Details

sample188.0ms

Algorithm

intervals

Results

95.0ms	90×	body	1280	valid
24.0ms	63×	body	640	valid
8.0ms	27×	body	320	valid
7.0ms	66×	body	80	valid
2.0ms	10×	body	160	valid

simplify37.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize14.0ms

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))

rewrite53.0ms

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))
13.0ms	(/ (* r (sin b)) (cos (+ a b)))
11.0ms	(cos (+ a b))

series278.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(* r (sin b))
180.0ms	(/ (* r (sin b)) (cos (+ a b)))
26.0ms	(cos (+ a b))

simplify3.2s

Counts

62 → 62

Iterations

Useful iterations: done (3.2s)

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

prune196.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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))

rewrite117.0ms

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:

22.0ms	(* r (sin b))
36.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
36.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms	(* (sin a) (sin b))

series575.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* r (sin b))
116.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
322.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
65.0ms	(* (sin a) (sin b))

simplify3.3s

Counts

98 → 98

Iterations

Useful iterations: done (3.3s)

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

prune517.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-r` `associate-l` `associate-/l*`
4×	`distribute-lft-neg-in` `expm1-log1p-u` `neg-mul-1` `distribute-rgt-neg-in` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `neg-sub0` `frac-2neg` `div-sub` `distribute-frac-neg` `div-exp` `clear-num` `fma-udef` `div-inv` `sin-mult`

Counts

4 → 94

Calls

4 calls:

14.0ms	(* r (sin b))
0.0ms	(fma (cos a) (- (cos b)) (* (sin b) (sin a)))
9.0ms	(/ (- (* r (sin b))) (fma (cos a) (- (cos b)) (* (sin b) (sin a))))
12.0ms	(* (sin b) (sin a))

series595.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* r (sin b))
139.0ms	(fma (cos a) (- (cos b)) (* (sin b) (sin a)))
352.0ms	(/ (- (* r (sin b))) (fma (cos a) (- (cos b)) (* (sin b) (sin a))))
51.0ms	(* (sin b) (sin a))

simplify3.9s

Counts

106 → 106

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	170	1709
1	339	1667
2	963	1542
3	4401	1540
done	5002	1537

prune501.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

61×	`times-frac`
57×	`add-sqr-sqrt`
50×	`add-cube-cbrt` `*-un-lft-identity`
37×	`associate-r`
21×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
8×	`pow1`
7×	`neg-mul-1`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `associate-/r*` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `distribute-frac-neg` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`neg-sub0` `frac-2neg` `div-sub` `associate-*r/` `clear-num` `distribute-rgt-neg-out` `fma-udef` `sin-mult`

Counts

4 → 146

Calls

4 calls:

0.0ms	(fma (cos a) (- (cos b)) (* (sin b) (sin a)))
33.0ms	(* r (/ (- (sin b)) (fma (cos a) (- (cos b)) (* (sin b) (sin a)))))
9.0ms	(/ (- (sin b)) (fma (cos a) (- (cos b)) (* (sin b) (sin a))))
12.0ms	(* (sin b) (sin a))

series775.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(fma (cos a) (- (cos b)) (* (sin b) (sin a)))
368.0ms	(* r (/ (- (sin b)) (fma (cos a) (- (cos b)) (* (sin b) (sin a)))))
195.0ms	(/ (- (sin b)) (fma (cos a) (- (cos b)) (* (sin b) (sin a))))
65.0ms	(* (sin b) (sin a))

simplify3.5s

Counts

158 → 158

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	226	3187
1	489	3091
2	1375	2884
3	4718	2880
done	5000	2875

prune773.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes253.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	19
1	19	19
2	23	19
3	26	19
done	26	19

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.5s	2814×	body	1280	valid
1.7s	1927×	body	640	valid
903.0ms	769×	body	320	valid
249.0ms	2165×	body	80	valid
82.0ms	327×	body	160	valid