Details

sample644.0ms

Algorithm

intervals

Results

229.0ms	90×	body	1280	valid
45.0ms	27×	body	320	valid
42.0ms	63×	body	640	valid
14.0ms	66×	body	80	valid
3.0ms	10×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize24.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
5.5b	(cos (+ a b))

rewrite57.0ms

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:

26.0ms	(* r (sin b))
15.0ms	(/ (* r (sin b)) (cos (+ a b)))
13.0ms	(cos (+ a b))

series191.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* r (sin b))
119.0ms	(/ (* r (sin b)) (cos (+ a b)))
29.0ms	(cos (+ a b))

simplify3.0s

Counts

62 → 62

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	96	575
1	207	562
2	572	484
3	2172	482
done	5000	480

prune218.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(- (* (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))

rewrite133.0ms

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))
21.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
52.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
36.0ms	(* (sin a) (sin b))

series583.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* r (sin b))
133.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
311.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
84.0ms	(* (sin a) (sin b))

simplify3.7s

Counts

98 → 98

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	152	1364
1	370	1324
2	1158	1196
3	4168	1081
done	5000	1078

prune479.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

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` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

17.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
14.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
14.0ms	(* (sin a) (sin b))

series637.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* r (sin b))
133.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
372.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
73.0ms	(* (sin a) (sin b))

simplify2.4s

Counts

86 → 86

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	127	1087
1	273	1071
2	770	917
3	2734	915
done	5001	912

prune555.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

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 a) (sin b))))
27.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
19.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
28.0ms	(* (sin a) (sin b))

series700.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
371.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
165.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
69.0ms	(* (sin a) (sin b))

simplify2.4s

Counts

106 → 106

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	153	1831
1	326	1797
2	879	1603
3	2442	1599
done	5001	1572

prune585.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes195.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	16	18
done	16	18

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.5s	2814×	body	1280	valid
1.7s	1927×	body	640	valid
623.0ms	769×	body	320	valid
351.0ms	2165×	body	80	valid
79.0ms	327×	body	160	valid