Details

sample189.0ms

Algorithm

intervals

Results

59.0ms	87×	body	1280	valid
22.0ms	54×	body	640	valid
10.0ms	29×	body	320	valid
7.0ms	73×	body	80	valid
3.0ms	13×	body	160	valid

simplify100.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.8b	(cos (+ a b))

rewrite79.0ms

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:

21.0ms	(* r (/ (sin b) (cos (+ a b))))
21.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

series271.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms	(* r (/ (sin b) (cos (+ a b))))
79.0ms	(/ (sin b) (cos (+ a b)))
44.0ms	(cos (+ a b))

simplify765.0ms

Counts

82 → 82

Iterations

Useful iterations: done (761.0ms)

Iter	Nodes	Cost
0	122	955
1	283	928
2	1071	842
done	5000	836

prune351.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite260.0ms

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:

36.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
127.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
33.0ms	(* (sin b) (sin a))
58.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series684.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
352.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
73.0ms	(* (sin b) (sin a))
156.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify1.3s

Counts

122 → 122

Iterations

Useful iterations: 2 (424.0ms)

Iter	Nodes	Cost
0	187	2200
1	467	2145
2	2154	1957
done	5001	1957

prune775.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite153.0ms

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:

38.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
20.0ms	(* r (sin b))
26.0ms	(* (sin b) (sin a))
65.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series608.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
46.0ms	(* r (sin b))
66.0ms	(* (sin b) (sin a))
377.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify1.1s

Counts

98 → 98

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	157	1364
1	395	1324
2	1969	1180
done	5001	1174

prune636.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

25.0ms	(* (sin b) (sin a))
1.0ms	(expm1 (log1p (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
24.0ms	(/ (* r (sin b)) (expm1 (log1p (- (* (cos a) (cos b)) (* (sin b) (sin a))))))
2.0ms	(log1p (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series874.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sin b) (sin a))
206.0ms	(expm1 (log1p (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
460.0ms	(/ (* r (sin b)) (expm1 (log1p (- (* (cos a) (cos b)) (* (sin b) (sin a))))))
151.0ms	(log1p (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify988.0ms

Counts

78 → 78

Iterations

Useful iterations: done (984.0ms)

Iter	Nodes	Cost
0	132	1258
1	306	1149
2	1462	993
done	5001	989

prune324.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes329.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b 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

sample5.6s

Algorithm

intervals

Results

3.4s	2880×	body	1280	valid
1.0s	1895×	body	640	valid
287.0ms	728×	body	320	valid
261.0ms	2139×	body	80	valid
145.0ms	359×	body	160	valid