Details

sample248.0ms

Algorithm

intervals

Results

67.0ms	90×	body	1280	valid
47.0ms	11×	body	160	valid
30.0ms	61×	body	640	valid
10.0ms	69×	body	80	valid
7.0ms	25×	body	320	valid

simplify18.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.1b	(cos (+ a b))

rewrite459.0ms

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*` `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 → 53

Calls

3 calls:

9.0ms	(* r (sin b))
11.0ms	(/ (* r (sin b)) (cos (+ a b)))
11.0ms	(cos (+ a b))

series399.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* r (sin b))
272.0ms	(/ (* r (sin b)) (cos (+ a b)))
85.0ms	(cos (+ a b))

simplify1.1s

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
2	883
1	220
0	98

prune469.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite116.0ms

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×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

14.0ms	(* r (sin b))
33.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
20.0ms	(* (sin a) (sin b))
46.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* r (sin b))
124.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
84.0ms	(* (sin a) (sin b))
308.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.0s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1688
1	389
0	153

prune692.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

rewrite54.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

8.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
19.0ms	(* (sin a) (sin b))
26.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series548.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* r (sin b))
102.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
82.0ms	(* (sin a) (sin b))
324.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify1.4s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	1342
1	301
0	129

prune616.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite182.0ms

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×	`expm1-log1p-u` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `associate-*r/`

Counts

4 → 110

Calls

4 calls:

25.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
38.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
19.0ms	(* (sin b) (sin a))
94.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

series730.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
161.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
65.0ms	(* (sin b) (sin a))
345.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

simplify2.0s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	2084
1	468
0	188

prune1.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes442.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
2	20
1	18
0	12

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.9s	2883×	body	1280	valid
920.0ms	1829×	body	640	valid
726.0ms	808×	body	320	valid
404.0ms	2146×	body	80	valid
81.0ms	336×	body	160	valid