Details

sample405.0ms

Algorithm

intervals

Results

200.0ms	57×	body	640	valid
92.0ms	93×	body	1280	valid
12.0ms	22×	body	320	valid
10.0ms	70×	body	80	valid
5.0ms	14×	body	160	valid

simplify81.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
5	20
4	19
3	17
2	14
1	12
0	8

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize43.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.4b	(cos (+ a b))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `times-frac` `associate-r` `associate-l*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 56

Calls

3 calls:

13.0ms	(* r (sin b))
16.0ms	(/ (* r (sin b)) (cos (+ a b)))
17.0ms	(cos (+ a b))

series298.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(* r (sin b))
187.0ms	(/ (* r (sin b)) (cos (+ a b)))
48.0ms	(cos (+ a b))

simplify4.4s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
3	2510
2	606
1	223
0	101

prune794.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize78.0ms

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))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `cos-mult` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `div-inv` `associate-/l*`

Counts

4 → 90

Calls

4 calls:

46.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
13.0ms	(* r (sin b))
23.0ms	(* (sin a) (sin b))
76.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series1.0s

Counts

4 → 12

Calls

4 calls:

181.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
96.0ms	(* r (sin b))
123.0ms	(* (sin a) (sin b))
629.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify7.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	4640
2	1164
1	392
0	157

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `associate-*r/`

Counts

4 → 114

Calls

4 calls:

24.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
177.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
24.0ms	(* (sin a) (sin b))
49.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series1.2s

Counts

4 → 12

Calls

4 calls:

199.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
570.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
114.0ms	(* (sin a) (sin b))
351.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.8s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	1544
1	469
0	186

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize127.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
0.2b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
23.5b	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

rewrite569.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
29×	`sin-mult`
23×	`add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down`
14×	`cbrt-div`
11×	`frac-times` `associate-*l/`
10×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
9×	`associate-/r/`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-*r/` `cos-mult` `frac-sub`
4×	`expm1-log1p-u` `associate-r` `associate-l` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac`
2×	`cbrt-undiv` `pow-plus` `div-exp` `*-commutative`
1×	`cbrt-prod` `pow2` `clear-num` `frac-2neg` `flip3--` `pow1/3` `swap-sqr` `pow3` `rem-cbrt-cube` `div-inv` `flip--` `associate-/l*` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

17.0ms	(* (sin a) (sin b))
196.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
103.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
237.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

series963.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sin a) (sin b))
619.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
155.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
109.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

simplify4.1s

Counts

127 → 127

Iterations

Iter	Nodes
done	5002
2	1811
1	535
0	210

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes890.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.9s	2902×	body	1280	valid
1.2s	1902×	body	640	valid
730.0ms	724×	body	320	valid
370.0ms	2112×	body	80	valid
89.0ms	361×	body	160	valid