Details

sample273.0ms

Algorithm

intervals

Results

80.0ms	90×	body	1280	valid
36.0ms	63×	body	640	valid
11.0ms	27×	body	320	valid
10.0ms	66×	body	80	valid
3.0ms	10×	body	160	valid

simplify95.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	20	9
4	21	9
done	21	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize28.0ms

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))

rewrite95.0ms

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:

37.0ms	(* r (/ (sin b) (cos (+ a b))))
21.0ms	(/ (sin b) (cos (+ a b)))
23.0ms	(cos (+ a b))

series252.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(* r (/ (sin b) (cos (+ a b))))
55.0ms	(/ (sin b) (cos (+ a b)))
32.0ms	(cos (+ a b))

simplify3.3s

Counts

82 → 82

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	122	955
1	260	924
2	659	834
3	1814	830
done	5001	824

prune377.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

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:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
110.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
37.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms	(* (sin a) (sin b))

series774.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
353.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
199.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
92.0ms	(* (sin a) (sin b))

simplify3.1s

Counts

122 → 122

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	181	2200
1	430	2141
2	1243	1949
3	3731	1826
done	5000	1821

prune706.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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))

rewrite103.0ms

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:

17.0ms	(* r (sin b))
28.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
39.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms	(* (sin a) (sin b))

series675.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* r (sin b))
134.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
390.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
86.0ms	(* (sin a) (sin b))

simplify3.6s

Counts

98 → 98

Iterations

Useful iterations: done (3.6s)

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

prune470.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin b) (log1p (expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
0.3b	(log1p (expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.4b	(expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

26.0ms	(/ (sin b) (log1p (expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
25.0ms	(* (sin a) (sin b))
0.0ms	(log1p (expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
1.0ms	(expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series794.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(/ (sin b) (log1p (expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
95.0ms	(* (sin a) (sin b))
208.0ms	(log1p (expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
218.0ms	(expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify4.9s

Counts

84 → 84

Iterations

Useful iterations: 4 (3.1s)

Iter	Nodes	Cost
0	129	1396
1	253	1263
2	611	1145
3	1472	1136
4	4769	1109
done	5000	1109

prune476.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes326.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	15	16
done	15	16

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.9s	2814×	body	1280	valid
962.0ms	1927×	body	640	valid
551.0ms	327×	body	160	valid
526.0ms	769×	body	320	valid
376.0ms	2165×	body	80	valid