Details

sample351.0ms

Algorithm

intervals

Results

151.0ms	97×	body	1280	valid
46.0ms	56×	body	640	valid
16.0ms	69×	body	80	valid
12.0ms	19×	body	320	valid
5.0ms	15×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	20
5	20
4	19
3	17
2	14
1	12
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize33.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.8b	(cos (+ a b))

rewrite28.0ms

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×	`associate-/r` `times-frac` `associate-r` `associate-l*` `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 → 47

Calls

3 calls:

7.0ms	(* r (sin b))
11.0ms	(/ (* r (sin b)) (cos (+ a b)))
8.0ms	(cos (+ a b))

series231.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(* r (sin b))
132.0ms	(/ (* r (sin b)) (cos (+ a b)))
29.0ms	(cos (+ a b))

simplify680.0ms

Counts

56 → 56

Iterations

Iter	Nodes
3	2224
2	564
1	200
0	92

prune521.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

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×	`prod-exp` `associate-/r/` `cbrt-unprod` `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 → 81

Calls

4 calls:

7.0ms	(* r (sin b))
8.0ms	(* (cos a) (cos b))
14.0ms	(* (sin a) (sin b))
52.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series982.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* r (sin b))
63.0ms	(* (cos a) (cos b))
61.0ms	(* (sin a) (sin b))
796.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify4.3s

Counts

93 → 93

Iterations

Iter	Nodes
3	4504
2	1165
1	380
0	158

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

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×	`prod-exp` `cbrt-unprod` `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 → 105

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
9.0ms	(* (sin a) (sin b))
76.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
22.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series649.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos a) (cos b))
72.0ms	(* (sin a) (sin b))
328.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
200.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify5.8s

Counts

117 → 117

Iterations

Iter	Nodes
3	4386
2	1466
1	457
0	188

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin b) (sin a))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
0.3b	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
27.6b	(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))

rewrite353.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
29×	`sin-mult`
23×	`add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down`
14×	`cbrt-div`
11×	`frac-times` `associate-*l/`
10×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
9×	`associate-/r/`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-*r/` `cos-mult` `frac-sub`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up` `add-log-exp`
3×	`associate-/r*` `times-frac`
2×	`cbrt-undiv` `pow-plus` `div-exp` `*-commutative`
1×	`cbrt-prod` `pow2` `clear-num` `frac-2neg` `flip3--` `pow1/3` `swap-sqr` `pow3` `rem-cbrt-cube` `div-inv` `flip--` `associate-/l*` `unswap-sqr`

Counts

4 → 103

Calls

4 calls:

16.0ms	(* (sin b) (sin a))
156.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
37.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
142.0ms	(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))

series524.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin b) (sin a))
324.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
74.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
58.0ms	(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))

simplify4.5s

Counts

115 → 115

Iterations

Iter	Nodes
3	6590
2	1679
1	493
0	202

prune1.7s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes342.0ms

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
2	15
1	15
0	12

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.2s	3000×	body	1280	valid
2.0s	1822×	body	640	valid
451.0ms	729×	body	320	valid
431.0ms	2106×	body	80	valid
192.0ms	343×	body	160	valid