b))
18.0ms	(* r (sin b))
53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))

series508.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos a) (cos b))
60.0ms	(* r (sin b))
304.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
88.0ms	(* (sin a) (sin b))

simplify1.4s

Counts

105 → 105

Iterations

Iter	Nodes
done	5002
2	1817
1	411
0	170

prune617.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
19×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`clear-num` `frac-2neg` `associate-*r/`

Counts

4 → 117

Calls

4 calls:

16.0ms	(* (cos a) (cos b))
88.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
13.0ms	(* (sin a) (sin b))
27.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series640.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (cos a) (cos b))
325.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
78.0ms	(* (sin a) (sin b))
174.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.6s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	2055
1	486
0	200

prune870.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(* (sin b) r)
0.2b	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
0.2b	(* (sin b) (sin a))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `div-inv` `flip--` `associate-/l*` `sub-div`

Counts

4 → 93

Calls

4 calls:

15.0ms	(* (cos a) (cos b))
17.0ms	(* (sin b) r)
41.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
15.0ms	(* (sin b) (sin a))

series595.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos a) (cos b))
67.0ms	(* (sin b) r)
399.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
74.0ms	(* (sin b) (sin a))

simplify1.8s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
2	2000
1	406
0	172

prune683.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes361.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.1s	2918×	body	1280	valid
1.6s	1912×	body	640	valid
449.0ms	2095×	body	80	valid
414.0ms	705×	body	320	valid
163.0ms	370×	body	160	valid