Details

sample299.0ms

Algorithm

intervals

Results

87.0ms	89×	body	1280	valid
74.0ms	73×	body	80	valid
34.0ms	50×	body	640	valid
14.0ms	34×	body	320	valid
3.0ms	10×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 13.4b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.8b	(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:

23.0ms	(* r (sin b))
25.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

series291.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* r (sin b))
190.0ms	(/ (* r (sin b)) (cos (+ a b)))
45.0ms	(cos (+ a b))

simplify765.0ms

Counts

62 → 62

Iterations

Useful iterations: done (763.0ms)

Iter	Nodes	Cost
0	96	575
1	215	562
2	880	492
done	5001	482

prune252.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

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))))
0.2b	(* (sin a) (sin b))

rewrite126.0ms

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:

18.0ms	(* r (sin b))
38.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms	(* (sin a) (sin b))

series647.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* r (sin b))
138.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
350.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
87.0ms	(* (sin a) (sin b))

simplify1.0s

Counts

98 → 98

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	152	1364
1	386	1324
2	1777	1182
done	5002	1174

prune561.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite210.0ms

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:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
42.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
131.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
14.0ms	(* (sin a) (sin b))

series733.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
195.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
362.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
56.0ms	(* (sin a) (sin b))

simplify1.6s

Counts

122 → 122

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	181	2200
1	467	2145
2	2131	1957
done	5001	1883

prune685.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
0.2b	(* (sin b) (sin a))
0.3b	(pow (* (sin b) (sin a)) 3)
29.7b	(cbrt (pow (* (sin b) (sin a)) 3))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`times-frac`
8×	`cbrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `pow-prod-down` `associate-/r/` `unswap-sqr`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-exp` `*-commutative` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `pow1/3` `associate-*r/` `div-exp` `cos-mult` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv`

Counts

4 → 103

Calls

4 calls:

178.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
15.0ms	(* (sin b) (sin a))
14.0ms	(pow (* (sin b) (sin a)) 3)
9.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

series561.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
63.0ms	(* (sin b) (sin a))
122.0ms	(pow (* (sin b) (sin a)) 3)
55.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

simplify1.8s

Counts

115 → 115

Iterations

Useful iterations: 2 (531.0ms)

Iter	Nodes	Cost
0	196	1688
1	534	1394
2	2620	1266
done	5000	1266

prune681.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes349.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.4s	2913×	body	1280	valid
1.0s	1797×	body	640	valid
358.0ms	788×	body	320	valid
244.0ms	2129×	body	80	valid
80.0ms	374×	body	160	valid