Details

sample417.0ms

Algorithm

intervals

Results

177.0ms	91×	body	1280	valid
88.0ms	56×	body	640	valid
30.0ms	9×	body	160	valid
11.0ms	25×	body	320	valid
10.0ms	75×	body	80	valid

simplify69.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize25.0ms

Local error

Found 3 expressions with local error:

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

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×	`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 (+ b a)))
10.0ms	(cos (+ b a))

series413.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* r (sin b))
229.0ms	(/ (* r (sin b)) (cos (+ b a)))
124.0ms	(cos (+ b a))

simplify770.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
2	963
1	219
0	99

prune420.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

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:

22.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
10.0ms	(* r (sin b))
9.0ms	(* (sin b) (sin a))
21.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series600.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
68.0ms	(* r (sin b))
70.0ms	(* (sin b) (sin a))
325.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify924.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1926
1	398
0	158

prune702.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

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/` `cos-mult` `fma-udef`

Counts

4 → 94

Calls

4 calls:

16.0ms	(* (cos a) (cos b))
0.0ms	(fma (- (sin b)) (sin a) (* (cos a) (cos b)))
23.0ms	(* r (/ (sin b) (fma (- (sin b)) (sin a) (* (cos a) (cos b)))))
8.0ms	(/ (sin b) (fma (- (sin b)) (sin a) (* (cos a) (cos b))))

series717.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos a) (cos b))
125.0ms	(fma (- (sin b)) (sin a) (* (cos a) (cos b)))
360.0ms	(* r (/ (sin b) (fma (- (sin b)) (sin a) (* (cos a) (cos b)))))
187.0ms	(/ (sin b) (fma (- (sin b)) (sin a) (* (cos a) (cos b))))

simplify729.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1486
1	381
0	165

prune853.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-cbrt-cube` `add-exp-log`
18×	`add-sqr-sqrt`
16×	`times-frac`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`cbrt-undiv` `div-exp`
10×	`associate-/r*`
8×	`pow1` `prod-exp` `cbrt-unprod`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `fma-udef` `associate-/l` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`

Counts

4 → 105

Calls

4 calls:

8.0ms	(* r (sin b))
19.0ms	(/ (* r (sin b)) (/ (* (fma (sin a) (sin b) (* (cos a) (cos b))) (fma (- (sin b)) (sin a) (* (cos a) (cos b)))) (fma (sin a) (sin b) (* (cos a) (cos b)))))
11.0ms	(* (fma (sin a) (sin b) (* (cos a) (cos b))) (fma (- (sin b)) (sin a) (* (cos a) (cos b))))
15.0ms	(/ (* (fma (sin a) (sin b) (* (cos a) (cos b))) (fma (- (sin b)) (sin a) (* (cos a) (cos b)))) (fma (sin a) (sin b) (* (cos a) (cos b))))

series810.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* r (sin b))
352.0ms	(/ (* r (sin b)) (/ (* (fma (sin a) (sin b) (* (cos a) (cos b))) (fma (- (sin b)) (sin a) (* (cos a) (cos b)))) (fma (sin a) (sin b) (* (cos a) (cos b)))))
264.0ms	(* (fma (sin a) (sin b) (* (cos a) (cos b))) (fma (- (sin b)) (sin a) (* (cos a) (cos b))))
122.0ms	(/ (* (fma (sin a) (sin b) (* (cos a) (cos b))) (fma (- (sin b)) (sin a) (* (cos a) (cos b)))) (fma (sin a) (sin b) (* (cos a) (cos b))))

simplify1.9s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
2	3621
1	508
0	183

prune909.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes422.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.8s	2928×	body	1280	valid
1.5s	1797×	body	640	valid
512.0ms	339×	body	160	valid
293.0ms	2178×	body	80	valid
260.0ms	758×	body	320	valid