Details

sample490.0ms

Algorithm

intervals

Results

262.0ms	95×	body	1280	valid
80.0ms	48×	body	640	valid
18.0ms	68×	body	80	valid
18.0ms	27×	body	320	valid
8.0ms	18×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
4	21
3	20
2	16
1	12
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.1b	(cos (+ a b))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 76

Calls

3 calls:

13.0ms	(* r (/ (sin b) (cos (+ a b))))
10.0ms	(/ (sin b) (cos (+ a b)))
26.0ms	(cos (+ a b))

series199.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(* r (/ (sin b) (cos (+ a b))))
48.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify1.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
2	1075
1	286
0	126

prune492.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
19×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`clear-num` `frac-2neg` `associate-*r/`

Counts

4 → 117

Calls

4 calls:

9.0ms	(* (cos a) (cos b))
133.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
28.0ms	(* (sin a) (sin b))
51.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series627.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos a) (cos b))
322.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
74.0ms	(* (sin a) (sin b))
177.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.5s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	2055
1	486
0	200

prune815.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (* (sin a) (sin b)))
0.1b	(* r (/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
18×	`associate-r`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-l`
5×	`expm1-log1p-u`
4×	`associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `prod-exp` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `div-inv` `flip--`
1×	`log1p-udef` `clear-num` `frac-2neg` `log1p-expm1` `associate-*r/` `sin-mult`

Counts

4 → 103

Calls

4 calls:

0.0ms	(log1p (* (sin a) (sin b)))
45.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))))
11.0ms	(* (sin a) (sin b))
28.0ms	(/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))

series700.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(log1p (* (sin a) (sin b)))
342.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))))
64.0ms	(* (sin a) (sin b))
197.0ms	(/ (sin b) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))

simplify1.2s

Counts

115 → 115

Iterations

Iter	Nodes
done	5001
2	1983
1	452
0	185

prune862.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (* (sin a) (sin b)))
0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))

rewrite63.0ms

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`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`log1p-udef` `clear-num` `frac-2neg` `flip3--` `log1p-expm1` `div-inv` `flip--` `sin-mult` `associate-/l*`

Counts

4 → 81

Calls

4 calls:

0.0ms	(log1p (* (sin a) (sin b)))
8.0ms	(* r (sin b))
27.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))
27.0ms	(* (sin a) (sin b))

series604.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(log1p (* (sin a) (sin b)))
51.0ms	(* r (sin b))
394.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))
54.0ms	(* (sin a) (sin b))

simplify1.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5002
2	1696
1	380
0	156

prune621.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes327.0ms

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	17
1	17
0	14

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.6s	2918×	body	1280	valid
2.3s	1912×	body	640	valid
459.0ms	705×	body	320	valid
403.0ms	2095×	body	80	valid
163.0ms	370×	body	160	valid