Details

sample208.0ms

Algorithm

intervals

Results

63.0ms	77×	body	80	valid
45.0ms	79×	body	1280	valid
26.0ms	67×	body	640	valid
5.0ms	22×	body	320	valid
2.0ms	11×	body	160	valid

simplify18.0ms

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: 14.2b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.0b	(cos (+ a b))

rewrite75.0ms

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:

31.0ms	(* r (sin b))
16.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

series262.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* r (sin b))
179.0ms	(/ (* r (sin b)) (cos (+ a b)))
33.0ms	(cos (+ a b))

simplify2.7s

Counts

62 → 62

Iterations

Useful iterations: done (2.7s)

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

prune289.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

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

rewrite99.0ms

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:

11.0ms	(* r (sin b))
22.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
13.0ms	(* (sin a) (sin b))
48.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series663.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* r (sin b))
142.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
75.0ms	(* (sin a) (sin b))
395.0ms	(/ (* 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	1162	1174
3	4193	1081
done	5000	1078

prune548.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

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

Counts

4 → 74

Calls

4 calls:

17.0ms	(* r (sin b))
1.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
28.0ms	(* (sin a) (sin b))
13.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series644.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* r (sin b))
138.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
81.0ms	(* (sin a) (sin b))
356.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify2.2s

Counts

86 → 86

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	127	1087
1	273	1071
2	775	921
3	2734	915
done	5000	912

prune439.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin b) (sin a))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
0.3b	(pow (* (sin b) (sin a)) 3)
26.7b	(cbrt (pow (* (sin b) (sin a)) 3))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

13.0ms	(* (sin b) (sin a))
76.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
18.0ms	(pow (* (sin b) (sin a)) 3)
9.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

series590.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sin b) (sin a))
345.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
104.0ms	(pow (* (sin b) (sin a)) 3)
65.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

simplify1.6s

Counts

104 → 104

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	175	1493
1	406	1226
2	1531	1096
done	5000	1039

prune543.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes211.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	18	16
2	20	16
done	20	16

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.4s	2908×	body	1280	valid
1.0s	1810×	body	640	valid
352.0ms	766×	body	320	valid
334.0ms	2127×	body	80	valid
151.0ms	392×	body	160	valid