Details

sample179.0ms

Algorithm

intervals

Results

58.0ms	51×	body	640	valid
55.0ms	100×	body	1280	valid
7.0ms	28×	body	320	valid
6.0ms	68×	body	80	valid
4.0ms	9×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize14.0ms

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))

rewrite72.0ms

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:

40.0ms	(* r (sin b))
16.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series283.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(* r (sin b))
166.0ms	(/ (* r (sin b)) (cos (+ a b)))
45.0ms	(cos (+ a b))

simplify2.6s

Counts

62 → 62

Iterations

Useful iterations: done (2.6s)

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

prune233.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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))))

rewrite85.0ms

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:

29.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* r (sin b))
13.0ms	(* (sin a) (sin b))
31.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series518.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(* r (sin b))
53.0ms	(* (sin a) (sin b))
311.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (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	1166	1174
3	4192	1081
done	5002	1078

prune509.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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))

rewrite264.0ms

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:

23.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
56.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
149.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
33.0ms	(* (sin a) (sin b))

series714.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
161.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
363.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
74.0ms	(* (sin a) (sin b))

simplify3.0s

Counts

122 → 122

Iterations

Useful iterations: done (3.0s)

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

prune670.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

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))) (* (* 0 (sin a)) (sin b))))

rewrite69.0ms

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` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `clear-num` `cos-mult` `flip-+` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

11.0ms	(* (cos a) (cos b))
0.0ms	(fma (- (sin a)) (sin b) (* (cos a) (cos b)))
20.0ms	(* r (sin b))
35.0ms	(/ (* r (sin b)) (+ (fma (- (sin a)) (sin b) (* (cos a) (cos b))) (* (* 0 (sin a)) (sin b))))

series590.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos a) (cos b))
122.0ms	(fma (- (sin a)) (sin b) (* (cos a) (cos b)))
80.0ms	(* r (sin b))
342.0ms	(/ (* r (sin b)) (+ (fma (- (sin a)) (sin b) (* (cos a) (cos b))) (* (* 0 (sin a)) (sin b))))

simplify3.0s

Counts

88 → 88

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	153	1434
1	351	1284
2	1027	1028
3	3268	967
done	5000	965

prune472.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes272.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	14	16
done	14	16

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.9s	2954×	body	1280	valid
891.0ms	1762×	body	640	valid
731.0ms	2134×	body	80	valid
484.0ms	843×	body	320	valid
75.0ms	308×	body	160	valid