Details

sample378.0ms

Algorithm

intervals

Results

184.0ms	105×	body	1280	valid
51.0ms	58×	body	640	valid
18.0ms	71×	body	80	valid
10.0ms	16×	body	320	valid
2.0ms	6×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize46.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.9b	(cos (+ a b))

rewrite49.0ms

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*` `insert-posit16` `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 → 50

Calls

3 calls:

8.0ms	(* r (sin b))
21.0ms	(/ (* r (sin b)) (cos (+ a b)))
18.0ms	(cos (+ a b))

series253.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* r (sin b))
145.0ms	(/ (* r (sin b)) (cos (+ a b)))
32.0ms	(cos (+ a b))

simplify699.0ms

Counts

59 → 59

Iterations

Iter	Nodes
3	2151
2	565
1	203
0	95

prune583.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`associate-/r/` `insert-posit16`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `div-inv` `associate-/l*`

Counts

4 → 81

Calls

4 calls:

19.0ms	(* (cos a) (cos b))
34.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
30.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(* (sin a) (sin b))

series649.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (cos a) (cos b))
114.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
383.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
91.0ms	(* (sin a) (sin b))

simplify4.4s

Counts

93 → 93

Iterations

Iter	Nodes
3	4519
2	1186
1	390
0	160

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-*r/`

Counts

4 → 104

Calls

4 calls:

27.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
92.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
39.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))

series729.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
367.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
160.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
89.0ms	(* (sin a) (sin b))

simplify3.7s

Counts

116 → 116

Iterations

Iter	Nodes
3	4427
2	1415
1	435
0	175

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
3.1b	(log (exp (* (sin a) (sin b))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`log-prod` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `times-frac` `associate-r` `associate-l*` `log-pow` `associate--r+`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--`
1×	`exp-prod` `clear-num` `sub-neg` `frac-2neg` `exp-to-pow` `diff-log` `rem-log-exp` `pow-prod-down` `-commutative` `div-inv` `sin-mult` `associate-/l` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

13.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
27.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
11.0ms	(* (sin a) (sin b))
4.0ms	(log (exp (* (sin a) (sin b))))

series568.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
328.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
54.0ms	(* (sin a) (sin b))
52.0ms	(log (exp (* (sin a) (sin b))))

simplify1.8s

Counts

87 → 87

Iterations

Iter	Nodes
3	3836
2	999
1	340
0	146

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes305.0ms

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

sample7.5s

Algorithm

intervals

Results

3.7s	2928×	body	1280	valid
2.2s	1851×	body	640	valid
842.0ms	715×	body	320	valid
442.0ms	2209×	body	80	valid
107.0ms	298×	body	160	valid