Details

sample325.0ms

Algorithm

intervals

Results

39.0ms	91×	body	1280	valid
13.0ms	51×	body	640	valid
5.0ms	31×	body	320	valid
4.0ms	75×	body	80	valid
1.0ms	8×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	15	9
3	19	9
4	20	9
done	20	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.3b	(cos (+ a b))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

9.0ms	(* r (/ (sin b) (cos (+ a b))))
3.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

series162.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(* r (/ (sin b) (cos (+ a b))))
39.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify2.2s

Counts

82 → 82

Iterations

Useful iterations: 3 (756.0ms)

Iter	Nodes	Cost
0	122	955
1	264	924
2	872	834
3	4849	830
done	5000	830

prune244.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
25.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series454.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
46.0ms	(* (sin a) (sin b))
214.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
116.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify662.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (144.0ms)

Iter	Nodes	Cost
0	181	2200
1	429	2141
2	1465	1949
done	5000	1949

prune458.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (- (* (sin b) (sin a))))
4.0ms	(* (sin b) (sin a))
8.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin b) (sin a))))))
3.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))

series470.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(fma (cos a) (cos b) (- (* (sin b) (sin a))))
44.0ms	(* (sin b) (sin a))
223.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin b) (sin a))))))
117.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))

simplify607.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	154	1831
1	330	1797
2	1123	1603
done	5001	1603

prune402.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
0.3b	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
3.6b	(log (exp (* (sin a) (sin b))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

4.0ms	(* (sin a) (sin b))
23.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
10.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
2.0ms	(log (exp (* (sin a) (sin b))))

series433.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin a) (sin b))
220.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
114.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
49.0ms	(log (exp (* (sin a) (sin b))))

simplify622.0ms

Counts

116 → 116

Iterations

Useful iterations: 2 (122.0ms)

Iter	Nodes	Cost
0	172	2092
1	376	1828
2	1241	1658
done	5000	1658

prune443.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes204.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	17	18
done	17	18

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2913×	body	1280	valid
448.0ms	1767×	body	640	valid
140.0ms	773×	body	320	valid
128.0ms	2210×	body	80	valid
43.0ms	337×	body	160	valid