Details

sample422.0ms

Algorithm

intervals

Results

99.0ms	91×	body	1280	valid
44.0ms	67×	body	640	valid
9.0ms	23×	body	320	valid
8.0ms	60×	body	80	valid
4.0ms	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

localize40.0ms

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))

rewrite101.0ms

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×	`associate-l` `associate-/r` `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 → 67

Calls

3 calls:

51.0ms	(* r (/ (sin b) (cos (+ a b))))
21.0ms	(/ (sin b) (cos (+ a b)))
22.0ms	(cos (+ a b))

series311.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(* r (/ (sin b) (cos (+ a b))))
78.0ms	(/ (sin b) (cos (+ a b)))
55.0ms	(cos (+ a b))

simplify3.5s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	3166
2	807
1	267
0	116

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize58.0ms

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))

rewrite286.0ms

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`
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` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

25.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
150.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
78.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
26.0ms	(* (sin a) (sin b))

series896.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
423.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
238.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
98.0ms	(* (sin a) (sin b))

simplify2.6s

Counts

112 → 112

Iterations

Iter	Nodes
done	5002
2	1567
1	432
0	170

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

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))

rewrite167.0ms

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×	`associate-/r/` `cos-mult`
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` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

20.0ms	(* r (sin b))
37.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
79.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
27.0ms	(* (sin a) (sin b))

series751.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* r (sin b))
154.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
420.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
100.0ms	(* (sin a) (sin b))

simplify4.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	4589
2	1147
1	360
0	140

prune927.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

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

rewrite218.0ms

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×	`associate-/r/`
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 → 96

Calls

4 calls:

115.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
53.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
36.0ms	(* (sin a) (sin b))
10.0ms	(log (exp (* (sin a) (sin b))))

series810.0ms

Counts

4 → 12

Calls

4 calls:

414.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
225.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
84.0ms	(* (sin a) (sin b))
87.0ms	(log (exp (* (sin a) (sin b))))

simplify5.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
3	4611
2	1293
1	385
0	164

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes562.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample7.3s

Algorithm

intervals

Results

4.0s	2850×	body	1280	valid
1.9s	1867×	body	640	valid
458.0ms	2196×	body	80	valid
449.0ms	747×	body	320	valid
104.0ms	340×	body	160	valid