Details

sample377.0ms

Algorithm

intervals

Results

183.0ms	91×	body	1280	valid
41.0ms	67×	body	640	valid
18.0ms	23×	body	320	valid
8.0ms	60×	body	80	valid
5.0ms	15×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize42.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
5.5b	(cos (+ a b))

rewrite150.0ms

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:

91.0ms	(* r (/ (sin b) (cos (+ a b))))
23.0ms	(/ (sin b) (cos (+ a b)))
27.0ms	(cos (+ a b))

series357.0ms

Counts

3 → 9

Calls

3 calls:

211.0ms	(* r (/ (sin b) (cos (+ a b))))
84.0ms	(/ (sin b) (cos (+ a b)))
62.0ms	(cos (+ a b))

simplify4.0s

Counts

82 → 82

Iterations

Iter	Nodes
done	5005
3	3207
2	875
1	279
0	122

prune856.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize63.0ms

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))))
0.3b	(* (sin a) (sin b))

rewrite302.0ms

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:

41.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
151.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
72.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
31.0ms	(* (sin a) (sin b))

series998.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
483.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
238.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
108.0ms	(* (sin a) (sin b))

simplify3.0s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1541
1	460
0	181

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
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×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

22.0ms	(* r (sin b))
41.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
79.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms	(* (sin a) (sin b))

series897.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* r (sin b))
176.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
508.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
130.0ms	(* (sin a) (sin b))

simplify2.9s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1204
1	386
0	152

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.3b	(* (sin a) (sin b))
2.8b	(log (exp (* (sin a) (sin b))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

39.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
27.0ms	(* (sin a) (sin b))
10.0ms	(log (exp (* (sin a) (sin b))))

series872.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
471.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
118.0ms	(* (sin a) (sin b))
106.0ms	(log (exp (* (sin a) (sin b))))

simplify2.9s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1329
1	420
0	167

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes619.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.2s	2850×	body	1280	valid
1.6s	1867×	body	640	valid
798.0ms	340×	body	160	valid
656.0ms	747×	body	320	valid
481.0ms	2196×	body	80	valid