Details

sample263.0ms

Algorithm

intervals

Results

81.0ms	91×	body	1280	valid
31.0ms	56×	body	640	valid
10.0ms	25×	body	320	valid
9.0ms	75×	body	80	valid
2.0ms	9×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.3b	(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))
9.0ms	(/ (* r (sin b)) (cos (+ a b)))
10.0ms	(cos (+ a b))

series215.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(* r (sin b))
113.0ms	(/ (* r (sin b)) (cos (+ a b)))
34.0ms	(cos (+ a b))

simplify713.0ms

Counts

56 → 56

Iterations

Useful iterations: done (711.0ms)

Iter	Nodes	Cost
0	92	535
1	211	525
2	870	453
done	5001	443

prune344.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

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×	`sin-mult`
4×	`associate-/r/` `cos-mult`
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 → 76

Calls

4 calls:

26.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms	(* r (sin b))
26.0ms	(* (sin a) (sin b))
31.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
54.0ms	(* r (sin b))
55.0ms	(* (sin a) (sin b))
358.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify939.0ms

Counts

88 → 88

Iterations

Useful iterations: done (935.0ms)

Iter	Nodes	Cost
0	141	1256
1	365	1224
2	1577	1084
done	5000	1024

prune681.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite157.0ms

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`
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 → 100

Calls

4 calls:

14.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
19.0ms	(* (sin a) (sin b))
83.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
39.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series636.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
51.0ms	(* (sin a) (sin b))
316.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
178.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify899.0ms

Counts

112 → 112

Iterations

Useful iterations: done (896.0ms)

Iter	Nodes	Cost
0	171	2072
1	441	2028
2	1858	1842
done	5001	1766

prune663.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-cbrt-cube` `add-exp-log`
30×	`sin-mult`
29×	`cos-mult`
24×	`frac-times`
19×	`times-frac` `associate-/l/`
18×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/r*` `flip3-+` `frac-add` `flip-+`
12×	`cbrt-undiv` `div-exp`
10×	`associate-/r/`
8×	`pow1` `flip3--` `associate-*l/` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `sub-div`
6×	`associate-r` `associate-l` `associate-*r/`
4×	`div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `associate-/l` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 145

Calls

4 calls:

9.0ms	(* (sin b) (sin a))
37.0ms	(/ (* r (sin b)) (/ (* (- (* (cos a) (cos b)) (* (sin b) (sin a))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
78.0ms	(* (- (* (cos a) (cos b)) (* (sin b) (sin a))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
64.0ms	(/ (* (- (* (cos a) (cos b)) (* (sin b) (sin a))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))

series759.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin b) (sin a))
329.0ms	(/ (* r (sin b)) (/ (* (- (* (cos a) (cos b)) (* (sin b) (sin a))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
261.0ms	(* (- (* (cos a) (cos b)) (* (sin b) (sin a))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
96.0ms	(/ (* (- (* (cos a) (cos b)) (* (sin b) (sin a))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify458.0ms

Counts

157 → 157

Iterations

Useful iterations: done (447.0ms)

Iter	Nodes	Cost
0	273	6438
1	950	5082
done	5001	4306

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes323.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	15	16
done	15	16

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.5s	2928×	body	1280	valid
1.2s	1797×	body	640	valid
806.0ms	758×	body	320	valid
649.0ms	2178×	body	80	valid
138.0ms	339×	body	160	valid