Details

sample347.0ms

Algorithm

intervals

Results

167.0ms	100×	body	1280	valid
43.0ms	56×	body	640	valid
17.0ms	23×	body	320	valid
11.0ms	62×	body	80	valid
7.0ms	15×	body	160	valid

simplify41.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	20
5	20
4	19
3	17
2	14
1	12
0	8

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize71.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.2b	(cos (+ a b))

rewrite61.0ms

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:

15.0ms	(* r (sin b))
25.0ms	(/ (* r (sin b)) (cos (+ a b)))
19.0ms	(cos (+ a b))

series269.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* r (sin b))
175.0ms	(/ (* r (sin b)) (cos (+ a b)))
41.0ms	(cos (+ a b))

simplify704.0ms

Counts

65 → 65

Iterations

Iter	Nodes
3	2189
2	582
1	212
0	101

prune691.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize54.0ms

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))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite101.0ms

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:

23.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
16.0ms	(* r (sin b))
24.0ms	(* (sin a) (sin b))
36.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series524.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(* r (sin b))
50.0ms	(* (sin a) (sin b))
320.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.4s

Counts

102 → 102

Iterations

Iter	Nodes
3	4407
2	1152
1	382
0	157

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

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))
0.3b	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

rewrite42.0ms

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`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 78

Calls

4 calls:

9.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
11.0ms	(* (sin a) (sin b))
21.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series644.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* r (sin b))
149.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
83.0ms	(* (sin a) (sin b))
342.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify1.6s

Counts

90 → 90

Iterations

Iter	Nodes
3	3910
2	887
1	294
0	133

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))
0.1b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

24.0ms	(- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))
21.0ms	(* r (sin b))
20.0ms	(* (sin a) (sin b))
40.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))

series700.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))
54.0ms	(* r (sin b))
58.0ms	(* (sin a) (sin b))
416.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))))

simplify2.0s

Counts

101 → 101

Iterations

Iter	Nodes
3	4093
2	1102
1	392
0	168

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes369.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	18
1	18
0	14

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.2s	2885×	body	1280	valid
2.1s	1883×	body	640	valid
453.0ms	732×	body	320	valid
449.0ms	2174×	body	80	valid
119.0ms	328×	body	160	valid