Details

sample216.0ms

Algorithm

intervals

Results

78.0ms	59×	body	640	valid
60.0ms	95×	body	1280	valid
10.0ms	32×	body	320	valid
5.0ms	61×	body	80	valid
2.0ms	9×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	9
1	15	9
2	20	9
done	20	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.9b	(cos (+ a b))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

20.0ms	(* r (sin b))
25.0ms	(/ (* r (sin b)) (cos (+ a b)))
22.0ms	(cos (+ a b))

series278.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(* r (sin b))
177.0ms	(/ (* r (sin b)) (cos (+ a b)))
44.0ms	(cos (+ a b))

simplify9.1s

Counts

62 → 62

Iterations

Useful iterations: done (9.1s)

Iter	Nodes	Cost
0	96	575
1	1394	562
done	5001	483

prune203.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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

rewrite139.0ms

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:

19.0ms	(* r (sin b))
36.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
24.0ms	(* (sin a) (sin b))
56.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series589.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* r (sin b))
127.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
61.0ms	(* (sin a) (sin b))
339.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify10.1s

Counts

98 → 98

Iterations

Useful iterations: done (10.1s)

Iter	Nodes	Cost
0	152	1364
1	1867	1322
done	5001	1173

prune625.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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

Counts

4 → 74

Calls

4 calls:

14.0ms	(* (cos b) (cos a))
10.0ms	(* r (sin b))
0.0ms	(fma (sin b) (- (sin a)) (* (cos b) (cos a)))
12.0ms	(/ (* r (sin b)) (fma (sin b) (- (sin a)) (* (cos b) (cos a))))

series637.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (cos b) (cos a))
58.0ms	(* r (sin b))
143.0ms	(fma (sin b) (- (sin a)) (* (cos b) (cos a)))
367.0ms	(/ (* r (sin b)) (fma (sin b) (- (sin a)) (* (cos b) (cos a))))

simplify8.5s

Counts

86 → 86

Iterations

Useful iterations: done (8.5s)

Iter	Nodes	Cost
0	135	1098
1	1607	1080
done	5000	923

prune426.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

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

rewrite261.0ms

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:

24.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
153.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
26.0ms	(* (sin a) (sin b))
52.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series688.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
364.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
68.0ms	(* (sin a) (sin b))
163.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.6s

Counts

122 → 122

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	181	2200
1	2274	2141
done	5000	1949

prune656.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes282.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	18
1	19	18
done	19	18

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.9s	2939×	body	1280	valid
975.0ms	1778×	body	640	valid
334.0ms	2138×	body	80	valid
233.0ms	811×	body	320	valid
95.0ms	335×	body	160	valid