Details

sample277.0ms

Algorithm

intervals

Results

89.0ms	91×	body	1280	valid
33.0ms	60×	body	640	valid
13.0ms	31×	body	320	valid
8.0ms	65×	body	80	valid
3.0ms	9×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize74.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
2.3b	(cos (+ a b))

rewrite35.0ms

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:

7.0ms	(* r (sin b))
11.0ms	(/ (* r (sin b)) (cos (+ a b)))
15.0ms	(cos (+ a b))

series258.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* r (sin b))
157.0ms	(/ (* r (sin b)) (cos (+ a b)))
39.0ms	(cos (+ a b))

simplify1.1s

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
2	883
1	220
0	98

prune441.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

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:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
12.0ms	(* (sin a) (sin b))
43.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series571.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
49.0ms	(* r (sin b))
76.0ms	(* (sin a) (sin b))
324.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1708
1	389
0	153

prune934.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

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))

rewrite152.0ms

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 a) (sin b)))
63.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
40.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms	(* (sin a) (sin b))

series744.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
343.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
190.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
84.0ms	(* (sin a) (sin b))

simplify1.8s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1967
1	467
0	182

prune959.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
16×	`associate-r`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `prod-exp` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `frac-2neg` `associate-*r/` `fma-udef` `sin-mult`

Counts

4 → 94

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
14.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
8.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
9.0ms	(* (sin a) (sin b))

series736.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
348.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
162.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
91.0ms	(* (sin a) (sin b))

simplify1.7s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1701
1	374
0	156

prune818.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes386.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.3s	2868×	body	1280	valid
1.4s	1875×	body	640	valid
332.0ms	2150×	body	80	valid
260.0ms	768×	body	320	valid
87.0ms	339×	body	160	valid