Details

sample590.0ms

Algorithm

intervals

Results

222.0ms	28×	body	320	valid
128.0ms	100×	body	1280	valid
39.0ms	51×	body	640	valid
10.0ms	68×	body	80	valid
7.0ms	9×	body	160	valid

simplify41.0ms

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: 13.4b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.3b	(cos (+ a b))

rewrite98.0ms

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:

22.0ms	(* r (sin b))
26.0ms	(/ (* r (sin b)) (cos (+ a b)))
27.0ms	(cos (+ a b))

series208.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* r (sin b))
116.0ms	(/ (* r (sin b)) (cos (+ a b)))
37.0ms	(cos (+ a b))

simplify2.5s

Counts

62 → 62

Iterations

Useful iterations: done (2.5s)

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

prune236.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

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:

24.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* r (sin b))
18.0ms	(* (sin a) (sin b))
31.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series675.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
69.0ms	(* r (sin b))
94.0ms	(* (sin a) (sin b))
358.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (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	1166	1174
3	4192	1081
done	5002	1078

prune491.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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))

rewrite276.0ms

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:

33.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
56.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
158.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
25.0ms	(* (sin a) (sin b))

series747.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
160.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
391.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
66.0ms	(* (sin a) (sin b))

simplify2.9s

Counts

122 → 122

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	181	2200
1	430	2141
2	1248	1955
3	3750	1826
done	5000	1821

prune590.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

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

Counts

4 → 74

Calls

4 calls:

28.0ms	(* (cos a) (cos b))
0.0ms	(fma (- (sin a)) (sin b) (* (cos a) (cos b)))
10.0ms	(* r (sin b))
12.0ms	(/ (* r (sin b)) (fma (- (sin a)) (sin b) (* (cos a) (cos b))))

series653.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (cos a) (cos b))
165.0ms	(fma (- (sin a)) (sin b) (* (cos a) (cos b)))
50.0ms	(* r (sin b))
366.0ms	(/ (* r (sin b)) (fma (- (sin a)) (sin b) (* (cos a) (cos b))))

simplify2.2s

Counts

86 → 86

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	136	1098
1	290	1080
2	817	925
3	2752	921
done	5000	919

prune434.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes261.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	19
1	18	19
done	18	19

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.5s	2954×	body	1280	valid
1.2s	1762×	body	640	valid
387.0ms	843×	body	320	valid
224.0ms	2134×	body	80	valid
74.0ms	308×	body	160	valid