Details

sample427.0ms

Algorithm

intervals

Results

198.0ms	68×	body	640	valid
119.0ms	83×	body	1280	valid
15.0ms	21×	body	320	valid
12.0ms	76×	body	80	valid
4.0ms	8×	body	160	valid

simplify852.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
5	21
4	20
3	18
2	16
1	12
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize39.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
3.0b	(cos (+ a b))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 87

Calls

3 calls:

37.0ms	(/ (sin b) (cos (+ a b)))
54.0ms	(* r (/ (sin b) (cos (+ a b))))
29.0ms	(cos (+ a b))

series298.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(/ (sin b) (cos (+ a b)))
183.0ms	(* r (/ (sin b) (cos (+ a b))))
45.0ms	(cos (+ a b))

simplify2.3s

Counts

96 → 96

Iterations

Iter	Nodes
done	5014
3	3379
2	927
1	303
0	134

prune516.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite639.0ms

Algorithm

rewrite-expression-head

Rules

280×	`add-sqr-sqrt`
188×	`*-un-lft-identity`
144×	`prod-diff`
119×	`associate-r`
117×	`associate-l`
115×	`add-cube-cbrt`
67×	`times-frac`
64×	`unswap-sqr`
36×	`distribute-lft-out--` `difference-of-squares`
27×	`*-commutative`
22×	`associate-/r*`
17×	`associate-*r/`
13×	`add-cbrt-cube` `add-exp-log`
12×	`fma-neg`
8×	`pow1` `associate-/r/`
7×	`sin-mult` `associate-/l*`
6×	`cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `sub-div`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `un-div-inv` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 350

Calls

4 calls:

133.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
99.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
13.0ms	(* (sin b) (sin a))
378.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

series695.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
168.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
66.0ms	(* (sin b) (sin a))
349.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

simplify2.8s

Counts

362 → 362

Iterations

Iter	Nodes
done	5003
2	2704
1	988
0	418

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite420.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
56×	`add-cube-cbrt`
43×	`times-frac`
42×	`associate-r`
36×	`prod-diff`
27×	`associate-l`
18×	`distribute-lft-out--` `difference-of-squares`
16×	`unswap-sqr`
14×	`associate-/r*`
13×	`add-cbrt-cube` `associate-*r/` `add-exp-log`
12×	`fma-neg`
8×	`pow1`
7×	`associate-/l*` `add-log-exp`
6×	`*-commutative`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `flip3--` `prod-exp` `cbrt-unprod` `flip--`
2×	`cbrt-undiv` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `un-div-inv` `div-inv`
1×	`log1p-udef` `sub-neg` `sin-mult`

Counts

4 → 201

Calls

4 calls:

76.0ms	(- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a)))))
74.0ms	(/ (sin b) (- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a))))))
15.0ms	(* (sin b) (sin a))
248.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a)))))))

series784.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a)))))
204.0ms	(/ (sin b) (- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a))))))
62.0ms	(* (sin b) (sin a))
362.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a)))))))

simplify2.1s

Counts

213 → 213

Iterations

Iter	Nodes
done	5001
2	1832
1	642
0	275

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a)))))
0.2b	(* (sin b) (sin a))
0.2b	(/ (- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a))))) (sin b))
0.3b	(/ r (/ (- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a))))) (sin b)))

rewrite339.0ms

Algorithm

rewrite-expression-head

Rules

214×	`add-sqr-sqrt`
186×	`*-un-lft-identity`
180×	`times-frac`
114×	`add-cube-cbrt`
36×	`prod-diff` `distribute-lft-out--` `difference-of-squares`
33×	`associate-l`
31×	`associate-/r*`
23×	`unswap-sqr`
17×	`associate-/l*`
15×	`associate-r` `associate-/r/`
13×	`add-cbrt-cube` `add-exp-log`
12×	`fma-neg`
7×	`add-log-exp`
6×	`pow1` `div-inv`
5×	`*-commutative`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`clear-num` `frac-2neg` `flip3--` `flip--`
2×	`diff-log`
1×	`log1p-udef` `sub-neg` `div-sub` `pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`

Counts

4 → 274

Calls

4 calls:

54.0ms	(- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a)))))
26.0ms	(* (sin b) (sin a))
124.0ms	(/ (- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a))))) (sin b))
123.0ms	(/ r (/ (- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a))))) (sin b)))

series824.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a)))))
53.0ms	(* (sin b) (sin a))
171.0ms	(/ (- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a))))) (sin b))
409.0ms	(/ r (/ (- (* (cos b) (cos a)) (log1p (expm1 (* (sin b) (sin a))))) (sin b)))

simplify2.5s

Counts

286 → 286

Iterations

Iter	Nodes
done	5028
2	2967
1	962
0	384

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes327.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.8s	2839×	body	1280	valid
2.2s	1837×	body	640	valid
475.0ms	766×	body	320	valid
459.0ms	2216×	body	80	valid
166.0ms	344×	body	160	valid